(BRAINLIEST) A baker sells cupcakes and bases her prices on the number of cupcakes purchased.

The graph shows a piecewise function with one piece increasing from the point 0 comma 0 through the point 12 comma 18 to the endpoint 24 comma 36 and another piece going from the point 24 comma 36 through the point 48 comma 60 and increasing to the right.

Based on the graph, what is the pricing the baker uses for her sales?

The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 24 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.
The first 36 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.
The first 36 cupcakes cost $1 each, and all cupcakes after that cost $1.50 each.

Answers

Answer 1

Answer: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.

Step-by-step explanation:

The graph shows two pieces of the function, with one increasing from the point (0, 0) through the point (12, 18) to the endpoint (24, 36) and the other increasing from the point (24, 36) through the point (48, 60) to the right.

This means that the first 24 cupcakes cost $1.50 each and all cupcakes after that cost $1 each, as shown by the first piece of the function. The second piece of the function shows that the price per cupcake does not increase after 36 cupcakes, so option 3 and option 4 can be eliminated.

Therefore, the correct answer is: The first 24 cupcakes cost $1.50 each, and all cupcakes after that cost $1 each.


Related Questions

A pool charges $4 each visit or you can buy a membership for $100. Write and solve an inequality to find how many times a person should use the pool so that a membership is less expensive than paying each time. Write an inequality and solve. PLEASE HELP ME!!

Answers

Answer:

Let's say the number of visits to the pool is represented by the variable 'x'.

If a person chooses to pay per visit, the cost will be 4x dollars.

If a person chooses to buy a membership, the cost will be a one-time payment of $100.

We want to find out when the cost of buying a membership becomes less expensive than paying per visit. In other words, we want to solve the inequality:

4x > 100

To solve for x, we need to isolate the variable. We can do this by dividing both sides by 4:

x > 25

So, if a person plans to visit the pool more than 25 times, it's more cost-effective to buy a membership instead of paying per visit.

Find the are 22ft 37ft 38. 09ft 109degrees 138degrees

Answers

Answer:

B.

Step-by-step explanation:

I just took the test

Hi! im new to this i i coudnt go to school today becuase im sick and im trying to do mah and i cant figure this out anyone can help,

surface area of the prism.
5yd 4yd 2yd

Answers

The surface area is

[tex]2(5\times4)+2(5\times2)+2(4\times2)=[/tex]

[tex]40+20+16=[/tex]

76 square yards

Answer:

The surface area of the prism.

5 yd, 4 yd, 2 yd

76 square yards

Step-by-step explanation:

You're welcome.

Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO

Answers

I don't know but i can help a little

Step-by-step explanation:

But If the slops are the same and the y-intercepts are different, the lines are parallel...


What is √45 rounded to the nearest whole number

Answers

exact form: 3√5

decimal form: 6.70820393…

nearest whole number: 7

Answer:

3√5

Step-by-step explanation:

|x-3|\ge11 ∣x−3∣≥11 please anwser quickly

Answers

The given inequality is [tex]|x-3|/11 \geq 1[/tex]and the solution to the inequality is [tex]x \leq -8[/tex] or [tex]x \geq 14.[/tex]

We want to solve for [tex]x[/tex], which means we want to find all possible values of [tex]x[/tex] that satisfy the inequality.

To start, we multiply both sides of the inequality by 11, which gives us:

[tex]| x - 3 | \geq 11[/tex]

Now we have an inequality without any fractions. The absolute value sign means that we need to consider two cases: one where [tex]x-3[/tex] is positive, and one where [tex]x-3[/tex] is negative.

Case 1: [tex]x-3[/tex] is positive

If [tex]x-3[/tex] is positive, then [tex]| x - 3 |[/tex] is equal to [tex]x-3[/tex]. So we can rewrite the inequality as:

[tex]x - 3 \geq 11[/tex]

Adding 3 to both sides, we get:

[tex]x \geq 14[/tex]

This means that if [tex]x[/tex] is greater than or equal to 14, then the inequality is satisfied.

Case 2: [tex]x-3[/tex] is negative

If [tex]x-3[/tex] is negative, then [tex]| x - 3 |[/tex] is equal to [tex]-(x - 3)[/tex]. So we can rewrite the inequality as:

[tex]-(x - 3) \geq 11[/tex]

Multiplying both sides by -1, we get:

[tex]x - 3 \leq -11[/tex]

Adding 3 to both sides, we get:

[tex]x \leq -8[/tex]

This means that if [tex]x[/tex] is less than or equal to -8, then the inequality is satisfied.

Putting these two cases together, we get:

[tex]x \leq -8[/tex] or [tex]x \geq 14[/tex]

These are all the possible values of [tex]x[/tex] that satisfy the inequality.

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The complete question is:

Solve the equation: | x - 3 | / 11 ≥ 11 and determine the type of solution.

Help please, I will give brainiest


Type the correct answer in each box. Round your answers to the nearest hundredth.

City Cat Dog

Lhasa Apso Mastiff Chihuahua Collie

Austin 24. 50% 2. 76% 2. 86% 3. 44% 2. 65%

Baltimore 19. 90% 3. 37% 3. 22% 3. 31% 2. 85%

Charlotte 33. 70% 3. 25% 3. 17% 2. 89% 3. 33%

St. Louis 43. 80% 2. 65% 2. 46% 3. 67% 2. 91%

Salt Lake City 28. 90% 2. 85% 2. 78% 2. 96% 2. 46%

Orlando 37. 60% 3. 33% 3. 41% 3. 45% 2. 78%

Total 22. 90% 2. 91% 2. 68% 3. 09% 2. 58%

The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.


The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is ______%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is ______%

Answers

The probability that a randomly selected orphan pet in an animal shelter in Austin is a dog is 11.71%. The probability that a randomly selected orphaned dog in the same animal shelter in Austin is a Chihuahua is 29.37%.

The probability that a haphazardly chosen vagrant pet in a creature covered in Austin is a canine is 11.71%.

The probability that a haphazardly chosen stranded canine in a similar creature cover in Austin is a Chihuahua is 29.37% .

2.76% + 2.86% + 3.44% + 2.65% = 11.71%

11.71/3.44 = .2937

.2937 = 29.37%

Probability is just the way that logical something is to occur.

Whenever we're uncertain about the result of an occasion, we can discuss the probabilities of specific results — how likely they are. The investigation of occasions represented by probability is called statistics.

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Spaceship Earth is a major tourist at Epcot. It is a sphere whose volume is
approximately 65, 417 m³. What is the approximate circumference of Spaceship
Earth? Use π = 3. 14. Round to the nearest whole number. Do not label.

Answers

The approximate circumference of Spaceship Earth is approximately 138.02 meters.

What is circumference of a circle?

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

The volume of the sphere is given as:

V = (4/3)πr³

Substituting the values:

[tex]r = (3(65,417)/4(3.14))^{(1/3)} = 21.96 meters[/tex]

The circumference of the circle is:

C = 2πr

Substituting the value of r:

C = 2(3.14)(21.96) = 138.02 meters

Hence, the approximate circumference of Spaceship Earth is approximately 138.02 meters.

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what is x2=20 show your work

Answers

Answer:

x=10

Step-by-step explanation:

x2=20

2*x=20

2*10=20

so, x=10

A rocket is launched from the top of a 90 foot cliff with an initial velocity of 160 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16t^2+160t+90. How long after the rocket is launched will it be 30 feet from the ground?

Answers

The rocket will be 30 feet from the ground approximately 0.4 seconds or 9.6 seconds after it is launched.

To solve this problem, we need to find the value of t for which the height of the rocket is 30 feet. We can use the given equation to set up an equation for this as follows:

-16t² + 160t + 90 = 30

Simplifying and rearranging, we get:

-16t² + 160t + 60 = 0

Dividing by -4, we get:

4t² - 40t - 15 = 0

Using the quadratic formula, we get:

t = [40 ± √(40² - 4(4)(-15))] / (2×4)

t = [40 ± √(1840)] / 8

t = [40 ± 2×√(460)] / 8

t = 5 ± (1/2)×√(460)

Therefore, the rocket will be 30 feet from the ground at t = 5 - (1/2)×√(460) seconds or t = 5 + (1/2)×√(460) seconds. These are the two possible solutions to the equation. We can simplify them as follows:

t = 0.4 seconds or t = 9.6 seconds

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Como expresar

[tex]\frac{20*19*18}{4*3*2*1}[/tex]

:>

Answers

Based on the information, we can infer that the whole number equivalent to this fraction is 285.

How to isolate the fraction to get a whole number?

To clear the fraction and obtain an integer we must perform all the mathematical operations that are in the fraction, in this case it is a division and seven multiplications. Here we show you the result:

20*19*18/4*3*2*16,840 / 4*3*2*16,840 / 24285

As evidenced in the procedure, the multiplications were cleared and later the fraction was divided. In this case the result would be the integer 285.

Note: This question is incomplete. Here is the complete information:

How to express this fraction in whole numbers?

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PLEASE HELP FAST (giving brainliest)

Answers

Answer:

Answer is B The data is asymetrical.

Step-by-step explanation:

14. When finding the volume of prisms and pyramids, a unit cube can be used. Why is a unit sphere not a good unit of volume measurement for all spheres?​

Answers

Therefore, for spheres of different sizes, we need to use different measuring units, unlike prisms and pyramids, where a unit cube can be used as a standard unit for all shapes with the same base and height.

What is volume?

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the measure of the total amount of space that an object takes up. The standard unit of volume is the cubic meter (m³) in the International System of Units (SI), but other units such as cubic centimeters (cm³) and cubic inches (in³) are also commonly used. The volume of an object can be calculated using different formulas depending on its shape and dimensions.

Here,

A unit sphere is not a good unit of volume measurement for all spheres because spheres come in various sizes and diameters. The unit sphere has a radius of 1, and while it can be used to measure the volume of spheres with radii equal to 1, it cannot be used to measure the volume of spheres with different radii.

For example, if we want to find the volume of a sphere with a radius of 2, we cannot use the unit sphere as a measuring unit. Instead, we would need to use a larger sphere with a radius of 2 as our measuring unit.

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PLS HELP (SORRY I KEEP ASKING QUESTIONS I HATE MATH SO I DONT RLLY PAY ATTENTION THAT WELL)

Answers

The graph shows that the rise is 3 and the run is 3, and the hypotenuse is the length between the two points.

let hypotenuse = x

using Pythagorean theorem:

x^2= 3^2 + 3^2

x^2 = 9 + 9

x= sqrt 18

x = 4.2426....

rounding to the nearest 10th:

x = 4.2

the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. the distribution is likely to be .

Answers

The distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

What is a skewed distribution?

A skewed distribution is one in which the data is not uniformly distributed but rather concentrated on one side. In simple words, a skewed distribution is one in which one tail has a greater number of observations than the other tail, with the majority of data falling in the tail with the greater number of observations.

In a symmetric distribution, the data is uniformly distributed on both sides of the median, with half of the data lying to the right and half to the left.

Thus, the distribution of test scores shows that most students did not do well on the test; some did fine and only a few did exceedingly well. The distribution is likely to be skewed.

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An instrument that can be used to measure height,age and shoe size of learners

Answers

A stadiometer can be used to measure height, age, and shoe size of learners. It is a simple device consisting of a ruler mounted on a vertical board, and the measurements can be taken in the Frankfort Plane position.

An instrument that can be used to measure height, age, and shoe size of learners is a stadiometer. A stadiometer is a device designed to measure the height of an individual, typically from the floor to the crown of the head. It consists of a ruler, graduated in metric or imperial units, mounted on a vertical board. To measure a person's height, they must stand against the board with their feet together and their head in the Frankfort Plane. The Frankfort Plane is an imaginary line running from the top of the ears to the bottom of the eyes. Once the person is standing in this position, the height is read off the ruler and recorded.

In addition to height measurement, a stadiometer can also be used to measure age and shoe size of learners. To measure age, the stadiometer must be calibrated with the average height of the population by age. Then, when the person is standing in the Frankfort Plane position, their age can be read off the ruler. To measure shoe size, the stadiometer must be calibrated with the average height of a person with a certain shoe size. Once the person is standing in the Frankfort Plane position, their shoe size can be read off the ruler.

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pls help me with both of them

Answers

The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994

The dimensions of the rectangle, given the area of the rectangle would be:

Length : 12. 8 meters Width : 6.9 meters

How to find the year ?

The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.

164 = 0.93x² + 2.2x + 130

0.93x² + 2.2x + 130 - 164 = 0

0.93x² + 2.2x - 34 = 0

x = 2.5

Now, we'll find the year by adding the value of x to 1990:

Year = 1990 + 2.5 = 1992.5

= 1994 which is the closest year in options

How to find the dimensions of the rectangle ?

The area of the rectangle is given by:

Area = width × length

91 = (x + 2)(2x + 3)

91 = 2x² + 3x + 4x + 6

91 = 2x² + 7x + 6

2x² + 7x - 85 = 0

When solved differently:
x = 4.9

x = -3.5

Using the positive values:

Width = x + 2 ≈ 4.9 + 2 = 6.9 meters

Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters

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a line that passes through (3,5) and (4,13)

Answers

Answer:

y = 8x-19

Step-by-step explanation:

The first step is to find the slope.

m= ( y2-y1)/(x2-x1)

  = ( 13-5)/(4-3)

   = 8/1

  = 8

Then we can use the slope intercept formula.

y = mx+b

y = 8x+b

Substitute a point to find the intercept.

5 = 8*3+b

5 = 24+b

-19 = b

The formula is

y = 8x-19

Answer:

y = 8x - 19

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 5 ) and (x₂, y₂ ) = (4, 13 )

m = [tex]\frac{13-5}{4-3}[/tex] = [tex]\frac{8}{1}[/tex] = 8 , then

y = 8x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 5 )

5 = 8(3) + c = 24 + c ( subtract 24 from both sides )

- 19 = c

y = 8x - 19 ← equation of line

100 POINTS AND WILL MARK BRAINLIEST!
Law of Cosines Of A Triangle -

GIVEN:

C (the degree)

20

22

18 (the base)

C = ?°

Round your final answer to the nearest tenth.

Answers

Law of Cosines Of A Triangle -GIVEN: C (the degree) 20, 22,18 (the base). C is 26.5 degrees.

To solve for the angle C using the law of cosines, we use the formula:

[tex]c^2 = a^2 + b^2[/tex] - 2ab cos(C)

where c is the angle C's opposite side.

Substituting the given values, we get:

[tex]18^2 = 20^2 + 22^2[/tex] - 2(20)(22)cos(C)

324 = 1048 - 880cos(C)

880cos(C) = 724

cos(C) = 724/880

C = [tex]cos^{(-1)}[/tex](724/880)

C ≈ 26.5 degrees

Therefore, the measure of angle C is approximately 26.5 degrees.

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55 divided by 11 * 7 x (2 + 14)

Answers

560

1) PEMDAS so 2+14=16

2)55/11=5

3)5x7=35

4)35(16)=560

Consider the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family.


Yes No Totals

Men 106 141 247

Women 92 161 253

Totals 198 302 500


a. Develop the joint probability table for these data and use it to answer the following questions

b. What are the marginal probabilities?

c. What is the probability of living with family given you are an 18- to 34-year-old marn in the U. S. ?

d. What is the probability of living with family given you are an 18- to 34-year-old woman in the U. S. ?

e. What is the probability of an 18- to 34-year-old in the U. S. Living with family?

f. If, in the U. S. , 49. 4% of 18-to 34-year-olds are male, do you consider this a good representative sample? Why?

Answers

After considering the following hypothetical survey results of 18- to 34-year-olds in a certain country, in response to the question "Are you currently living with your family?" we get the following probabilities.

a. The joint probability table for the given data is:

             Yes      No      Totals

Men          0.212   0.282   0.494

Women        0.184   0.322   0.506

Totals       0.396   0.604   1

b. The marginal probabilities for living with family and not living with family are:

                 Yes No

Men        0.212 0.282

Women 0.184 0.322

Totals 0.396 0.604

c. The probability of living with family given you are an 18- to 34-year-old man in the U.S. is 0.212/0.396 = 0.5354 or approximately 53.54%.

d. The probability of living with family given you are an 18- to 34-year-old woman in the U.S. is 0.184/0.506 = 0.3636 or approximately 36.36%.

e. The probability of an 18- to 34-year-old in the U.S. living with family is 0.396 or 39.6%.

f. We cannot determine whether the sample is representative solely based on the percentage of males in the survey.

A good representative sample should be randomly selected to accurately reflect the population being studied. The percentage of males in the sample is relevant only if it differs significantly from the percentage of males in the population being studied.

The joint probability table was developed for the survey results of 18- to 34-year-olds on living with family. Marginal probabilities were calculated and the probability of living with the family was found for both men and women. The overall probability of living with the family was also determined. It is unclear if the sample is representative without additional information.

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The amount A, in milligrams, of a 10-milligram dose of a drug remaining in the body after t hours
is given by the formula A = 10(08)t Find, to the nearest tenth of an hour, how long it takes for half
of the drug dose to be left in the body.

Answers

It takes 3.1 hour  for half of the drug dose to be left in the body.

Milligram

In the metric system the unit measurement of mass is known as mg .

mg is equal to one thousandth of a gram ie.1/1000. The unit is often used in medical field for weighing out small quantities of  ingredients.

prons

it is precise and it can be used to measure small quantities of items.

It is easy to convert mg to other units of measure.

cons:

It is a very small unit of measurement, it is difficult to measure the values accurately.

It is also a very commonly used unit of measurement, it get easily  confuse with other units

10*1/2=10(0.8)^t

0.8^t=1/2

t=log0.8*1/2

t=3.1

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The baker receives an order of 80 chocolate pies for a community festival. The baker needs 3 cups of milk to make each pie. How much milk, in gallons, is needed to make the 80 pies for the festival?

Answers

the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival. To find out how much milk is needed to make 80 chocolate pies, we need to first determine the total amount of milk required for one chocolate pie. We know that the baker needs 3 cups of milk to make one chocolate pie.

To convert cups to gallons, we need to divide by 16 since there are 16 cups in a gallon. So, one chocolate pie requires 3/16 gallons of milk.

To find out how much milk is needed to make 80 chocolate pies, we can multiply the amount of milk required for one pie by the number of pies. This gives us:

(3/16) gallons of milk per pie x 80 pies = 15 gallons of milk

Therefore, the baker needs 15 gallons of milk to make 80 chocolate pies for the community festival.

It's important to make sure we convert units correctly when solving these types of problems. In this case, we had to convert cups to gallons to make sure we were using the same unit of measurement for both the amount of milk needed for one pie and the total amount needed for 80 pies. By following these steps, we can accurately determine the amount of ingredients needed to fulfill an order, which is important for bakers and other food service professionals.

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Can You fail 5th grade elementary? i have a 68 in math and im scared

Answers

Answer: I mean technically no. grades don't really matter until high school. You can get held back but that's up to your parents if you do

answer:

probobly not because it can also depend on the fsa or fast test u have to take but a 68 is not bad its a d+ really close to 70 so i dont think u will dont worry.

In ΔSTU, u = 980 inches, t = 700 inches and ∠T=161°. Find all possible values of ∠U, to the nearest degree.

Answers

Answer:<U=27.1

Step-by-step explanation:

undoing the law of sines to find <U:

[tex]\frac{sin161}{700} =\frac{sinU}{980}[/tex]

[tex]sin U 700=980sin161[/tex]

[tex]Sin U =\frac{980sin161}{700}[/tex]

[tex]< U=27.1[/tex]

Assume that TDW Corporation (calendar year-end) has 2022 taxable income of $650,000 for purposes of computing the §179 expense. The company acquired the following assets during 2022: (Use MACRS Table 1, Table 2, Table 3, Table 4 and Table 5. ) Asset Placed in Service Basis Machinery September 12 $ 2,270,000 Computer equipment February 10 263,000 Furniture April 2 880,000 Total $ 3,413,000 a. What is the maximum amount of §179 expense TDW may deduct for 2022?

Answers

The maximum amount of §179 expense TDW may deduct for 2022 is $257,000.

To determine the maximum amount of §179 expense that TDW Corporation can deduct for 2022, we first Add up the cost of all the assets acquired in 2022:

$2,270,000 (machinery) + $263,000 (computer equipment) + $880,000 (furniture) = $3,413,000

Now we determine the amount of the §179 deduction limit for the tax year.

For tax year 2022, the §179 deduction limit is $1,050,000.

Check if the cost of the assets exceeds the §179 deduction limit.

Since the cost of the assets ($3,413,000) is greater than the §179 deduction limit ($1,050,000), we need to calculate the phase-out limit.

Now we determine the phase-out limit.

For tax year 2022, the phase-out limit is $2,620,000.

Calculate the §179 expense deduction.

Since the cost of the assets ($3,413,000) is greater than the phase-out limit ($2,620,000), we need to reduce the §179 deduction by the excess over the phase-out limit.

The excess over the phase-out limit is $793,000 ($3,413,000 - $2,620,000).

The §179 expense deduction is the lesser of the §179 deduction limit and the cost of the assets reduced by the excess over the phase-out limit.

The §179 expense deduction is $1,050,000 - $793,000 = $257,000.

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Need help too figure out these questions these are 2 outa 10 i have too do but these the hardest

Answers

Answer:

1. I don't know

2. 10

Step-by-step explanation:

[tex]c=\sqrt{a^{2}+b^{2} } = \sqrt{6^{2}+8^{2} } = \sqrt{36+64} = \sqrt{100} = 10[/tex]

Answer is
1) area of shaded area = 14.13 m
area of the remainder of circle = 345.87

2) hypotenuse = 10cm

Step by step
1)
Area of a circle is A=TT r^2
A= (3.14) (6)^2
A= 3.14 x 36
A= 113.04
Now we want to find out just the shaded area

There is 360 degrees in a circle
We are finding 45 degrees of 360 = 1/8
1/8 of 113.04 = 14.13 m

2) hypotenuse is found using formula
a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2

√100 = √c^2
10 cm = c

a supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. (a) what is the expected number of container drops needed to hit a target?

Answers

The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.

       

       To find out the expected number of container drops needed to hit a target, we can use the formula given below;            

                      E(X) = (1/p) E(X)

                             = (1/0.37)E(X)

                             = 2.7027

          Thus, the expected number of container drops needed to hit a target is approximately 2.7027.

An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).

            The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.

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Newton's 2nd law says that when a larger force is applied to an object of mass m, the object will experience a larger acceleration. At the same time, you've learned that all objects experience the same acceleration in a free fall, even if their weights (the forces of gravity acting on them) are different. That sounds like a contradiction: on one hand, from the Newton's 2nd law, a larger force means larger acceleration, on the other hand when applied to motion under gravity - a larger weight (force) means the same acceleration for all objects. How do you reconcile these statements? Why isn't it a contradiction? Does gravity violate the Newton's second law or is there another explanation. Be as thorough and clear in your explanation as possible.

Answers

It is important to understand that the force of gravity acting on an object does not violate Newton's second law. It is an external force that acts on an object and produces an acceleration in it. Therefore, the acceleration due to gravity does not violate Newton's second law.

According to the Newton's second law, a force acting on a body of mass m produces an acceleration a in the body which is directly proportional to the force and inversely proportional to the mass. For instance, If a body of mass m is acted upon by a force F, then the acceleration produced in the body is given by F/m.As per the law, a larger force will produce a larger acceleration in the object.

When a body falls under gravity, it is said to experience weight. The weight of an object is the force of gravity acting on the object. According to Newton's law of gravitation, every object attracts every other object with a force proportional to their masses and inversely proportional to the square of their distance. In general, the weight of an object can be given by the formula weight = mass x acceleration due to gravity.

Therefore, as the acceleration due to gravity is the same for all objects, the weight of an object is proportional to its mass. It implies that a heavier object has more weight, while a lighter object has less weight.As per the above facts, a heavier object would require a larger force to move it than a lighter object. However, when they fall under gravity, both objects fall at the same rate. It appears as a contradiction, but the reason for it is the difference between weight and mass.

The mass of an object is a measure of the amount of matter in it, while the weight of an object is the force exerted on it by gravity.The acceleration produced in an object by an external force is not the same as the acceleration due to gravity. A force F produces an acceleration F/m, whereas the acceleration due to gravity is the same for all objects.

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to begin a bacteria study, a petri dish had 2800 bacteria cells. each hour since, the number of cells has increased by 3.3%. let t be the number of hours since the start of the study. let y be the number of bacteria cells. write an exponential function showing the relationship between y and t.

Answers

[tex]y = 2800(1.033)^t[/tex] is the exponential function for starting population of 2800 bacterium cells that is shown to multiply exponentially over time using this function, increasing by a factor of 1.033 every hour.

We can use an exponential function of the type y = abt to simulate the development of bacteria cells over time, where y stands for the number of cells, t for the number of hours, and a and b for constants that we must establish.

Since we now know there are 2800 bacterium cells, we can enter this number into the equation to obtain:

[tex]2800 = ab^0[/tex]

By simplifying this equation, we obtain a = 2800, which informs us that there are 2800 bacterium cells in the initial population.

We must use the knowledge that the number of cells rises by 3.3% every hour to get the value of b. By dividing this percentage growth by 100, we can convert it to a decimal, yielding a growth rate of 0.033. The value of b can then be obtained by multiplying this growth rate by 1:

b = 1 + 0.033 = 1.033

These values of a and b are what we obtain when we enter them into our exponential function:

[tex]y = 2800(1.033)^t[/tex]

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