The graph represents the journey of a bus from the bus stop to different locations:

The title for the graph is Bus Journey. The label on the y-axis is Distance in miles, and the label on the x-axis is Time in hours. The graph shows 5 parts. The part labeled 1 is a smooth curve going up from the origin. The part labeled 2 is a straight horizontal line. The part labeled 3 is a smooth curve going up. The part labeled 4 is a straight horizontal line. The part labeled 5 is a smooth curve going down that touches the x-axis.
Part A: Use complete sentences to describe the motion of the bus in parts 1, 2, 3, 4, and 5 of the journey. (4 points)

Part B: In which parts of the graph is the function increasing, decreasing, and constant? (4 points)

Part C: Is the graph linear or non-linear? Explain your answer. (2 points)

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

Since the length of 15 is divided between the circumference of the circle and the perimeter of the square,

2πr + 4s = 15 ⇒ s = (15 - 2πr ) / 4

A = πr2 + s2 = πr2 + [ (15 - 2πr ) / 4]2 = πr2 + (225 - 60πr + 4π2r2) / 16

A = π(1 + π/4)r2 - (15/4)πr + 225/16

dA/dr = 2π(1 + π/4)r - (15/4)π = 0 ⇒ r = (15/4)π / [2π(1 + π/4)] = 15 / (8 + 2π)

Since A(r) is concave up, it has a minimum at

r = 15 / (8 + 2π)

Since  s = (15 - 2πr ) / 4 and s > 0, the maximum r is 15/(2π).  This same r will also maximize the area.

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Answer:

B

Step-by-step explanation:

Answer:

John = 14 ; Van = 26

Step-by-step explanation:

V = 12 + J

V - 2 = 2(J-2)

12 + J - 2 = 2J - 4

J + 10 = 2J - 4

2J - J = 10 + 4

J = 14

V = 12 + 14

V = 26

Answer:

Width is 5.

Length is 11.

Step-by-step explanation:

Let the width be x.

x = width

The length is 6 feet longer.

x + 6 = length

Area is

length × width

Area is 55 (given)

55 = x(x+6)

Use distributive property.

55 = x^2 + 6x

Set equal to 0 and factor to solve. See image.

We have to toss out a solution that doesn't make sense. A measure of a side of a rectangle cannot be negative.

see image.

Step-by-step explanation:

30/4=7.4

30/5=6

6/3=2

Alex went to the moves 4 times that year.

Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

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Answer:Pemdas

Step-by-step explanation:Comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2²

The expressions are given in the question as:

(8 + 3² - 2·6)/(7 - 1·2) and (3/4 + 1/8) + 1/8 - 2²

As per the PEMDAS rule, the required solution would be as:

⇒ (8 + 3² - 2·6)/(7 - 1·2)

⇒ (8 + 9 - 12)/(7 - 2)

⇒ (17- 12)/5

⇒ 5/5

⇒ 1

⇒ (3/4 + 1/8) + 1/8 - 2²

⇒ (6 + 1)/8 + 1/8 - 4

⇒ 7/8 + 1/8 - 4

⇒ (7 + 1)/8 - 4

⇒ 8/8 - 4

⇒ 1 - 4

⇒ -3

Here 1 > -3

Thus, comparing the given expression as per the solution:

(8 + 3² - 2·6)/(7 - 1·2) > (3/4 + 1/8) + 1/8 - 2².

Answer:

                  1

log₂√2 = ------

                  2

Step-by-step explanation:

I'm assuming the equation looks like this:

2¹⁽² = √2

                  1

log₂√2 = ------

                  2

I hope this helps!

The equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

What is a polynomial function?

Polynomial functions are defined for all values of x and have a finite number of roots (x-values at which the function is equal to 0). The roots of a polynomial function can be found by solving the equation f(x) = 0.

By using the given table, we can plot the points on the graph and we can draw a graph

• Fitted coefficients:

a = 9

b = -9

c = -1

d = 1

Then we can prepare the polynomial as

y = 9 - 9x - x² + x³

Now write down in the standard form, we get

f(x) = x³ - x² -9x + 9

Hence, the equation of the cubic polynomial is f(x) = x³ - x² -9x + 9.

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Share of the each person is 1/12. And the above situation can be represented in the given picture.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire.

When we cut a piece of cake from the entire thing in real life, that could be the best example for Fractions.

To represent a fraction in a diagram we choose a closed polygon like a circle, square, etc.

First, divide the polygon into the number of parts as given in the denominator and shade the number of taken parts that are given in the numerator.

Here we have

6 people equally share 1/2 a pan of macaroni and cheese  

As we know 1/2 means half

By the given data, Half of the macaroni and cheese is shared by 6 people which means Half of the pan of macaroni and cheese again divided into 6 parts

=> (1/2) ÷ 6 =  [tex]\frac{ \frac{1}{2} }{6}[/tex]  = [tex]\frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]  

Therefore,

Share of the each person is 1/12. And the above situation can be represented in the given picture.

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It will take 220.8 hour, Teresa to knit 265 squares

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that the relationship between the number of hours Teresa spends

knitting and the number of squares she completes for a blanket.

We need to find the hours does it take Teresa to knit 265 squares.

Now Based on the equivalent ratios  we have;

Teresa's Knitting /Completed Squares

10/12 = x / 265

Thus, Now cross multiplication we get;

x = 265(10/12)

x = 220.8

The answer is 220.8

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Answer: z=3x+1

Step-by-step explanation:

1. Distribute 6 through the parentheses

18x=6z-6

2. Move the z variable to the left side and x variable to the right

-6z= -6-18x

3. Divide both sides by -6 in order to get z by itself

z=1+3x

4. Reorder the terms using commutative property

z=3x+1

Answer:

x = 222:2 and x = 2

Step-by-step explanation:

(2x-123):3=33

(2x – 123):3 = 33

2x – 123 = 33.3

2x – 123 = 99

2x = 99 + 123

2x = 222

x = 222:2

x = 111

200-8.(2x+7)=112

200 – 8.(2x + 7) = 112

-8.(2x + 7) = 112 – 200

-8.(2x + 7) = -88

2x + 7 = (-88):(-8)

2x + 7 = 11

2x = 11 – 7

2x = 4

x = 4:2

   x = 2

I hope my answer helps you.

Answer: A residual is the difference between the observed value of a dependent variable and the predicted value based on a given model. In this case, the manager of the water park has produced a least squares regression equation of the form y = -3110 + 51.2x, where y is the number of customers entering the park and x is the daily high temperature. This equation can be used to predict the number of customers based on a given temperature.

On the day in question, the high temperature was 93F and 1700 customers entered the park. Using the given equation, we can predict the number of customers that would be expected based on this temperature:

y = -3110 + 51.2x

= -3110 + 51.2 * 93

= -3110 + 4768.6

= 1658.6

The residual for this observation is the difference between the observed value of 1700 and the predicted value of 1658.6, which is 1700 - 1658.6 = 41.4. This is the residual for this observation.

To determine how much data is enough to estimate the average weight of this population with a 95% confidence and an error not superior to 15 grams, we would need to use a statistical sample size calculator or consult a statistical table. Factors that would need to be considered include the desired confidence level, the desired margin of error, and the standard deviation of the population.

Using a sample size calculator, we can input these values and determine the required sample size. For example, with a 95% confidence level, a margin of error of 15 grams, and a standard deviation of 87 grams, the required sample size would be approximately 38 children. This means that we would need to measure the weight of at least 38 male children who are 10 weeks old in order to estimate the average weight of the population with a 95% confidence and an error not superior to 15 grams.

It is important to note that this is just an estimate and the actual sample size may vary depending on the specific characteristics of the population being studied. Additionally, it is always a good idea to consult with a statistician or other expert to ensure that the appropriate sample size is used in any statistical analysis.

Answer: 1/2

Step-by-step explanation:

Use rise over run. Up 1, over 2.

And so on. Find nice points on the graph to practice slope with!

The change represents growth and rate of increase is 4.2%

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Given that, an exponential function y = 970(1.042)ˣ

When the growth rate is greater than 1, then the function represents a growth.

The general form equation is:

y(x)= a(1+r)ˣ such that r is the growth percent.

So,

1+r = 1.042

r = 0.042

r = 4.2%

Hence, the growth rate is 4.2%

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The equations that model the total cost of the meal are:

A. x = 3 * 4 + 29

C. x = 41

We know that the family has 4 members and they buy:

Then the total cost is the $29 for the dinner plate plus four times the $3 for the dessert, this is:

x = $29 + $4*3

x = $29 + $12

x  = $41

Then the correct options are A and C.

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Answer:

always true , because 120+60=180

Answer:

[tex]85 \sqrt{5} [/tex]

We would expect 198 of the intervals to contain the mean.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

Given that Mary wishes to estimate the mean height of women aged 18-24.

picks a sample of 100

Women aged between 18 and 24 and constructs a 99% confidence interval for the population mean.

If Mary were to repeat this procedure 200 times in total, she would obtain

200 different confidence intervals.

A confidence interval of a parameter gives an interval in which the parameter is expected to be found. Because the interval either contains or doesn't contain the parameter, the probability is either 0 or 100%, which is not helpful.  A 95% CI says that if we construct 100 intervals, 95% will contain the parameter. That is a true percentage, not a confidence. We don't know which 95, however, since the parameter is still unknown or unknowable.

I would expect 99%×200 or 198 of the intervals to contain the mean.

Hence, would expect 198 of the intervals to contain the mean.

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The equation represents that, Miles could rent the meeting room for t ≤ 16 hours.

What is inequality?

The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.

The total cost for Miles to rent the meeting room for t hours is given by the equation C = 21 + 4t. We are trying to find the number of hours t for which C is equal to or less than $85.

We can solve this problem by setting up the inequality 21 + 4t ≤ 85 and solving for t.

Subtracting 21 from both sides gives us 4t ≤ 64.

Dividing both sides by 4 gives us t ≤ 16.

Thus, Miles can rent the meeting room for t hours, where t is less than or equal to 16. This means that he can rent the room for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, or 16 hours.

Hence, the equation represents that, Miles could rent the meeting room for t ≤ 16 hours.

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Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

As per the given,

5 machines take 9 days,

5 x 9 = 45 machines day

45/15 = 3 days

Hence "Total machine days are 5 9 = 45 thus, it will take 3 days to complete the same test with 15 machines".

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Answer: x>2

Step-by-step explanation:

To solve for x, we want to use inverse operations to isolate x.

[tex]-\frac{x}{2} < -1[/tex]            [multiply both sides by -2]

[tex]x > 2[/tex]

Answer:(-6 5/6)

Step-by-step explanation:

-12.5=-12-1/2

-5 2/3= -5-2/3

=(-12 3/6)-(-5 4/6)

=(-6 5/6)

gimme brainlliest

The equivalent expression is (x + 2√3i) (x - 2√3i).

What is a Polynomial Equation?

The equations formed with variables, exponents and coefficients are called as polynomial equations. It can have different exponents, where the higher one is called the degree of the equation.

Given polynomial is,

x² + 12

We need to find it's equivalent expression for that see the options

Solve the option (a)

(x + 2√3i) (x - 2√3i)

Now, solve this if we get equal to x² + 12 that means that option is answer

x(x - 2√3i) + 2√3i(x - 2√3i)

x² - 2xi√3 + 2xi√3 -  2√3i *  2√3i

x²  -  12 i²

we know, i² = -1

so, we get

x² + 12

We get the answer by 1st option. If you solve other options you'll get different answer.

Hence, the equivalent expression is (x + 2√3i) (x - 2√3i).

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The expression that is equivalent to the given expression, (ab⁷)⁴, is a⁴b²⁸. The correct option is the last option a4b28

From the given information, we are to determine the expression that is equivalent to the given expression

The given expression is

(ab⁷)⁴

To determine the expression that is equivalent to this expression, we will expand the given expression

Expanding the expression

(ab⁷)⁴

Applying the distributive exponent law of indices,

(a)⁴ × (b⁷)⁴

Simplifying

a⁴ × b²⁸

= a⁴b²⁸
Hence, the equivalent expression is a⁴b²⁸

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Answer:

I think it's a4b28

Step-by-step explanation:

Answer:

Step-by-step explanation:

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The required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

Given,
To determine the value of the unknowns in the matrix,

A matrix is a collection of numbers that are arranged in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,
[tex]2\left[\begin{array}{ccc}w&2\\5&z\end{array}\right] +3\left[\begin{array}{ccc}2&x\\-2&-6\end{array}\right] = 4\left[\begin{array}{ccc}4&7\\y&3\end{array}\right][/tex]
From the above matrix,
Equation formed,
2w + 6 = 16,
w = 5,

2z -18 = 12
z = 15

10 - 6 = 4y
y = 1

Thus,  the required value of the unknowns in the given sum of the matrix are w = -5, z = 15, and y = 1.

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Answer:

5 cups

Step-by-step explanation:

6bananas =2cups

6(2cups)+6(2cups)+3(1cup)= 15 bananas

5cups of blueberries