The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. What is the probability that a randomly selected broiler weighs more than 1,454 grams?

Answer:

A. H(x) is an inverse of F(x)

Step-by-step explanation:

The given functions are:

[tex]F(x)=\sqrt{x-2}[/tex]

[tex]G(x)=(x-2)^2[/tex]

[tex]H(x)=x^2+2[/tex]

We compose F(x) and G(x) to get:

[tex](F\circ G)(x)=F(G(x))[/tex]

[tex](F\circ G)(x)=F((x-2)^2)[/tex]

[tex](F\circ G)(x)=\sqrt{(x-2)^2-2}[/tex]

[tex](F\circ G)(x)=\sqrt{x^2-4x+4-2}[/tex]

[tex](F\circ G)(x)=\sqrt{x^2-4x+2}[/tex]

[tex](F\circ G)(x)\ne x[/tex]

Hence G(x) is not an inverse of F(x).

We now compose H(x) and G(x).

[tex](F\circ H)(x)=F(H(x))[/tex]

[tex](F\circ H)(x)=F(x^2+2)[/tex]

[tex](F\circ H)(x)=\sqrt{x^2+2-2}[/tex]

We simplify to get:

[tex](F\circ H)(x)=\sqrt{x^2}[/tex]

[tex](F\circ H)(x)=x[/tex]

Since [tex](F\circ H)(x)=x[/tex], H(x) is an inverse of F(x)

Answer:

the answer is 90

Step-by-step explanation:

296-96=90

Answer:

$5151.42

Step-by-step explanation:

The formula you need is

[tex]A(t)=P(1+\frac{r}{n})^{(n)(t)}[/tex]

where A(t) is the amount after the compounding, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings per year, and t is time in years.  The info we have is

A(t) = 8000

P = ?

r = .09

t = 5

Filling in we have

[tex]8000=P(1+\frac{.09}{2})^{(2)(5)}[/tex]

Simplifying a bit and we have[tex]8000=P(1+.045)^{10}[/tex]

Now we will add inside the parenthesis and raise 1.045 to the 10th power to get

8000 = P(1.552969422)

Divide away the 155... on both sides to solve for P.

P = $5151.42

Answer:

  $1516.69 per month less

Step-by-step explanation:

The formula for the monthly payment A on a loan of principal P, annual rate r, for t years is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

For the 18.5% loan, the monthly payment is ...

  A = 150000(.185/12)/(1 -(1 +.185/12)^(-12·30)) ≈ 2321.92

For the 5% loan, the monthly payment is ...

  A = 150000(.05/12)/(1 -(1 +.05/12)^-360) ≈ 805.23

The mortgage at 5% would be $1516.69 less per month.

Final answer:

To determine how much less per month a $150,000 30-year mortgage would be at a 5% interest rate compared to an 18.5% rate, calculate monthly payments for both scenarios and subtract the lower payment from the higher one.

Explanation:

The question asks to compare monthly mortgage payments in two different interest rate scenarios for a 30-year, $150,000 mortgage: first at an 18.5% interest rate which was the average in the 1980s, and second at the current rate of 5%. To find out how much less the monthly payment would be at 5% compared to 18.5%, we can use the formula for calculating monthly mortgage payments:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where:

M is your monthly payment.

P is the principal loan amount, $150,000 in this case.

i is your monthly interest rate. The annual rate needs to be divided by 12.

n is the number of payments (the number of months you will be paying the loan).

Calculating the monthly payment for an 18.5% interest rate over 30 years:

P = $150,000

i = 18.5% annual interest rate / 12 months = 1.5417% monthly interest rate

n = 30 years * 12 months/year = 360 payments

Doing the same calculation at a 5% interest rate:

P = $150,000

i = 5% annual interest rate / 12 months = 0.4167% monthly interest rate

n = 30 years * 12 months/year = 360 payments

After computing the monthly payments for both interest rates, we then subtract the monthly payment at 5% from the monthly payment at 18.5% to determine how much less it would be. As this is a high school-level mathematics problem, we use algebraic operations and functions to answer the question.

Answer:

cool

Step-by-step explanation:

Answer: The ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]

Step-by-step explanation:

Since we have given that

Radius of first sphere = 5 inches

Radius of second sphere = 10 inches

We need to find the ratio of volume of first sphere to volume of second sphere:

As we know the formula for "Volume of sphere ":

[tex]Volume=\dfrac{4}{3}\pi r^3[/tex]

So, it becomes,

Ratio of first volume to second volume is given by

[tex]\dfrac{4}{3}\pi (5)^3:\dfrac{4}{3}\pi (10)^3\\\\=5^3:10^3\\\\=125:1000\\\\=1:8[/tex]

Hence, the ratio is [tex]1:8\ or\ \dfrac{1}{8}[/tex]

The ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches is 1/8.

To find the ratio of the volume of a sphere with a radius of 5 inches to the volume of a sphere with a radius of 10 inches, we can use the formula for the volume of a sphere, which is V = (4/3)πr³. Let's calculate the volumes of the two spheres:

For the sphere with a radius of 5 inches:

V1 = (4/3)π(5)³ = (4/3)π(125) = 500π inches³

For the sphere with a radius of 10 inches:

V2 = (4/3)π(10)³ = (4/3)π(1000) = 4000π inches³

Therefore, the ratio of the two volumes is:

R = V1/V2 = (500π)/(4000π) = 1/8

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Answer:

11

Step-by-step explanation:

-2×pi is approximately-6.28

3×sqrt(2) is approximately 4.24

Now if you really need... just list out the integers between those two numbers and then count like so: -6,-5,-4,-3,-2,-1,0,1,2 3,4

That is 11 integers

The question is about finding the number of integers between -2π and 3√2. This involves understanding the definition of the function a*b, and then applying this to the given values. The correct answer is 11.

The function a*b defined in this problem represents the number of integers greater than a and less than b.

When we substitute a with -2π and b with 3√2, we are basically finding the number of integers between -2π and 3√2.

Knowing that -2π is approximately -6.28, and 3√2 which is approximately 4.24, we count the integers that fall between these two numbers.

Our list of integers will be: -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4. Hence, the answer is 11 (option c).

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Answer:

Part 1) [tex]y=80,000(1.035)^{x}[/tex]

Part 2) The table in the attached figure

Part 3) The graph in the attached figure

Step-by-step explanation:

Part 1) Find the population function

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> is the population

x ----> the time in years

a is the initial value (a=80,000 people)

b is the base (b=100%+3.5%=103.5%=1.035)

substitute

[tex]y=80,000(1.035)^{x}[/tex]  

Part 2) Construct the table

For x=0 years  

substitute in the function equation

[tex]y=80,000(1.035)^{0}=80,000\ people[/tex]  

For x=10 years

substitute in the function equation

[tex]y=80,000(1.035)^{10}=112.848\ people[/tex]

For x=20 years

substitute in the function equation

[tex]y=80,000(1.035)^{20}=159,183\ people[/tex]

For x=40 years

substitute in the function equation

[tex]y=80,000(1.035)^{40}=316,741\ people[/tex]

For x=50 years

substitute in the function equation

[tex]y=80,000(1.035)^{50}=446,794\ people[/tex]

For x=75 years

substitute in the function equation

[tex]y=80,000(1.035)^{75}=1,055,884\ people[/tex]

For x=100 years  

substitute in the function equation

[tex]y=80,000(1.035)^{100}=2,495,313\ people[/tex]

Part 3) The graph in the attached figure  

Answer:

The area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

Step-by-step explanation:

We need to find the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28.

The standard normal table represents the area under the curve.

[tex]P(z<-2.94)\cup P(z>-2.28)=P(z<-2.94)+P(z>-2.28)[/tex]          .....(1)

According to the standard normal table, we get

[tex]P(z<-2.94)=0.0016[/tex]

[tex]P(z>-2.28)=1-P(z<-2.28)=1-0.0113=0.9887[/tex]

Substitute these values in equation (1).

[tex]P(z<-2.94)\cup P(z>-2.28)=0.0016+0.98807=0.9903[/tex]

Therefore the area under the standard normal curve to the left of z=−2.94 and to the right of z=−2.28 is 0.9903 square units.

The area under the standard normal curve to the left of z  = −2.94 and to the right of z = −2.28 is 0.9903 square units.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The area under the standard normal curve to the left of z = −2.94 and to the right of z = −2.28 will be

The standard normal table represents the area under the curve.

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = P(z < -2.94) + P(z > -2.28)[/tex] ...1

According to the standard normal table, we have

[tex]\rm P(z < -2.94) = 0.0016\\\\P(z > -2.94) = 1- P(z < -2.94) = 1-0.0113 = 0.9887[/tex]

Substitute these values in equation 1, we have

[tex]\rm P(z < -2.94) \cap P(z > -2.28) = 0.0016 + 0.9887 = 0.9903[/tex]

More about the normal distribution link is given below.

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Answer:

The area of the glass in region BCIH is 11 to the nearest feet²

Step-by-step explanation:

* Lets explain the figure

- The window is a semicircle with center G and radius 6 feet

- There is a small semicircle with center G and radius GF

∵ GE is 6 feet and EF is 3 feet

∵ GE = GF + FE

∴ 6 = GF + 3 ⇒ subtract 3 from both sides

∴ 3 = GF

∴ The radius of the small semicircle is 3 feet

∵ m∠BGC = 45°

- The area of sector BGC is part of the area of the semicircle

∵ The area of semi-circle is 1/2 π r²

∵ The measure of the central angle of the semicircle is 180°

∵ The measure of the central angle of the sector BGC is 45°

∴ The sector = 45°/180° = 1/4 of the semi-circle

∴ The area of the sector is 1/4 the area of the semicircle

∵ The area of the semicircle = 1/2 π r²

∵ r = 6 feet

∴ The area of the semicircle = 1/2 π (6)² = 1/2 π (36) = 18 π feet²

∴ Area of the sector = 1/4 (18 π) = 4.5 π feet²

- The small sector HGI has the same central angle of the sector BGC

∴ The area of the sector HGI is 1/4 The area of the small semicircle

∵ The area of the small semicircle = 1/2 π r²

∵ r = 3 feet

∴ The area of the small semicircle = 1/2 π (3)² = 1/2 π (9) = 4.5 π feet²

∴ Area of the sector HGI= 1/4 (4.5 π) = 1.125 π feet²

- The area of the glass in region BCIH is the difference between the

  area of sector BGC and the area of the sector HGI

∴ The area of the glass in region BCIH = 4.5 π - 1.125 π ≅ 11 feet²

Answer:

11 feet to the nearest square foot.

Step-by-step explanation:

The area of sector BCG

= 45/180 * 1/2 π r^2

= 1/4 * 1/2 π r^2

= 1/8 * π * 6^2

= 4.5 π ft^2.

The radius of the inner semicircle is 6 - 3 = 3 feet.

The area of sector HIG = 1/4 * 1/2 π  3^2

= 1.125 π ft^2.

So the area of BCIH

= area of BCG - area HIG

=  4.5  π - 1.125  π

=  3.375  π

= 10.6 square feet.

Answer:

First type of fruit drinks: 48 pints

Second type of fruit drinks: 32 pints

Step-by-step explanation:

Let's call A the amount of first type of fruit drinks. 55% pure fruit juice

Let's call B the amount of second type of fruit drinks. 80% pure fruit juice

The resulting mixture should have 65% pure fruit juice and 80 pints.

Then we know that the total amount of mixture will be:

[tex]A + B = 80[/tex]

Then the total amount of pure fruit juice in the mixture will be:

[tex]0.55A + 0.8B = 0.65 * 80[/tex]

[tex]0.55A + 0.8B = 52[/tex]

Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -0.8 and add it to the second equation:

[tex]-0.8A -0.8B = -0.8*80[/tex]

[tex]-0.8A -0.8B = -64[/tex]

[tex]-0.8A -0.8B = -64[/tex]

               +

[tex]0.55A + 0.8B = 52[/tex]

--------------------------------------

[tex]-0.25A = -12[/tex]

[tex]A = \frac{-12}{-0.25}[/tex]

[tex]A = 48\ pints[/tex]

We substitute the value of A into one of the two equations and solve for B.

[tex]48 + B = 80[/tex]

[tex]B = 32\ pints[/tex]

To create an 80-pint batch of 65% pure fruit juice, the Royal Fruit Company needs to solve two equations representing the volume and percent mixture of the two juices. These equations can be solved simultaneously to find the required volumes of each juice.

The subject of this question falls under Mathematics, particularly dealing with proportions and algebra. Given that the first type of juice is 55% pure fruit and the second type is 80% pure fruit, we can define our variables: let's denote X as the volume of the first type of drink and Y as the volume of the second one. We know that the total volume is 80 pints, so we have our first equation: X + Y = 80. The second equation derives from the percentage of fruit juice: 0.55X + 0.80Y = 0.65*80.

Now we can solve these two equations to find the volumes of X and Y. The solution to these equations will provide us with the volume needed from each of the two types of juice to achieve a 65% pure fruit juice drink.

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Answer:

After how many years is the fish population 100?

x=3.97 years

Step-by-step explanation:

The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation

[tex]f (x) = 20 (1.5) ^ x[/tex]

Where x represents the number of years elapsed f(x) represents the amount of fish.

Given this situation, the following question could be posed

After how many years is the fish population 100?

So we do [tex]f (x) = 100[/tex] and solve for the variable x

[tex]100 = 20 (1.5) ^ x\\\\\frac{100}{20} = (1.5)^x\\\\ 5= (1.5)^x\\\\log_{1.5}(5) = log_{1.5}(1.5)^x\\\\log_{1.5}(5) = x\\\\x =log_{1.5}(5)\\\\x=3.97\ years[/tex]

Observe the solution in the attached graph

Answer:

Step-by-step explanation:

Given:

  Total interest earned on two investments is $29,220.

  An amount is invested at 7%.

  $24,000 more than 4 times that amount is invested at 8%.

Find:

  The amount invested at each rate.

Solution:

  Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

  interest on 7% account + interest on 8% account = total interest

  0.07x + 0.08(24000+4x) = 29220

  0.39x + 1920 = 29220 . . . . . . . . . . . simplify

  0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

  x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

  24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

  7% interest + 8% interest = 29,220

  0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

Comment on 6-step method

We have tried to hit the highlights. Your steps appear to be ...

Answer:

a) The volume in cubic inches is 36000

b) The volume in cubic feet is 125/6

c) The volume in cubic yard is 125/162

Step-by-step explanation:

* Lets study the information of the problem to solve it

- The dimensions of the piece of cardboard are 90 inches by 70 inches

- The side of the cutting square is 15 inches

- The squares are cutting from each corner

∴ Each dimension of the cardboard will decrease by 2 × 15 inches

∴ The new dimensions of the piece of cardboard are;

90 - (15 × 2) = 90 - 30 = 60 inches

70 - (2 × 15) = 70 - 30 = 40 inches

- The dimensions of the box will be:

# Length = 60 inches

# width = 40 inches

# height = 15 inches

- The volume of any box with three different dimensions is

V = Length × width × height

∵ The length = 60 inches

∵ The width = 40 inches

∵ The height = 15 inches

∴ V = 60 × 40 × 15 = 36000 inches³

a) The volume in cubic inches is 36000

* Now lets revise how to change from inch to feet

- 1 foot = 12 inches

∵ 1 foot = 12 inches

∴ 1 foot³ = (12)³ inches³

∴ 1 foot³ = 1728 inches³

∵ The volume of the box is 36000 inches³

∴ The volume of the box in cubic feet = 36000 ÷ 1728 = 125/6  

b) The volume in cubic feet is 125/6

* Now lets revise how to change from feet to yard

- 1 yard = 3 feet

∵ 1 yard = 3 feet

∴ 1 yard³ = (3)³ feet³

∴ 1 yard³ = 27 feet³

∵ The volume of the box is 125/6 feet³

∴ The volume of the box in cubic yard = 125/6 ÷ 27 = 125/162  

c) The volume in cubic yard is 125/162

Answer:

3600 cubic inches , 2.08 cubic feet , 0.0771 cubic yards

Step-by-step explanation:

Here we are given that the open box has been constructed from a card board with length 90 inches and width 70 inches by

1. cutting  a square card board

2. of each side 15 inches

Hence when we are done with folding it for our cuboid , we find our new

1. Length = 90-15-15 = 60 inches

2. width = 70-15-15 = 40 inches

3. Height = 15 inches

Now we know the volume of any cuboid is given as

V= Length * width * height

 = 60*40*15

 = 3600 cubic inches

Part 2 . Now let us convert them into  cubic feet

1 cubic inch = 0.000578704 cubic feet

Hence 3600 cubic inches = 3600 * 0.000578704  cubic feet

                                           =2.083 cubic feet

Part 3. Now let us convert them into  cubic yards

1 cubic inch = 0.0000214335 cubic yards

Hence 3600 cubic inches = 3600 * 0.0000214335 cubic yards

                                           = 0.0771 cubic yards

Answer:

G.P. is, 450, 360, 288, 230.4,......

The sum is 2250.

Step-by-step explanation:

Given,

The first total spending in the resort city = $ 450 million,

Also, 80% of that revenue is again spent in the resort city, and of that amount approximately 80% is again spent in the same city, and so on.

Thus, there is a G.P. that represents the given situation,

450, 360, 288, 230.4,......

Which is an infinite geometric series having first term, a = 450,

Common ratio, r = 0.8,

Hence, the sum of the series,

[tex]S_n=\frac{a}{1-r}[/tex]

[tex]=\frac{450}{1-0.8}[/tex]

[tex]=\frac{450}{0.2}[/tex]

[tex]=2250[/tex]

Answer:

Function which represents the product of these two numbers is:

(23+x)(28+2x)

Step-by-step explanation:

The first number is the sum of 23 and x

i.e. First number=23+x

The second number is 18 less than two times the first number.

i.e. Second number=2(23+x)-18

                                = 46+2x-18

                                = 28+2x

Product of the two numbers=(23+x)(28+2x)

Hence, function which represents the product of these two numbers is:

(23+x)(28+2x)

Answer: Our required probability is 47.3%.

Step-by-step explanation:

Since we have given that

Probability of schools or district in a country use digital content = 86% = 0.86

Probability of schools or district uses digital content as a part of their curriculum out of 86% = [tex]\dfrac{11}{20}[/tex]

So, Probability that a selected school or district uses digital content and uses it as a part of their curriculum is given by

[tex]\dfrac{86}{100}\times \dfrac{11}{20}\\\\=0.86\times 0.55\\\\=0.473\\\\=47.3\%[/tex]

Hence, our required probability is 47.3%.

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3% and this can be determined by using the given data.

Given :

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is given by:

[tex]=\dfrac{11}{20}\times \dfrac{86}{100}[/tex]

Now, multiply 11 by 86 and also multiply 20 by 100 in the above expression.

[tex]=\dfrac{11\times 86}{20\times 100}[/tex]

SImplify the above expression.

[tex]=\dfrac{946}{2000}[/tex]

= 0.473

So, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 47.3%.

For more information, refer to the link given below:

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Dave and Ellen could annually save $27 by installing dead-bolts and $9 by installing smoke detectors. This amounts to a significant discount on their homeowner's insurance premium.

Dave and Ellen's annual homeowner's insurance premium is $450. If they install dead-bolts on all the exterior doors, they would receive a 6 percent discount, while smoke detector installations would fetch them a 2 percent discount. Let's calculate these discounts:

A. Dead-bolts discount: 6 percent of $450 translates to $(450*(6/100)) which equals $27.

B. Smoke detectors discount: 2 percent of $450would be $(450*(2/100)) that equals $9.

To summarize, the couple could annualy save $27 by installing dead-bolts and $9 by installing smoke detectors, which is a substantial reduction on the insurance premium.

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Dave and Ellen can save $27 annually by installing dead-bolt locks and $9 annually by installing smoke detectors. Total savings from both installations would be $36 annually.

Let's break down the problem step by step to calculate the discounts that Dave and Ellen will receive if they install dead-bolt locks and smoke detectors.

Part (a): Discount for Dead-Bolt Locks

1. Annual premium: $450

2. Discount for dead-bolt locks: 6%

The discount amount is calculated as follows:

[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]

So, for the dead-bolt locks:

Discount amount for dead-bolt locks = 450 × [tex]\frac{6}{100} \][/tex]

Discount amount for dead-bolt locks = 450 × 0.06

Discount amount for dead-bolt locks = 27

Thus, Dave and Ellen will receive an annual discount of $27 if they install dead-bolt locks on all exterior doors.

Part (b): Discount for Smoke Detectors

1. Annual premium: $450

2. Discount for smoke detectors: 2%

The discount amount is calculated as follows:

[tex]\[ \text{Discount amount} = \text{Annual premium} \times \frac{\text{Discount percentage}}{100} \][/tex]

So, for the smoke detectors:

Discount amount for smoke detectors} = 450 × [tex]\frac{2}{100}[/tex]

Discount amount for smoke detectors} = 450 × 0.02

Discount amount for smoke detectors} = 9

Thus, Dave and Ellen will receive an annual discount of $9 if they install smoke detectors on each floor of their house.

Answer:

  The bottleneck of this process is Workstation C, at 30 minutes per unit.

Step-by-step explanation:

The throughput of each workstation is ...

Since each process must be executed once per finished product, the bottleneck is the station with the lowest throughput. It is clearly Workstation C.

The bottleneck of this process is workstation D, where the time per unit is 15 minutes.

The bottleneck of this process is workstation D, where the time per unit is 15 minutes. This means that workstation D takes the longest time to complete one unit compared to other workstations. The bottleneck determines the maximum output rate of the entire process, as the other workstations cannot work faster than the slowest one.

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Answer:

  (-9, 6)

Step-by-step explanation:

It's all about pattern matching.

A circle centered at (h, k) with radius r has the equation ...

  (x -h)^2 + (y -k)^2 = r^2

Comparing this pattern to the equation you have, you can see that ...

Then the center is (h, k) = (-9, 6).

Answer:

 (-9, 6)

Step-by-step explanation:

i took the test

Final answer:

To find the probability of the mean weight of 25 randomly selected ice cream cartons being greater than 20.06 ounces, we can use the Central Limit Theorem. By calculating the standard error, finding the z-score, and using a z-table or calculator, we can determine the probability.

Explanation:

To find the probability that the mean weight of 25 randomly selected ice cream cartons is greater than 20.06 ounces, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means from a population with any distribution will be approximately normal, as long as the sample size is large enough.

First, we need to find the standard error of the mean (SE). The formula for SE is SE = standard deviation / √(sample size). In this case, the standard deviation is 0.3 ounces and the sample size is 25. So, SE = 0.3 / √25 = 0.06 ounces.

Next, we calculate the z-score, which measures how many standard deviations the mean is from the population mean. The formula for z-score is z = (sample mean - population mean) / standard error. In this case, the sample mean is 20.06 ounces, the population mean is 20.1 ounces, and the standard error is 0.06 ounces. So, z = (20.06 - 20.1) / 0.06 = -0.67.

We can use a z-table or a calculator to find the probability associated with the z-score. From the table or calculator, we find that the probability of getting a z-score greater than -0.67 is approximately 0.748. Therefore, the probability that the mean weight of the 25 ice cream cartons is greater than 20.06 ounces is approximately 0.748.

ANSWER

[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]

See attachment for the graph

EXPLANATION

The standard equation of the vertical ellipse with center at the origin is given by

[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]

where

[tex] {a}^{2} \: > \: {b}^{2} [/tex]

The ellipse has its vertices at (0,±17).

This implies that:a=±17 or a²=289

The foci are located at (0,±15).

This implies that:c=±15 or c²=225

We use the following relation to find the value of b²

[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]

[tex] \implies \: 289 - {b}^{2} = 225[/tex]

[tex] - {b}^{2} = 225 - 289[/tex]

[tex] - {b}^{2} = - 64[/tex]

[tex] {b}^{2} = 64[/tex]

We substitute into the formula for the standard equation to get:

[tex]\frac{ {x}^{2} }{ 64 } + \frac{ {y}^{2} }{ 289 } = 1[/tex]

Answer:

[tex]4a^{2}[/tex]

Step-by-step explanation:

We need to simplify the following expression:

[tex]y=\frac{32a^{3}b^{2}}{8ab^{2}}[/tex]

We know that: [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]. Applying this rule, we have that:

[tex]y = \frac{32a^{3}b^{2}}{8ab^{2}} = 4a^{3-1}b^{2-2} = 4a^{2}[/tex]

Then, the solution is: [tex]4a^{2}[/tex]

Answer:

678

Step-by-step explanation:

Answer:

a) 43

b) 5.7

c) 2.54

Step-by-step explanation:

The metric system is so easy to work with, everything is in base of 10, and all measures use a prefix. Here, we're talking about length, with the main measure being the meter.

1 m = 100 centimeters (centi- = 1/100)

1 m = 1000 millimeters (milli- = 1/1000)

So, for each centimeter, you have 10 millimeters.

a) How many millimeters are in 4.3 centimeters?

1 cm = 10 mm as shown above, so 4.3 cm = 43 mm

b) How many centimeters are in 57 millimeters?

10 mm = 1 cm so, 57 mm = 5.7 cm

c) Approximately how many centimeters are in an inch?

There are approximately 2.54 cm in an inch.  No real calculation to make here, it's just a unit conversion between systems, done following a known reference table.

Answer:

F or G = {7,8,9,10,11,12,13,14}

n(F or G) = 8

n(S) = 12

By counting the no. of outcome

P(F or G) = n(F or G) / n(S)

P(F or G) = 8 /12

P(F or G) = 2/3

By using the general addition rule

P(F or G) = P(F) + P(G) - P(F and G)

= 6/12 + 4/12 - 2/12

= 2/3

ANSWER

[tex]80 {ms}^{ - 1} [/tex]

EXPLANATION

The average velocity of the ball is the rateof displacement over the total time.

The height of the ball, in feet, after t seconds is given by the function:

[tex]f(t)=-16t^2+192t[/tex]

At time t=1, the height of the ball is

[tex]f(1)=-16(1)^2+192(1)[/tex]

[tex]f(1)=-16+192 = 176ft[/tex]

At time t=6, the height of the ball is

[tex]f(6)=-16(6)^2+192(6)[/tex]

[tex]f(6)=-16(36)+192(6)[/tex]

[tex]f(6)=-576+1152 = 576[/tex]

The average velocity

[tex] = \frac{f(6) - f(1)}{6 - 1} [/tex]

[tex]= \frac{576- 176}{6 - 1} [/tex]

[tex]= \frac{400}{5} [/tex]

[tex] = 80 {ms}^{ - 1} [/tex]

Answer: 0.8021

Step-by-step explanation:

The given problem is a binomial distribution problem, where

[tex]n=14,\ p=0.2, q=1-0.2=0.8[/tex]

The formula of binomial distribution is :-

[tex]P(X=r)=^{n}C_{r}p^{r}q^{n-r}[/tex]

The probability that the lot will fail inspection is given by :_

[tex]P(X\geq2)=1-(P(X\leq1))\\\\=1-(P(0)+P(1))\\\\[/tex]

[tex]=1-(^{14}C_{0}(0.2)^{0}(0.8)^{14-0}+^{14}C_{1}(0.2)^{1}(0.8)^{14-1})\\\\=1-((1)(0.8)^{14}+(14)(0.2)(0.8)^{13})\\\\=0.802087907\approx0.8021[/tex]

Hence, the required probability = 0.4365

Answer:

8,000-24x

Step-by-step explanation:

Let

y ----> depreciated value of the car

x---> rate of depreciation

t ----> the time in months

we know that

The linear equation that represent this situation is

y=8,000-xt

For

t=2 years=2*12=24 months

substitute

y=8,,000-x(24)

y=8,000-24x