Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Kathy and her brother Clay recently ran in a local marathon. The distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes. The distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes. The finishing time for Clay was 289 minutes. Calculate and interpret the standardized score for Clayâs marathon time. Show your work.

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Answer:

5.18 miles each day

Step-by-step explanation:

3 weeks × 6 days = 18 days

93.24 miles in 18 days gives an average of 93.24 ÷ 18 = 5.18 miles per day

f

(

x

)

=

x6

+2x(tothepowerof5)

−

2

x

(tothepowerof3

)−

2x

Answer: + 8 degrees

Step-by-step explanation: average (-8+24)/2= 16/2 degrees

Mr.West ate 23 ounces of grapes in 11 days by eating 2 1/11 ounces of grapes each day.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Mr.West ate grapes for 11 days. He ate 2 1/11 ounces of grapes each day.

Therefore, The total number of grapes Mr.West ate is,

= 11×(2 1/11) grapes.

= 11×(23/11) grapes.

= 23 grapes.
So, He ate 23 ounces of grapes in 11 days.

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The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Answer:

the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Step-by-step explanation:

Let the original price of each costume be $x. The sale price of each costume will be $(x-3.50). Ms. Monroe ordered 24 costumes, so the cost of 24 costumes at the sale price will be:

24 × (x-3.50) = $24x - $84

Ms. Monroe paid $516 in all, so we can write:

24x - 84 = 516

Adding 84 to both sides, we get:

24x = 600

Dividing both sides by 24, we get:

x = 25

Therefore, the original price of each costume was $25, and the sale price was $(25-3.50) = $21.50.

Answer: so Ms.Monroe got $84 off her entire purchase

Step-by-step explanation: I hope it helps

Answer:

t=In(37/20)/0.046

Step-by-step explanation:

p=2000

r=0.046

A=3700

t=?

3700=2000e^0.046t

switch sides

2000e^0.046t=3700

Divide both sides by 2000

$2000e^0.046t/2000=$3700/2000

Simplify

e^0.046=37/20

Apply exponent rules

0.046=37/20

Solve 0.046t = ln(37/20)

t=In(37/20)/0.046

Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

The cost to cover one-third of the land is 36 dollars.

It cost $108 to cover 1 meter square with matted grass.  The cost to cover one-third of the land can be calculated as follows:

1 / 3 of the land = 1 / 3 of 1 metres squared = 1 / 3 metres square

Using proportion,

1 metre square = 108 dollars

1 / 3 meters square = ?

cross multiply

The cost to cover one-third of the land = 108 ÷ 1 / 3

The cost to cover one-third of the land = 108 / 3

The cost to cover one-third of the land = 36 dollars

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The amount it will cost to cover 1 / 3 of the land area is 36 dollars.

It cost 108 dollars  to cover an area of 1 metre square with matted grass.  The amount of money it will take to cover 1 / 3 of the land area can be calculated as follows:

let's find 1 / 3 of the land area.

1 / 3 of the land area = 1 / 3 × 1 = 1 / 3 metres square

Therefore,

1 metres square = 108 dollars

1 / 3 metres square = ?

cross multiply

Hence,

amount to cover 1 / 3 of land = 1 / 3 × 108

amount to cover 1 / 3 of land = 108 / 3

amount to cover 1 / 3 of land = 36 metres square.

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Step-by-step explanation:

The width of each interval is Δx = (4−1)/6 = 1/2.

a) Evaluate the function at the beginning and end of each interval.

f(x) = 7√(ln x)

f(1) = 7√(ln 1) = 0

f(1.5) = 7√(ln 1.5) ≈ 4.4573300

f(2) = 7√(ln 2) ≈ 5.8278823

f(2.5) = 7√(ln 2.5) ≈ 6.7006153

f(3) = 7√(ln 3) ≈ 7.3370295

f(3.5) = 7√(ln 3.5) ≈ 7.8348826

f(4) = 7√(ln 4) ≈ 8.2418702

Calculate the area of each trapezoid.

T₁ = ½ (0 + 4.4573300) (1/2) = 1.1143325

T₂ = ½ (4.4573300 + 5.8278823) (1/2) = 2.5713031

T₃ = ½ (5.8278823 + 6.7006153) (1/2) = 3.1321244

T₄ = ½ (6.7006153 + 7.3370295) (1/2) = 3.5094112

T₅ = ½ (7.3370295 + 7.8348826) (1/2) = 3.7929780

T₆ = ½ (7.8348826 + 8.2418702) (1/2) = 4.0191882

The total area is therefore:

T = 1.1143325 + 2.5713031 + 3.1321244 + 3.5094112 + 3.7929780 + 4.0191882

T = 18.139337

b) Evaluate the function at the midpoint of each interval.

f(1.25) = 7√(ln 1.25) ≈ 3.3066651

f(1.75) = 7√(ln 1.75) ≈ 5.2365230

f(2.25) = 7√(ln 2.25) ≈ 6.3036165

f(2.75) = 7√(ln 2.75) ≈ 7.0404861

f(3.25) = 7√(ln 3.25) ≈ 7.5996115

f(3.75) = 7√(ln 3.75) ≈ 8.0477348

Calculate the area of each rectangle.

M₁ = (3.3066651) (1/2) = 1.6533325

M₂ = (5.2365230) (1/2) = 2.6182615

M₃ = (6.3036165) (1/2) = 3.1518082

M₄ = (7.0404861) (1/2) = 3.5202431

M₅ = (7.5996115) (1/2) = 3.7998057

M₆ = (8.0477348) (1/2) = 4.0238674

The total area is therefore:

M = 1.6533325 + 2.6182615 + 3.1518082 + 3.5202431 + 3.7998057 + 4.0238674

M = 18.767318

c) Simpson's rule can be calculated as:

S₆ = Δx/3 [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + 4f(x₅) + f(x₆)]

S₆ = (1/2)/3 [0 + 4(4.4573300) + 2(5.8278823) + 4(6.7006153) + 2(7.3370295) + 4(7.8348826) + 8.2418702]

S₆ = 18.423834

Answer:

About 7

Step-by-step explanation:

245/35 = 7

So, 246/35 = 7.02, which is about 7.

Hope this helps!

Plz name brainliest if possible!

Step-by-step explanation:

Using the various theorems relating inscribed and external angles to intercepted arcs, we can write the following relations:

  angle A = 1/2(arc BP) . . . . . . . . . . . inscribed angle

  angle A = 1/2(arc CD -arc CP) . . . external angle at tangent/secant

  angle CPD = 1/2(arc CD) . . . . . . . inscribed angle

  angle CPB = 1/2(arc CP) + 1/2(arc BP) . . . . . sum of angles at the mutual tangent

Equating the expressions for angle A, we have ...

  1/2(arc BP) = 1/2(arc CD -arc CP)

Adding arc CP gives ...

  1/2(arc BP +arc CP) = 1/2(arc CD)

Substituting the last two equations for angles from above, this gives ...

  angle CPB = angle CPD

Hence PC bisects angle BPD.

Answer: D

Step-by-step explanation:

1 in.=1488 milesx5=7440 miles.

Area= pi x r^2

=pi x (7440)^2 or option D.

Hope this helps :)

Answer:

8 hours/day is the answer.

Answer:

10.526% or 0.10526

Step-by-step explanation:

The probability of choosing a blue marble would be 5/20, or 0.25 and then the probability of choosing a green marble next would be 8/19, or about 0.421.  Multiply these probabilities together to get your answer.  

Hope this helps:)

Answer:

a = 2 , b = 1

Step-by-step explanation:

\(\frac{8-i}{3-2i}*\frac{3+2i}{3+2i}\)

=> \(\frac{(8-i)(3+2i)}{9+4}\)

=> \(\frac{24+13i-2i^2}{13}\)

=> \(\frac{26+13i}{13}\)

Comparing it with a+bi

a = 26/13 , b = 13/13

a = 2, b = 1

Answer:

a = 2

b = 1

Step-by-step explanation:

\(\frac{8-i}{3-2i}\)

Write the fraction in this form:

\(\frac{a+bi}{c+di}\:=\:\frac{\left(c-di\right)\left(a+bi\right)}{\left(c-di\right)\left(c+di\right)}=\:\frac{\left(ac+bd\right)+\left(bc-ad\right)i}{c^2+d^2}\)

\(\frac{\left(8(3)+-1(-2)\right)+\left(-1(3)-8(-2)\right)i}{3^2+-2^2}\)

Evaluate.

\(\frac{26+13i}{13}\)

Factor the numerator.

\(\frac{13\left(2+i\right)}{13}\)

\(2+1i\)

Answer: 0.5

Step-by-step explanation: it should be but  wait for other answers

The conditional relative frequency that a participant has brown hair, given that he/she has brown eyes is 0.71

We would solve this using Baye's Theorem:

Let R represent brown hair

Let B represent brown eyes

\(P = \frac{R}{B} = P\frac{(RnB)}{P(B)}\)

P(RnB)= 10

P(B)= 2 + 2 + 10 = 14

Therefore

\(P(\frac{R}{B} ) = \frac{10}{14}\)

= 0.71

Therefore, the correct answer is option D.

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The percentage of our new facility's seating is full will be 76%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

Our new training room can seat 150 employees.

If 6 tables consisting of 6 chairs are now taken.

Then the number of occupied seats by tables will be

⇒ 6 x 6

⇒ 36

Then the percentage of our new facility's seating is full will be

P = [(150 - 36) / 150]  x 100

P = (114/150) x 100

P = 0.76 x 100

P = 76%

The percentage of our new facility's seating is full will be 76%.

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Answer:

143°

Step-by-step explanation:

supplementary angles are angles that combine to form a straight line (and we know that a straight line = 180 degrees)

you can think of an angle as needing another angle to "supplement" it into being a full line.

So, we know that one angle = 37°

And that: one angle + supplementary angle = 180 degrees

                 37° + x  = 180°

                - 37           -37

                     x    = 143

So, the measure of this angle's supplement is 143°

hope this helps!!

Answer:

143 degrees

Step-by-step explanation:

180 - 37 = 143

The rate of the proportional relationship is k = 200 rows per minute.

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is the constant of proportionality or rate of change.

Using a pair of values of (x, y) and replacing them in the equation above, we can find the value of k.

The first point is (1, 200), replacing these values:

200 = k*1

200/1 = k

So Cole rows 200 meters per minute.

If we use the second point (2, 200) we will get the same rate:

400 = k*2

400/2 = k

200 = k

And so on if we use any point.

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at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly.

h(t)  h'(t)

0   0

2.5   -200

4   -400

5   -600

h'(4.5) = -400 ft/s

h'(5) = -600 ft/s

h'(5.5) = -800 ft/s

The bungee jumper is rising most rapidly at t = 5.

h"(5) = -200 ft/s^2

The bungee jumper's height at time t (in seconds) is given in the table. Using the given data, we can estimate h'(4.5), h'(5), and h'(5.5) to be -400 ft/s, -600 ft/s, and -800 ft/s respectively. It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly. We can also estimate h"(5) to be -200 ft/s^2, which is the rate of change of the velocity of the bungee jumper. This means that at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.

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Option c. $400 is the correct answer. The marginal revenue product of the fourth worker is $400.

The efficient organizations compare to its competitor generates higher marginal revenue product at each level of labour input. They invest heavily in training, skilling, and re-skilling their labour force with a transparent organizational culture.

The incremental total revenue earned for additional labour recruited is termed as marginal revenue product. The marginal revenue product of the fourth worker is calculated as under

The total revenues generated by employing three labourers is $1,120

The total revenues generated by employing four labourers is $1,520

Marginal revenue product of the fourth worker = Total revenues generated by employing four labourers - Total revenues generated by employing three labours

=$1,520 - $1,120

=$400

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Answer:

x=25/3

Step-by-step explanation:

I'm not sure if it is correct but. . .

Answer: x=25/3

Step-by-step explanation:

Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

Area  = 10

Step-by-step explanation:

(\(\sqrt{50}\)×\(\sqrt{8}\))  ÷ 2 = 10

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Answer:

It's asking what 3^k+2 is in terms of m. That is where the 2 comes from.

Please let me know if this helped <3

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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