Homework 1: Parallel Lines & Transversal

Answer:

8(x-4)

= 8x - 32

hope it helps

a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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The phrase that is identical to 7(d - 4) in option B is -4(d+ 7). A mathematical expression is a statement that contains a minimum of two numbers .

A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's basic components are as follows: Expression is (Number/Variable, Math Operator, Number/Variable). A mathematical expression is a statement that contains a minimum of two numbers or variables and at least one mathematical operation. Let's learn how to write expressions. A number is 6 more than half of another number, and that other number is called x. In a mathematical expression, this statement is represented as x/2 + 6.

given

The correct response is 4 less than 7, since 4 is less than 7.

Thus, 7-4=3 could be considered.

The first section of 7–4 appears to be answer B.

The phrase that is identical to 7(d - 4) in option B is -4(d+ 7).

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Answer:

A

Step-by-step explanation:

You take the 64 teams, split it in half, and then the exponent is r

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The equation that represents the number of teams t that remained in the tournament after r rounds is t = 64 x \((1/2)^{r}\)

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 3x + 3 = 4 is an equation.

We have,

Number of teams = 64

The number of teams eliminated after each round = Half the team.

The equation represents the number of teams t that remained in the tournament after r rounds.

t = 64 x \((1/2)^{r}\) ____(1)

Put r = 1, we must get 32 teams.

t = 64 x 1/2 = 32

Put r = 2 we must get 16 teams.

t = 64 x (1/2)² = 64 x 1/4 = 16

We see that (1) is the correct equation to represent the number of teams t that remained in the tournament after r rounds.

Thus,

The equation that represents the number of teams t that remained in the tournament after r rounds is t = 64 x \((1/2)^{r}\)

Option A is the correct answer.

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T test is used to compute the confidence interval, when the mean and standard deviation is given.

What is Standard Deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be very close to the set mean. The lower case Greek letter (sigma), again for population standard deviation, or even the Latin letter s, again for sample standard deviation, are most frequently used in mathematical texts and equations to represent standard deviation. Standard deviation may be abbreviated as SD. A random variable, specimen, statistical population, data set, as well as probability distribution's standard deviation is equal to the square root of its variance. When the number in a sample, sample mean and sample standard deviation is given, the test statistic that should be used when computing a confidence interval is t test

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The difference between a set of expected and observed values is known as residual standard deviation, which refers to the standard deviation of the residual values.

In the given question we have to explain the standard deviation of the residual values in the regression output.

Regression analysis is a statistical technique used to demonstrate the relationship between two different variables and to assess how well one variable can be predicted based on the behaviour of another.

The standard deviation of points surrounding a fitted line or the standard error of estimate are other names for residual standard deviation.

The difference between a set of expected and observed values is known as residual standard deviation, which refers to the standard deviation of the residual values.

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Answer:

B

Step-by-step explanation:

IDGAF

First you will get 4dz

By rewriting a relation we will see that there are 0.5 fluid ounces in a tablespoon.

We know the relation between the different units:

1 fluid ounce = 2 tablespoons.

To see how many fluid ounces are in a tablespoon, we just need to work with the relation above and write "1 tablespoon" on the right side.

So if we take our relation:

1 fluid ounce = 2 tablespoons.

And we divide both sides by 2 then we will get:

1/2 fluid ounce = 2/2 tablespoons.

0.5 fluid ounces = 1 tablespoon.

then we can conclude that there is 0.5 fluid ounces in a tablespoon.

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The amount raised by a booster club compared with the number of  raffle tickets sold shows a constant rate of change;

A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.

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The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.

To solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;

8x - 4y = -4

add 4y to both sides

8x - 4y + 4y= -4 + 4y

8x = - 4 + 4y

also to make y the subject;

- 4 + 4y = 8x

add 4 to both sides

- 4 + 4 + 4y = 8x + 4

4y = 8x + 4

factorize the right hand side

4y = 4(2x + 1)

divide through by the coefficient of y

4y/4 = [4(2x + 1)]/4

y = 2x + 1

Hence, the equation 8x - 4y = -4 has y = 2x + 1

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Answer:

8 3/4

Step-by-step explanation:

There are 5 jobs that required less than 2 1/2 gallons.

For the equation, you'll just be adding all these up

1 1/2 + 1 1/2 + 1 3/4 + 2 + 2

Which will give you 8 3/4

Answer:

-1⅓÷2⅖=-4/15

Step-by-step explanation:

this my answer negative 4/15

The area οf the given figure is 44.5 cm²

A cοmpοsite figure is a shape made up οf twο οr mοre simple shapes, such as triangles, rectangles, circles, οr pοlygοns, that are cοmbined οr intersected tο create a new shape.

Tο find the area οf the given figure find the area οf individual parts rectangle and triangle.

Here we have

A cοmpοsite figure fοrmed by οne rectangle and οne triangle

Frοm the figure dimensiοns οf the rectangle are 3 × 9 cm

Since the οppοsite sides οf the rectangle are equal take the missing side οf the rectangle as 3 cm

Area οf the rectangle = Lenght × Width

= 3 cm × 9 cm = 27 cm²

Given the height οf the triangle as 5 cm

Base οf triangle = (2 + 3 + 2) cm = 7 cm

Hence, Area οf the triangle = 1/2(5) × (7) = 17.5 cm²  

Here area οf the cοmpοsite figure = Area οf rectangle + Area οf triangle

= 27 cm² + 17.5 cm²

= 44.5 cm²

Therefοre,

The area οf the given figure is 44.5 cm²  

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Answer:

3:5

Step-by-step explanation:

3, 6, 9.

5, 10, 15.

always see which numbers fit and which numbers dont

Answer:

9:24 is the ratio.

Step-by-step explanation:

Answer:

(0,0), (1,2), (2,4), (3,6), (4,8), (5,10)

Step-by-step explanation:

Hi again,

Once again, this equation does not have the "b" for y = mx + b. Therefore, this linear graph will run through the origin (0,0).

To find the y coordinates, you can substitute the x value into y = 2x.

For example, if you put in 2  into y = 2x, you would get 4 for the y-coordinate.

Hope this explains the process. Cheers.

Answer:

the answer is a

Step-by-step explanation:

x=0 the first equation gives -4

andx= 2 6/2 = 3-4= -1

Answer:

Step-by-step explanation:

m∠1 = 35°

m∠1 +m∠2 = 90°    {The two angles are compliments}

35 + m∠2  = 90°

          m∠2 = 90 - 35

         m∠2 = 55°

m∠2 + m∠3 = 90°      {The two angles are compliments}

55 + m∠3 = 90°

       m∠3 = 90° - 55°

m∠3 = 35°

Answer:

C) d=400t

Step-by-step explanation:

400mph means 400 miles per hour. (So every hour 400miles is covered due to the fact that its constant)

Therefore, to have the total distance, we take the 400 and multiply it by the amount of Time spent. (T in this inatance)

Answer:

20

Step-by-step explanation:

To determine the number of 9s between 1 and 100, we can consider the numbers from 1 to 99 since we want to exclude 100.

In the range from 1 to 99, we can observe the following patterns:

There is one 9 in each of the units' places (9, 19, 29, ..., 89, 99), giving us 10 occurrences.

There is one 9 in each of the tens' places (90, 91, 92, ..., 99), giving us 10 occurrences.

Therefore, there are a total of 10 + 10 = 20 occurrences of the digit 9 between 1 and 100.

Answer:

14.7

Step-by-step explanation:

Answer:

https://brainly.com/question/19844359?answeringSource=feedPublic%2FhomePage%2F1

Step-by-step explanation:

here's a link to the answers

Answer:

B. {-5, -4, 2}

Step-by-step explanation:

brainliest

Answer:

function A

Step-by-step explanation:

_______________

Answer:

let DEC=x

x-135=180

x=45°

supplementary angles

Answer:

around 45 minutes

Step-by-step explanation:

it takes about 15 minutes to do 1 mile, do the correct math, it'll take about 45 minutes to do 3 miles

As per the volume of the rectangular tank, the dimensions are 13.78 x 379.82 x 13.78

Volume of rectangle:

The general formula to calculate the volume of the rectangle is

V = length x width x height.

Given,

A rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness.

Here we need to find the dimensions of the rectangular tank,

As per the given volume of rectangular tank, when we equate this with the formula, then we get,

=> 5234 = length x width x height.

Let us consider the length and the width are equal then we get the value of height as.

=> height = 5234/length

So, the value is calculated by using the surface area formula,

=> A = length² + 5234/length

When we differentiate the surface area with respect to

=> dA/dl = 2l - 5234/l²

To minimize the surface area, so dA/dl = 0,

=> 2l = 5324/l²

=> 2l³ = 5234

=> l³ = 2617

=> l = ∛2617

Therefore, the value of length is 13.78

Then the height is calculated as.

=> h = 5234/13.78 = 379.82

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Answer:

17 + 6i

Step-by-step explanation:

(2 + 3i)(4 - 3i) ← expand product using FOIL

= 8 - 6I + 12I - 9I² ( note i² = - 1 )

= 8 + 6i - 9(- 1)

= 8 + 6i + 9

= 17 + 6i

Answer:

$160

Step-by-step explanation:

Diane sold some stuffs at a garage sale.

Let the total value of the money Diane made = x

She spent one-half of the money she made on a new bicycle.

Amount spent on a Bicycle = 1/2 × x = 1/2x

Next,

Amount left

= x - 1/2x = 1/2x

She spent one-half of what was left on a portable stereo.

Amount spent spent on Portable stereo

= 1/2 × 1/2x

= 1/4x

If Diane had $40.00 left,

Hence:

The fraction of what was left is calculated as:

= x - (1/2x + 1/4x)

= x - (3/4x)

= 1/4x

Hence:

1/4x = $40

We can find the value of x now.

1/4 × x = $40

x/4 = $40

x = $40 × 4

x = $160

Therefore, the amount she made from the garage sale is $160

Answer:

Hey hey guys, it is 160.00

Step-by-step explanation:

Answer:  430000

Step-by-step explanation: you have to do pemdas

Answer: 430,000. /four hundred thirty thousand

Step-by-step explanation:

The value of 4.3 x 10^5 is 430,000.

To understand this, the notation 4.3 x 10^5 represents a number in scientific notation, where 4.3 is the coefficient or significand, and 10^5 is the exponent. The exponent of 10 tells us how many places to move the decimal point to the right. In this case, the exponent 5 means we need to move the decimal point five places to the right.

Starting with 4.3, we move the decimal point five places to the right to get 430,000. So, 4.3 x 10^5 is equivalent to 430,000.

Answer:

d. 6, 4 (1/2), 3, 1 (1/2), ...

Step-by-step explanation:

A geometric sequence is any sequence that is exponentially growing/decaying, so analyze the slopes. The slope for D is a constant -1.5, so it is a linear (not geometric) sequence.