4. The three graphs represent the progress
of three runners in a 400-meter race.
The solid line represents runner A. The
dotted line represents runner B. The
dashed line represents runner C.
distance (meters)
400
300
200
100
10
40
20 30
time (seconds)
a. One runner ran at a constant rate throughout the race. Which one?
b. A second runner stopped running for a while. Which one? During which interval
of time did that happen?
c. Describe the third runner's race. Be as specific as possible.
d. Who won the race? Explain how you know.

Maggie is 30 years old, and Bobby is 15 years old if in 3 years, Maggie's age will be 50% greater than Bobby's age and years ago when Maggie was 25 years old, Bobby was 10 years old.

Maggie is 15 years older than Bobby. We have to determine Bobby's age.

Let's suppose that Bobby's age is x, so Maggie's age would be x + 15 years.

1) In 3 years, Maggie's age will be 50% greater than Bobby's age.

The age of Maggie in 3 years would be (x + 15) + 3, and the age of Bobby would be x + 3.

According to the problem, Maggie's age in 3 years would be 50% greater than Bobby's age in 3 years.

So, (x + 15) + 3 = (1.5)(x + 3)

Simplifying the above equation, we get

x + 18 = 1.5x + 4

Now, we will solve for

x.x - 1.5x = -14-0.5x = -14x = 28

Therefore, Bobby is 28 years old now.

2) Years ago, when Maggie was 25 years old, Bobby was 10 years old.

Let's assume that x years ago Maggie was 25 years old. Thus, Bobby was 10 years old at that time.

So, x + 25 = (x + 10) + 15x = 15

Therefore, Maggie is 30 years old now. And Bobby is 15 years old now.

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The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.

A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.

The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t

Where:

Y is equal to the car's value after t years.

In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.

t equals the amount of years

The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t

By condensing the formula, we obtain the following result: y = 28,000(0.91)t

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Answer: h=4

Step-by-step explanation:

The length of the base of a parallelogram is 30 feet and the height is 40 feet.

Given that the height of a parallelogram is 10 feet more than the length of the base, and the area of the parallelogram is 1200 square feet. We have to find the length of the base and the height. Let the length of the base of a parallelogram be x. Then, the height of the parallelogram = x + 10.

We know that the area of a parallelogram is given by; A = base × height1200 = x(x + 10). Simplify the equation1200 = x² + 10x. Rearrange the equationx² + 10x - 1200 = 0. On solving this quadratic equation, we get; x = 30 and x = -40.

Since the length of the base cannot be negative, therefore, the length of the base is 30 feet. So, the height of the parallelogram is 30 + 10 = 40 feet. Therefore, the length of the base of a parallelogram is 30 feet and the height is 40 feet.

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The coefficient of determination measures goodness of fit.

The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.

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Answer: 126in

Step-by-step explanation:

ftc6yhunum8im

huju7kt6r

5+10=24

g5ghykn

To find the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade, we can use the complement rule.

The complement of the event "at least one of the cards is a spade" is "neither of the cards is a spade."

To find the probability that neither of the two cards is a spade, we can multiply the probabilities of drawing a non-spade on the first card and a non-spade on the second card:

P(neither is spade) = (39/52) x (38/51) = 0.4498 (rounded to four decimal places)

P(at least one is spade) = 1 - P(neither is spade)

P(at least one is spade) = 1 - 0.4498

P(at least one is spade) = 0.5502 (rounded to four decimal places)

Therefore, the probability that at least one of the two cards drawn from a standard deck of 52 playing cards is a spade is 0.5502 or approximately 55.02%.

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The required amount of money earned on the savings account by the end of the year is $4.50.

To calculate the amount of money earned on a savings account with a given Annual Percentage Rate (APR), we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the initial amount of money in the account

Rate is the annual interest rate (as a decimal)

Time is the length of time the money is invested (in years)

In this case, the principal is $100, the rate is 4.50% per year (or 0.045 as a decimal), and the time is one year. Therefore, the interest earned can be calculated as:

Interest = $100 x 0.045 x 1

Interest = $4.50

So, the amount of money earned on the savings account by the end of the year is $4.50.

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The equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1 (option D).

To derive the equation of a line, we need to use the point-slope formula, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. Plugging in the given values, we have:

y - (-5) = -3(x - 2)

Simplifying this expression, we get:

y + 5 = -3x + 6

y = -3x + 1

Thus, the equation that represents the line passing through the point (2, -5) with a slope of -3 is y = -3x + 1.

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Complete Question:

Choose the equation below that represents the line passing through the point (2, - 5) with a slope of −3.

A.) y = −3x − 13

B.) y = −3x + 11

C.) y = −3x + 13

D.) y = −3x + 1

Answer:

The answer is y = -3x + 1

Answer:

13 bags

Step-by-step explanation:

V = π(2^2)(1/2) = 2π = 6.28 cubic feet

6.28 ÷ .5 = 12.56

So Martin needs to buy at least 13 bags of sand.

To determine if the difference in years at the company between employees with a high school degree and those with an MBA is significant at the 95% confidence level, we can perform a hypothesis test for p-value.

We can run a hypothesis test to see if the difference in years spent at the organization between workers with a high school diploma and those with an MBA is significant at the 95% confidence level.

We must first specify our alternative hypothesis and null hypothesis. Our null hypothesis is that there is no discernible difference in the number of years that personnel with a high school diploma and those with an MBA have worked for the organization. Our alternate theory is that the two groups have significantly different average years of employment.

The probability of witnessing the data if the null hypothesis is correct can then be determined using a t-test. The null hypothesis can be rejected if the p-value is less than 0.05, and the difference in years spent at the company between workers with a high school diploma and those with an MBA is determined to be significant at the 95% level of confidence.

We can use a two-sample t-test to compare the means of the two groups if the data is normally distributed and the variances are identical.

If the t-test yields a p-value of less than 0.05, we can reject the null hypothesis and draw the conclusion that there is a significant difference in the number of years that employees with a high school diploma and those with an MBA have worked for the organisation. In contrast, if the p-value is higher than 0.05, we are unable to rule out the null hypothesis since there is insufficient data to support the existence of a significant difference.

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Answer: 40/7 or 5.7

Step-by-step explanation:

using angle bisector theorem we get,

x/5 = 8/7

Upon substituting our given values in above equation, we will get:

x/5 X 5 = 8/7 X 5

x = 40/7 or 5.7

Answer:

3.3

Step-by-step explanation:

Angle bisector theorem: In a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

       [tex]\dfrac{x}{8-x}=\dfrac{5}{7}[/tex]

Cross multiply,

    x *7 = 5*(8 - x)

        7x = 40 - 5x

   7x + 5x = 40

        12x   = 40

             [tex]x = \dfrac{40}{12}\\\\x = 3.3[/tex]

The area of the rectangular section in the garden is Area = (x₂ - x₁) x (y₂ - y₁)

Now, let's look at the rectangular section of the garden represented by the coordinate plane. We are told that the section is represented by Rectangle JKLM. The four corners of this rectangle can be represented by their respective coordinates:

Point J: (x₁, y₁)

Point K: (x₂, y₁)

Point L: (x₂, y₂)

Point M: (x₁, y₂)

To find the area of this rectangle, we need to use the formula:

Area = length x width

The length of the rectangle is the distance between points J and K, which is given by:

Length = x₂ - x₁

The width of the rectangle is the distance between points J and M, which is given by:

Width = y₂ - y₁

Therefore, the area of the rectangle is:

Area = (x₂ - x₁) x (y₂ - y₁)

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Complete Question:

Gina is growing lettuce in a section of a garden. She represents this section with Rectangle JKLM. Each unit in the coordinate plane represents 1 foot.

What is the area of the section where lettuce grows?

The given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b).

The y value of the y-intercept point is denoted by the symbol b in the formula.

The general form of a linear equation is y-y1=m(x-x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

So, in the given situation:
The point-slope form is: y = mx + b

Then y is y and b is the x value and m is the slope.

Now, insert values as follows:

y = mx + b

140 = -14x + 10

Graph the equation as follows:

(Refer to the graph attached below)

Therefore, the given values are inserted in the point-slope form which formed the equation 140 = -14x + 10 and has been graphed.

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The given equation of the circle is:

[tex] \rm \: x^2 + y^2 = 20[/tex]

We can write this equation in standard form by completing the square:

[tex] \rm x^2 + y^2 = 20[/tex]

[tex] \rm x^2 + y^2 - 20 = 0[/tex]

[tex] \rm (x^2 - 2x + 1) + (y^2 - 20) = 1[/tex]

[tex] \rm (x - 1)^2 + y^2 = 21[/tex]

Therefore, the center of the circle is (1, 0) and the radius is the square root of 21.

the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

To write a piecewise function to represent the total distance Carrie has traveled after t hours, we need to break down her journey into different parts and calculate the distance covered during each part.

Let's define the three different parts of her journey:

•Part 1: The first hour, during which she averaged 30 miles per hour

•Part 2: The next 4 hours, during which she averaged 65 miles per hour

•Part 3: The remaining 2 hours, during which she averaged 52 miles per hour

For Part 1, the distance covered can be calculated as:

d1 = 30t (where t is the time spent in the first hour, t ≤ 1)

For Part 2, the distance covered can be calculated as:

d2 = 260 + 65(t - 1) (where t is the time spent in the next 4 hours, 1 < t ≤ 5)

For Part 3, the distance covered can be calculated as:

d3 = 520 + 52(t - 5) (where t is the time spent in the remaining 2 hours, 5 < t ≤ 7)

Now, we can combine these three equations to form a piecewise function for the total distance traveled by Carrie:

d(t) = 30t, 0 ≤ t ≤ 1

d(t) = 260 + 65(t - 1), 1 < t ≤ 5

d(t) = 520 + 52(t - 5), 5 < t ≤ 7

Therefore, the function d(t) represents the total distance (in miles) traveled by Carrie after t hours, where t is the time elapsed since the start of her journey.

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This equation represents the linear relationship between the dependent variable (y) and the independent variable (x) with a slope of 2 and a y-intercept of -3.

However, I can provide a general example using common terms in algebra:
Terms: Dependent variable (y), independent variable (x), slope (m), and y-intercept (b).
To represent a linear relationship between two variables, we can use the equation of a straight line, which is often written as:
[tex]y = mx + b[/tex]
Here's what each term in the equation represents:
1. y: This is the dependent variable, meaning its value depends on the value of the independent variable (x). In a graph, it is usually represented on the vertical axis.
2. x: This is the independent variable, which can take any value within a given range. It is usually represented on the horizontal axis in a graph.
3. m: This is the slope of the line, representing the rate at which the dependent variable (y) changes with respect to the independent variable (x). A positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.
4. b: This is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
simply plug in the values for the slope (m) and y-intercept (b). For example, if the slope is 2 and the y-intercept is -3, the equation would be:
[tex]y = 2x - 3[/tex]

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The sky Train from the terminal to the Cental car and long-term parking center is supposed to arrive every 6 minutes. The waiting times for the train are known to follow a uniform distribution. The 60th percentile of the waiting times is 3 minutes.

Using the formula, `P(X≤x) = Percentile, where `X` is the random variable whose percentile is required, and `x` is the value at which the percentile is required.

Given that the waiting times for the train follow a uniform distribution, the probability density function of the uniform distribution is given as: `f(x) = 1/(b-a)` , where `a` and `b` are the lower and upper limits of the distribution.

Now, it is given that the sky train is supposed to arrive every 6 minutes. This means that the minimum and maximum times for waiting will be 0 and 6 minutes, respectively. Hence, `a = 0` and `b = 6`.

Using the formula for the uniform distribution, we have `f(x) = 1/(6 - 0) = 1/6`. Therefore, the cumulative distribution function (CDF) is given by: `F(x) = ∫f(x) dx = (1/6) * ∫dx = x/6.

`Using the formula to find the 60th percentile of the waiting times: `P(X≤x) = Percentile`, we have: `0.6 = P(X≤x)`. Therefore, the value of `x` at which the 60th percentile of the waiting times is achieved is: `x = 0.6 * (b - a) + a = 0.6 * (6 - 0) + 0 = 3`. Thus, the 60th percentile of the waiting times is 3 minutes.

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The equation that represents the total area of the pool and deck is: A(x) = 2x² + 24x + 64.

In algebra, a binomial is a polynomial that consists of two terms connected by either an addition or a subtraction operator. A binomial can be written in the form (ax + b) or (ax - b), where "a" and "b" are constants and "x" is a variable.

Binomials are used in a variety of algebraic operations, such as factoring, expanding, and solving equations. They also appear in binomial probability distributions and binomial theorem.

Let's start by drawing a diagram to visualize the problem:

___________      

|                       |    4 ft

|   _________|_________

|   |                   |                    |

|   |                   |                    |

|  |                    |                    |   2x

|  |                    |                    |

|  |_________|_________ |

|                       |    4 ft

|__________ |

      2w

The rectangular pool is twice as wide as it is long, so we can let the length be x, and the width be 2x.

The deck around the pool is 4 feet wide on each side, so the total width of the pool and deck is (2x + 8), and the total length is (x + 8).

Therefore, the total area of the pool and deck can be represented as:

(2x + 8)(x + 8)

Expanding the expression, we get:

2x² + 24x + 64

So the equation that represents the total area of the pool and deck is:

A(x) = 2x² + 24x + 64

where A(x) is the area of the pool and deck, and x is the length of the pool.

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For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:

P(N=n,K=k) = P(N=n) * P(K=k)If this condition is not satisfied, then N and K are dependent.

The distribution of K given that N=2 can be calculated using the conditional probability formula:

P(K=k|N=2) = P(K=k and N=2) / P(N=2)

Let X be the outcome of the coin flip. Then the joint probability mass function of N and K can be expressed as:

P(N=n,K=k) = P(X=0) for n=0 and k=0

P(N=n,K=k) = P(X=1) for n=1 and k=0, 1

P(N=n,K=k) = P(X=2) for n=2 and k=0, 1, 2

P(N=n,K=k) = P(X=3) for n=3 and k=0, 1, 2

The marginal probability mass function of N can be obtained by summing over all possible values of K:

P(N=n) = P(N=n,K=0) + P(N=n,K=1) + P(N=n,K=2)

The marginal probability mass function of K can be obtained by summing over all possible values of N:

P(K=k) = P(N=0,K=k) + P(N=1,K=k) + P(N=2,K=k) + P(N=3,K=k)

The conditional probability mass function of N given that K=2 can be calculated using Bayes' theorem:

P(N=n|K=2) = P(K=2|N=n) * P(N=n) / P(K=2)

For N and K to be independent, the joint probability mass function should factorize into the product of the marginal probability mass functions:

P(N=n,K=k) = P(N=n) * P(K=k)

If this condition is not satisfied, then N and K are dependent.

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The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.

In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:

(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:

6⁽⁷⁻⁶⁾ = 6¹ = 6.

Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.

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a. Total purchase price: 15.The total selling price plus the sales tax.

b. Unit pricing: 18. Locating the best value for your money

c. Comparison shopping: 14. A technique that allows shoppers to compare prices

d. Coupons: 16. Discount

e. Rebates: 16. discount

f. Markdown: 17. regular selling price minus the markdown.

g. Markdown rate: 16. Discount

h. Sale price: 18. Locating the best value for your money

Selling price is the amount of money a customer pays for a product or service. It is the amount that a customer pays for the product or service after any discounts, taxes, or fees have been applied.

a. Total purchase price: The total selling price plus the sales tax. This amount is the total cost the customer pays for the good or service, including any taxes and fees.

b. Unit pricing: The cost per unit of a good or service. This allows shoppers to compare the cost of similar items and make an informed decision about which item offers the best value.

c. Comparison shopping: A technique that allows shoppers to compare prices, quality, and other factors when making a purchase.

d. Coupons: A form of discount that can be used when making a purchase. Coupons are often found in newspapers, magazines, or online and can be used to reduce the total purchase price.

e. Rebates: A form of discount where customers receive money back after making a purchase. Rebates are often found in the form of a check or a prepaid debit card.

f. Markdown: The regular selling price minus the markdown. The markdown is the amount that is discounted from the regular selling price.

g. Markdown rate: The percentage of the regular selling price that is discounted. This rate is used to calculate the amount of the markdown.

h. Sale price: The discounted price of a good or service. This is the amount the customer pays after any discounts or coupons have been applied.

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Answer:

22: 2

23: -7

25: 6

26: 3

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

Step-by-step explanation:

For 22: 2 * 2 * 2 = 8, therefore, 2

For 23:  -7 * -7 * -7 = -343. This results in a negative number because there is is an odd number of negative numbers (follows the odd-even negative rule).

For 25: Multiply both sides of the equation by -1/2 to get z^3 = 216. The cube root of 216 is 6

For 26: Add 11 to both sides to get 2h^3 = 54. Divide both sides by 2 to get h^3 = 27. Cube root of 27 is 3.

Let me know if this helped by clicking the help button or if not please comment with issues and I'll get right back to you!

The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.

Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.

This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.

This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.

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The domain for n in the arithmetic sequence is the one in the first option:

all integers where n ≥1

We have a arithmetic sequence defined by the general formula:

aₙ  = 4 - 3*(n - 1)

And we want to find the domain for the possible values of n that we can use in that formula.

Remember that the terms of a sequence are defined as:

a₁, a₂, a₃,...

So the values of n are positive whole numbers, in this case the first one is n = 1.

a₁ = 4 + 3*(1 - 1)

a₁ = 4

And then we can keep using any positive integer, then the correct option is:

all integers where n ≥1

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Answer:

Step-by-step explanation: 14 = x

Answer:

The answer to your question would be 14

Step-by-step explanation:

Simple equation

14 - 10 = 4

I hope this helps and have a wonderful day!

Answer:

$510,000

Step-by-step explanation:

Since we are rounding to the nearest thousand, we can use the hundreds place to determine the if we need to round down or up.

Remember, 4 or less, round down. 5 or more, round up.

Since the hundreds digit is 4, we do not need to round.

We only need to change the rest of the digits to 0.

So, our answer would be $510,000.

Answer: The answer is 38.5 cm^2

Step-by-step explanation:

Given:

           Radius(r) = 7/2

            Pie (π) = 22/7

We know that:

          The area of Circle is = πr^2 = π * r * r

           So, ans is = (22/7) * 7/2 * 7/2 = 38.5 cm^2

Answer:

A≈ 38.5cm^2

Step-by-step explanation:

Given:

The approximation of pi is 22/7 or 3.141592

The radius is 7/2 or 3.5

Work:

A=πr(2)=π·3.5(2)≈38.48451

now let's round it to 38.5cm^2

Answer:

orthocentre

Step-by-step explanation:

this is the answer to your question