on their next training run, pepe averaged a speed of 2/3 of a mile in 5 minutes, while paula averaged 1/4 of a mile in 2 minutes. if pepe and paula each ran at their individual pace for 60 minutes, how many total miles did they cumulatively run?

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

4.8 minutes

Step-by-step explanation:

First, set up the proportion as  \(\frac{2}{10} = \frac{x}{24}\)

Next, you cross multiply.

This gives you 10x = 48

Now, divide 10 by both sides.

This gives you x = 4.8

An equation of the line of best fit is y = 0.19x + 308.93.

The slope is 0.19 and it represent the yearly attendance per the cost of advertising.

The y-intercept is 308.93 and it represent the initial attendance.

A scatter plot of the residuals would show a linear relationship.

Yes, there is a casual relationship in the data.

The predicted attendance when the advertising cost is $89,000 would be 17,219 people.

In order to determine a linear equation for the line of best fit that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the advertising cost (in dollars) would be plotted on the x-axis of the scatter plot while the attendances would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data, a linear equation for the line of best fit is given by:

y = 0.19x + 308.93

Next, we would determine the predicted attendance when x = $89,000:

y = 0.19(89,000) + 308.93

y = 17,218.93 ≈ 17,219 people.

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Answer:

$7.50

Step-by-step explanation:

you add 40.50 + 4.50 which then equals 45 and you divide that by 6 and you get 7.50

One ticket costs $7.50 without the coupon this we obtained by dividing total cost before discount  by Number of tickets

Let us find the total cost of the tickets before the coupon is applied. We can do this by adding the discount amount ($4.50) to the final cost ($40.50):

Total cost before discount = Final cost + Discount amount

Total cost before discount = $40.50 + $4.50

Total cost before discount = $45.00

Now we can divide the total cost before discount by the number of tickets

(6) to find the cost of one ticket:

Cost of one ticket = Total cost before discount / Number of tickets

Cost of one ticket = $45.00 / 6

Cost of one ticket = $7.50

Therefore, one ticket costs $7.50 without the coupon.

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The intersection points are: (0, -3) and (10, 2)

The bounded area is -20.83 unit²

(a) The  intersection points of the line and curve are the points where the line and curve meet. Thus, the intersection points are:

(0, -3) and (10, 2)

(b) The integral terms of y which gives the area bound are:

a = -3, b = 2 (These are the y values of the intersection points)

Since we have x = y² + 3y and x = 2y + 6, we can say:

y² + 3y = 2y + 6

y² + 3y - 2y - 6 = 0

y² + y - 6 = 0

Thus, h(y) =

Using a = -3 and b = 2  with h(y) = y² + y - 6, we have the bounded area as:

\(Area = \int\limits^b_a {y} \, dy\)

\(Area = \int\limits^{2}_{-3} {(y^{2} + y - 6}) \, dy\)

Integrating the area:

Area = [y³/3 + y²/2 - 6y + C]²₋₃

Area = [2³/3 + 2²/2 - 6(2)] - [(-3)³/3 + (-3)²/2 - 6(-3)]

Area = [8/3 + 2 - 12] - [-9 + 4.5 + 18]  

Area = [-22/3] - [27/2]

Area = -125/6

Area = -20.83 unit²

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Answer:

\(\sqrt{1}\)

Step-by-step explanation:

We know that a rational number cannot have roots. All of the answer choices cannot be simplified except for \(\sqrt{1}\), which can become 1. Therefore, our answer is \(\sqrt{1}\).

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.

The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.

To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:

Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.

In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.

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The solution to the equation below rounded to two decimals is x = 2.77.

A number that may be entered for the variable to produce a true number statement is the answer to an equation.

The solution to the equation \(3^x=21\) is x = 2.77 (rounded to two decimal places).

To solve this equation, we can take the logarithm of both sides using any base. Let's use the natural logarithm (ln):

\(3^x = 21\\\\ln(3^x) = ln(21)\)

Using the power rule of logarithms, we can bring down the exponent x:

x ln(3) = ln(21)

Finally, we can solve for x by dividing both sides by ln(3):

x = ln(21) / ln(3) = 2.769...

Rounding to two decimal places gives x = 2.77.

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The confidence interval for  mean number of hours of sleep on a typical night for the students is  [ 94.58,105.42 ] .

Using the mean, standard deviation, number of samples, and desired confidence interval as inputs, the following formula is used to compute the interval:

X + / -( Z * ( σ / √n))

where z comes from the reference's standard distribution tables and has a 95% confidence interval of 1.96.

100 + / - (1.96 * (17.50/40^1/2))

= [ 94.58,105.42 ]

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.

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Answer:

23

Step-by-step explanation:

31+23=54

\(54-x=31\)

Simplify:

\(-x+54=31\)

Subtract 54 from both sides:

\(-x+54-54=31-54\)

\(-x=-23\)

Divide both sides by -1:

\(\dfrac{-x}{-1} =\dfrac{-23}{-1}\)

\(=\fbox{x = 23}\)

Answer:

eeeeee

Step-by-step explanation:

eeeeeeee

The current value of Avery’s car is $12,480.

First step is to calculate the Net Worth

Bank accounts    $3,900

Credit card debt ($2,950)

Real estate         $37,425

Student loans    ($1,700)

Investments        $4,600

Net worth           $41,275

Second step is to calculate the current value of Avery’s car

Current value=$53,755-$41,275

Current value=$12,480

Inconclusion the current value of Avery’s car is $12,480.

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Answer:

ok so the numbers are 21%, 3/20, 25.6%, 2.24, and .24 we are ordering from least to greatest

Step-by-step explanation: First we need to figure out what 3/20 is and its 0.15 so 3/20 comes first then 0.24 then 2.24 then 21% then 25.6%

Answer:

3 weeks 5 days

Step-by-step explanation:

A week is 7 days

26/7 = 3 remainder 5

3 weeks 5 days

The best type of graph for the data set below is a bar graph. So the correct option is A.

The pictorial representation of data which is generally grouped, in the form of vertical or horizontal rectangle-shaped bars is called a bar graph. In this type of graph, the length of bars is a representation of the measure of data. They are also called bar charts. In statistics, bar graphs are one of the ways of data handling.

Statistics is the collection, presentation, analysis, organization, and interpretation of data observations. There are various methods for the representation of this statistical data. These can be tables, bar graphs, pie charts, histograms, frequency polygons, etc.

There are three main characteristics of bar graphs. These are:

It helps in comparing the different sets of data among different groups.

The relationship using two axes is shown where the categories are on one axis and the values are on the other axis.

Major changes in data over time are shown.

Therefore the correct option is A.

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The complete question is:

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

I have learned a lot in math, although it was years ago on of my favorite things to learn was to multiply and divide. They were not only easy but also fun.

Step-by-step explanation:

Answer:

x = pi n

Step-by-step explanation:

6 sec^2(x) − 6 = 0

Add 6 to each side

6 sec^2(x) − 6+6 = 0+6

6 sec^2(x)=6

Divide by 6

 sec^2(x)  = 1

Take the square root of each side

sqrt(  sec^2(x) ) = ±sqrt(1)

 sec(x)  =± 1

sec (x) = 1       sec(x) = -1

Take the inverse sec of each side

sec^-1(sec (x)) = sec^-1(1)       sec^-1(sec (x)) = sec^-1(-1)

x = 2 pi n                                    x = pi + 2 pi n   where n is an integer

Combining

x = pi n

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Answer:

(2, 8), (0, 8), (-1, 5), (-1, 3), (-2, 3)} is {-1, 0, 2, 3}

Step-by-step explanation:

Answer:

i agreee

Step-by-step explanation:

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer:

Step-by-step explanation:

I forgot to add the last reason is AAS (two angles one side are congruent = triangles are congruent)

S.

1.Given

2. AE = EC

3. <AEB = <CED

4. <CDE = <ABE

5. triangles congruent

R.

1. Given

2. Segment bisector theorem

3. Vertical angles theorem

4. PAI Theorem

Hope this helps!

Cone B does not have volume 48bold pi cubic units with these dimensions, but it does have the same volume as Cone A because they both have volume 48bold pi cubic units.

A cone, also known as a vertex, is a three-dimensional polygonal object with a flat base and a soft tapering apex. In a plane with no vertices, a cone is formed by connecting a story arc of lines, half-lines, but rather routes those are common to all focuses on the outpost. A cone is a muti structure with just a peaceful transition from a flat, round or, base towards the vertex and apex, which represents as the base's axis. A three-dimensional polygonal shape with only an upwardly flat curved surface is known as a cone.

Because Cone A has a volume of 48bold pi cubic units, we can use the volume of a cone formula to calculate its height:

Cone volume = 1/3 * base area * height

1/3 * pi * 62 * 4 = 48bold pi

48pi = 48bold pi

As a result, Cone A's height is 4 units. The radius is also 6 units, as we can see.

Cone volume = 1/3 * base area * height

\(1/3 * pi * r2 * h = 48\\144 = r^2 * h\\144 = 8^2 * 3\\144 = 192\)

Cone B does not have volume 48bold pi cubic units with these dimensions, but it does have the same volume as Cone A because they both have volume 48bold pi cubic units.

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Answer:

1 boy 4 girls, 2 boys 8 girls, 3 boys 12 girls, 4 boys 16 girls

\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)