The heights of young American women, in inches, are approximately Normally distributed with mean μ and standard deviation σ = 2.4. If I want to construct a 99% confidence interval with a margin of error of no more than ± 1 inch, what is the smallest sample I can select?

Answer:

Step-by-step explanation:

Answer:

for a vertical line the value of x, in this case 9, will never change. this will be true for any value of y. therefore the equction for vertical line line passing through this point is; x=9 likewise, for a horizontal line the value of y, in this case -4 will never change. this will be true for any value of x. therefore the equation for a horizontal line passing through this points is; y=-4

Step-by-step explanation:

hope this helpful and you welcome!

tell me if you have anything to help you with.

Answer:

47

Step-by-step explanation:

Let's solve your equation step-by-step.

−4x−3(−44−23)=13

Step 1: Simplify both sides of the equation.

−4x+201=13

Step 2: Subtract 201 from both sides.

−4x+201−201=13−201

−4x=−188

Step 3: Divide both sides by -4.

−4x

−4

=

−188

−4

x=47

Answer: 76°

Step-by-step explanation: The 76° and X are Alternate Interior Angles hence they are congruent to each other.

H(x) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. H(x) can take any value between 0 to 12.

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\). O(x) is a probability distribution of the random variable x. The expected value of x is 2.4. The standard deviation of x is 1.385.

Explanation: Given, the number of applicants (n) = 12.

The probability of a lie detector test suggesting a truthful person as deceptive = 0.2.

The probability of a lie detector test suggesting a truthful person as truthful = 0.8.

Let x be the number of people who the lie detector says are being deceptive.

a) The distribution of x (the number of people who the lie detector says are being deceptive) is binomial because the following conditions are satisfied: There are n independent trials, where n = 12.

Each trial has only two possible outcomes – either the lie detector test suggests that the applicant is deceptive or the lie detector test suggests that the applicant is truthful. The probability of the lie detector test suggesting that a truthful person is deceptive (p) remains the same in each trial, where p = 0.2. The outcomes of each trial are independent of each other. Therefore, the distribution of x is given by:

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\)

Where C is the symbol of combination. It can be calculated as follows:

\(C = (12Cx) = 12! / [x! \times (12 - x)!]\)

b) The expected value of x is given by:

E(x) = np

E(x) = 12 × 0.2

= 2.4

The standard deviation of x is given by:

\(\sigma(x) = \sqrt{np(1-p)}\)

\(\sigma(x) = \sqrt{12 \times 0.2 \times 0.8}\)

σ(x) = √(1.92)

σ(x) = 1.385

Hence, H(x) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Here, H(x)  can take any value between 0 to 12.

\(O(x) = (12Cx)(0.2)^x(0.8)^{(12-x)]\)

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the mathematical property demonstrated is associative property (3rd option)

Given:

To find:

the mathematical property

The property with the same arrangement as the given expression is associative property as it has to do with grouping.

Hence, the mathematical property demonstarted is associative property (3rd option)

The domain of a function is the set of all inputs for which the function remains valid. Since the graph shows the number of coffee stores after 1992. The domain will only makes sense for positive numbers, since a negative year doesn't make any sense. Therefore, the domain is:

The largest possible value of the expression (12 - x)/3x is 3.

Expression

In algebra, expression is the combination of variables, numbers and constants.

Given,

Here we have the expression (12 - x)/3x.

Now we have to find the  largest possible integer value.

As we have given in the question that the x takes only the non negative integer, then the values must be 1, 2, 3, ….

So, we have to apply the values on the given expression ,

Then we get the values,

=> x = 1 = > (12 - 1)/3(1) = 11/3 = 3.6

=> x = 2 => (12 - 2) / 3(2) = 10/6 = 1.6

=> x = 3 => (12 - 3) / 3(3) = 9/9 = 1

Therefore, the resulting value is 3.

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The executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

Let x be the number of days the executive stayed in London, y be the number of days he stayed in Paris, and z be the number of days he stayed in Rome.

We can set up the following equations to represent the given information:

180x + 230y + 160z = 2660 (hotel bills)

110x + 120y + 90z = 1520 (meal expenses)

x = y + z (he spent as many days in London as he did in Paris and Rome combined)

We can rearrange the third equation to get y + z - x = 0 and substitute it into the first two equations to eliminate x:

180x + 230y + 160z = 2660

110x + 120y + 90z = 1520

-180y - 180z + 180x = 0

Adding the first and third equations gives us:

360x + 50y - 20z = 2660

Adding the second and third equations gives us: 290x - 60y - 90z = 1520

We can now solve for x by multiplying the first equation by 3 and the second equation by 5 and subtracting them:

1080x + 150y - 60z = 7980

-1450x + 300y + 450z = 7600

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

1630x - 150y - 510z = 380

Solving for x gives us:

x = (150y + 510z + 380) / 1630

Substituting this back into the third equation gives us:

y + z - (150y + 510z + 380) / 1630 = 0

Multiplying by 1630 and rearranging gives us:

1480y + 490z = 380

We can now solve for y by multiplying the first equation by 490 and the second equation by 50 and subtracting them:

490(360x + 50y - 20z) = 490(2660)

50(290x - 60y - 90z) = 50(1520)

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

19600x + 24500y - 9800z = 1303400

-14500x + 3000y + 4500z = 76000 --------------------------------------------------

4100x - 21500y - 14300z = 1227400

Solving for y gives us:

y = (4100x + 14300z - 1227400) / 21500

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480(4100x + 14300z - 1227400) / 21500 + 490z = 380

Multiplying by 21500 and rearranging gives us:

606800x + 2054200z - 1817320000 = 0

Solving for z gives us:

z = (1817320000 - 606800x) / 2054200

Substituting this back into the equation x = y + z gives us:

x = y + (1817320000 - 606800x) / 2054200

Multiplying by 2054200 and rearranging gives us: 606800x^2 - 2054200xy - 2054200x + 1817320000y + 3707618640000 = 0

Using the quadratic formula, we can find the value of x:

x = (2054200y + 2054200 ± √[(2054200y + 2054200)^2 - 4(606800)(1817320000y + 3707618640000)]) / (2*606800)

Plugging in the value of y from earlier gives us:

x = (2054200(4100x + 14300z - 1227400) / 21500 + 2054200 ± √[(2054200(4100x + 14300z - 1227400) / 21500 + 2054200)^2 - 4(606800)(1817320000(4100x + 14300z - 1227400) / 21500 + 3707618640000)]) / (2*606800)

Simplifying and solving for x gives us:

x = 10

Substituting this back into the equation x = y + z gives us:

10 = y + z

Substituting this back into the equation 1480y + 490z = 380 gives us:

1480y + 490(10 - y) = 380

Solving for y gives us:

y = 6

Substituting this back into the equation 10 = y + z gives us: 10 = 6 + z

Solving for z gives us:

z = 4

Therefore, the executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.

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Step-by-step explanation:

\((a + {b)}^{2} = {a}^{2} + 2ab + {b}^{2} \)

Step-by-step explanation:

Answer:

Point D

Hope it helps! <3

Answer:

The measure of the vertex angle is 100°

Step-by-step explanation:

In Δ MNO

∵ Δ MNO is an isosceles triangle with base MO

∴ NM = NO

→ In an isosceles triangle, the base angles are equal in measures

∵ ∠M and ∠O are the base angles isosceles ΔMNO

∴ m∠M = m∠O

∵ m∠M = (3x + 10)°

∵ m∠O = (5x - 10)°

→ Equate their measures

∴ 5x - 10 = 3x + 10

→ Add 10 to both sides

∵ 5x - 10 + 10 = 3x + 10 + 10

∴ 5x = 3x + 20

→ Subtract 3x from both sides

∴ 5x - 3x = 3x - 3x + 20

∴ 2x = 20

→ Divide both sides by 2 to find x

∵ \(\frac{2x}{2}\) = \(\frac{20}{2}\)

∴ x = 10

→ Substitute the value of x in the measures of ∠M and ∠O to find them

∵ m∠M = 3(10) + 10 = 30 + 10

∴ m∠M = 40°

∵ m∠O = 5(10) - 10 = 50 - 10

∴ m∠O = 40°

→ The sum of the measures of the interior angles of a Δ is 180°

∵ m∠M + m∠O + m∠N = 180°

∵ 40 + 40 + m∠N = 180

→ Add the like terms

∴ 80 + m∠N = 180

→ Subtract 80 from both sides

∴ 80 - 80 + m∠N = 180 - 80

∴ m∠N = 100°

∵ ∠N is the vertex angle of Δ MNO

∴ The measure of the vertex angle is 100°

The value of the function f(−2/3) will give the value 8/3.

A function is important to show the expression that's given.

Given: f(x) = 3x^2 −5x−2.

To find f(-2/3), we substitute x = -2/3  into the equation:

f(-2/3) = 3 x (-2/3)^2  - 5(-2/3) - 2

         = 3 x 4/9 + 10/3 -2

         = 12/9 + 10/3 - 2

         = (12 + 30 - 18) / 9

         = 24 /9

        = 8/3

Therefore, f(-2/3) evaluates to 8/3.

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Answer:1700

Step-by-step explanation:

Answer:

50:75

Step-by-step explanation:

2+3=5

125/5=25

25*2=50

25*3=75

50:75

Hope this helped! :)

Answer:

If two of the angles are the same, the third angle is the same and the triangles are similar.

Step-by-step explanation:

If two of the angles are the same, the third angle is the same and the triangles are similar.

The situations that can be modeled by uniform distribution include;

Option 2) is: When each discrete value is

equally likely to occur.

Option 3) is:  When each value of a continuous random variable is equally likely to occur.

Since each value has an equal chance of occurrence, thus this situation can be  modelled by Uniform distribution.

Since each value of a continuous random variable is equally likely to occur, that it follows a continuous uniform distribution.

A uniform distribution is a type of probability distribution in statistics in which all outcomes are equally likely. A deck of cards has uniform distributions because the chances of drawing a heart, a club, a diamond, or a spade are all equal. When you sample a random element, you do so according to some distribution.

The term "uniformly" refers to sampling from a uniform distribution, i.e., from a set in which drawing each element is equally likely. In statistics, it is a type of probability distribution in which every possible outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

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Answer:

Yes this is true.

Step-by-step explanation:

If you took a true ''if-then'' statement, inserted a not in each clause and reversed the clauses, the new statement would also be true - yes this is true.

If the conditional (if, then) is true, then the contra- positive (reversed; if not, then not) will be also true.

Example:

Statement 1: If you study hard, then you get good grades.

Statement 2: If you do not study hard, then you do not get good grades.

We can see that these sentences are same.

So, the answer is true.

Answer: Yi did not list all the factors of 63

Step-by-step explanation:

Given That :

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

Factors of 63: 1, 7, 9, 63

The greatest common factor is 7

Find the error in the calculation above :

Not all factors of 63 were listed

Answer:

Yi did not list all the factors of 63. or B/2

I took the test (Edge 2020/2021) :)

Step-by-step explanation:

Answer:

4h

Step-by-step explanation:

Expression: 4h-8h=4h

Because both 4h and 8h end in the same variable they can be subtracted when you subtract 4 and 8 you get 4. and You can't forget your variable so you end with 4h

Your expression is a group of terms without an equal sign. 4h and 8h are your terms as well as your answer.

Your expression ends as 4h-8h=4h

Answer:

2296 unit^2

Step-by-step explanation:

The area is the sum of the  6 rectangles in the net.

= 38*10 + 38*16 + 38*10 + 38*16 + 10*16 + 10*16

= 380 + 608 + 380 + 608 + 160 + 160

= 2296.

Answer:

The surface area is 8

and volume is 12.

Let me know if wrong!! :))

Step-by-step explanation:

Answer:

1+2=3 is answer

Step-by-step explanation:

so what help u need?

hope this helps you out if i doesnt just comment and ill see what i can do

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of surface areas and volumes.

To get the volume of the whole irregular shape, we have to divide it into two regular parts, find the individual volume and then add up them to getthe whole volume.

Here we divide it into two separate parts. so we get as,

after solving, we get total volume as 1140 cm^3

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

D. (0, 9.5) and (10, 1.5)

Step-by-step explanation:

The line of best fit, runs closest to most points.

i hope this helps :)

(0, 9.5) and (10, 1.5) can be joined to draw most accurately the line of best fit on this scatter plot.

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

It is that line which is closest to all the points. For example, in this question, the line joining points (0,9.5) and (10,1.5) is the line of best fit.

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Answer:

1:6

Step-by-step explanation:

Answer:

1/6.... 1:6.... one to six

Henry needs to wait approximately 8 years before he can afford to buy a car that costs $12,430, assuming he doesn't make any additional deposits or withdrawals from his bank account.

The number of years Henry needs to wait before buying a car, we can use the formula for compound interest and solve for the number of years.

The formula for compound interest is:

Future Value = Present Value × (1 + Interest Rate)^n

Present Value (PV) = $5,500

Future Value (FV) = $12,430

Interest Rate (r) = 9% (0.09)

We want to find the number of years (n).

Rearranging the formula, we have:

(1 + r)^n = FV / PV

Substituting the given values, we get:

(1 + 0.09)^n = $12,430 / $5,500

Simplifying the equation:

1.09^n = 2.260

To solve for n, we can take the logarithm of both sides:

n × log(1.09) = log(2.260)

Dividing both sides by log(1.09):

n = log(2.260) / log(1.09)

Using a calculator, we can calculate:

n ≈ 8.12 (rounded to two decimal places)

Therefore, Henry needs to wait approximately 8.12 years before buying the car.

Using the formula for compound interest, we can calculate the number of years Henry needs to wait before buying a car.

In this case, the present value of Henry's bank account is $5,500, and the future value needed for the car is $12,430. The interest rate is 9% (0.09).

By rearranging the formula and substituting the given values, we obtain the equation (1 + 0.09)^n = $12,430 / $5,500.

Simplifying further, we have 1.09^n = 2.260.

To solve for n, we take the logarithm of both sides. Dividing both sides by log(1.09), we find n = log(2.260) / log(1.09).

Calculating this expression using a calculator, we get approximately 8.12 years.

Therefore, Henry needs to wait approximately 8.12 years before buying the car.

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