The ages of 12 runners in a recent marathon are listed.

35, 17, 34, 14, 28, 20, 18, 15, 14, 19, 17, 31

Find the median and interpret its meaning as it relates to the runners.

The median is 18.5, and it represents the typical age of the runners.
The median is 20.5, and it represents the typical age of the runners.
The median is 21.5, and it represents the difference in the lowest and highest ages of runners.
The median is 23.5, and it represents the difference in the lowest and highest ages of runners.
Question 10(Multiple Choice Worth 2 points)

Answer:

Option D) 10mi

Step-by-step explanation:

A rectangle has 90 degree angles. When a line cuts it diagonally, it makes a right angle.

When there is a right angle we think about the Pythagorean theorem.

a²± b² = c²

Plug the values:

8²+6²= c²

Simplify:

64+36 = c²

Combine like terms:

100 = c²

Rooting hypotenuse we get

10 = c

The length of the path is 10 miles.

The solution is, a) Negative linear; b) about 48

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

a) Type of correlation

The graph shows a negative linear correlation.

b) Prediction

It looks like a student who makes 60 in Science would make about 48 in English.

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The pendulum will swing at the velocity of 3.06 m/s at the bottom of the swing.

Velocity is the rate of change of position of an object, usually measured in meters per second (m/s). It is a vector quantity, which means it has both magnitude and direction. Velocity is an essential notion in physics since it is used to describe motion and is one of the fundamental principles of classical mechanics. It is connected to other notions such as acceleration, momentum, and force. Velocity is a measure of how rapidly an item moves in a specific direction, and it is computed by dividing the distance travelled by the time it takes for the object to traverse that distance.

The speed of the pendulum at the bottom of its swing can be calculated using the formula:

v = √(2gh)

where v = velocity, g = gravitational acceleration (9.8m/s2), h = height (1.22m)

Therefore, the speed of the pendulum at the bottom of its swing is:

v = √(2*9.8*1.22)

v = 3.06 m/s

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La ecuación de la circunferencia que pasa por los puntos (0, 0), (3, 4) y (6, 2) es x² + y² - (55 / 9) · x - (5 / 3) · y = 0.

Según la geometría analítica, la fórmula general de una circunferencia contiene tres coeficientes reales (D, E, F) en la siguiente expresión:

x² + y² + D · x + E · y + F = 0

En consecuencia, se requiere el conocimiento de tres puntos distintos para determinar las condiciones de la ecuación. Es preciso construir un sistema de ecuaciones lineales, cuya forma es:

D · x + E · y + F = - x² - y²

Si sabemos que (x₁, y₁) = (0, 0), (x₂, y₂) = (3, 4) y (x₃, y₃) = (6, 2), entonces tenemos el siguiente sistema de ecuaciones lineales:

F = 0

3 · D + 4 · E + F = - 25

6 · D + 2 · E + F = - 40

Cuya solución se obtiene mediante métodos numéricos:

(D, E, F) = (- 55 / 9, - 5 / 3,  0)

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Answer:

Step-by-step explanation:

Wow, that is a lot. You got to give me a brainliest ! Lol

1) 9²+12²=x², x=15

2)10²+24²=x², x=26

3)3²+7²=x², x=7.6

4)6²+x²=10², x=8

5)x²+6²=24², x=23.2

6)1²+1²=x², x=1.4

7)x²+8²=21², x=19.4

8)x²+24²=30², x=18

9)5²+9²=x², x=10.3

The required volume of figure 1 is given as 55 ft³, and the volume of all the figures is evaluated by following the same procedure.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
Volume  = 1/3 area of base × height - - - - -(1)

(1)
Area of base = area of triangle = 1/2 × base × height

Area of base = 1/2 × 5 * 6 = 15
Put this value in equation 1
Volume =  1 /3 ×15 × 11
Volume = 55 ft³

Similarly, the volume of each figure can be evaluated.

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The expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

An expression is combination of variables, numbers and operators.

The given expression is (X+1)(2x-8)

Apply distributive property

(X+1)(2x-8)

x(2x-8)+1(2x-8)

2x²-8x+2x-8

Trinomial is an expression which has three terms.

2x²-6x-8

Hence, the expression (X+1)(2x-8) in the form of trinomial is 2x²-6x-8

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The equation that represents the given graph is: D. y = 2/5x - 3.

The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

here, we have,

To find the equation of a line that passes through two points (x1, y1) and (x2, y2), we can use the following steps:

Find the slope (m) using the formula

m = (y2 - y1) / (x2 - x1).

Plug in the slope and one of the points into the equation

y = mx + b to find b.

So, for the line that passes through the points (0, -3) and (5, -1),

the slope is (-1 - (-3)) / (5 - 0)

                 = 2/5,

and the y-intercept can be found by plugging in the slope and the point (0, -3) into the equation y = mx + b:

-3 = (2/5) * 0 + b

-3 = b

Therefore, the equation of the line that passes through (0, -3) and (5, -1) is:  y = (2/5)x - 3

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Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.

Mathematics includes the study of numbers, various variations, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship variable between the number of inputs and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a domain. The letter f is frequently used to denote functions (x).

Here,

Given :

=> f(−4) = −2

=> ƒ'(−4) = 6

=> f(-5) = −4

=> f'(-5) = 1

To find :

=> g(x) = ƒ(2x + 3)

=> g(4) = f(2(-4) + 3)

=> g(4) = f(-5)

=> f(-5) = -4

=> f'(-5) = 1

Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.

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Answer:

12 ft

Step-by-step explanation:

To find the height of a rectangular box with a base measuring 3 feet by 6 feet and a volume of 72 cubic feet, we need to use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the volume of the box and the length and width, so we can substitute the values and solve for the height:

72 = 3 x 6 x Height

72 / (3 x 6) = Height

12 = Height

So, the height of the box is 12 feet.

If the point (4, -1) is a point on the graph of f, then f(4) = -1.

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

Point ​(4,−​1) is a point on the graph of​ f

The expression "f(4)" represents the output value of the function f, when 4 is plugged into it as the input.

If the point (4, -1) is on the graph of f, it means that for the input value of 4, the output value of the function is -1.

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Answer:

C is the answer.

Step-by-step explanation:

Switzerland uses the currency called Switzerland Franc.

PLEASE MARK ME BRAINLIEST.

Answer:

A ≈ 5568.2 cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

here the diameter = 84.2 , then r = 84.2 ÷ 2 = 42.1 , then

A = π × 42.1² = π × 1772.41 ≈ 5568.2 cm² ( to 1 decimal place )

The probability that Deborah's first flight was delayed can be found to be 0. 85.

To find the probability that Deborah's first flight from Boston to Denver was delayed, use the following formula :

= 1 - probability that the flight takes off on time

Probability that the flight takes off on time = 0. 15 .

The probability that Deborah's first flight from Boston to Denver was delayed is therefore :

= 1 - 0. 15

= 0. 85

In conclusion, there is an 85 % probability that the first flight was delayed.

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Answer: The total value of the loan with quarterly compounded interest  is $60,109.34.

Step-by-step explanation:

To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A = final amount (loan + interest)

P = principal (the original amount of the loan)

r = annual interest rate as a decimal

n = number of times the interest is compounded in a year

t = time in years

For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.

Substituting the values into the formula, we get:

A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)

A = $50,000 * (1.015375)^(15.7532)

A = $50,000 * 1.22186888

A = $60,109.34

Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.

225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required to get 600 pounds of a new blend costing $3.50

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of Earl Grey tea and y represent the amount of Orange Pekoe tea.

Earl Grey tea sells for $6 per pound while Orange Pekoe tea sells for $2 per pound. Both teas were mixed to get 600 pounds of a new blend selling at $3.50. Hence:

x + y = 600    (1)

Also:

6x + 2y = 3.5(600)    (2)

From both equations:

x = 225, y = 375

225 pounds of the Earl Grey tea and 375 pounds of Orange Pekoe tea are​ required

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Answer: 3

Step-by-step explanation:

The graph of the equation can be seen on the image at the end, and when she uses 17 cups of flour, she will use 76.5 cups of honey.

We assume that the relation is linear.

Remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the linear equation passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we have the two pairs:

(27, 6)

(45, 10)

First, you can graph these two points and connect them with a line, that will be the graph of our equation.

The slope is:

a = (10 - 6)/(45 - 27)

a = 4/18

a = 2/9

y = (2/9)*x + b

To find the value of b we can replace the values of the point (27, 6)

6 = (2/9)*27 + b

6 = 2*3 + b

6 = 6 + b

0 = b

So the equation is just:

y = (2/9)*x

And for 17 cups of flour, she will use:

17 = (2/9)*x

(9/2)*17 = x

76.5 = x

She needs to use 76.5 cups of honey.

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Answer:

216.25

Step-by-step explanation:

First multiply 4 × 37 = 148

Then add 148 + 68.25 = 216.25

Answer:

The "one number" is equal to 4 and "another number" is equal to 6.

Step-by-step explanation:

1. We can write an equation for "one number": X = 2n - 8 (X is one number and another number is N)

2. Since their sums are 10 we can write it was X + N

3. Plug in the value of X to get: 2n - 8 + N = 10

4. Put 8 to the other side to get + 8 --> 2n + N = 10 + 8

5. Now you form the equation 3n = 18

6. N = 18 / 3 which is 6

7. To get X you do 10 - 6 which is equal to 4

8. To make sure the answer is correct plug in the values into the equation: 4 = 2(6) - 8 which simplifies to 4 = 12 - 8

Therefore, one number is equal to 4 and another number is equal to 6

Answer:

Each bucket will be [tex]\dfrac{1}{2}[/tex] full

Step-by-step explanation:

First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.

Adding up the fractions we get the expression:

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}[/tex]

To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3

This is the smallest number divisible by all 3 numbers without a remainder

There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3

We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly

Multiply each of the fractions by the LCM

12 x 5/12 = 5

12 x 3/4 = 9

12 x 1/3 = 4

These will become the numerators in the addition with the common denominator of 12

[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}\\\\= \dfrac{5 + 9 + 4}{12}\\\\= \dfrac{18}{12}\\\\[/tex]

This is how many buckets it will take to hold the water from all three buckets

Divide numerator and denominator by 6 to reduce to lowest fraction

[tex]\dfrac{18 \div 6}{12\div6} = \dfrac{3}{2}[/tex]

This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket

[tex]\dfrac{3}{2} \div 3\\\\= \dfrac{3}{2} \times \dfrac{1}{3}\\\\= \dfrac{1}{2}[/tex]

So each bucket will be half full

Answer:

SA = 439.8 in²

Step-by-step explanation:

the surface area (SA) is the total area of the 6 triangular faces and the base

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 10 and h = 6 , then

A = [tex]\frac{1}{2}[/tex] × 10 × 6 = 5 × 6 = 30 in²

so area of 6 triangles = 6 × 30 = 180 in²

Then

SA = 180 + 259.8 = 439.8 in²

A positive and a negative coterminal angle for each given angle is

A. 13π/4 and -3π/4.

B. 97π/36 and -47π/36.

What is the coterminal angle?

Coterminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). Coterminal angles are the angles that have the same initial side and share the terminal sides.

Here, we have

A. 5π/4

We have to find the coterminal angle.

5π/4 + 2π = 13π/4

5π/4 -  2π = -3π/4

Hence, a positive and a negative coterminal angle for each given angle is 13π/4 and -3π/4.

B. 25π/36

We have to find the coterminal angle.

25π/36 + 2π = 97π/36

25π/36 -  2π = -47π/36

Hence, a positive and a negative coterminal angle for each given angle is 97π/36 and -47π/36.

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Kevin has $3840 invested in stocks in total.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Annual interest in first investment - 11%

Annual interest in other investment - 14%

Total interest annually - $480

Let us assume, x is the investment in each stock

or, total investment = 2x

then, making an equation for the total interest

0.11x+.14x=480

Multiplying everything by 100

11x+14x=48000

25x=48000

Divide both sides by 25

x=1920

then, by total investment = 2x

2×(1920) = 3840

Hence, Kevin has $3840 invested in stocks in total.

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The bedroom's area in meters squared is 55.1693 m².

finding the area of the basement:

The length of the basement is 2 * 10.5 m = 21 m

The width of the basement is 8 m / 4 = 2 m

The area of the basement is 21 m * 2 m = 42 m²

Next, let's find the equivalent area of the 10 square feet tile in meters:

1 square foot = 0.092903 m²

10 square feet = 10 * 0.092903 m^2 = 0.92903 m²

finding the area of the bedroom:

The length of the bedroom is 10.5 m - 6 m = 4.5 m

The width of the bedroom is 8 m * 34 = 2.72 m

The area of the bedroom is 4.5 m * 2.72 m = 12.24 m²

So the total area covered with carpet and tile is:

12.24 m² + 42 m² + 0.92903 m²

  = 55.1693 m²

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In order to buy four bananas, then the number of apples that he bought will be 8.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50.

Let 'x' be the number of apples and 'y' be the number of bananas. Then the equation is given as,

1x + 0.50y = 10

x + 0.50y = 10

In order to buy four bananas, then the number of apples that he bought is given as,

x + 0.50 (4) = 10

x + 2 = 10

x = 8

In order to buy four bananas, then the number of apples that he bought will be 8.

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Answer: 4

Step-by-step explanation: i took the test

Answer:

The equation for the new graph is e^(x -6)

On solving the provided question we can say that by fraction, Mike can fill 18 X 1/3 = 6 cups with water

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Each jar holds 1/3 cup.

Mike has 18 cups of water

by fraction, Mike can fill 18 X 1/3 = 6 cups with water

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The correct question is -

Mike will fill jars with water for an experiment. Each jar holds 1/3 cup. Mike has 18 cups of water. How many jars can Mike fill with water?

Answer:

It isn't measured, but it gives you a ruff representation of what the subject looks like.

Step-by-step explanation: