The time taken by Nick to do his statistics homework follows a normal distribution with a mean of 25 minutes and a standard deviation of 5 minutes. Jasmin’s homework time also follows a normal distribution with a mean of 50 minutes and a standard deviation of 10 minutes. They hate each other’s guts and never work together so we can assume that Nick’s homework completion is independent of Jasmine’s homework completion.

a) Define the random variable D to be the difference between the amount of time spent on a randomly selected assignment of Jasmin’s and a randomly selected assignment of Nick’s. So D = N – J. Find the mean and the standard deviation of D.

b) Calculate the probability that Nick spent longer doing his assignment than Jasmin did. Show your method clearly.

Answer:

see below

Step-by-step explanation:

You will need the hypotenuse   12 ^2 + 9^2 = h^2   h = 15

In a right triangle:

S O H   C A H  T O A

sin s  =   S A H  = Opposite / Hypotenuse =   12/15

cos r = C A H  = Adjacent / Hypotenuse    = 12/ 15

Tan s = T O A =  12 / 9

cos (theta) = cos s  = 9 / 15

Tan r = 9/12

arc cos(theta) = theta = arccos(9/15) = 53.13 degrees

Answer:

answer is c

Step-by-step explanation:

hope you get it right

Answer:

x=28

Step-by-step explanation:

PEMDAS

parenthesis first...

5x-8+(6x-3x-24+6)=6x+30 *remember to distribute the negative sign*

5x-8+(3x-18)=6x+30

8x-26=6x+30

2x=56

x=28

A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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Answer:

i belive the awnser to this is m= –4

Answer:

Slope m = -4

Step-by-step explanation:

In order to solve this problem, we need to use \(\frac{y2-y1}{x2-x1}\). After plugging in we get \(\frac{2-6}{9-8}\). 2 - 6 = -4 and 9 - 8 = 1. Because we don't need to write the 1 when it is in the denominator, the answer is just -4.

Answer:

16cm and 48 degrees

Step-by-step explanation:

Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail

We are told in the question that

Linda walked 3/4 of the length of the Tremont Trail before stopping for a rest.

From the question, the length of the Tremont Trail = 3 1/2 miles

Hence, the distance (how far )Linda has walked =

3/4 of 3 1/2 miles

= 3/4 × 3 1/2 miles

= 3/4 × 7/2 miles

= 21/8 miles

= 2 5/8 miles or 2.625 miles

Therefore, Linda had walked 2 5/8 miles or 2.625 miles on the Tremont trail.

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The domain in a relation y(x) is the set of values for which the relation is defined (the values on x, where y is defined)

In this relation the values wich the relation is defined is: the coordinates of x where there are a point:

The range in a relation y(x) is the set of all the values that y(x) takes (the values of y)

In this relation the values that takes y(x) are the coordinates of y where there are a point:

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

i have no more money to buy a candle shop full of dogs with cats and people

Step-by-step explanation:

ur mae

Answer:

None

Step-by-step explanation:

The triangle with side lengths √35 , √14 , 7 is a right triangle.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

p² + b² = h² ( In a right-angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p² + b² = h² (In a right-angled triangle)

In Option D

(√35)² + (√14)² = 7²

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Hence, The triangle with side lengths √35, √14, 7 is a right triangle.

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The ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder is 4:3, or 4/3.

To find the ratio of the surface areas of the two similar cylinders, we need to consider the ratio of their corresponding dimensions. Since the two cylinders are similar, their radii are proportional to their heights. Let's denote the height of the smaller cylinder as h1, the height of the larger cylinder as h2, the radius of the smaller cylinder as r1, and the radius of the larger cylinder as r2.

Given:

h1 = 15 inches

h2 = 20 inches

The ratio of the heights is:

h2 / h1 = 20 / 15 = 4 / 3

Since the cylinders are similar, the ratio of their radii is the same as the ratio of their heights:

r2 / r1 = 4 / 3

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The solution of inequality is,

⇒ x < 2

Given that;

The inequality is;

⇒ 2x + 1 < 5

We have to solve the inequality.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

The inequality is given as;

⇒ 2x + 1 < 5

Solve as;

2x + 1 < 5

Subtract 1 from both side,

2x + 1 - 1 < 5 - 1

2x < 4

Divide 2 from both sides,

x < 2

Hence, The solution of inequality is,

⇒ x < 2

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Answer:

the correct answer is x<2

Step-by-step explanation:

y = 3x² + 1

Differentiate both sides with respect to t :

dy/dt = 6x dx/dt

We're given that dy/dt = +3 units/second, so when x = 2 we find

3 u/s = 6 • 2 dx/dt

dx/dt = 3/12 u/s = 1/4 u/s

which means x is increasing at a rate of 1/4 units per second.

Answer:

AB is not a tangent. The lengths 4, 12, and 13 do not form a right triangle.

√(4^2 + 12^2) = √160, which is not equal to 13.

Answer:

No

Step-by-step explanation:

if AB is a tangent the the angle BAC = 90°

using Pythagoras' theorem

then square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

BC² = 13² = 169

AB² + AC² = 12² + 4² = 144 + 16 = 160

since BC²≠ AB² + AC²

then Δ ABC is not a right triangle so AB is not a tangent

Answer:

Explanation:

Given the functions:

We want to find:

First of all, we need to find:

This is done by inserting the value of h(x) into f(x)

So, we have:

Substituting 7 for x in f[h(x)], we have f[h(7)]

Which is what we are looking for.

Answer: 150

Step-by-step explanation:

You got it right, just divide 300 by 2 :)

Answer:

150

Step-by-step explanation:

50% is half if everything... half of 300 is 150

Answer:

5.66 years

Step-by-step explanation:

450 x 1.025^(n) = 450 + 67.50

450 x 1.025^(n) = 517.50

1.025^(n) =(517.50 / 450)

1.025^(n) = 1.15

n = ln(1.15) / ln(1.025)

n = 5.66

Answer:meep

Step-by-step explanation:

meep

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

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Answer:

5009.206

Step-by-step explanation:

The answer is 5009.206. We see that the first portion of this question asks, "(5×1,000)+(9×1)". 5x1000 is 5000. 9x1 is 9. 5000+9= 5009. The second portion of this question asks for the numbers that go after the decimal. 2x1/10 is 2/10. 6x1/1000 is 6/1000. The decimal place stands for one. So we do .206. If the decimal stands for ones that means in this case the 2 is in the tenths place (like it should be since the question asks for 2/10) and the 6 is in the 1000 place (like it should be since the question asks for 6/1000). We add this up together and our answer is 5009.206. Hope this explanation helps! Happy learning!

3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

Answer:

-9z=11-2

-9z=9

z=9+9

z=18

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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The triangles include:

4) To determine if a triangle is right, obtuse, or acute, we need to use the Pythagorean Theorem to determine if the square of the longest side equals the sum of the squares of the other two sides.

Here, the longest side is 9, and the other two sides are 6 and 7.

9² = 6² + 7²

81 = 36 + 49

81 = 85

Since 81 is not equal to 85, the triangle is not a right triangle. To determine if it's obtuse or acute, we need to check the cosine of the largest angle using the Law of Cosines.

cos A = (b² + c² - a²) / 2bc

Let's choose 9 as side a, since it's the largest side:

cos A = (6² + 7² - 9²) / (84)

cos A = 0.048

Since cos A is positive, angle A is acute. Therefore, the triangle is acute.

5) Using the same process as above:

16² = 10² + 12²

256 = 100 + 144

256 = 244 + 12

Since 256 is greater than 244, the triangle is obtuse.

6) Again, using the same process as above:

(8√6)² = 8² + 16²

192 = 64 + 256

192 = 320

Since 192 is less than 320, the triangle is obtuse.

7) 29² = 20² + 21²

841 = 400 + 441

841 = 841

Since 841 is equal to 841, the triangle is a right triangle.

8) √73 is greater than 8 and 3, so it must be the largest side.

(√73)² = 8² + 3²

73 = 64 + 9

73 = 73

Since 73 is equal to 73, the triangle is a right triangle.

9) 12² = 8² + 10²

144 = 64 + 100

144 = 164 - 20

Since 144 is less than 164, the triangle is obtuse.

10) 15² = 9² + (3√34)²

225 = 81 + 306

225 = 387 - 162

Since 225 is less than 387, the triangle is obtuse.

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Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer: The surface area of the rectangular prism is approximately 4 square yards.

Step-by-step explanation: Given that the volume of the rectangular prism is 160 cubic yards, we can find the dimensions of the prism using the formula:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

So, we have:

160 = lwh

Now, we need to find two other measurements in order to calculate the surface area of the rectangular prism. However, we do not have enough information to find all three dimensions. Therefore, we will assume one dimension and find the other two.

Let's assume that the height of the rectangular prism is 10 yards. Then, we can rearrange the formula for the volume to solve for the product of the length and width:

lw = V/h = 160/10 = 16

Now, we have two equations:

lw = 16

wh = 160/10 = 16

Solving for w in the first equation, we get:

w = 16/l

Substituting this expression for w in the second equation, we get:

l(16/l)h = 16

Simplifying, we get:

h = 1

Therefore, the dimensions of the rectangular prism are:

length = l

width = 16/l

height = 10

Now, we can calculate the surface area of the rectangular prism using the formula:

SA = 2lw + 2lh + 2wh

Substituting the values we found, we get:

SA = 2(l(16/l)) + 2(l(10)) + 2((16/l)(10))

SA = 32/l + 20l + 160/l

To find the minimum value of this expression, we can take its derivative with respect to l and set it equal to zero:

dSA/dl = -32/l^2 + 20 + (-160/l^2)

0 = -32/l^2 + 20 - 160/l^2

52/l^2 = 20

l^2 = 52/20

l ≈ 1.44

Substituting this value of l back into the expression for SA, we get:

SA ≈ 4 square yards

Therefore, the surface area of the rectangular prism is approximately 4 square yards.

Answer:

Part A: 146°

Part B: 70°

Part C: 104°

Step-by-step explanation:

Part A:

m<SHI = 34° (given)

m<SHI + m<MIH = 180° (same side interior angles of a transversal are supplementary)

34° + m<MIH = 180° (Substitution)

Subtract 34° from each side

m<MIH = 180° - 34°

m<MIH = 146°

Part B:

m<HAL = 110° (given)

m<HAV + m<HAL = 180° (linear pair)

m<HAV + 110° = 180° (substitution)

Subtract 110° from each side

m<HAV = 180° - 110°

m<HAV = 70°

m<AVM = m<HAV (alternate interior angles are congruent)

m<AVM = 70°

Part C:

The obtuse angle formed = m<HAV + SHI (exterior angle of a triangle = the sum of two opposite interior angles of a ∆)

The obtuse angle formed = 70° + 34° = 104°