You and a friend start biking in opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. How far apart are you and your friend after 15 minutes? Round to the nearest hundredth of a mile.

Answer:

84% of 151.1 being reduced from 151.1 is what we need to find.

Thus we shld find 84% of 151.1

12,692.4÷100

126.924

Now subtracting 126.924 from 151.1

151.1 - 126.924

24.176

Answer:

24.176

Step-by-step explanation:

Let's find 84% first of 151.1 before we decrease it.

Since we have 84%, we can turn into a decimal and use it for our sum.

84% = 0.84

We multiply 151.1 by 0.84 in order to find the amount (strange right? I thought it was divide).

151.1 × 0.84 = 126.924

Now that we have 84% of 151.1, let's decrease it. We need to take them both away from each other, biggest number first!

151.1 - 126.924 = 24.176

And that is the final answer!

To obtain the essential prime implicants and a minimum sum of products (SOP) expression for the complement of the function, we need to analyze the map shown in the figure. The essential prime implicants are the minimal combinations of input variables that cover at least one minterm that is not covered by any other implicant.

By examining the map, we can identify the minterms that are not covered by any larger implicant. These minterms correspond to the "don't care" or "X" entries in the map. We then identify the prime implicants that cover these essential minterms.

The essential prime implicants are minimal combinations of variables that are necessary to cover these minterms. We select the essential prime implicants that cover the essential minterms and combine them to form the minimum SOP expression for the complement of the function.

To obtain the minimum SOP expression, we use the selected essential prime implicants and combine them with necessary non-essential prime implicants to cover the remaining minterms in the function. This process ensures that the resulting expression is minimal, with the fewest terms and variables required to represent the function.

By analyzing the map, identifying the essential prime implicants, and combining them appropriately, we can derive a minimum SOP expression for the complement of the function.

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To find the approximate area of a regular 13-gon with sides of length 16 yards, we can divide the polygon into 13 congruent triangles, where each triangle has a central angle of 360/13 degrees.

The central angle of each triangle is 360/13 degrees, and the radius of the circumcircle of the polygon is half the length of the diagonal of the 13-gon. To find the diagonal, we can divide the 13-gon into 10 isosceles triangles, where each triangle has base length 16 yards and base angles of 180/13 degrees. We can then use the law of cosines to find the length of the diagonal:

d^2 = 16^2 + 16^2 - 21616*cos(180/13)

d ≈ 176.28 yards

The area of each triangle can be found using the formula:

A = (1/2)bh

where b is the length of the base (16 yards) and h is the height of the triangle. The height of the triangle can be found using the Pythagorean theorem:

h^2 = d^2 - (b/2)^2

h ≈ 174.15 yards

Thus, the area of each triangle is:

A = (1/2)(16)(174.15) ≈ 1394.38 square yards

The total area of the 13-gon is therefore:

A_total = 13A ≈ 18,121.94 square yards

Therefore, the approximate area of the regular 13-gon is 18,121.94 square yards.

Answer:

3^12

Step-by-step explanation:

9³=(3²)³=3^6

27²=(3³)²=3^6

So together, it is 3^12

Answer:

3^12

Step-by-step explanation:

9^3 x 27^2

Rewrite 9 as 3^2 and 27 as 3^3

3^2^3  * 3^3^2

We know that a^b^c = a^(b*c)

3^(2*3)  * 3^(3*2)

3^6   * 3^6

We know that a^b  * a^c = a^(b+c)

3^(6+6)

3^12

The correct answer is b) 15.87%, indicating that approximately 15.87% of NFL players have a retirement age less than 31 years old.

To find the percentage of players whose age is less than 31, we can use the standard normal distribution and z-scores.

First, we need to calculate the z-score for the value 31 using the formula:

z = (x - μ) / σ

where x is the value we want to find the percentage for, μ is the mean, and σ is the standard deviation.

In this case, x = 31, μ = 33, and σ = 2. Plugging these values into the formula, we get:

z = (31 - 33) / 2 = -1

Next, we can look up the cumulative probability associated with the z-score -1 in the standard normal distribution table. The cumulative probability represents the percentage of values that are less than the given z-score.

From the standard normal distribution table, the cumulative probability for z = -1 is approximately 0.1587, which corresponds to 15.87%.

Therefore, the correct answer is b) 15.87%, indicating that approximately 15.87% of NFL players have a retirement age less than 31 years old.

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The transformation that map ∆ABC to ∆A′B′C′ are reflection about y= x and 10 units to the right and 4 units up.

Given:

Mapping of ∆ABC to ∆A′B′C′.

From the figure, it can be seen that the coordinates are swapped.

and, In a transformation that swaps the x-coordinates with the y-coordinates of points in a plane is the reflection about y= x.

Now, Coordinates of A (-6, 2)

and, coordinates A'(-2, 12)

This, means that points of the triangle 10 units to the right and 4 units up in the coordinate plane.

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Answer:

x = 5/2,2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

We'll give Sucely the variable s and Liz l.

s = 3(l - 5)

21 = 3(l - 5) distribute the 3

21 = 3l - 15 add 15 to each side

36 = 3l divide each side by 3

12 = l

So, Liz sent 12 texts

The probability (in percentage) that a score will fall between a -3z and +2 z scores is 97.59%.

Assuming a standard normal distribution, the probability that a score falls between -3z and +2z can be calculated as the difference between the cumulative probabilities of +2z and -3z.

Using a standard normal distribution table or calculator, we find that the cumulative probability of +2z is approximately 0.9772, and the cumulative probability of -3z is approximately 0.0013.

Therefore, the probability that a score falls between -3z and +2z is:

0.9772 - 0.0013 = 0.9759

Converting to a percentage, we get:

0.9759 x 100% ≈ 97.59%

So the probability that a score falls between -3z and +2z is approximately 97.59%.

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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75. To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms.

For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395

For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266

For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122

To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923

Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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Based on the given data, the probability of a room being occupied on any particular weekend night is 0.75.

To calculate the probability that at least 4 out of the 7 rooms are occupied on a weekend night, we can use the binomial probability formula. By summing up the probabilities for 4, 5, 6, and 7 occupied rooms, we find that the probability is approximately 0.923.

To calculate the probability, we can use the binomial probability formula, which states that the probability of getting exactly k successes in n independent Bernoulli trials, each with a probability p of success, is given by the formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

In this case, we want to find the probability of at least 4 out of 7 rooms being occupied on a weekend night. We can calculate this by summing up the probabilities of getting 4, 5, 6, and 7 occupied rooms. For 4 occupied rooms:
P(X = 4) = (7 choose 4) * 0.75^4 * (1 - 0.75)^(7 - 4) = 0.339

For 5 occupied rooms:
P(X = 5) = (7 choose 5) * 0.75^5 * (1 - 0.75)^(7 - 5) = 0.395
For 6 occupied rooms:
P(X = 6) = (7 choose 6) * 0.75^6 * (1 - 0.75)^(7 - 6) = 0.266
For 7 occupied rooms:
P(X = 7) = (7 choose 7) * 0.75^7 * (1 - 0.75)^(7 - 7) = 0.122
To find the probability of at least 4 occupied rooms, we sum up the probabilities for 4, 5, 6, and 7 occupied rooms:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.339 + 0.395 + 0.266 + 0.122 = 0.923. Therefore, the probability that at least 4 out of the 7 hotel rooms are occupied on any weekend night is approximately 0.923, or 92.3% when rounded to three decimal places.

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\(10 - d = - 34 - 5d\)

Because we cannot subtract or add up constants and variables, we simply move the same variable term to the same side and constant term to the same constant side.

\(10 + 34 = - 5d + d \\ 44 = - 4d \\ \frac{44}{ - 4} = d \\ - 11 = d\)

Substitute d = -11 in the equation.

\(10 - ( - 11) = - 34 - 5( - 11) \\ 10 + 11 = - 34 + 55 \\ 21 = 21\)

The equation is true for d = -11.

\( \large \boxed{d = - 11}\)

Answer:

d=-11

Step-by-step explanation:

10-d=-34-5d

+5d +5d

10+4d=-34

-10 -10

4d=-44

÷4 ÷4

d=-11

just do the opposite

The equation has no solution as 10 + x ≠ 5 + x

When the value of x is 2, the equation also have no solution as 12 ≠ 7

Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, factors and coefficients.

These algebraic expressions are expressions that are identified with arithmetic operations, such as;

From the information given, we have;

6 + x + 4 = 2 + x  + 3

collect the like terms, we have

10 + x = 5 + x

But we know that 5 is not equal to x and thus, the equation has no solution

Now, let's substitute the value of x as 2, we have;

10 + 2 = 5 + 2

This gives;

12 = 7

This is not true and thus, the equation has no solution

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The most appropriate choice for profit and loss will be given by

Uncle Ben will feed his cows 2 pounds of grain supplement.

What is profit and loss?

If the selling price is more than the cost price, then the difference between the selling price and the cost price will give the profit.

If the selling price is less than the cost price, then the difference between the selling price and the cost price will give the loss.

Here,

For 1 pound

Cost price of grain supplement  = \(0.70 \times 1\)

                                                      = $\($0.70\)

Selling price of milk = \(0.20 \times 5\)

                                 = $\(1\)

Profit = $(\(1 - 0.70\))

         = $0.30

For 2 pounds

Cost price of grain supplement  = \(0.70 \times 2\)

                                                      = $\($1.40\)

Selling price of milk = \(0.20 \times 9\)

                                 = $\(1.80\)

Profit = $(\(1.80 - 1.40\))

         = $0.40

For 3 pounds

Cost price of grain supplement  = \(0.70 \times 3\)

                                                      = $\($2.10\)

Selling price of milk = \(0.20 \times 12.3\)

                                 = $2.46

Profit = $(\(2.46 - 2.10\))

         = $0.36

For 4 pounds

Cost price of grain supplement  = \(0.70 \times 4\)

                                                      = $\($2.80\)

Selling price of milk = \(0.20 \times 15.5\)

                                 = $3.1

Profit = $(\(3.1 - 2.80\))

         = $0.30

For 5 pounds

Cost price of grain supplement  = \(0.70 \times 5\)

                                                      = $\($3.50\)

Selling price of milk = \(0.20 \times 18\)

                                 = $3.60

Profit = $(\(3.60 - 3.50\))

         = $0.10

For 6 pounds

Cost price of grain supplement  = \(0.70 \times 6\)

                                                      = $\($4.20\)

Selling price of milk = \(0.20 \times 20\)

                                 = $4

Loss = $(\(4.20 - 4\))

         = $0.20

For 7 pounds

Cost price of grain supplement  = \(0.70 \times 7\)

                                                      = $\(4.90\)

Selling price of milk = \(0.20 \times 21.5\)

                                 = $\(4.30\)

Loss = $(\(4.90 - 4.30\))

         = $0.60

For 8 pound

Cost price of grain supplement  = \(0.70 \times 8\)

                                                      = $\($5.60\)

Selling price of milk = \(0.20 \times 22.5\)

                                 = $\(4.50\)

Loss = $(\(5.60 - 4.50\))

         = $1.10

For 9 pounds

Cost price of grain supplement  = \(0.70 * 9\)

                                                      = $\(6.30\)

Selling price of milk = \(0.20 * 23\)

                                 = $\(4.60\)

Loss = $(\(6.30 - 4.60\))

         = $1.70

Since profit from 2 pounds of grain supplement is the most, Uncle Ben will feed his cows 2 pounds of grain supplement.

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Complete Question

Farmer Ben knows that feeding a grain supplement to his cows will produce more milkaccording to the following schedule:

ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?

The table has been attached here

Answer:

8 inches

Step-by-step explanation:

Use Pythagorean theorem,

Base² + altitude² = hypotenuse²

15²+ altitude² = 17²

225 + altitude² = 289

           altitude² = 289 - 225 = 64

altitude = √64 = 8 in

Answer:

The altitude of triangle is 8 in.

Step-by-step explanation:

Solution :

Here, we have given that the two sides of triangle are 17 in and 15 in.

Finding the third side of triangle by pythagoras theorem formula :

\({\longrightarrow{\pmb{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}}\)

Substituting all the given values in the formula to find the third side of triangle :

\(\begin{gathered}\qquad{\longrightarrow{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15)}^{2} + {(Altitude)}^{2} = {(17)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15 \times 15)} + {(Altitude)}^{2} = {(17 \times 17)}}}}\\\\\quad{\longrightarrow{\sf{{(225)} + {(Altitude)}^{2} = {(289)}}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = {(289)} - (225)}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 289 - 225}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 64}}}\\\\\quad{\longrightarrow{\sf{Altitude = \sqrt{64}}}}\\\\\quad{\longrightarrow{\sf{Altitude = 8 \: in}}}\\\\\quad{\star{\underline{\boxed{\sf{\red{Altitude = 8 \: in}}}}}}\end{gathered}\)

Hence, the altitude of triangle is 8 in.

\(\rule{300}{2.5}\)

Answer:

sorry

.......... ................

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level is that the true mean score improvement on the outcomes assessment test is equal to or less than 3%.

The null hypothesis is a statement that assumes there is no significant difference or relationship between two variables in a population, or that any observed difference or relationship is due to chance or sampling error. It is usually denoted by "H0" and is used in statistical hypothesis testing to determine whether there is evidence to support an alternative hypothesis.

In the given question,

The null hypothesis to test the faculty member's claim that the improvement is no more than 3% at the 5% significance level would be:

H0: The true mean score improvement on the outcomes assessment test is equal to or less than 3%.

This hypothesis assumes that there is no significant improvement in the mean score on the outcomes assessment test as a result of the review course. The alternative hypothesis would be:

Ha: The true mean score improvement on the outcomes assessment test is greater than 3%.

This hypothesis assumes that there is a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

To test these hypotheses, we would use a one-tailed t-test with a significance level of 0.05 and calculate the t-value and p-value based on the sample data. If the p-value is less than 0.05, we would reject the null hypothesis and conclude that there is evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course. If the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis and conclude that there is no evidence of a significant improvement in the mean score on the outcomes assessment test as a result of the review course.

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To find c, cdf and P(. 1 ≤ X <. 5), the calculation is given.

Suppose that X has the density function f (x) = cx² for 0 ≤ x ≤ 1 and f (x) = 0 otherwise.
a. Find c.
To find c, we need to use the fact that the integral of the density function over the entire range of x should equal 1. That is,
∫0¹ f(x) dx = 1
Substituting the given density function, we get
∫0¹cx² dx = 1
Integrating and simplifying, we get
c(1/3) = 1
Solving for c, we get
c = 3
So, the value of c is 3.
b. Find the cdf.
The cdf is the integral of the density function from the lower limit of x to a given value of x. That is,
F(x) = ∫₀ˣ f(t) dt
Substituting the given density function and simplifying, we get
F(x) = ∫₀ˣ 3t²dt
Integrating and simplifying, we get
F(x) = x³
So the cdf is F(x) = x³
c. What is P(.1 ≤ X < .5)?
To find this probability, we need to find the difference between the cdf at the upper limit and the cdf at the lower limit. That is,
P(.1 ≤ X < .5) = F(.5) - F(.1)
Substituting the cdf that we found earlier, we get
P(.1 ≤ X < .5) = (0.5)³ - (0.1)³
Simplifying, we get
P(.1 ≤ X < .5) = .125 - .001
P(.1 ≤ X < .5) = 0.124
So the probability that X is between .1 and .5 is .124.

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The correct option is (a) 3 cups of sugar .

To make 3 times the recipe, 3 cups of sugar are needed.

let's first determine the amount of sugar needed to make 1 pound of fudge. We know that it takes 1/2 cup of sugar to make 3/4 pounds of fudge.

If 3/4 pounds of fudge require 1/2 cup of sugar, then we can calculate the amount of sugar needed for 1 pound of fudge by scaling up the amount of sugar in proportion to the weight of fudge:

(1/2 cup) / (3/4 pounds) = (1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3 cup of sugar per pound of fudge.

Now, if we want to make 3 times the recipe, which is equivalent to 3 pounds of fudge, we can multiply the amount of sugar needed for 1 pound by 3:

(2/3 cup of sugar per pound) * 3 pounds = 2/3 * 3 = 6/3 = 2 cups of sugar.

To make 3 times the recipe, 3 cups of sugar are needed.

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do you think it could be x+y=800

To make the given statements true, $967.72 should be invested in the account today, with no additional deposits or withdrawals being made.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:

B = P(1 + r/n)^t

where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year

Based on the given information, P is the unknown and

B = $2174. 30

t = 18

r = 4. 6% = 0.046

n = 1

Plug in the values and solve for P or the amount that should be invested today.

B = P(1 + r/n)^t

$2174. 30 = P(1 + (0.046/1))^18

$2174. 30 = P(1.046)^18

P = $2174. 30 / (1.046)^18

P = $967.72

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Answer:

<A=79°

<B=112°

Step-by-step explanation:

this shape is Quadrilateral

so C+A=180°

D+B=180°

the easiest way to solve division is to first use calculator if you don't have it you can count the number by dividing them

Answer:

the missing values is 5

I hope it's helps you to

Answer:

+5

Step-by-step explanation:

-5=-10+5

-5=-5

-+-=-

+-+=+

Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

A child's ability to learn to read is the result of both natural cognitive development and environmental factors, with the interaction between nature and nurture being important for reinforcing the learning process.

Learning to read is a complex process that involves both nature (maturation) and nurture (environmental factors). Here are some reasons why:

Maturation: There is a natural process of cognitive development that occurs in children, which enables them to learn to read. For example, their brains develop the ability to recognize and differentiate between sounds, which is necessary for decoding words.

Nurture: The environment in which a child grows up can also have a significant impact on their ability to learn to read. For example, exposure to books, reading materials, and literacy-rich environments can enhance a child's vocabulary and comprehension skills.

Interaction: Finally, the interaction between nature and nurture is also important. For example, a child's natural curiosity and motivation to learn may be influenced by the support and encouragement of caregivers, teachers, and peers.

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u²= s²+t²

= 4.3²+4.9²

= 42.5

u= V42.5

= V170 /2

≈6.52

Answer:

6.519 cm

Step-by-step explanation:

Mmkay, so, you have to use the Pythagorean Theorem to find the actual length, which is a^2 + b^2 = c^2

a = 4.9 cm

b = 4.3 cm

4.9^2 is 24.01

4.3^2 is 18.49

Now add the two together:

24.01 + 18.49 = 42.5

Finally, we need to find the square root of 42.5

sqrt(42.5) = 6.519 cm

(rounding to nearest thousandth cuz it said so right by the answer box lol)

Hope this helped :D