Mathematics High School

## Answers

**Answer 1**

The slopes and **y-intercepts** of a given system of equations and its graph, find the coefficients of the x-terms and the constant terms in each equation. Compare these values to understand the relationship between the lines in the system.

To determine the slopes and y-intercepts of the given system of equations and its graph, please follow these steps:

Identify the equations in the system. Unfortunately, you haven't provided the specific equations or the graph. However,

I'll explain the general process for **determining** slopes and y-intercepts.

Determine the slopes of each line. For each equation in the system, find the **coefficient** of the x-term. This coefficient is

the slope of the line.

If the equation is in the form y = mx + b, then the slope (m) is the coefficient of the x-term.

Determine the y-intercepts of each line. For each **equation** in the system, find the constant term (b). This is the y-intercept of the line.

In the equation y = mx + b, the y-intercept (b) is the constant term.

Compare the slopes and y-intercepts. Once you have found the slopes and y-intercepts for each line in the system of

equations, you can **compare** them to determine if the lines are parallel, intersecting, or the same line.

In summary, to determine the slopes and y-intercepts of a given system of equations and its graph, find the coefficients of the x-terms and the **constant** terms in each equation. Compare these values to understand the relationship between the lines in the system.

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## Related Questions

I need help on this asap!

This question is worth more points, but i unfortunately don't have many left till i go and answer some questions.

### Answers

The **quadrilateral **is a square and a square is a parallelogram

The **quadrilateral **is a square and a square is a special type of rectangle

The length of the sides and the **angle **at the vertices is required for the classification as square

The length of **hypotenuse **EF = 5 units

How to classify the quadrilateral

The quadrilateral is classified by calculating the **length **of the **sides**

To find the lengths of the sides of the given **quadrilateral**, we need to find the distance between each pair of consecutive vertices.

Using the **distance formula**, the length of each side can be calculated as follows:

Side HE:

Length = sqrt((2 - (-1))^2 + (3 - (-1))^2) = sqrt(3^2 + 4^2) = 5

Side EF:

Length = sqrt((6 - 2)^2 + (0 - 3)^2) = sqrt(4^2 + (-3)^2) = 5

Side FG:

Length = sqrt((3 - 6)^2 + (-4 - 0)^2) = sqrt((-3)^2 + (-4)^2) = 5

Side GH:

Length = sqrt((-1 - 3)^2 + (-1 - (-4))^2) = sqrt((-4)^2 + 3^2) = 5

Therefore, all sides of the quadrilateral have a length of 5.

Using **Pythagoras** **theorem**

hypotenuse = 4² + 3²

hypotenuse = 16 + 9

hypotenuse = √25

hypotenuse = 5

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The standard deviation of a sample of 100 elements taken from a very large population is determined to be 60. The variance of the population

a) can not be larger than 60

b) can not be larger than 3600.

c.must be at least 100.

d.can be any value greater or equal to zero.

### Answers

The **variance** of the **population**(b) can not be larger than 3600.

The reason for this is that the variance of a population is always equal to or greater than the variance of a **sample** taken from that population. Since the sample size in this case is relatively large (n=100) and assuming the sample is representative of the population, the sample standard deviation of 60 can be used as an estimate for the population standard deviation.

The formula for variance is the square of the **standard deviation**, therefore the population variance cannot be larger than (60)^2 = 3600. It is important to note that the variance could be any value greater than or equal to zero, as there is no lower bound for the variance of a population.

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.

Which of the following is a solution to the equation sin (x) + 2 = 1?

270 degrees

180 degrees

60 degrees

30 degrees

### Answers

The equation sin(x) + 2 = 1 can be rearranged as sin(x) = -1.

However, the range of sine function is -1 to 1. Since there is no angle whose sine value is greater than 1 or less than -1, this equation has no solution in real numbers.

Therefore, none of the provided answer choices (270 degrees, 180 degrees, 60 degrees and 30 degrees) are solutions to the given equation.

There are 48 people in gym class. What fraction represents the number of people running?

5/8 of the people were in spin class.

1/3 of the people were lifting weights

The remaining people were running

A. 1/8

B. 1/24

C. 1/12

D. 23/24

### Answers

Answer:B

Step-by-step explanation:

5/8 of 48 is 30.

1/3 of 48 is 16.

So 30 people are spinning and 16 are lifting weights.

48-30-16=2

There are two people left out of 48.

2/48 reduces to 1/24.

suppose that two unrelated women who are having normal pregnancies, devondra and miranda, are given the first trimester screen. what is the probability that devondra gets a positive result and miranda gets a negative result? if 100 unrelated women with normal pregnancies are tested with the first trimester screen, what is the probability that at least 1 woman will receive a positive result?

### Answers

The **probability **that at least one woman will receive a positive result if 100 unrelated women with normal pregnancies are tested with the first-trimester screen is 99.52%.

Suppose that two unrelated women, Devondra and Miranda, who are having **normal **pregnancies, are given the first-trimester screen.

This screen is a prenatal test that evaluates the risk of the fetus having certain chromosomal abnormalities, including Down syndrome.

The probability that Devondra gets a positive result and Miranda gets a negative result will be determined below.

For this purpose, the probability of getting a positive result on a first-trimester screen is 0.03, and the probability of getting a negative result is 0.97.

Therefore, the probability of Devondra getting a positive result and Miranda getting a negative result is:

P(Devondra gets a positive result AND Miranda gets a negative result) = P(Devondra gets a positive result) * P(Miranda gets a negative result)= 0.03 * 0.97

= 0.0291

= 2.91%.

Therefore, the probability that Devondra gets a positive result and Miranda gets a negative result is 2.91%.

Now, let's find out the probability that at least one woman will receive a positive result if 100 unrelated women with normal pregnancies are tested with the first-trimester screen.

The probability of getting a positive result is 0.03, and the probability of getting a negative result is 0.97.

We want to find the probability of at least one woman receiving a positive result.

It means that we will calculate the probability of no woman receiving a positive result and subtract it from 1.

Let's denote this probability by P(no woman receives a positive result).

P(no woman receives a positive result)

= P(first woman gets a negative result AND second woman gets a negative result AND ... AND hundredth woman gets a negative result)

= P(first woman gets a negative result) * P(second woman gets a negative result) * ... * P(hundredth woman gets a negative result) = 0.97 * 0.97 * ... * 0.97 (100 times)≈ 0.0048.

The probability that at least one woman will receive a positive result is:

P(at least 1 woman receives a positive result)= 1 - P(no woman receives a positive result)

= 1 - 0.0048

= 0.9952

= 99.52%.

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any help and explanation is greatly appreciated!! I'm struggling with understanding the question and how to find the answer :")

1. "in the figure below. angle GAF is as twice as the abgle DAG. Find X.

*picture of diagram attached below*

### Answers

**Answer:**

x=10

**Step-by-step explanation:**

GAF is 2 times of DAG, so DAG times 2 is GAF.

So, DAG times 2, which is 35*2=70, is GAF.

So now 2x+50=70.

Both sides minus 50 for 2x = 10.

Then divided by 2, for x=10.

Which graph represents the function f(x) = (x – 3)2? On a coordinate plane, a parabola opens up. It goes through (negative 6, 8), has a vertex at (negative 3, 0), and goes through (negative 0, 8). On a coordinate plane, a parabola opens up. It goes through (negative 4, 7), has a vertex at (0, negative 9), and goes through (4, 7). On a coordinate plane, a parabola opens up. It goes through (1, 4), has a vertex at (3, 0), and goes through (5, 4). On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (0, 3), and goes through (2, 7).

### Answers

The third graph is the correct representation of the **function** f(x) = (x - 3[tex])^{2}[/tex].

**What is a** **function?**

A mathematically defined statement, rule, or law that describes the relationship between two independent variables and one dependent **variable** is called a function.

We are given a function as f(x) = (x - 3[tex])^{2}[/tex]. Along with this, we are also given four different graphs of which one is the correct representation of the function.

Since, the given function is a square function so, it will form a **parabola**.

So, on the coordinate plane, a parabola opens up which has a vertex at (3, 0), and goes through (1,4) and (5, 4).

Hence, the third graph is the correct representation of the **function**

f(x) = (x - 3[tex])^{2}[/tex].

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The prices of two different brands of hot chocolate are shown below. What is the difference in price between the two brands when buying 900 g of hot chocolate? Give your answer in pounds (£). Brand A HOT CHOCOLATE £2.70 150 g Brand B HOT CHOCOLATE £3.05 180 g

### Answers

Using the** arithmetic operations**, the price difference between the two brands when buying 900 g of hot chocolate is £0.90.

**What is arithmetic operation?**

A subject of mathematics known as **arithmetic operations** deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and **division** are included.

To compare the prices of the two brands of hot chocolate, we need to calculate the price per gram for each brand.

For Brand A, the price per gram is -

Use the arithmetic operation** **of divison.

£2.70 ÷ 150 g = £0.018 per gram

For Brand B, the price per gram is -

Use the arithmetic operation of **division**.

£3.05 ÷ 180 g = £0.017 per gram

So Brand A is more expensive per gram than Brand B, but we need to calculate the difference in price when buying 900 g of hot chocolate.

For Brand A, 900 g will cost -

Use the arithmetic operation of multiplication.

900 g × £0.018 per gram = £16.20

For Brand B, 900 g will cost -

Use the **arithmetic operation** of multiplication.

900 g × £0.017 per gram = £15.30

Therefore, the difference in price between the two brands when buying 900 g of hot chocolate is -

Use the arithmetic operation of **subtraction**.

£16.20 − £15.30 = £0.90

So Brand A is £0.90 more expensive than Brand B when buying 900 g of hot chocolate.

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Say that you (or your parents) are purchasing a house for $235,000 and have an excellent credit score. If you pay $1,678. 93 at the end of the first month, how much is applied to the principal balance?

### Answers

**Answer:**

**The amount applied to the principal balance can be found by subtracting the interest from the total payment. Assuming a monthly interest rate of r and a principal balance of P, the interest for the first month can be calculated as:**

**interest = r * P**

**Since the payment of $1,678.93 is made at the end of the first month, the interest has not yet accrued, so the full payment goes towards the principal. Therefore, the amount applied to the principal balance is simply:**

**amount applied to principal = $1,678.93**

**So the full payment of $1,678.93 is applied to the principal balance of the house purchase.**

Can someone help me fast!?!?

Trying to get better at doing word problems like this is would help a lot.

A baker plans to sell $560 of baked goods online each week. This week, she is within $42 of her goal.

Define the variable and write an absolute value equation to represent the scenario.

After that solve the equation, showing all steps.

Last, what are the minimum and maximum amounts that the baker received for her baked goods?

### Answers

**Step-by-step explanation:**

Let's define the variable "x" as the amount of baked goods the baker sold this week.

The absolute value equation to represent the scenario is:

|560 - x| = 42

This equation states that the absolute value of the difference between the baker's goal ($560) and the actual amount of baked goods sold (x) is equal to $42.

To solve this equation, we need to consider two cases:

Case 1: 560 - x = 42

In this case, the amount of baked goods sold is:

x = 560 - 42 = 518

Case 2: 560 - x = -42

In this case, the amount of baked goods sold is:

x = 560 + 42 = 602

Therefore, the minimum amount the baker received for her baked goods is $518, and the maximum amount is $602.

. Is there more than one fraction you could use to

estimate 27% of 200? Explain.

### Answers

**Yes**, there are multiple **fractions** that we could use to estimate 27% of 200.

**What is fraction?**

An **element** of a whole is a fraction. The number is represented mathematically as a **quotient**, where the numerator and **denominator **are split.

27% of 200 = 0.27 × 200 = 54

Now, we can find **fractions** that are close to 0.27 and use them to estimate 27% of 200. For **example**:

1/4 = 0.25, which is close to 0.27. So we can **estimate** 27% of 200 as 1/4 of 200:

27% of 200 ≈ (1/4) × 200 = 50

3/11 = 0.2727..., which is also close to 0.27. So we can estimate 27% of 200 as 3/11 of 200:

27% of 200 ≈ (3/11) × 200 ≈ 54.55...

As we can see, both of these fractions give us estimates that are close to the actual **value** of 27% of 200.

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Martins grandma gave him a $100 gift certificate to his favorite restaurant.every day for four days Martin went to the restaurant and bought a drink for $1.19 and fries for f dollars.write a simplified expression for how much money Martin has left on his gift certificate

### Answers

**Answer:**

95.24 - 4f

**Step-by-step explanation:**

100 - 4(1.19) -4f

100 - 4.76 - 4f

95.24 - 4f

Helping in the name of Jesus.

I think the answer would be 95.24 - 4f

1.19 x 4 = 4.76

F x 4 = 4f

100 - 4.76 = 95.24

95.24 - 4f

HELP PLEASE NOW IM SO STUCK

### Answers

The question is invalid or there is an error in the **dimensions** provided.

**What is rectangular prism ?**

A rectangular prism, also known as a rectangular parallelepiped, is a three-dimensional solid object that has six rectangular faces. Each face of a rectangular prism is a rectangle, and **opposite** faces of a rectangular prism are parallel and congruent. Rectangular prisms are commonly encountered in everyday life, for example, in boxes and packages.

The volume of a rectangular prism can be calculated using the formula V = l × w × h, where l, w, and h are the **lengths** of the three edges of the prism. The surface area of a rectangular prism can be calculated using the formula SA = 2lw + 2lh + 2wh, where l, w, and h are the lengths of the three edges of the prism.

We can see that triangle ABC is a **right triangle**, since BC is the longest side and the other two sides are AD and DC. Using the Pythagorean theorem, we can find AB:

AB² = BC² - AC²

AB² = 65² - (30² + 63²)

AB² = 4225 - 4689

AB² = -464

Since we cannot take the **square root of **a negative number, it means that there is no real value for AB that satisfies the given dimensions.

Therefore, the question is invalid or there is an error in the dimensions provided.

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In the rectangular prism below AD=30,DC=63,andBC=65 Find the length of AB

Todd is playing a game. each turn he rolls the die (labeled with the numbers 1-6) and spins the spinner . to win, he needs to roll a 2 and spin a 5 on his next turn. calculate the probability he will on his next turn.

### Answers

The **probability **of Todd winning the game on his next turn is 1/48 or approximately 0.02 or 2%.

**What is the probability?**

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and **possible cases**.

Assuming that the die and spinner are fair, the probability of Todd rolling a 2 and spinning a 5 on his next turn are independent **events**, so we can multiply their probabilities to get the overall probability:

P(rolling a 2) = **1/6** (since there is only one 2 on the die)

P(spining a 5) = **1/8** (since there is only one 5 on the spinner)

Therefore, the **probability **of Todd winning the game on his next turn is:

P(winning) = P(rolling a 2) x P(spining a 5) = (1/6) x (1/8) = 1/48

Hence, the probability of Todd **winning **the game on his next turn is 1/48 or approximately 0.02 or 2%.

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PLEASE ANSWER ASAP - NEED THE ANSWER IN 6 MINS

Line plot titled, Length of Hyacinth Bulbs. The line is labeled, Length in inches. There is a number line from 6 to 10 partitioned into thirds. There is one mark above six and one-third. There are two marks above six and two-thirds. There is one mark above seven and one-third. There are three marks above seven and two-thirds. There is one mark above eight and one-third. There is one mark above eight and two-thirds. There are two marks above nine and one-third. There is one mark above 10.

What is the total length of all the bulbs that are seven and two-thirds inches?

21 inches

twenty-one and two-thirds inches

twenty-two and one-third inches

23 inches

### Answers

**Answer:**

Based on the information provided in the line plot, there are three marks above seven and two-thirds inches. Therefore, there are three bulbs with a length of seven and two-thirds inches.

To calculate the total length of these bulbs, we need to multiply their length by the number of bulbs, which gives:

7 and 2/3 inches x 3 bulbs = 23 inches

Therefore, the total length of all the bulbs that are seven and two-thirds inches is 23 inches.

Triangle ABC is translated 8 units up to create a new triangle A’B’C.

Select the ordered pairs that show the coordinates of the vertices of triangle A’B’C.

To select the coordinates for a vortex, click the ordered pair. To deselect the coordinates, click on the ordered pair again.

(2, -2) (-6, 6) (-6, -10) (2, 6) (2, -10) (10, -7) (2, 1) (10, -2)

### Answers

The **coordinates **of the image of the **triangle** are (-6, 6), (2, 6) and (2, 1)

How to determine the image of the triangle

The **translation rule** for moving a point or object up 8 units is to add 8 to the y coordinates

So, we have

Image = (x, y + 8)

From the figure, we have the **coordinates **to be

(-6, -2), (2, -2) and (2, -7)

So, we have

Image = (-6, -2 + 8), (2, -2 + 8) and (2, -7 + 8)

Evaluate

Image = (-6, 6), (2, 6) and (2, 1)

So, the **image** is (-6, 6), (2, 6) and (2, 1)

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The children from a football club are put in rows in the sports hall

When put in rows of 9, there are two children left over

When put in rows of 12 there are two children left over

What is the least number if children in the football club

### Answers

**Answer: Let's call the total number of children in the football club "x".**

**According to the problem:**

**When the children are put in rows of 9, there are 2 children left over. This means that x is 2 more than a multiple of 9, or in other words: x ≡ 2 (mod 9).**

**When the children are put in rows of 12, there are 2 children left over. This means that x is also 2 more than a multiple of 12: x ≡ 2 (mod 12).**

**To find the least value of x that satisfies both of these congruences, we can use the Chinese Remainder Theorem (CRT).**

**First, let's rewrite the congruences in a standard form:**

**x ≡ 2 (mod 9) --> x = 9a + 2, for some integer "a"**

**x ≡ 2 (mod 12) --> x = 12b + 2, for some integer "b"**

**Now we can use CRT to solve for x:**

**Find the greatest common divisor (GCD) of 9 and 12: gcd(9, 12) = 3.**

**Divide both sides of each congruence by the GCD:**

**x/3 ≡ 2/3 (mod 3), where x/3 = 3a + 2/3**

**x/3 ≡ 2/3 (mod 4), where x/3 = 4b + 2/3**

**Multiply the first congruence by 4 and the second congruence by -3:**

**4(x/3 ≡ 2/3 (mod 3)) --> 4(3a + 2/3) ≡ 8/3 (mod 4) --> 4(3a) + 4(2/3) ≡ 2 (mod 4) --> 3a + 1 ≡ 2 (mod 4)**

**-3(x/3 ≡ 2/3 (mod 4)) --> -3(4b + 2/3) ≡ -2 (mod 3) --> -3(4b) - 3(2/3) ≡ 1 (mod 3) --> b - 1 ≡ 1 (mod 3)**

**Solve for the remainders in each congruence:**

**3a + 1 ≡ 2 (mod 4) --> a ≡ 1 (mod 4)**

**b - 1 ≡ 1 (mod 3) --> b ≡ 2 (mod 3)**

**Substitute back to find x:**

**x = 9a + 2 = 9(4k + 1) + 2 = 36k + 11, where k is an integer (since a ≡ 1 (mod 4))**

**x = 12b + 2 = 12(3j + 2) + 2 = 36j + 26, where j is an integer (since b ≡ 2 (mod 3))**

**Check that x satisfies both original congruences:**

**x ≡ 11 (mod 9), which has a remainder of 2 when divided by 9 (as required)**

**x ≡ 26 (mod 12), which has a remainder of 2 when divided by 12 (as required)**

**Since we want the least value of x, we can take k = j**

**Step-by-step explanation:**

**Answer:**

38

**Step-by-step explanation:**

it would be 38 because we know that the children from a football club are put into rows in the sports hall.

- when putting rows of 9 children, there are 2 children left.

- When put into rows of 12 children, there are 2 left.

LOOK AT THE LCM HERE (LCM OF 9 and 12 = 36) :

9 = 3x3

12 = 2x2x3

= 4x3

= 12

2x2x3x3 = 36

GIVEN that when putting rows of 9 children, there are 2 children left over. Also when put into rows of 12 children, there are 2 left over.

So add the 2 rows with 36 due to there being 2 rows of children LEFT OVER!

36+2=38

The least number of children in the football club = 38.

a patient needs of a low-dose pain reliever. the pharmacy sends pills marked . how many should be administered? round to the nearest tenth of a pill.

### Answers

The pharmacy should send two pills **marked **for the patient to take.

To answer this question, we can use the formula below;

Dosage = (Amount of Drug x Patient's Weight) / Time

Since we don't have any **information **about the patient's weight or the time, we can't calculate the dosage.

However, we can calculate the number of pills required.

So, let's proceed with the calculation.

Each pill contains 2.5 mg of the pain reliever.

We need to **administer **a low dose, so let's assume the dose required is 5 mg.

To administer this dose, we need to give two pills, i.e., 2 x 2.5 = 5mg.

However, the question asks us to round the answer to the **nearest **tenth of a pill.

Since we can't divide a pill into parts, we need to round the answer up or down to the nearest whole pill.

In this case, since we need two pills, the answer is 2 pills.

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Part B Question Which statement is true about the difference of the sample means? The difference of the sample means is statistically significant because it falls outside the 5% significance level. The difference of the sample means is not statistically significant because it falls outside the 5% significance level. The difference of the sample means is not statistically significant because it falls within the 5% significance level. The difference of the sample means is statistically significant because it falls within the 5% significance level.\

### Answers

The difference of the sample **means **is not statistically significant because it falls within the 5% significance level. So correct option is B.

Describe Statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves methods and techniques for collecting, summarizing, and analyzing data to draw conclusions or make decisions. Statistics can be applied in a wide range of fields, including science, business, engineering, medicine, and social sciences.

Some of the key concepts in statistics include descriptive statistics, which involve summarizing and presenting data in a meaningful way, and inferential statistics, which involve using **sample **data to make inferences or draw conclusions about a larger population. Other important concepts include probability theory, hypothesis testing, regression analysis, and statistical modeling.

Statistics plays a critical role in many aspects of modern life, from scientific research and public policy to business decision-making and personal finance. By providing a rigorous framework for data analysis and interpretation, statistics helps us to understand the world around us, make informed decisions, and solve complex problems.

Since the 95% confidence interval includes 0 (i.e., it includes the **possibility **of no difference between the population means), we cannot reject the null hypothesis at the 5% level of significance. Therefore, the difference of the sample means is not statistically significant because it falls within the 5% significance level. The correct answer is:

The difference of the sample means is not statistically significant because it falls within the 5% significance level.

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The complete question is:

You calculated the standard deviation of the sample mean differences to be 0.69. You also calculated the sample mean difference to be 1.74. Now you’ll determine whether the difference is significant. For the purpose of constructing the confidence interval, assume that there’s no difference between the population means.

Part A

Question

Determine the 95% confidence interval for the difference of the sample means. Then complete the statements. The 95% confidence interval is -1.38 -3.44 -3.48 -1.26 to 1.38 3.44 1.26 3.48

The value of the sample mean difference is 1.74, which falls within outside the 95% confidence interval.

Part B

Question

Which statement is true about the difference of the sample means?

The difference of the sample means is not statistically significant because it falls outside the 5% significance level.

The difference of the sample means is not statistically significant because it falls within the 5% significance level.

The difference of the sample means is statistically significant because it falls within the 5% significance level.

The difference of the sample means is statistically significant because it falls outside the 5% significance level.

Find the hypotenuse of the triangle, the

distance between points (4, 4) and (-2,-2).

[?]

(4,4)

Enter the number that

6 goes beneath the radical

symbol.

(+242)

6

please give me a real answer i need this

### Answers

The **length** of the hypotenuse of the triangle is **6*sqrt(2) **if the two points in a coordinate plane are (4, 4) and (-2,-2).

The given points are,

point 1 = (4, 4)

point 2 = (-2,-2)

To **calculate** the length between two points in a coordinate plane, the distance formula is used:

**d = sqrt((x2 - x1)^2 + (y2 - y1)^2)**

Here we can assume (x1, y1) and (x2, y2) are the **coordinates** of the two points.

d = sqrt((-2 - 4)^2 + (-2 - 4)^2)

d = sqrt((-6)^2 + (-6)^2)

d = sqrt(36 + 36)

d = sqrt(72)

**d = 6 * sqrt(2)**

Therefore, the **length** of the hypotenuse of the triangle is **6 *sqrt(2)**.

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For a store's anniversary sale, 320 employees were asked their favorite color choice for sales tags. The results are shown in the circle graph. How many employees chose pink? Enter your answer in the box.

### Answers

The number of **employees** that chose **pink** would be = **128 employees.**

How to calculate the number of employees that chose pink?

To calculate the number of employees that chose **pink** is to convert the **percentage** values from the circle diagram to an ordinary value.

From the diagram, the **percentage** of pink = 40%

The total number of **employees** = 320

Therefore 40% of 320;

= 40/100×320

= 12800/100

= **128 employees.**

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Here is a diagram of the base of a bird feeder. Each square on the grid represents 1 square inch. What is the area of the base of the bird feeder?

### Answers

The **area** of the base of the bird feeder is 49 square inches.

**What is area of square?**

The area of a **square** is the amount of space inside the square, and it is calculated by multiplying the length of one side by itself.

To find the area of the base of the bird feeder, we need to find the areas of the **triangle** and the square and then add them together.

Area of the triangle = (base x height) / 2

= (7 x 4) / 2

= 14 square inches

Area of the square = length x width

= 5 x 7

= 35 square inches

Total area of the base = area of triangle + area of square

= 14 + 35

= 49 square inches

Therefore, the area of the base of the bird feeder is 49 square inches.

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Imagine you are the pastry chef at your favorite restaurant. The manager has just told you that you have a large crowd coming in for lunch tomorrow and you need to prepare. This project includes a recipe for cupcakes for dessert. You are expecting 108 people, but the recipe does not serve that many people, so you will need to adjust the ingredients so there will be enough. For example, if a recipe serves 8 people and you need to feed 32 people, what would you need to do? You would have to make 4 times as much as the original recipe makes, which means that you would need to multiply the amount of each ingredient by 4, since 8*4 = 32.

### Answers

**Answer:**

To adjust the cupcake recipe to serve 108 people, you will need to follow these steps:

Determine how many cupcakes the original recipe makes. Let's say the original recipe makes 12 cupcakes.

Calculate how many batches of cupcakes you will need to make to serve 108 people. To do this, divide the number of people by the number of cupcakes in one batch: 108 ÷ 12 = 9. You will need to make 9 batches of cupcakes.

Multiply the amount of each ingredient in the original recipe by 9. For example, if the original recipe calls for 2 cups of flour, you will need 18 cups of flour (2 cups x 9 batches).

Follow the same process for all of the ingredients in the recipe, making sure to adjust each one by the same factor.

Prepare the cupcakes according to the adjusted recipe, baking each batch separately.

By following these steps, you should be able to adjust the cupcake recipe to serve the large crowd coming in for lunch tomorrow.

**Step-by-step explanation:**

Please answer the questions in the photo (will mark brainliest if available + 20p )

### Answers

**Answer:**

-3x power 3+x power 4+5 is the answer

a rectangular pizza, 40 cm by 60 cm, is cut into 24 square pieces. two round pizzas, each cut into 12 slices, also give 24 pieces. so that the pizza slices are the same size, what must be the diameter of the round pizzas? round to the nearest centimeter. don't include units.

### Answers

A rectangular pizza, 40 cm by 60 cm, is cut into 24 square pieces. two round pizzas, each cut into 12 slices, also give 24 pieces. The **diameter** of the round pizzas is approximately 3.2 cm when the pizza slices are the same size.

The length of a straight line passing through the center of a circle and **connecting **two points on the circumference.

To find the diameter of the round pizzas, let's **assume** 'd' to be the diameter of the round pizzas.

Given,

The area of the **rectangular** pizza = 40 cm × 60 cm = 2400 cm²

The area of one **square **piece = 2400 / 24 = 100 cm²

The area of two round pizzas = 24 × 2 = 48

The area of one slice of **round** pizza = 48 / 12 = 4

The **area** of one slice of round pizza = π × (d/2)² => 4 = π × (d/2)²So, (d/2)² = 4/π=> d/2 = √(4/π)=> d = 2 × √(4/π) ≈ 3.183 cm≈ 3.2 cm (nearest centimeter).

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unit 8 right triangle and trigonometry homework 5 trigonometry: finding sides and angles. Helppp

### Answers

1. The **length** of x ≈ 14.3 , 2. x ≈41.4, 3. x ≈ 18.1 and 4. x ≈ 118.5 rounding to the nearest tenth in the given triangle.

**What is the** **length?**

1. Let us assume the given triangle as a ΔABC, Using **trigonometry**, we can find that sin(63°) = BC/16, which implies that BC ≈ 14.3. Rounding to the nearest tenth, we get x ≈ 14.3.

2. Let us assume the given **triangle** as a ΔABC, Using trigonometry, we can find that sin(39°) = BC/x, which implies that x ≈ 41.4. Rounding to the nearest tenth, we get x ≈ 41.4.

3. Let us assume the given triangle as a ΔABC, Using trigonometry, we can find that sin(49°) = BC/14, which implies that BC ≈ 10.9.

Then, using the **Pythagorean theorem**, we get x ≈ 18.1. Rounding to the nearest tenth, we get x ≈ 18.1.

4. Let us assume the given triangle as a ΔABC, Using trigonometry, we can find that sin(15°) = BC/x, which implies that x ≈ 120.3.

Then, using the Pythagorean theorem, we get AB ≈ 118.5. Rounding to the nearest tenth, we get x ≈ 118.5.

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List all pairs of congruent angles. Then write the ratios of the corresponding side lengths in a statement of proportionality. (Answer 8)

### Answers

7. Ratios of the **corresponding **side lengths= BD/MP = DG/PQ = BG/QM. 8. ratios of the corresponding side lengths= DE/HJ = EF/KL = FG/LK = GD/JH.

Describe Quadrilaterals?

A quadrilateral is a polygon with four sides and four angles. It is a two-dimensional shape that can be defined by the length of its sides, the measure of its angles, and its internal **geometry**. There are many different types of quadrilaterals, each with its own set of properties and characteristics.

The most basic type of quadrilateral is a rectangle, which has four right angles and opposite sides that are parallel and equal in length. A square is a special type of rectangle, where all four sides are equal in length. Another common type of quadrilateral is a parallelogram, which has opposite sides that are parallel and equal in length. A rhombus is a type of parallelogram where all four sides are equal in length.

7. Triangle BDG congruent to triangle MPQ:

Angle BGD is congruent to angle MQPAngle BDG is congruent to angle MPQAngle GBD is congruent to angle QMP

The ratios of the corresponding side lengths in a statement of **proportionality **can be written as:

BD/MP = DG/PQ = BG/QM

8. DEFG congruent to HJKL:

Angle DEF is congruent to angle HJKAngle EFG is congruent to angle JKLAngle DFE is congruent to angle HJLAngle GEF is congruent to angle KHL

The ratios of the corresponding side lengths in a statement of proportionality can be written as:

DE/HJ = EF/KL = FG/LK = GD/JH

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According to legend, the inventor of the game of chess requested payment as follows:

My request is a modest one. I humbly request one grain of rice on the first square of the chess board, two grains on the second square, four grains on the third square, and so on. Each square represents twice as many grains as the previous one.

The king agreed immediately.

Part a: Write an expression for the number of grains on square n of the chess board.

Part b: How many grains of rice are to be placed on the 20th

square?

Part c: There are 64 squares on a chess board; do you think the king was able to fulfill the request? Explain.

### Answers

After answering the provided question, we can conclude that Therefore, **function **there are [tex]2^19[/tex]grains of rice on the 20th square, which is equal to 524,288.

what is function?

In **mathematics**, a function is a relationship between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the **range**). In other words, a function takes **inputs **from one set and produces outputs from another. Inputs are frequently represented by the variable x, while outputs are represented by the variable y. A function can be described using an equation or a **graph**. The equation y = 2x + 1 depicts a linear function in which each value of x yields a distinct value of y.

a) Let's define a recursive function to represent the number of grains on square n, where n can be any positive integer:

[tex]f(n) = 1, if n = 1\\f(n) = 2*f(n-1), if n > 1[/tex]

b) To find the number of grains on the 20th square, we can simply plug in n=20 into the expression we derived above:

[tex]f(20) = 2f(19) = 2(2f(18)) = 2(2*(2*f(17))) = ... = 2^19[/tex]

Therefore, there are [tex]2^{19}[/tex] grains of rice on the 20th square, which is equal to 524,288.

c.

[tex]total_{grains} = f(1) + f(2) + f(3) + ... + f(64)\\total_{grains} = 2^0 + 2^1 + 2^2 + ... + 2^63\\sum = a*(1 - r^n)/(1 - r)\\total_{grains} = 1*(1 - 2^64)/(1 - 2) = 2^64 - 1\\[/tex]

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Taylor babysits four times as many hours on the weekend as she does during the week. She earns $10. 50 per hour. This week, she wants to earn at least $315. Will Taylor meet her goal by working 4 hours during the week

### Answers

Taylor needs to work at least 6 hours during the week to meet her goal of **earning **at least $315. However, since she is working only 4 hours during the week, she won't be able to meet her goal.

Taylor works "w" hours during the week and "4w" hours on the weekend. Therefore, her total **working hours** in a week are "5w". Taylor earns $10.50 per hour, so her weekly earning can be calculated as "10.50 * 5w = 52.5w".

Now, we need to find out if Taylor can meet her goal of earning at least $315.

We can set up an **inequality**:

52.5w ≥ 315

Dividing both sides by 52.5:

w ≥ 6

This means Taylor needs to work at least 6 hours during the week to meet her goal. Since she is working 4 hours during the week, she won't be able to meet her goal.

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Complete question:

Taylor babysits four times as many hours on the weekend as she does during the week. She earns $10. 50 per hour. This week, she wants to earn at least $315. Will Taylor meet her goal by working 4 hours during the week?

marsha pays $25 for the first ticket purchase to the roller coaster theme park. each ticket after the first is $10. write a function expressing the amount of money she pays for herself and friends to go to the roller coaster theme park. let x be the total number of people in the group

### Answers

The **function **expressing the amount of money Marsha pays for herself and friends to go to the** roller coaster** theme park is f(x) = $10x + $15.

Given that **Marsha **pays $25 for the first ticket purchase to the roller coaster theme park and each ticket after the first is $10.To express the amount of money she pays for herself and friends to go to the **roller coaster** theme park, we can write a function as follows; Let x be the total number of people in the group.

If Marsha and her friends are 'x' in number, then the total number of tickets they will have to purchase will be 'x'.Then the amount Marsha pays for herself is $25 and the amount Marsha pays for her** friends** is $10 per person. So, the amount Marsha pays for the friends is (x - 1) * $10Hence, the function can be **expressed** as:f(x) = $25 + (x - 1) * $10 = $25 + $10x - $10= $10x + $15.

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