Data regarding fuel efficiency of an 18-wheel truck were collected. The graph shows the correlation between the average speed above 40 miles per hour (in miles per hour) and the money spent on gas (n dollars): Estimate the average rate of change from x = 5 to x = 9.​

Answer:

a b c or d?

Step-by-step explanation:

Answer: If a superball is dropped from a height of h feet and left to bounce forever, the total time needed for all this bouncing to take place can be represented by the formula:

t = h / (r - 1)

where t is the total time, h is the height from which the ball is dropped, and r is the rebound ratio of the ball.

The rebound ratio of the ball is the fraction of the ball's initial height that it bounces back up after each bounce. For example, if a ball has a rebound ratio of 0.5, it will bounce back up to half its initial height after each bounce.

The total time needed for the ball to bounce forever is equal to the height from which the ball is dropped divided by the difference between the rebound ratio and 1. This is because the ball will bounce back up a fraction of its initial height after each bounce, and the total time needed for all the bounces to take place is determined by the difference between the height of the ball and the fraction of the height that it bounces back up.

The number of leaves on a tree which is 2 yards tall and receives 9 hours of sunlight is 324 leaves.

z = k × y × x

Where,

If y = 10 yards, x = 3 hours, z = 540 leaves

z = k × y × x

540 = k × 10 × 3

540 = 30k

k = 540/30

k = 18

Then, find z when y = 2 yards and x = 9 hours

z = k × y × x

= 18 × 2 × 9

z = 324 leaves.

In conclusion, given the constant of proportionality, the number of leaves on the tree is 324 leaves.

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Answer:

Step-by-step explanation:

I know that in point-slope form, the equation is y - y1 = m(x - x1)

Fill in y1 and x1 with the points given in the multiple choices.

If you look at Letter A, it shows the point (0,9). If you fill that in the formula. You solve the equation:

y - 9 = -3/4(x - 0)

y - 9 = -3/4x

+9.     =.  +9

y = -3/4x + 9

Therefore your answer is letter A.

Answer:

y = 2.5x

Step-by-step explanation:

When the relationship is proportional you can find the slope (or unit rate) by taking any point in the form y/x

20/8 = 2.5

30/12 = 2.5

This will work of every point n the line.

Answer: b

Step-by-step explanation:

3^2 + x^2 = 9^2

9 + x^2 = 81

x^2 = 72

x = sqrt(72)

Step-by-step explanation:

Let x = cost of cheese pizza

Let y = cost of pepperoni pizza

x + 6y = 136

2x + 2y = 49

Solve the system:

x = $14

y = $15

Answer:

-9.661

Step-by-step explanation:

Adding a negative is the same as subtracting a positive and you started with a negative number so:

-6.05

-3.611

------------

-9.661

Answer: -9.661

Step-by-step explanation:

A negative plus a negative will ALWAYS equal a negative. If you have an addition with two negatives, just add them normally and add the negative sign:
-6.05+(-3.611) = 6.05 + 3.611

6.05 + 3.611 = 9.661

Now add the negative sign:

9.661 = -9.661

Hope this helps!!

The y-intercept is the point the graph intersects the y-axis. It is represented by the constant c in the equation of a straight line graph, y = m·x + c

6. The y-intercept is 7

8. The y-intercept is 0

12 a. The error is taking the x-intercept as the y-intercept

b. Please find attached the graph of line with a y-intercept of 3 drawn with MS Excel

A straight line graph is the graph of a linear equation.

The slope-intercept form of the equation of a straight line graph is y = m·x + c, where;

m = The slope of the graph

c = The y-intercept

6 The y-intercept is the point the graph crosses the y-axis.

The line crosses the y-axis at the point (0, 7)

8. The point at which the graph crosses the y-axis is (0, 0)

12. The graph in the question is a straight line graph that passes through the points (3, 0), and (0, -4)

The x-intercept of the graph is 3

The y-intercept of the graph is -4

a. The possible error of the graph that is an example of a line with a y-intercept of 3 is therefore, mistaking the y-intercept for the x-intercept

b. Please find attached the graph of the line y = x + 3 that has a y-intercept of 3 drawn with MS Excel on the graph of the question with equation y = (4/3)·x - 4

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Answer:

$1471.49

Step-by-step explanation:

1571.13-80=1491.13

1491.13+456.82=1947.95

179.48+74.73+82.70+139.55=476.46

1947.95-476.46=1471.49

Answer:

it is B

Eplanation:

180-155=75 (straight line add up 180 degrees)

75+55+x=180

130+x=180(angles in triangle also add up 180 degrees)

x=180-130(rearranging formula)

x=50, which is option letter B

The x-intercepts of the parabola are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

What is the equation of a parabola?

The general equation of a parabola is given by y = a(x – h)2 + k or x = a(y – k)2 +h. Here (h, k) denotes the vertex.

To write the equation of the given parabola in the desired form, we can complete the square.

The equation of a parabola with vertex at (h, k) and axis of symmetry x = h is given by:

y = a(x - h)^2 + k

where a is a nonzero constant.

In this case, the vertex is (6, -5) and the y-intercept is (0, 175), so the equation of the parabola is of the form:

y = a(x - 6)^2 - 5

Substituting the y-intercept, we have:

175 = a(0 - 6)^2 - 5

Solving for a, we find that a = 15/4.

Thus, the equation of the parabola is:

y = 15/4(x - 6)^2 - 5

To find the x-intercepts, we need to find the values of x such that y = 0. Substituting y = 0 into the equation of the parabola, we have:

0 = 15/4(x - 6)^2 - 5

Adding 5 to both sides, we have:

5 = 15/4(x - 6)^2

Dividing both sides by 15/4, we have:

4/15 = (x - 6)^2

Taking the square root of both sides, we have:

x - 6 = +/- 2/3

Thus, the x-intercepts are at x = 6 +/- 2/3.

Therefore, the x-intercepts of the parabola are (x₁, y₁) = (6 + 2/3, 0) and (x₂, y₂) = (6 - 2/3, 0).

Rounded to the nearest hundredth, the x-intercepts are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

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Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.

The remainder is the amount left over after a division operation.

An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.

From the property of exponent:

We can rewrite 10^2023 as (10^13)^155 * 10^8:

10^2023 = (10^13)^155 * 10^8

We can then use the property of exponents to simplify:

10^2023 = (10^(13*155)) * 10^8

Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.

We can find the remainder by calculating 10^8 mod 13:

10^8 = 100000000

After dividing 100000000 by 13, we get a remainder of 9.

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The equation of the line joining the points (2,-8) and (5,6) is y = 14 / 3 x - 52 / 3

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2,-8) and (5,6). Let's find the slope.

m = 6 + 8 / 5 - 2

m = 14 / 3

Let's find the y-intercept using (5, 6).

y = 14 / 3 x + b

6 = 14 / 3 (5) + b

6 = 70 / 3 + b

b = 6 - 70 / 3

b =  18 - 70/ 3

b = -52 / 3

Therefore, the equation is y = 14 / 3 x - 52 / 3

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The amount of interest he will pay on this loan is $12,400.

Principal = $10,000

Rate = 8%

Time = 36 months, 1 year - 12 months

36 months - 36/12= 3 years

S.I. = PRT/100

10,000*8*3/100

240,000/100 = $2,400

A = P+I = 10,000+2,400= $12,400

The amount of interest he will pay on this loan $12,400.

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Answer:

35cm^2

Step-by-step explanation:

Things To Keep In Mind:

Height: 7 cm

Length: 10 cm

(L*H)/2=area of triangle

7*10=70

70/2=35

If there are any problems with this answer please feel free to tell me, thanks :)

By simplifying and solving, Tamala is not in class while she is at school is 0.5 hour.

Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.

Algebra is a branch of mathematics that involves the use of letters and symbols to represent unknown quantities, known as variables, in equations and formulas.

Tamala is in class for 6 * (7/6) = 7 hours.

Tamala is not in class for 7(1/2) - 7 = 1/2 hours.

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The number of hours when Jai and Keilantra are the same distance from the stadium is 3 hours.

Jai is 254 miles away from the stadium. Jai is driving along the highway at a speed of 41 miles per hour. This will be:

254 - 41h

Keilantra is 293 miles away from the stadium. Keilantra is driving at speed of 54 miles per hour. This will be:

293 - 54h

The equations will be:

254 - 41h = 293 - 54h

54h - 41h = 293 - 254

13h = 39

Divide

h = 39/13

h = 3

The number of hours is 3 hours.

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The equation of Total Charges will be $1.95 + ($2.7 * x)

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

The equation of Total Charges will be

Let, the total distance in miles be x

Then,

Total Charges = $1.95 + ($2.7 * x)

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Therefore the solution to this question is expression a=3/5 & expression b=6/5  3a+b=3 , and  10a+5b=6+6=12 .

Probability is the study of how likely it is for an event to occur or for a statement to be true, with numerical explanations of probability being a key component. An event's probability is represented by a number between 0 and 1, where, broadly speaking, 0 indicates that the event is impossible and 1 indicates that it is certain to occur.

Here,

Naturally, the total probability for x∉[0,1] is 0 and since the total probability must be 1, we have

∫01a+bx2dx=1

The left-hand side is

[ax+b[tex]x^{3}[/tex]/3] x=1 & x=0 => a+b3

3a+b=3

In general, for continuous probability distributions we have

E(x)=∫P(x)xdx

(If you have a sufficiently advanced version of integration, the restriction to continuous distributions may be lifted.)

In this case, it's

E(x)=[a[tex]x^{2}[/tex]/2+b[tex]x^{4}[/tex]/4]x=1 & x=0 => a/2+b/4

So,

a/2+b/4=3/5

10a+5b=12

Being shrewd with matrix inversion or anything of the sort is pointless. Just get rid of b:

15a+5b=15

5a=3

a=3/5

b=3(1−a)=6/5

and indeed  3a+b=3 , and  10a+5b=6+6=12 .

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18,564 different groups of 6 children can be driven.

Here we are given 18 Children in total and we can fit Only 6 Children out of them.

The number of different groups of 6 children that can fit into the van ca be calculated with a simple formula

The formula used will be -

n! = n(n-1)(n-2)(n-3).......1

n!= (18 x 17 x 16 x 15 x 14 x 13) / (6 x 5 x 4 x 3 x 2)

  = 18,564

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Profit is the money you have left after paying for business expenses.

The production of the products are given below with the profit as well:

a. Production of Product 1 = 50 units per week

b. Production of Product 2 = 0 units per week

c. Production of Product 3 = 145 units per week

d. Production of Product 4 = 10 units per week

e. Total Profit = $1250 per week

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Answer:

Step-by-step explanation:

A local manufacturing firm produces four different metal products, each of

which must be machined, polished and assembled. The specific time

requirements (in hours) for each product are as follows:

Machining,

hours

Polishing, hours Assembling,

hours

Product I 3 1 2

Product II 2 1 1

Product III 2 2 2

Product IV 4 3 1

Step-by-step explanation:

-4y = 5x - 12

4y = -5x + 12

y = -5/4x + 3

Answer:

∠ABC = 98°

Step-by-step explanation:

an isosceles triangles base angles have the same angle measures

so both are 71

add them and then subtract that from 180 to find ∠ABD

180 - (71 + 71)

180 - 142 = 38

that is ∠ABD

to find ∠ABC you must add ∠DBC to ∠ABD

all angles of an equilateral triangle are equivalent

they are also 60 degrees

so add 60 to 38

38 + 60 = 98

that is your answer

Answer:

There Are 40 Bicycles And 23 Tricycles

Step-by-step explanation:

Let, x be bicycles and y be tricycles

Condition 1;

: x + y= 63

: x =63-y

Condition 2;

Number Of Tires=149

:2x + 3y =149 [2x=Two Tires Of Bicycle And

3y=Three Tires Of Tricycle]

:x = 149-3y/2

Combination 1 & 2;

63-y = 149-3y/2

126-2y = 149-3y

y=23

x = 63-23

=40

The null hypothesis (H0) would be that the population mean number of hours married men in your area spend on child care per week is equal to the reported mean of 6.0 hours per week.

The population mean number is equal to the reported mean according to null hypothesis. The alternative hypothesis (HA) would be that the population mean differs from the reported mean.

H0: μ = 6.0 hours/week

HA: μ ≠ 6.0 hours/week

b. To find the sample mean, we need to add up all of the values in the sample and divide by the number of values. The sample mean is 6.34 hours/week.

To calculate the test statistic, we can use the formula:

t = (x' - μ0) / (s / √n)

where x' is the sample mean, μ0 is the hypothesized mean (in this case, 6.0 hours/week), s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (6.34 - 6.0) / (3.23 / √40) = 0.34 / (0.53 / 6.32) = 0.34 / 0.08 = 4.25

The p-value is the probability of getting a result as extreme as the one we observed, given that the null hypothesis is true. In this case, we would need to use a t-distribution table or a computer program to find the p-value, since the sample size is small and the population standard deviation is unknown.

c. If we select a level of significance of 0.05, then we can use the p-value to make a decision about the null hypothesis. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that the population mean differs from the reported mean. If the p-value is greater than 0.05, we do not have enough evidence to reject the null hypothesis and would conclude that the population mean is likely to be the same as the reported mean.

In this case, the p-value is greater than 0.207, so we do not have enough evidence to reject the null hypothesis. We would conclude that the population mean number of hours married men in your area spend on child care per week is likely to be the same as the reported mean of 6.0 hours per week.

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Answer:$441.05

Step-by-step explanation:

For this question you would multiply the amount of each DVD by the price and add them all up

like this:

11(27.95) +7(17.95)+1(7.95)=$441.05

Natural numbers and irrational numbers are two pairs of sets that have the same cardinality.

It is sufficient to demonstrate the existence of a bijection between the set of real numbers R and the set of irrational numbers RQ in order to demonstrate that both have the same cardinality:

For each positive integer n, map n to 2n to produce a countable number of holes in R. Be aware that these countable holes are located at all irrational locations (2n-1), as well. R should be mapped to itself. R should be mapped to itself. Feel free to use your preferred irrational number in the above in place of [tex]\pi[/tex].

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The system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C)

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Cost of theme park is = $20

Tickets for each ride and attraction are = $3 a piece

Number of tickets purchased = X

So, total cost of tickets is = 3 * X

Total cost of visit to the theme park is = Y

So, the equation we get

Y = 3X + 20

Hence, the system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C).

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The composition of translations for the first image is (x+1, y+5) and for the second image is (x-4, y).

What is a translation?

A transformation that moves a figure through its points using a given ruler—a translation vector—is referred to as a translation. Without altering the original geometry, this process moves each point in a picture both horizontally and vertically.

Given a graph of translation

The first image is translated as 1 unit upward and 5 units right side.

Then, translation (x,y) → (x+1, y+5)

And,

The second image is translated as 4 units downward only.

Then, translation (x,y) → (x-4, y)

Hence, the above is the required composition of translations.

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The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

The given coordinate point is (-1, 5) and slope=-4.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get

5=-4×(-1)+c

⇒ c=5-4

⇒ c=1

Substitute m=-4 and c=1 in y=mx+c, we get

y=-4x+1

Therefore, the slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

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