Sam and Liam raced up and then back down a hill. Sam's average speed up the hill
was 1 mph, and his average speed down the hill was 9 mph. Liam ran up the hill
and down the hill at 2 mph. If the trail from the bottom to the top of the hill is 1
mile long, how much time did it take each boy to finish? Who was the winner?

Answer:

C 76

Step-by-step explanation:

let x = 1st number

let x+ 2 = 2nd number

let x + 4 = 3rd number

let x + 6 = 4th number

Let x + 8 = 5th number

x + x + 2 + x+ 4 + x + 6 + x + 8 = 400  Combine like terms

5x + 20 = 400 Subtract 20 from each side

5x  = 380  Divide both sides by 5

x = 76

Check:

76 + 78 + 80 + 82 + 84 = 400

The probability of having fewer than three television sets in the apartment is 0.7

Probability is solved by finding the ratio of required outcome to the total sample

In the given problem the total sample space is the sum of the frequencies which

sum of the frequencies

= 1 + 6 + 14 + 7 + 2

= 30

The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added

= 1 + 6 + 14

= 21

The probability P(X < 3) = 0.7

= 21 / 30

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As per the given least square regression line, the correlation between the height and the arm span is (a) greater than zero.

Regression line:

In statistics, regression line refers the an estimate of the line that describes the true, but unknown, linear relationship between the two variables.

Given,

Here we need to find the correlation between the height and the arm span by using the given least square regression line.

Let us consider the following situation,

"Measurements on young children in Mumbai, India, found this least‐ squares line for predicting height (y) from arm span (x): predicted y = 6.4 + 0.93x. Measurements are in centimeters (cm)."

While we looking into this one we have identified that the predicted function y = 6.4 + 0.93x, is defines the value of height.

So, here y is the dependent variable and the x is the independent value.

This means that the value x is smaller comparatively y value.

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Coffee A is 12.241 pounds, Coffee B is 18.269 pounds and Coffee C is 24.482 pounds.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let a pounds of coffee A needed

Let b pounds of coffee B needed

Let c pounds of coffee C needed

c= 2a.................(1)

a+ b+c= 55..........(2)

and, 14.99 a+ 13.99 b + 10.39 c /55 = 12.61

1499a + 1399 b + 1039 c = 69,355...............(3)

Subtract (2) from (3), we get

  1499 a+ 1399 b + 1039 c= 69355

-  1039 a - 1039 b - 1039 c = 57145

_____________________________

  460 a + 360 b = 12210

 46a+ 36 b = 1221

b= 1221/ 36 - 46 a/ 36

b= 407 / 12 - 23 a / 18

Put b in Equation (2)

a + 407 / 12 - 23 a / 18 + 2a= 55

-5a / 18 + 2a + 407/ 12 = 55

31a/ 18 = 253/ 12

a= 4554 / 372

a = 2277/ 186

a= 759/ 62

a= 12.241

and, c=2a = 24.482

b= 33.91 - 15.641

b= 18.269

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Answer:

O y = mx + b

Step-by-step explanation:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

(A) Positive

When z and y are both positive, the expression{ [tex]\frac{-z}{-y}[/tex] }is equal to [tex]\frac{-z}{-y}[/tex]. Since both z and y are positive, -z is negative and -y is negative, so the expression [tex]\frac{-z}{-y}[/tex] is equal to the positive number [tex]\frac{z}{\\y}[/tex].

Therefore, the sign of {-z}/{-y} when z>0 and y>0 is positive.

So the correct answer is:

(A) Positive

What is sign?

In mathematics, a sign is a symbol that is used to represent the relative size or value of a number or expression. The most common signs used in mathematics are the plus (+) and minus (-) signs, which are used to represent positive and negative numbers, respectively.

For example, the number 5 is a positive number, and it is represented using the plus sign. On the other hand, the number -5 is a negative number, and it is represented using the minus sign.

In addition to the plus and minus signs, there are also other signs used in mathematics, such as the equal sign (=), which is used to indicate that two quantities are equal, and the inequality signs (>, <, ≥, ≤), which are used to indicate that one quantity is greater than or less than another.

Overall, signs play a vital role in mathematics as they help to indicate the size and value of numbers and expressions, and they are essential for performing various mathematical operations and solving mathematical problems.

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The option that can be the model when Dwayne has collected data on the number of occupants of cars travelling on the road is Table B.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true

Given the information, the probability for a will be illustrated as:

a. = 0.6 + 0.2 + 0.2 + 0.1 + 0.05 = 1.15 > 1

b. = 0.5 + 0.25 + 0.05 + 0.06 + 0.04 = 1

c. 2 + 1 + 0.1 + 0.1 + 0.4 = 3.6 > 1

d. 0.5 + 0.25 + 0.25 + 0.125 + 0.125 = 1.25 > 1

e. 0.5 + 0.2 + 0.1 + 0.05 + 0.05 = 0.9 < 1

The correct option that illustrates this is Table B.

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Answer:

No solution

Step-by-step explanation:

The absolute value function outputs non-negative values.

Answer:  No solutions

This is because absolute value is never negative. It represents distance, and negative distance does not make sense.

The smallest possible output of |x+5| is zero.

Answer:

Exact area = 81π ft²

Approximate area = 254 ft²

Step-by-step explanation:

A = πr²

A = π × (9 ft)²

A = 81π ft²

A = 81(3.14) ft²

A = 254 ft²

[tex] \Large{\boxed{\sf A = 81 \pi \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

The area of a circle is given by the following formula:

[tex] \Large{\sf A = \pi \times r^2 } [/tex]

Where:

[tex] \\ [/tex]

We know that the diameter of a circle is twice its radius. Therefore, we can find the value of the circle's radius by dividing its diameter by 2.

[tex] \sf Diameter =2 \times radius \Longleftrightarrow radius = \dfrac{Diameter}{2} \\ \\ \\ \star \: \sf r = \dfrac{18 \ ft}{2} = \boxed{\sf 9 \ ft} [/tex]

[tex] \\ [/tex]

Now, substitute the value of the radius into the formula:

[tex] \sf A = \pi \times (9 \ ft)^2 = \boxed{\boxed{\sf 81 \pi \ \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer:

1/8 or 0.125

Step-by-step explanation:

1/2×1/8

multiply the numerators 1×1=1 and multiply the denominators 2×4=8

Final answer =1/8 or 0.125

Answer:

31 [tex]\frac{3}{5}[/tex] miles per gallon.

Step-by-step explanation:

[tex]\frac{39\frac{1}{2} }{1\frac{1}{4} }[/tex]

39 [tex]\frac{1}{2}[/tex] ÷  1 [tex]\frac{1}{4}[/tex]

[tex]\frac{79}{2}[/tex] ÷ [tex]\frac{5}{4}[/tex]

[tex]\frac{79}{2}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{158}{5}[/tex] = 31 [tex]\frac{3}{5}[/tex] miles per gallon or 31.6 miles per gallon

let's take it from the basic of one dolla!, how long will it take for $1 to become $2, namely double, at 10.5%?

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2\\ P=\textit{original amount deposited}\dotfill & \$1\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ t=years \end{cases} \\\\\\ 2=1e^{0.105\cdot t} \implies \log_e(2)=\log_e(e^{0.105t})\implies \log_e(2)=0.105t \\\\\\ \ln(2)=0.105t\implies \cfrac{\ln(2)}{0.105}=t\implies 6.6\approx t\qquad \textit{about 6 years and 219 days}[/tex]

The of interest earned by Cedric's account  after 1 year and 9 months is $34.83.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for interest.

I = P × r × t

I = $796 × 2.5% × 21/12

I = $796 × 0.025 × 1.75

I = $796 × 0.025 × 1.75

I = $34.83

Therefore, the interest earned in the account is $34.83.

Option B is the correct answer.

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Answer: -48

Step-by-step explanation:

-18-30 = -48

The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

Solution:

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                          = 4.08

Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]

                                = [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]

                                = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

  sin T  = 0.61

∴  ∠T = [tex]sin^{-1}[/tex](0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

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The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                         = 4.08

Area of the triangle = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

 sin T  = 0.61

∴  ∠T = (0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

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The quantities we need circumference for are: A and C.

The quantities we need area for are: B and D.

The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.

On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².

Therefore:

For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.

For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.

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By solving the following trigonometric function of m(x)= x cos(-x) we get m(x) = cos(x).

What is trigonometry ?

Given that;

              m(x) = x cos(-x)

              m(x) = x cos (x)    [ we know that cos(-x) = cos(x) ]

           m(x)/x = x cos(x)/x   [divide both sides by x]

                   m = cos(x)

Therefore, m(x)=x cos(-x) ⇒cos(x)

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The image of the polygon after a reflection in the line y=x is having vertices at A'(-3, 6), B'(-2, 1) and C'(1, 4) as shown in the diagram attached.

A reflection is a sort of transformation that creates a new shape by flipping a shape, called the preimage, across a line, called the line of reflection (called the image). You may imagine what would occur if the form were turned over the line to graph a reflection.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image).

You can picture what would happen if you flipped the form over the line in order to graph a reflection.

If a point A(x, y) is reflected about the line y = x,

the new point would be at A'(y, x)

Given the polygon with vertices at A(6, -3), B(1, -2) and C(4, 1).

The image of the polygon after a reflection in the line y=x has vertices at:

A'(-3, 6), B'(-2, 1) and C'(1, 4)

The image of the polygon is attached.

Therefore, according to the attached graphic, the vertices of the polygon's image after a reflection in the line y=x are located at A'(-3, 6), B'(-2, 1), and C'(1, 4).

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Answer:

A. 147

Step-by-step explanation:

Divide the polygon into rectangles.

You will have 2 rectangles:

1) 3 x 10

2) 9 x 13

Now you just need to find the area of this 2 rectangles and add them up.

1. 177.441177

2. 354.882354

3. 118.294118

4. 473.176472

5. 236.588236

This raffle's expected value per ticket is $ 0.25.

Given that 5,000 tickets are sold at $1 apiece for a charity raffle, and tickets are to be picked at random, the following monetary prizes will be awarded.

To estimate the expected value of this raffle if you buy 1 ticket, apply the following calculation: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5.

⇒ (500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X

⇒ (500 + 600 + 50 + 100) / 5000 = X

⇒ 1250/5000 = X

Apply the division operation, and we get

⇒ 0.25 = X

Therefore, this raffle's expected value per ticket is $ 0.25.

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Answer:

y = [tex]\frac{1}{8}[/tex]x

Step-by-step explanation:

You need to find the unit rate.  In a proportional relationship,  you can find this by taking any point on the line and putting it the form y/x

Look at point (16,2)  y/x = 2/16 = 1/8

Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]

What is synthetic division?

Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.

Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]

First we find x from the divisor,

x+2=0

x=-2

Next, we arrange it in the division form with only the coefficients of the dividend terms.

[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]

             [tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]

 ----------------------------------

     [tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]

Therefore, we get the remainder as 24

And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].

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Answer: 17 packs

Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.

Answer:

25

Step-by-step explanation:

The value of x is 4.

What are vertical angles?

The opposing angles formed when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.

Here, we have

Given the following parameters

m∠A= (6x +29)° and

m∠B = (7x+25)°

Now, we equate both angles to find the value of x and we get

6x+29 = 7x + 25

6x-7x = 25 - 29

-x = -4

x = 4

Hence,  the value of x is 4.

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Answer:

Lucas 71 inches

Tamika 66 inches

The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

What is the equivalent measure?

In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.

The unit "qt" stands for quart, which is a unit of volume.

It is equal to 32 fluid ounces or 0.946 liters.

Therefore, 19 quarts is equal to 19 * 32 = 1932= 608  fluid ounces,

or 19 * 0.946 = 190.946 =18.094 liters.

Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

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The positive numbers are 36 and 47.

What is a positive number?

Any positive number is one that is higher than zero.

A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, increasing bigger as you move to the right.

Assume that the positive numbers be x and y.

Given that the difference x and y is 11.

Therefore x - y = 11

x = y + 11 ....(i)

The product of the numbers is 1692.

xy = 1692 .....(ii)

Putting x = y - 11 in equation (ii):

(y + 11)y = 1692

y² +11y = 1692

y² +11y - 1692 = 0

y² +47y - 36y - 1692 = 0

y(y + 47) - 36(y+47) = 0

(y + 47) (y-36)=0

y = -47 and 36

Since the numbers are positive, thus y = 36.

The value of x is 36 + 11 = 47

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Answer:

Below

Step-by-step explanation:

WOW! THIS is not 'jogging' :

4 miles / 1/5 hr = 20 m/hr