The volume of a cone is equal to the volume of a sphere.
The radius of the cone is four times the radius of the sphere.

Write down an expression for h
in terms of r.
You must simplify your answer.
h=

Applying the angle relationships, the measures are: 1. m<A = 18°; m<B = 40°; 2. m<A = 9°; m<B = 43°; 3. m<C = 123°; m<D = 158°; 4. m<C = 131°; m<D = 160°

The position of the angle relationships in the image shown will determine the measures of the angles involved.

Therefore, we have the following for Figure  A:

1. m<D = 162°; m<C = 122°

m<A = 180 - 162 = 18° [the angle relationship is linear pair]

m<B = 180 - 122 - 18 = 40° [triangle sum theorem]

2. m<D = 171°; m<C = 128°

m<A = 180 - 171 = 9° [the angle relationship is linear pair]

m<B = 180 - 128 - 9 = 43° [triangle sum theorem]

3. m<A = 22°; m<B = 35°

m<C = 180 - 22 - 35 = 123° [triangle sum theorem]

m<D = 180 - 22 = 158° [the angle relationship is linear pair]

4. m<A = 20°; m<B = 29°

m<C = 180 - 20 - 29 = 131° [triangle sum theorem]

m<D = 180 - 20 = 160° [the angle relationship is linear pair]

Therefore, we have the following for Figure  B:

9. m<A = 65° [given]

m<B = 180 - 65 = 115° [linear pair]

m<C = 65° [corresponding angles]

m<D = m<B [corresponding angles]

m<D = 115°

m<E = m<C = 65° [vertical angles]

m<F = 180 - 65 - 90 = 25

10. m<A = 70° [given]

m<B = 180 - 70 = 110° [linear pair]

m<C = 70° [corresponding angles]

m<D = m<B [corresponding angles]

m<D = 110°

m<E = m<C = 70° [vertical angles]

m<F = 180 - 70 - 90 = 20

11. m<F = 22° [given]

m<E = 180 - 90 - 22 = 68°

m<E = m<C = 68° [vertical angles]

m<A = m<C = 68° [corresponding angles]

m<B = 180 - 68 = 112° [linear pair]

m<D = m<B = 112° [corresponding angles]

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Therefore, the recursive formula for the population growth model is:

[tex]P_n = 0*P_n-1[/tex] And the explicit formula for [tex]P_n[/tex] is:

[tex]P_n = 80*(1+0) n\\P_n=80[/tex]

The exponential growth model is a mathematical function that describes the growth of a population or system over time, assuming that the rate of growth is proportional to the size of the population or system. In other words, the model assumes that the growth rate of the population or system increases as the population or system grows larger.

by the question.

To find the recursive formula for the population growth model, we need to use the equation:

[tex]P_n = r*Pn-1[/tex]

where [tex]P_n[/tex] represents the population size at time n, Pn-1 represents the population size at the previous time step (n-1), and r represents the growth rate.

Given that the population grows exponentially with Po = 80, we can use the formula:

[tex]P_n = Po *(1 + r)n[/tex]

where Po is the initial population size and n is the number of time steps.

Using the fact that [tex]P_1 = 80[/tex], we can solve for the growth rate r:

[tex]Pq = Po * (1 + r)1\\80 = 80* (1 + r)1\\1 + r = (80/80)^(1/1)\\1 + r = 1^(1/1)\\1 + r = 1\\r = 0[/tex]

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Based on the dot plots, it can be concluded the students in the second period had higher scores with a typical score of 3 on the essay.

The dot plots show the scores Ms. Munoz students got on their essays for two different periods. In these plots, we can observe that in the first period the scores were between 1 and 4, while in the second period, the scores were between 2 and 5.

This shows the scores were higher in the second period, moreover, the typical or the most common score was 3.

Note: This question is incomplete; below I attach the missing information.

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The Answer: 758.83 in³

Step-by-step explanation:

Volume of Solids

The volume of the solid is 758.83 in³

Step-by-step explanation:

Given that the cone and half sphere is hollow

The volume of the cone =

The Volume of the sphere  =

So the Volume of the half sphere =

The volume of solid = volume of cone + volume of the half sphere

Given

height h = 19 in

radius r = 5 in

 =

    = 1/3 × 3.14 × 5 × 5 × 19

    = 497.16 in³

  = 2/3 × 3.14 × 5 × 5 × 5

  = 261.67 in³

V =  497.16 in³ + 261.67 in³

 = 758.83 in³

Hence the volume of the solid is 758.83 in³

Volume of Solids

The volume of the solid is 2813 in³

Step-by-step explanation:

Given that the cone and half sphere is hollow

The volume of the cone  [tex]=1/3\pi r^2h[/tex]

The Volume of the sphere [tex]=4/3\pi r^3[/tex]

So the Volume of the half sphere [tex]=2/3\pi r^3[/tex]

The volume of solid = volume of cone + volume of the half sphere

[tex]V=V_1+V_2[/tex]

Given

height h = 26 in

radius r = 8 in

[tex]V_1=1/3\pi r^2h[/tex]

    [tex]= 1/3 \times 3.14 \times 8 \times 8\times 26[/tex]

    [tex]=1741.65 \ in^3[/tex]

[tex]V_2=2/3\pi r^3[/tex]

 [tex]= 2/3 \times 3.14 \times 8 \times 8\times 8[/tex]

  [tex]= 1071.78 \ in^3[/tex]

[tex]V = 1741.65 \ in^3 + 1071.78 \ in^3[/tex]

[tex]2813 \ in^3[/tex]

Hence the volume of the solid is 2813 in³

Answer:

C

Step-by-step explanation:

Since C is the largest half, then C is part of the largest whole.

Answer: C

Answer:

4 5/8

Step-by-step explanation:

7 7/8= 63/8

3 1/4= 13/4= 26/8

63/8 - 26/8= 37/8

37/8= 4 5/8

Answer:

per hour he earns 416/8= 52$

in 2.8 hours he will earn = 52×2.8= 145.6$

Step-by-step explanation:

i hope you find it helpful, have a nice day

The first thing we must know is how much David earns per hour.

$416 ÷ 8 hrs = $52/hr

$52/hr  x 2.8hrs = $145.6

David earns $145.6 in 2.8 hours.

If a triangle has one side length of 9cm and another side of .12cm . The 3 possible answers for the third side​ are:  17, 20, and 21.

To determine the possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Using this theorem, the possible lengths for the third side can be found by checking which of the following inequalities hold:

   9 + 12 > x

   9 + x > 12

   12 + x > 9

Simplifying these inequalities, we get:

   x > -3 (always true)

   x > -9 (always true)

   x > -3 (always true)

Therefore, the possible lengths for the third side of the triangle must satisfy x > -9, which eliminates the answer 3 (which is less than 9 - 12 = -3).

The possible lengths for the third side are:

   9 + 12 > x, so x < 21

   9 + x > 12, so x > -3

   12 + x > 9, so x > -3

Therefore, the possible lengths for the third side of the triangle are:

   17 (9 + 12 = 21, which is greater than 17)

   20 (9 + 12 = 21, which is greater than 20)

   21 (9 + 12 = 21, which is equal to 21)

So, the three possible lengths for the third side of the triangle are 17, 20, and 21.

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The complete question is:

A triangle has one side length of 9

centimeters (cm) and another side length of 12

cm.

Which answers are possible lengths for the third side?

Select three that apply

17

22

9

21

20

3

Assuming the rate is constant, 125,000,000 years agο the cοasts were tοuching.

It is a term that basically defines the change in sοme quantity with respect tο anοther quantity. In mathematics it alsο defines ratiο where the numeratοr is οne physical quantity and denοminatοr is anοther quantity.

Given that, the twο cοast are separated by 5,000km.

Alsο given that Africa and Sοuth America are mοving away frοm each οther at a rate οf 4 centimetres per year.

The rate is cοnstant.

Nοw 5000km= 500,000,000 cm

distance = rate × time

distance/rate = time

sο, 500,000,000/4 = 125,000,000

Hence, the cοasts were tοuching  125,000,000 years agο.

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Answer:

Step-by-step explanation:

Using Pythagoras theorem, the value of c is √193.

What is Pythagoras' theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given:  the right triangle and given sides.

We have to find the value of c.

We apply here Pythagoras theorem and we get

a² + b² = c²

a = 7

b = 12

c = ?

(7)² + (12)² = c²

49 + 144 = c²

193 = c²

c = √193

Hence, the value of c is √193.

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Applying equations, the number of each type of pancake are originally: 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.

Let's use the following variables to represent the number of each type of pancake:

From the problem statement, we know that:

x + y + z = 150 (total number of pancakes)

1/3 x blueberry pancakes are left

4/5 y plain pancakes are left

1/2 z chocolate chip pancakes are left

There are now an equal number of each type of pancake

From the last statement, we can set up the following equations:

1/3 x = y = 1/2 z

Multiplying all sides of each equation by the least common multiple of the denominators, we get:

2x = 6y = 3z

Dividing all sides of each equation by 2, we get:

x = 3y = 3/2 z

Now we can use the equation x + y + z = 150 to substitute for x in terms of y and z:

3y + y + 2/3(3/2z) = 150

Simplifying and solving for z, we get:

5z = 270

z = 54

Substituting z = 54 into x = 3/2 z, we get:

x = 81

Substituting z = 54 into y = x/3, we get:

y = 27

Therefore, there were originally 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.

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Therefore, the angle of depression from Lisa's line of sight to the cat is approximately 12.21 degrees.

An angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, called the vertex. The rays are also called the sides or legs of the angle. Angles are usually measured in degrees, with a full circle measuring 360 degrees. Angles are used to describe the direction of an object, the orientation of a shape, or the position of a line. They are also used in trigonometry to calculate distances and heights in triangles, and in many other areas of mathematics and science.

Here,

In the diagram above, we have Lisa standing at point L and looking out the window of the building at her lost cat at point C, which is 58.5 meters away from the building. The height of the window from the ground is 12.6 meters. Let's call the angle of depression from Lisa's line of sight to the cat as ∠WLC. To find this angle, we need to use the tangent function, which relates the opposite side (12.6 meters) and adjacent side (58.5 meters) of ∠WLC.

tan ∠WLC = opposite / adjacent

tan ∠WLC = 12.6 / 58.5

Using a calculator, we get:

∠WLC = tan⁻¹(12.6 / 58.5)

∠WLC ≈ 12.21 degrees

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hi i also need help me toppers

Answer:

Step-by-step explanation:

To find the total number of text messages sent per month by the 23 million people aged 13-17 in the United States, we can multiply the average number of text messages per person (800) by the number of people (23,000,000):

Total number of text messages = 800 text messages/person/month x 23,000,000 people

Total number of text messages = 18,400,000,000 text messages/month

To express this number in scientific notation, we can move the decimal point 10 places to the left, since there are 10 digits to the right of the decimal point:

Total number of text messages = 1.84 x 10^10 text messages/month

Therefore, the total number of text messages sent per month by the 23 million people aged 13-17 in the United States is approximately 1.84 x 10^10 text messages.

Answer: 10

Step-by-step explanation:

500 divided 50

The total cost for one admission and r rides is $10 for admission and $2 multiplied by r for the rides, which can be expressed as the formula: Cost = $10 + $2r.

The problem statement provides two pieces of information: the admission cost and the ride cost. We are asked to find the total cost for one admission and r rides.

The admission cost is straightforward - it is a fixed cost of $10. This means that regardless of how many rides you go on, you will always pay $10 just to get into the fair.

The ride cost is based on the number of rides you go on. Each ride costs $2, so if you go on r rides, you will pay $2 multiplied by r, or 2r, for the ride portion of the cost.

To find the total cost for one admission and r rides, we simply add the admission cost of $10 to the ride cost of 2r, which gives us the formula:

Cost = $10 + $2r

This formula tells us that the cost of one admission and r rides is equal to $10 plus $2 multiplied by the number of rides (r) that the person goes on.

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Answer:

The probability of Meikel wearing khakis and sandals is

Step-by-step explanation:

3 ÷ 12 which should give us

1/4

Answer:

Step-by-step explanation:

We know the the total of angles for a triangle is 180 degrees.

So in this case we'd want to set up adding all of our angles and setting them equal to 180

17 + 126 + b = 180

then solve for b

143 + b = 180

b = 37 degrees

So the answer would be 37 degrees for angle b

The probability of drawing two yellow marbles without replacement is approximately 0.412 or 41.2%.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability is used to make predictions, analyze risks, and make decisions in various fields such as science, economics, and finance.

The probability of drawing a yellow marble on the first draw is 9/14, since there are 9 yellow marbles out of a total of 14 marbles in the bag. Since the first marble is not replaced before the second draw, there will be 8 yellow marbles left in the bag out of a total of 13 marbles.

So, the probability of drawing a yellow marble on the second draw, given that the first marble was yellow, is 8/13.

To find the probability of both marbles being yellow, we need to multiply the probability of drawing a yellow marble on the first draw by the probability of drawing a yellow marble on the second draw, given that the first marble was yellow:

P(both yellow) = P(first yellow) x P(second yellow | first yellow)

= 9/14 x 8/13

= 0.412

Therefore, the probability of drawing two yellow marbles without replacement is approximately 0.412 or 41.2%.

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Answer:

Step-by-step explanation:

5

The dimensions of the bookmark  length = (-18 + 2sqrt(117))/9 cm

A quadratic equation is an equation of the form:

ax² + bx + c = 0

where x is the variable, and a, b, and c are constants, with a ≠ 0.

The term "quadratic" comes from the fact that the highest power of x in the equation is 2 (i.e., x is raised to the second power).

Quadratic equations can be solved using a variety of methods, including factoring, completing the square, and using the quadratic formula.

Let's assume the length of the bookmark to be 'l' and the width to be 'w'.

We know that the perimeter of a rectangle is given by:

Perimeter = 2(length + width)

Substituting the values, we get:

18 = 2(l + w) --- (1)

We also know that the area of a rectangle is given by:

Area = length x width

Substituting the values, we get:

18 = l x w --- (2)

We can use equation (2) to solve for one variable in terms of the other:

l = 18/w

Substituting this in equation (1), we get:

18 = 2(18/w + w)

Simplifying, we get:

9 = 9/w + w

Multiplying both sides by 'w', we get:

w² + 9w - 18 = 0

Using the quadratic formula, we get:

w = (-9 + √(117))/2 or w = (-9 - √(117))/2

Since the width of the bookmark can't be negative, we discard the second solution.

Therefore, the width of the bookmark is:

w = (-9 + √(117))/2

We can use equation (2) to find the length of the bookmark:

l = 18/w

Substituting the value of w, we get:

l = 18/(-9 + √(117))

Simplifying, we get:

l = (-18 + 2√(117))/9

Therefore, the dimensions of the bookmark are:

length = (-18 + 2√(117))/9 cm

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1.  The probability that the mean salary of the sample is less than $60,000 is 0.0150.

2. Interpretation: There is a 1.50% probability that a random sample of 37 environmental compliance specialists will have a mean salary of less than $60,000,

To solve for the probability, we use the equation

(Sample mean - population mean)

    standard deviation / sqrt (n)

Therefore it becomes;

z = 60,000 - 62, 0000

5600/ sqrt (37)

z = -2000

      919.26

Using a standard normal distribution table or a calculator, we can find the probability that a z-score is less than -2.17.

The probability is approximately 0.0150 (rounded to four decimal places).

Therefore, the probability that the mean salary of the sample is less than $60,000 is 0.0150.

The above answer is based on the question below;

Find the probability and interpret the result. If convenient, use technology to find the probability.

The population mean annual salary for environmental compliance specialist is about $62, 000. A random sample of 37 specialists is drawn from the population. what is the probability that the mean salary of the sample is less than $60, 000? Assume б = $5,600

The probabiility that the mean salary is less than $60,000 is ................ Round to 4 decimal places is necessary.

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FIFO Method:

1. Determine the cost of the oldest inventory items available for sale (i.e., the items purchased first.

2.Multiply the cost per item by the number of items sold to determine the COGS.

3.Subtract the COGS from the total cost of the oldest inventory items to determine the value of the last inventory.

LIFO Method: The only difference between FIFO and LIFO method is that in LIFO method, newest inventory cost and value are determined in the first and last step respectively.

The average cost method is a way of determining the cost of inventory by taking the average of the cost of each item in the inventory. FIFO and LIFO are two other methods of determining the cost of inventory.

Average Cost Method:

Determine the total cost of all inventory items available for sale.

Determine the total number of inventory items available for sale.

Divide the total cost of inventory by the total number of items to get the average cost per item.

Multiply the average cost per item by the number of items sold to determine the cost of goods sold (COGS).

Subtract the COGS from the total cost of inventory to determine the value of the ending inventory.

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Answer:

[tex]2x-7 \geq -29[/tex]

Step-by-step explanation:

the difference means subtract, at least means  [tex]\geq[/tex], and a number can be represented by x. So twice a number is 2x, a difference of that is - 7, and at least 29 is [tex]\geq 29[/tex]

The required residual for Dianna's iguana is $0.05.

To find the residual for Dianna's iguana, we need to first calculate the predicted value of weekly food cost for the iguana using the given regression equation:

[tex]$\hat{y} = 0.4 + 0.15x$[/tex]

where x is the weight of the iguana in pounds.

Substituting x = 11 into the equation, we get:

[tex]$\hat{y} = 0.4 + 0.15(11) = 2.05$[/tex]

So the predicted weekly feed cost for Dianna's iguana is $2.05.

To find the residual, we subtract the predicted value from the actual value:

[tex]$residual = actual\ value - predicted\ value = 2.10 - 2.05 = 0.05$[/tex]

Therefore, the residual for Dianna's iguana is $0.05.

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Answer:

125cm²

Step-by-step explanation: