The average rate of change of the function f(x) = x on the interval [3, 3 + h] is given as follows:h + 6.How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. The function in this problem is given as follows:f(x) = x.Then the outputs are obtained as follows:f(3) = 3 = 9.f(3 + h) = h + 6h + 9.The change in the output is given as follows:h + 6h + 9 - 9 = h + 6h.The change in the input is given as follows:3 + h - 3 = h.Hence the rate is:r = (h + 6h)/h.r = h(h + 6)/hr = h + 6.More can be learned about the average rate of change of a function at brainly.com/question/11627203#SPJ1

Mathematics College

f(x) = x² on [3, 3+h]

Answers

Answer 1

The average rate of change of the function f(x) = x² on the interval [3, 3 + h] is given as follows:

h + 6.

How to obtain the average rate of change?

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The function in this problem is given as follows:

f(x) = x².

Then the outputs are obtained as follows:

f(3) = 3² = 9.f(3 + h) = h² + 6h + 9.

The change in the output is given as follows:

h² + 6h + 9 - 9 = h² + 6h.

The change in the input is given as follows:

3 + h - 3 = h.

Hence the rate is:

r = (h² + 6h)/h.

r = h(h + 6)/h

r = h + 6.

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Related Questions

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Which dimensions can create more than one triangle?
three angles measuring 25°, 65°, and 90°
three angles measuring 50°, 50°, and 50°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 10 ft
10

Answers

The dimensions that can create more than one triangle are given as follows:

three angles measuring 25°, 65°, and 90°.

What is the law of sines?

Suppose we have a triangle in which:

Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the measures of the internal angles of a triangle is of:

180º.

Meaning that the first option is correct and the second is not.

Considering the law of sines, an infinite number of triangles can be formed, as long as:

sin(25º)/a = sin(65º)/b = sin(90º)/c.

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Directions: Read the scenario below and solve. Show your
work.
If given x > 0 and y> 0, in which quadrant or axis will each
ordered pair described below lie? Explain your answer.
a. (-x, y)
b. (-x, 0)
c. (x, -y)
d. (0. y)

Answers

The quadrant or axis for each of the given ordered pairs is:

a. (-x, y) - second quadrant

b. (-x, 0) - X-axis

c. (x, -y) - fourth quadrant

d. (0, y) - Y-axis

How to determine the quadrants

a. (-x, y):

As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.

b. (-x, 0):

The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.

c. (x, -y):

The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.

d. (0, y):

In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.

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Posted a image so that you can see it

Answers

The missing values are b = 4.37, C = 11° and A = 134°

Given is a triangle, we need to find the missing lengths and angles,

So,

Using the cosine rule,

b² = a²+c² - 2ac Cosb

b = √4²+7²-2(4)(7)cos35°

b = √16+49-45.87

b = √19.13

b = 4.37

Now, using the sine rule,

Sin C / 7 = Sin 35° / 4.37

C = 11°

Applying the angle sum property of triangles,

A = 180°-(11°+35°)

A = 134°

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12.
What is the product of
3 and 10?

Answers

Answer:

Any number multiplied by 10 equals to the number and a 0 at the end

Therefore 3×10=3

Based only on the information given in
theorems or postulates could be given as reasons why AHIJKLM?
Check all that apply.
H
A. LL
L
a
K
B. AAS
C. ASA
D. LA
☐E. HA
OF. HL
MA

Answers

The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

What is triangle congruency?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

If two triangles meet all 5 requirements for congruence, then they are congruent.

They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).

So, according to the given, we can observe that:

2 pairs of angles are congruent one pair of which is 90°.

And 1 pair of sides are congruent.

Then, the rules that satisfy here will be:

AAS and HA

Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.

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Complete question:

Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?

Which of the following points is in the solution set of y < x^2 - 2x - 8?

Answers

The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

What is the solution about?

When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.

1 < (-2)² - 2(-2) - 8

-1 < 4 + 4 - 8

-1 < 0

Hence:

(-2,-1) can be in the solution

( 0,-2) Cannot

(4,0) will not.

Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)

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See full question below

Which of the following points is in the solution set of y < x2 - 2x - 8?

(-2, -1)(0, -2)(4, 0)

. To determine how funny the jokes were, the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a “lawyer joke” as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD).
Assuming that these data are normally distributed,
1. What was the rating that marks the cutoff for the top 10% of participant ratings for this joke?

Answers

If the "Lawyer's-Joke" is rates as the funniest, then the rating which is the top 10% of participant rating for this joke is 20 marks.

A "Normal-Distribution" is defined as a probability distribution that is symmetric, bell-shaped, and characterized by its mean and standard deviation.

First, we standardize the rating of 14.48 using the formula:

⇒ z = (x - μ) / σ;

where x is = rating of 14.48, μ is = mean rating, and σ is = standard deviation,

⇒ z = (14.48 - 14.48) / 4.38,

⇒ z = 0,

Next, we take the "z-score" that corresponds to the top 10% of the standard normal distribution. We know that the "z-score" is approximately 1.28,

Substituting the value in formula,

We get,

⇒ z = (x - μ) / σ ⇒ 1.28 = (x - 14.48)/4.38,

⇒ x - 14.48 = 1.28 × 4.38,

⇒ x = 20.97 ≈ 20 marks.

Therefore, the rating that marks the cutoff for the top 10% of participant ratings for this joke is approximately 20 on the scale of 1 to 21.

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Parking lots A and B charge a set fee. A charges 36.50 for 5 hours. B charges 38.00 for 5 hours. Lot A charges 49.50 for 7 hours and lot B charges 50.00 for 7 hours. How many hours are needed to park where it would cost the same?

Answers

Answer:

if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

Step-by-step explanation:

Let's assume that the cost of parking for x hours in both lots is the same, then we can set up the following equations:

For 5 hours of parking:

36.50 = 38.00

This is not true, so we know that the cost for parking in both lots will not be the same for 5 hours.

For 7 hours of parking:

49.50 = 50.00

This is also not true, so we know that the cost for parking in both lots will not be the same for 7 hours either.

Let's try setting up the equation for x hours of parking:

Fee for parking in Lot A = Fee for parking in Lot B

36.50 + (x-5)*7 = 38.00 + (x-5)*7

Simplifying the equation, we get:

36.50 + 7x - 35 = 38.00 + 7x - 35

Solving for x, we get:

x = 12

Therefore, if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.

What is the side length

Answers

Check the picture below.

Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}

Answers

A recursive definition for the set S can be given as follows:

What is recursion?

Recursion is a programming technique where a function calls itself to solve a problem.

Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.

Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.

In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.

The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.

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An arrow is launched upward with a velocity of 256
feet per second from the top of a 80
-foot stage. What is the maximum height attained by the arrow?

Answers

The maximum height attained by the arrow is 2128 feet

What is kinematic equation for vertical motion?

The kinematic equation for vertical motion is [tex]h = h_0 + v_0 \times (\frac{1}{2} )t - gt^2[/tex]

where:

h = height attained by the arrow (maximum height)

[tex]h_0 = [/tex]initial height (80 feet)

[tex]v_0 = [/tex]initial velocity (256 feet per second)

g = acceleration due to gravity (-32 feet per second squared)

t = time taken to reach maximum height

At the maximum height, the velocity of the arrow is zero. So we can use the fact that the final velocity is zero to find the time taken to reach the maximum height,

[tex]0 = v_0 - g \times t \\ t = \frac{ v_0}{g}[/tex]

Substituting this value of t into the first equation, we get:

[tex]h = h_0 + v_0 \times ( \frac{v_0}{g}) - ( \frac{1}{2} )g( \frac{v_0}{g})^2 \\ h = 80 + (256) \frac{256}{(-32)} - ( \frac{1}{2} )(-32)\frac{256^2}{(-32)^2} \\ h = 80 + 4096 - ( \frac{1}{2} ) \frac{(256)^2}{(32)} \\ h = 80 + 4096 - 2048 \\ h = 2128 \: feet[/tex]

Therefore, the maximum height attained by the arrow is 2128 feet.

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What’s the current yield of a 4.95 percent coupon corporate bond quoted at a price of 102.53?

Answers

The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.

What is the current yield of a 4.95% coupon bond?

The current yield of bond means return on an investment based on its current market price.

To calculate the current yield, we will use (annual interest payment/current market price * 100).

Annual interest payment = $1,000 face value x 4.95% coupon

Annual interest payment = $49.50

Current market price = 102.53% of the face value

Current market price = $1,025.30

Current yield = $49.50 / $1,025.30 x 100

Current yield = 4.82%

Answers

On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1

How to calculate the ratio

Total married male employees = 80% × 50% = 40%

Total male Trade Union members = 91.67%

Total male non-Trade Union members = 100% - 91.67% = 8.33%

Married male Trade Union members = 40% × 91.67% = 36.67%

Married male non-Trade Union members = 40% - 36.67% = 3.33%

Now, let's find the number of married female non-members:

The ratio based on the information is 3 to 1.

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please answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

(a) Lena got 33 more

(b) Last one

34°
ength of b
3
C
10
First, complete the equation.
c²= a² + b² - 2abcosC
c²=32 10²-2(3)([?]) cos
Enter the side length that belongs in the green box.
Enter

Answers

The complete equation for the cosine rule is c² = 3² + 10² - 2(3)(10) × cos(34).

What is cosine rule?

The cosine rule, also known as the law of cosines, is a formula used to find the lengths of sides or measures of angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. The cosine rule is typically used when you have a triangle with at least one known side length and its opposite angle, and you want to find either another side length or another angle in the triangle.

The cosine rule is given by the following formula:

c² = a² + b² - 2ab × cos(C)

where:

c is the length of the side opposite to angle Ca and b are the lengths of the other two sidesC is the measure of the angle opposite to side ccos(C) is the cosine of angle C

For the given side c;

c² = 3² + 10² - 2(3)(10) × cos(34)

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Scarlett Squirrel teaches a hula dancing class to young squirrels.
14
1414 squirrels showed up to class on Monday,
10
1010 squirrels on Tuesday,
8
88 squirrels on Wednesday,
10
10squirrels on Thursday, and
12
12squirrels on Friday.
Find the mean number of squirrels.

Answers

Answer:

10.8

Step-by-step explanation:

14+10+8+10+12

_______________

= 54/5

= 10.8

I need help on this

Answers

Answer:

1.5=slope

Step-by-step explanation:

To do this, we need to solve the slope.

We will use rise/run

0-3=-3

0-2=-2

-3/-2=1.5

Please help
Question in image

Answers

Answer:

55.5

Step-by-step explanation:

Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5

Cassie uses 1 quart cranberry juice, 1/2 gallon ginger ale, and 1 1/2 pint orange juice to make friut punch .How many 6- ounce servings can she make

Answers

She can make 20 6-ounce servings to make fruit punch

How to determine this

Cassie uses 1 quart cranberry juice,

1/2 gallon ginger ale,

1 1/2 pint orange juice.

1 quart of cranberry juice when converted to ounce

1 quart = 32 ounces

1/2 gallon of ginger ale when converted to ounce

1 gallon = 128 ounces

1/2 gallon = 128/2

1/2 gallon = 64 ounces

1 1/2 pint orange juice to make fruit punch

1 pint = 16 ounces

1 1/2 pint = 16 + 16/2 ounces

= 16 + 8

= 24 ounces

How many 6-ounces servings can she make

32 + 64 + 24

= 120 ounces

6-ounces that can be made

= 120 ounces/6 ounces

= 20 servings

Therefore, 20 6-ounce servings can be make for fruit punch

Answers

Answer:

y = 4

Step-by-step explanation:

[tex]y = -3*-2 - 2\\y = 4[/tex]

4X Minus 3y Equal 21

Answers

Step-by-step explanation:

The given equation is:

4x - 3y = 21

To solve for y, we can rearrange the equation as follows:

4x - 21 = 3y

Dividing both sides by 3, we get:

y = (4x - 21) / 3

Therefore, the solution to the equation is:

y = (4x - 21) / 3

The figure below shows roads near a pond. Each segment of the triangle represents a road or a path, except AB which represents the distance across the pond. Are the two triangles similar?

Answers

Answer:

Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.

what is the length of a scaled drawing with a width of 9cm and the scale factor 3/4?

Answers

The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm

Calculating the length of a scaled drawing

From the question, we have the following parameters that can be used in our computation:

Width = 9cm

Scale factor = 3/4

Using the above as a guide, we have the following:

Length of a scaled drawing = Width * Scale factor

Substitute the known values in the above equation, so, we have the following representation

Length of a scaled drawing = 9 * 3/4

Evaluate

Length of a scaled drawing = 6.75

Hence, the length of a scaled drawing is 6.75 cm

Answers

Check the picture below, so the angle looks more or less like so.

now, let's recall that the value pair in a terminal point is the adjacent and opposite sides

[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]

How to draw a quilt of isosceles triangular

Answers

The creation of an isosceles triangle quilt can only be achieved through a number of discreet steps:

The Steps

Initially, select the bespoke size of both individual triangles and the full-scale length and breadth of the snug.

Subsequently, draft a lattice on either a sheet of paper or digital drafting software, with each square serving as a single triangular unit.

Commencing your task from the bottom row, resonate along the equidistant bases while drawing with precision to ensure an immaculate line-up.

Then, for the succeeding section, diverge by slightly altering the position of the point of each triangle in accordance with the intermediary gap that exists between two triangles below it.

Continue repeating this pattern while constructing rows, enveloping further ground until fully complete coverage has been ensured.

Last but not least, rigorously maintain accuracy by exploiting straight edges strategically laid beside precise measuring instruments.

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Which functions have a y-intercept that is greater than the y-intercept of the function g(x)=x+31 +4? Check three
options.

f(x)=-2 (x-8)²

Oh(x) = -5 1x1 + 10

(x)=-4(x + 2)² +8

K(x)=(x-4)²+4

m(x)=x-81+6

Answers

The functions which have a y-intercept which is greater than the y-intercept of the function g(x) = |x + 3| + 4 are :

h(x) = -5 |x| + 10

k(x) = 1/4 (x - 4)² + 4

m(x) = 1/4 |x - 8| + 6

Given function is,

g(x) = |x + 3| + 4

y intercept of a function is the value of the function when the input value is 0.

g(0) = |0 + 3| + 4 = 7

f(x) = -2 (x - 8)²

f(0) = -2 (0 - 8)² = -128

h(x) = -5 |x| + 10

h(0) = 10

j(x) = -4(x + 2)² + 8

j(0) = -4 (0 + 2)² + 8 = -8

k(x) = 1/4 (x - 4)² + 4

k(0) = 1/4 (0 - 4)² + 4 = 8

m(x) = 1/4 |x - 8| + 6

m(0) = 1/4 |0 - 8| + 6 = 8

Hence the functions h(x) = -5 |x| + 10, k(x) = 1/4 (x - 4)² + 4 and m(x) = 1/4 |x - 8| + 6 have the y intercept greater than that of g(x) = |x + 3| + 4.

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At a college financial aid office, students who applied for a scholarship were classified according to their class rank: Fr = freshman, So = sophomore, Jr = junior, Se = senior. Construct a frequency distribution for the data.
Fr Fr So Jr Se
Se Fr Jr Fr Fr
Fr Fr So So Fr
Jr Se Se Se Jr
Jr So Fr So Jr
Fr So Jr Se Se

Answers

Answer:

Class Rank | Frequency

--- | ---

Fr | 7

So | 3

Jr | 4

Se | 6

Question 1(Multiple Choice Worth 2 points)

(Slope-Intercept Form MC)

The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.

coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0

Determine the slope of the line and explain its meaning in terms of the real-world scenario.

The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Question 2(Multiple Choice Worth 2 points)

(Systems of Linear Equations MC)

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks
Question 3(Multiple Choice Worth 2 points)

(Identifying Transformations LC)

Polygon ABCD is rotated to get polygon A′B′C′D′.

Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5, point B at negative 2 comma 8, point C at negative 2 comma 4, and point D at negative 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7, point B prime at 8 comma 2, point C prime at 4 comma 2, and point D prime at 3 comma 4

Determine the direction and angle of rotation.

270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation
Question 4(Multiple Choice Worth 2 points)

(Scatter Plots MC)

Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.

scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 2 comma 5, 2 comma 5.5, 3 comma 5.5, 4 comma 5, 4 comma 5.5, 5 comma 4.5, 6 comma 3.5, 7 comma 2, 8 comma 1, and 9 comma 0.5

Which of the following describes the pattern of association for the scatter plot?

There is a weak, positive linear association.
There is a weak, negative linear association.
There is a strong, positive nonlinear association.
There is a strong, negative nonlinear association.
Question 5(Multiple Choice Worth 2 points)

(Similar Triangles MC)

Triangle ABC ~ triangle DEF.

triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2

Determine the measurement of FD.

FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Question 6(Multiple Choice Worth 2 points)

(Slope MC)

What is the slope of the line that contains the points (−3, −1) and (3, −10)?

Undefined
0
negative two thirds
negative three halves
Question 7(Multiple Choice Worth 2 points)

(Experimental Probability MC)

An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.

Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35

What is the P(No Heads)?
85%
75%
50%
25%
Question 8(Multiple Choice Worth 2 points)

(Dilations MC)

Triangle ABC is dilated to produce triangle A′B′C′.

Graph of a triangle ABC with vertices at A 10 comma 2, B 18 comma 2, C 18 comma 10. Triangle A prime B prime C prime with vertices at A prime 5 comma 1, B prime 9 comma 1, C prime 9 comma 5.

Determine the scale factor used to create the image.

one fourth
one half
2
4

Answers

The slope of the line is -4, which means that the swimmer will complete 4 laps every minute. For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).

The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.

To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x

10x + 25 = 5x + 50

5x = 25

x = 5

So, after 5 weeks, the two siblings will have the same amount of money saved.

The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.

The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.

Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles

AB/DE = BC/EF = CA/FD

Plugging in the known values, we get

11/2.2 = 7.9/EF = 7.6/FD

Solving for FD, we get

FD = (7.6 * 2.2)/11 = 1.52

So, FD has a length of 1.52 units.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula

slope = (y2 - y1)/(x2 - x1)

Plugging in the given values, we get

slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2

So, the slope of the line is negative three halves.

The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials

P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%

So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.

Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.

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Question 1
Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 7.75 dollars.

Question 2
A tennis ball is dropped from a certain height. Its height in feet is given by h(t)=-16t^2+14 where t represents the time in seconds after launch. What is the ball’s initial height?

Answers

The quadratic regression equation is y = -140.61x² + 2,954.23x - 7,512.85 and the ball's initial height is 14 feet.

Writing the quadratic regression equation

Given the set of data

Using a graphing tool, we have

C = -7,512.85B = 2,954.23A = -140.61

A quadratic regression equation is represented as

y = Ax² + Bx + C

So, we have

y = -140.61x² + 2,954.23x - 7,512.85

When the selling price is 7.75, we have

y = -140.61(7.75)² + 2,954.23(7.75) + -7,512.85

Evaluate

y = 6937

The initial height

The ball's initial height is the height when t = 0, which means we need to evaluate the function h(0).

h(0) = -16(0)^2 + 14

h(0) = 0 + 14

h(0) = 14

Therefore, the ball's initial height is 14 feet.

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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. If the container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.

Answers

The total weight of the contents is 141.33 pounds.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.

The volume of the container is calculated as:

5 ft× 14.5 ft× 6.5 ft= 471.125 ft³

Then, the total weight of the contents is calculated as:

471.125 ft³× 0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds

Hence, the total weight of the contents is 141.33 pounds.

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