A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in
miles, , and her running speed, in miles per hour, when she runs:

Answer:

Step-by-step explanation:-b± √b²-4ac. X =

Answer:

y=6

Step-by-step explanation:

4(y-4)=8

4×y-16=8

4×y=8+16

4×y=24

y=6

4(6-4)=8

4×2=8

The length and the width of the rectangle are 61 inches and 19 inches, respectively

The mathematical statement from the question is given as

Length of a rectangle is four more than triple its width.

Mathematically, this can be represented as

Length = 3Width + 4

The perimeter is given as

Perimeter = 160 meters

The perimeter is calculated as

Perimeter = 2 x (Length + Width)

So, we have

2 x (3Width + 4 + Width) = 160

Divide by 2

3Width + 4 + Width = 80

This gives

4Width= 76

Divide by 4

Width = 19

Recall that

Length = 3Width + 4

So, we have

Length =  3 * 19 + 4

Evaluate

Length =  61

Hence, the dimensions are 61 inches by 19 inches

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The parallel line has an equation of y = 2x + 3

The equation is given as

2y = 4x + 14

Make y the subject

2y = 4x + 14

Divide through by 2

y = 2x + 7

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 2

This means that the slope of 2y = 4x + 14 is 2

The slopes of parallel lines are equal

This means that the slope of the other line is 2

i.e. m = 2

Recall that:

The equation of a line can be represented as

y = mx + c

Where

slope = m

So, we have

y = 2x + c

Assume any value for c

This gives

y = 2x + 3

Hence, the equation of the parallel line is y = 2x + 3

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Answer:

False

Step-by-step explanation:

The numerical coefficient is 14, not 4.

Answer:

it's False

Step-by-step explanation:

Trust me IT worth it

Answer:

22x + 20

Step-by-step explanation:

= (5)(3x) + (5)(4) + 7x

= 15x + 20 + 7x

= 15x + 20 + 7x

= (15x + 7x) + (20)

= 22x + 20

Answer:

22x +20

Step-by-step explanation:

5(3x + 4) + 7x

5 x 3x + 5 x 4 +7x

15x + 5 x 4 + 7x

15x + 20 + 7x

22x + 20

The maximum or minimum value of the function y = -2x² + 32x - 12 is (8, 116) and the range of the function y = -2x² + 32x - 12 lies in the interval

(−∞ ,116).

Given, the function is y = -2x2 + 32x - 12

According to the question we have to extract the maximum or minimum value of the function.

The maximum or minimum of a function which is a quadractic function occurs at the point x = -b/2a.

If a is negative, then the maximum value of the function is f(-b/2a).

If a is positive, then the minimum value of the function is f(-b/2a).

According to this, we can derive the general equation as

fmax(x) =ax²+bx+c occurs at x = -b/2a.

From the given equation, comparing we get

a = -2, b = 32, c = -12

Substitute the value of a and b in in the general equation and we get

x = -32/2(-2)

x = -32/-4

x = 8

Put x = 8 in the given general equation,

y = -2(8)² + 32(8) - 12

y = -2(64) + 256 - 12

y = -128 + 256 - 12

y = 256 - 140

y = 116

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Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].

If Mr. Fitch applies for the 5-year loan, the amount  he will pay in interest  with the 3-year loan is: $565.24.

First step is to find the cost of replacement left

Cost of replacement  = $4,348 x 6.5%

Cost of replacement =$282.62

Second step is to calculate the amount of  5-year loan

Loan = $282.62 x 5

Loan = $1413.1

Third step is to calculate the amount of the 3-years loan

Loan = $282.62 x 3

Loan = $847.86

Now let find the amount he will pay in interest with the 3-year loan

Amount = $1,413.1- $847.86

Amount =$565.24

Therefore the interest amount is $565.24.

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Answer:

3√10 units

Step-by-step explanation:

[tex] \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \sqrt{10} = 5 \sqrt{10} [/tex]

[tex]3x + 2x = 5 \sqrt{10} [/tex]

[tex]5x = 5 \sqrt{10} [/tex]

[tex]x = \sqrt{10} [/tex]

So the length of the longer piece is 3√10 units.

The slope of the line that passes through (9, 1) and (-8, 2) is -1/17

If we have a linear equation or a segment that passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

In this case, we know that the two points are (9, 1) and (-8, 2), using the above formula we can find the slope to be:

slope = (2 - 1)/(-8 - 9)

slope = 1/-17 = -1/17

That is the slope of the line or segment that passes through the given points.

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Answer:

c=40n+10

Step-by-step explanation:

They charge 40$ per night from which we get 40n

The extra 10$ is from the bathing fee

The rest of the information they give us isn't useful in this case because they didn't ask us the cost per hour

Answer:

Step-by-step explanation:

Which one adds up to 14 is the question?  There are dots on the dice which correspond to numbers. The dots are saying that they are numbers. And if you get to 14 with the dices, you pick it.

Using the z test the value of z is -0.9404 and  the value of z the research team should 0 - retain the null hypothesis.

In the given question,

They randomly selects a sample of 12 people, and with their permission, provides them a treatment.

So n = 12

The mean for their sample is 99.

x = 99

The mean for the population is 102.

μ=102

A standard deviation of 11.

σ = 11

Test statistic z:

z = (x-μ)/σ /√n

Now putting the value

z = 99-102/11/√12

z=-3/11/3.45

z=-3/3.19

z= -0.9404

Test statistic z = -0.9404

From the value of z the research team should 0 - retain the null hypothesis.

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Answer:$26

Step-by-step explanation:

52+22=74

100-74=26

Answer:

9:40

Step-by-step explanation:

Distance = rate x time

Let t = time

40 = 60t  Divide both sides by 60

[tex]\frac{40}{60}[/tex] = t  An hour would be 60 minutes so the number of minutes out of the total would be 40.

Train B is traveling faster because it traveled 100 meters in four seconds.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

We have to determine which train is moving faster based on the image.

We can tell by looking at the train speeds.

As per the formula,

distance/time = speed

Train A travels 12.5 metres in one second = 12.5/1 = 12.5 metres per second

Train B travels 100 meters in four seconds, hence its speed is 100/4 = 25 meters per second.

This is because it traveled 100 meters in four seconds, whereas train A covered 12.5 meters in one second.

Hence, train B is traveling faster.

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The question seems to be incomplete the correct question has been in attached file

Probability Theory

P (K) =[tex]\frac{n (K) }{n (S)}[/tex]

P(K) : probability of selected K

n (K) : number of occurence of K

n (S) : number of all occurence

In question is not contain information about the number of students who curry a gun, knife, or other weapon and the number of all students. so, we can desribe that :

n (A) : the number of occurence of students who curry a gun

n (B) : the number of occurence of students who curry a knife

n (C) : the number of occurence of students who curry other weapon

and the number of all students is n ( A U B U C) -> union of sets

how many randomly selected student? in question, there is no specific about the student. so, we can answer with :

1) probability of students who curry a gun

P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex]

2) probability of students who curry a knife

P (B) = [tex]\frac{n (B) }{n (AUBUC)}[/tex]

3) probability of students who curry other weapon

P (C) = [tex]\frac{n (C) }{n (AUBUC)}[/tex]

and if question want to estimate with percentage, we can multiply with 100%. example :

1) percentage of probability of students who curry a gun

P (A) = [tex]\frac{n (A) }{n (AUBUC)}[/tex] x 100%

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x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

According to the question,

The two numbers are positive and the sum of the two numbers is 16 and the sum of the squares of the two numbers is the minimum.

Now to solve the question we will consider,

x and y are the two numbers, such that x > 0 and y > 0

Sum of the numbers : x + y = 16

Sum of squares of the numbers: S = x²+ y²

x + y = 16 y = (16 - x)

Assume, S = x² + y²

S = x² + (16 - x)²

Now we will differentiate with respect to x

dS/dx = 2x+ 2(16-x)(-1)

2x-2(16-x)=0

2x-32+2x=0

4x-32=0

4x=32

x=32/4

x=8

As x > 0, x = 8

d²S/dx² = d/dx [2x+ 2(16-x)(-1)]

d²S/dx² = d/dx (2x) - 2 d/dx (16-x)

d²S/dx² = 2 - 2[0-1]

d²S/dx² = 4

Now when x=8

d²S/dx²  = 4 ≥0

Therefore, the function S = sum of the squares of the two numbers is minimum at x = 8.

y = 16-8 = 8

Therefore, x = 8 and y = 8 are the two positive numbers whose sum is 16 and the sum of the squares is minimum.

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Answer:14

Step-by-step explanation:All you have to do is Divide 378 by 27 to get x

Hope This Helps!

Answer:

Step-by-step explanation:

Answer:

b= c + t (the amount bought)

Step-by-step explanation:

Answer:

-5/3 or -1.67

Step-by-step explanation:

Answer:

-5/3

Step-by-step explanation:

Oh it's you again, I am just gonna copy paste my format from your previous question.

Use the slope formula: s=(y2-y1)/(x2-x1)

It doesn't matter the order.

Let's say -6 is x2 and 8 is y2; 3 is x1 and -7 is y1

Plug in the equation: s=[(8)-(-7)]/[(-6)-(3)]

Simplify and solve: s=[8+7]/[-9]

                               s = -15/9

                               s = -5/3

Answer:

Step-by-step explanation:

The relationship between the mean and median of the collected data is that the mean will be smaller than the median.

Since the SAT Math scores for these students will be mostly high scores, the distribution will be skewed to the left. Thus, the few low scores (outliers) will make the mean smaller than the median.

Outliers that do not change the mean have an impact just on the mean. As a result, the mean is frequently lower than that of the median when the distribution of data is skewed to the left. The mean is frequently higher than the median when the distribution is tilted toward the right. We anticipate that the mean and median in symmetrical distribution will be about identical in value. This is a crucial link between the connection here between mean and median as well as the distribution's form. Nevertheless, it isn't applicable to all sets of data. Collections of data sets are where exceptions happen much more frequently.

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The Perimeter of the Rectangle is 144cm;

What is the Perimeter of a Rectangle?

The sum of a rectangle's boundary lengths on all sides is known as its perimeter. A rectangle's perimeter is a linear measurement that can be expressed in meters, feet, inches, or yards. Let's first comprehend the two fundamental characteristics of a rectangle.

A rectangle has four 90° angles.

The lengths of a rectangle's diagonals are equal. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.

According to the question

Let the length of the rectangle be x cm;

So, The breadth of the rectangle will be:  (x+2) cm;

And, we have the diagonal = 52 cm;

So,

we can use the Pythagoras triangle to find the value of x cm;

⇒[tex]x^{2} + (x+2)^{2} = (52)^{2}[/tex]

⇒[tex]2x^{2} +4+4x = 2704;\\[/tex]

⇒[tex]2x^{2} +4x = 2700[/tex]

⇒[tex]2x^{2} +4x - 2700 =0;[/tex]

By solving the above equation, we get:

x = 35 cm;

So, the length of the rectangle = is 35 cm;

Breadth of the rectangle = 37 cm;

and
Perimeter of the Rectangle = 2(35 + 37) cm;

The perimeter of the Rectangle = = 144 cm;

Hence,

The perimeter of the Rectangle = = 144 cm;

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Students taking both honors courses and prefer basketball to football is 450.

Total number of students at a high school = 6000

Number of students who has taken honors courses = 1500

Number of students who prefer watching basketball to football = 1800

Let event of taking honors courses be A

and event of preferring watching basketball be B

P(A) = 1500 / 6000 = 0.25

P(B) = 1800 / 6000 = 0.3

If both the event of taking honors courses and preferring watching basketball is independent then

By using property of independent events ,

P(A∩B) = P(A) . P(B)

= (0.25)(0.3) = 0.075

Number of students taking both honors courses and prefer basketball to football = 0.075 × 6000

= 450 Students

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The range of the given relation is (-6, -3, 0, 3, 6).

Range:

Basically the set contains 2 elements in it, in which set contains all the second elements, on the other hand, is known as the range of the relation.

Given,

Here we have the relation (-5,6), (-3,3), (-1,0), (1,-3) and (3,-6)

Here we need to find the range of the relation.

According to the definition of the relation,

Range refers the y values of the coordinates,

So, based on this the value of the given coordinates are extracted as,

(-5, 6) => 6

(-3, 3) => 3

(-1, 0) => 0

(1, -3) => -3

(3, -6) => -6

Now we have arrange the range values from the smallest to largest,

Therefore, the range of the relation is (-6, -3, 0, 3, 6).

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The volume of the given rectangular box is given by 225 cubic inches.

We know that the volume of the rectangular box with length L and width W and height H is given by,

V = LWH

So given the length of rectangular box is = 12 1/2 inches = 25/2 inches

The width of rectangular box is = 4 1/2 inches = 9/2 inches

The height of box is = 4 inches

So the volume of the rectangular box = (25/2)*(9/2)*4 = 25*9 = 225 cubic inches.

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The average apple weight's 95% confidence interval is (119.14, 125.86).

According to one manufacturer, an apple weighs 120 grams on average with a 12-gram standard variation. According to statistics generated from a sample of 49 apples randomly selected from a shipment, the average weight per apple was 122. 5 grams.

Let, 

n = 49

x = 122.5 

σ = 12

To figure up and analyze a 95% confidence interval for the average apple weight; 

The formula for a 95% confidence interval is

(x ± 1.96*σ√n) 

(122.5 ± 1.96*12/√49)

(119.14, 125.86)

Consequently, a 95% confidence interval for the average apple weight is (119.14, 125.86).

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Answer: 7 comic books would be left after putting them into groups of 8.

Step-by-step explanation: There will be 326 groups of comic books. 326 x 8 = 2,608 which means that there will be 7 comic books left after putting them all into groups of 8.