Please find it quickly

Answer:

To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Given that the sample size is n = 69, the mean diameter of the population is μ = 209 inches, and the standard deviation of the population is σ = 2.4 inches.

We need to find the probability that the mean diameter of the sample shafts would be less than 209.1 inches, which can be written as:

P(X < 209.1)

To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

Given that the sample size is n = 69, the mean diameter of the population is μ = 209 inches, and the standard deviation of the population is σ = 2.4 inches.

We need to find the probability that the mean diameter of the sample shafts would be less than 209.1 inches, which can be written as:

P(X < 209.1)

To standardize this value, we need to calculate the z-score as follows:

z = (X - μ) / (σ / sqrt(n))

z = (209.1 - 209) / (2.4 / sqrt(69))

z = 0.4639

We can now find the probability using the standard normal distribution table or a calculator:

P(Z < 0.4639) = 0.6779

Therefore, the probability that the mean diameter of the sample shafts would be less than 209.1 inches is approximately 0.6779, rounded to four decimal places.

In this case, the population mean is 209 inches, and the sample mean we're interested in is 209.1 inches. So the z-score would be:
z = (209.1 - 209) / 0.2898 = 0.3456
Therefore, the probability that the mean diameter of the sample shafts would be less than 209.1 inches is 0.6368, rounded to four decimal places.

To answer your question, we will use the Central Limit Theorem and the z-score formula. Here are the steps:

we can use the formula for the z-score of the sample mean, which is:
z = (sample mean - population mean) / standard error

1. Find the mean (μ) and standard deviation (σ) of the population.
  μ = 209 inches
  σ = 2.4 inches

2. Determine the sample size (n) and the mean diameter you want to calculate the probability for (x).
  n = 69
  x = 209.1 inches

3. Calculate the standard error (SE) of the sample mean using the formula: SE = σ / √n
  SE = 2.4 / √69 ≈ 0.2892

4. Calculate the z-score using the formula: z = (x- μ) / SE
  z = (209.1 - 209) / 0.2892 ≈ 0.3455

5. Find the probability that the mean diameter of the sample shafts would be less than 209.1 inches by looking up the z-score in a z-table or using a calculator that can compute normal probabilities.
  P(Z < 0.3455) ≈ 0.635

The probability that the mean diameter of the sample shafts would be less than 209.1 inches is approximately 0.6350 or 63.50%.

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Answer:

midpoint = (-3,-0.5)

Step-by-step explanation:

To work out the x-axis of the midpoint, take the two x-axis values of the coordinates given and find the difference of the two values. So the equation becomes 2--8 which equals 10. Now the midpoint means half way so we half 10 to get 5. Now we can take (2,-6)  and minus 5 from the x-axis to get the x-axis of the midpoint. 2 - 5 = -3. The x-axis of the midpoint is -3.

To work out the y-axis of the midpoint, take the two y-axis values of the coordinates given and find the difference of the two values. So the equation becomes -6-5=-11 Now the midpoint means half way so we half -11 to get -5.5. Now we can take (2,-6) and add 5.5 from the y-axis to get the y-axis of the midpoint. -6 + 5.5 =-0.5. The y-axis of the midpoint is -0.5

The probability of obtaining a head on the next toss of a coin after obtaining two heads from two tosses is still 1/2 or 50%.

This is because each coin toss is an independent event, and the outcome of one toss does not affect the outcome of another toss. Therefore, the fact that two heads have been obtained in the previous two tosses does not change the probability of obtaining a head on the next toss, which is always 1/2 or 0.5 for a fair coin.

Probability is the likelihood of an event occurring. The values are between 0 and 1. The closer it is to 1, the greater the probability.

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The 95% confidence interval for the average of the numbers in the box is 5.4 ± (1.984 × 0.2), or (5.0, 5.8).

To calculate the confidence interval for the average of the numbers in the box, we need to use the central limit theorem since we have a sample size of 100, which is relatively large. The central limit theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases.

We need to calculate the sample mean by dividing the sum of the numbers on the tickets by the sample size: 540/100 = 5.4.

We need to calculate the standard error of the mean, which is equal to the standard deviation of the population divided by the square root of the sample size. Since we do not know the standard deviation of the population, we can use the standard deviation of the sample instead:

[tex]2/ \sqrt{} (100)[/tex]

= 0.2.

The 95% confidence interval for the population mean can be calculated by multiplying the standard error of the mean by the critical value from the t-distribution with n-1 degrees of freedom (99 degrees of freedom in this case) and adding/subtracting this value from the sample mean.

Using a t-distribution table or calculator, we can find that the critical value for a 95% confidence level with 99 degrees of freedom is 1.984. This means we are 95% confident that the true population mean falls within this interval.

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The quarts of paint used by Mieko to paint his living room is equal to 3 quarts.

Total paint bought by Mieko = 2 gallons

Amount of paint used  to paint bedroom = 1/4 of the paint.

Amount of paint used on the hallway = 3 quarts

Since 1 gallon is equal to 4 quarts.

Convert gallons to quarts.

Mieko bought 2 gallons of paint, which is equivalent to 8 quarts

She used 1/4 of the paint on her bedroom,

which is 1/4 x 8 quarts = 2 quarts.

She also used 3 quarts of paint on the hallway.

This implies,

The total amount of paint used on the bedroom and hallway is equal to,

2 quarts + 3 quarts = 5 quarts

The amount of paint used in the living room is the remaining amount of paint is equal to,

8 quarts - 5 quarts = 3 quarts

Therefore, Mieko used 3 quarts of paint in the living room.

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The above question is incomplete, the complete question is:

Mieko bought 2 gallons of paint. She used 1/4 of the paint on her bedroom, 3 quarts on the hallway, and the rest of the paint in the living room. How many quarts of paint did Mieko use in the living room?

The value of the car decreases from year to year by 15%.

A kind of function that would explain this type of pattern is an exponential decay function [tex]f(x) = 10000(0.15)^x[/tex].

You need the decay rate to find the function the actuary is using.

In Mathematics and Statistics, a population or physical asset (car) that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or physical asset that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Next, we would determine the constant ratio in each representation as follows;

Constant ratio, r = a₂/a₁ = a₃/a₂ = a₄/a₃ = a₅/₄

Constant ratio, r = 8520/10,000 = 7213/8250 = 6,100/7213 = 768/192

Constant ratio, r = 85.

By substituting the given parameters, we have the following:

P(t) = I(1 - r)^t

f(x) = 10,000(1 - 85/100)^x

f(x) = 9,600(1 - 0.85)^x

f(x) = 9,600(0.15)^x

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The measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees in the triangle.

In a triangle, the sum of the measures of the three angles is always 180 degrees.

Let the angle enclosed by the 19 inch and 23 inch sides x.

The Law of Cosines states that for a triangle with sides a, b, and c, and angle C opposite side c:

c² = a² + b² - 2ab cos(C)

Let's choose the 27 inch side as side c.

Then we have:

27² = 19² + 23²- 2(19)(23)cos(x)

729 = 850 - 874cos(x)

-121 = -874cos(x)

cos(x) = 0.1386

x=81 degrees

Hence, the measure of the angle enclosed by the 19 inch and 23 inch sides is  81 degrees.

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Answer:

49 text messages

Step-by-step explanation:

3.49/68 = 0.05 oer text

we can use this unit rate for text sent $2.45

$2.45/.05 per text message = 49 text messages

Answer:

A ratio of 3:1 means that there are 4 parts altogether. The fractions from the ratio can therefore be deduced as. 43 and 41. These represent the percentages: 75%:25%

Answer:

Step-by-step explanation:

The ratio can be converted into a fraction

therefore we can divide by the denominator in order to convert 30 Euros to a 3:1 ratio.

The fraction =3/4 and 1/4

so we have to divide 30 by 4

= 7.5 Euros

so;

3:1

(22.5):(7.5)

(45/2):(15/2)

45:15

divide by 15

3:1

A slope of 15 simply means that the rate of change of the value on the y-axis with respect to the x-axis is equal to 15.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting an assumed data points into the slope formula, we have the following;

Slope (m) = (80 - 20)/(6 - 2)

Slope (m) = 60/4

Slope (m) = 15.

In this context, we can reasonably infer and logically deduce that a slope of 15 denotes the rate of change of a straight line on a graph.

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Answer:

MO/KO = NO/LO

5/10 = 3/LO

5/10 = 3/x

Step-by-step explanation:

Since KLO and MNO are similar, that means the corresponding sides share a common proportion:

Note how corresponding sides MO and KO are given measurements, that means we can find the common proportion by dividing MO/KO (which is 5/10). Knowing the proportion between the corresponding sides between MO and KO, we can find LO by finding its corresponding side and setting up a proportion. LO's corresponding side is NO (with a measurement of 3):

5/10 = 3/LO

Other options also work:

MO/KO = NO/LO               since MO = 5 units, KO = 10 units, & NO = 3 units

5/10 = 3/x                           since any value can be set to a variable, LO = x

Answer:

18 - x

Step-by-step explanation:

f(x) = 6 - x

g(x) = x/3 + 8

f(2x) = 6 - (2x) => 6 - 2x

g(3x + 9) = (3x+9)/3 + 9 = x + 3 + 9 => x + 12

(6 - 2x) + (x + 12)

Simplified:

18 - x

Given that the triangles are congruent, we can conclude that

From the question, we are to determine what can be concluded from the fact that triangle QGL and triangle BRN are congruent

If ΔQGL and ΔBRN are congruent, we can infer that

QG = BR

LG = NR

QL = BN

Also, in terms of angles

∠LGQ = ∠NRB

∠QLG = ∠BNR

∠LQG = ∠NBR

In addition,

If two triangles are congruent, the areas of the triangles will be equal to each other

Thus,

We can conclude that

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Answer:

Step-by-step explanation:

If 9 units = 36 inches,

then 9 ÷ 9 = 36 ÷ 9 inches

∴ 1 unit = 36/9 inches

Answer:

The answer is 4/1(in)

Step-by-step explanation:

1/9 yard to in

1yd=36in

1/9yards=4in

and

9unit=36in

1 unit=36/9

1unit=4in

therefore 1unit=1/9yards

a) Number of elements in sample size is 11.

b) Probability P(E) is 0.45.

a) The sample space is the set of all possible outcomes when drawing a single card from the deck. Since there are 11 cards in total, the sample space has 11 elements.

b) We want to find the probability of drawing an even-numbered card, which includes the red cards numbered 2, 4, and 6, and the black cards numbered 2 and 4. There are five such cards in total, so the probability of drawing an even-numbered card is:

P(E) = number of even-numbered cards / total number of cards

P(E) = 5 / 11

P(E) = 0.4545 or approximately 0.45

Therefore, the probability of drawing an even-numbered card from the deck is about 0.45.

Correct Question:

A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.

R = card drawn is Red

E = card drawn is even-numbered

a) How many elements are there in the sample space.

b) What is the probability P(E).

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The selling price of the item after a percentage of markup by 15 % is given by S = $ 23

Given data ,

Let the initial price of the item be A = $20

Now , let the selling price of the item after percentage mark up be S

where percentage markup = 15 %

So , the amount of markup is M = ( 15 )% x 20

M = 20 x 0.15

M = $ 3

And , the selling price S = A + M

S = $ 20 + $ 3

S = $ 23

Hence , the selling price is S = $ 23

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2880 minutes in 2 days.

One day has 24 hours in it.

One hour = 60 minutes

One day in minutes = 24*60 = 1440 minutes

Two days in minutes = 1440 * 2 = 2880 minutes.

Answer:

2880

Step-by-step explanation:

4320÷3=1440

1440+1440=2880

Hope this helps!

For the equation  x²+6x+8 the roots are -4 and -2.

The given equation is x²+6x+8

We have to find the roots of the equation

x²+6x+8

Let us factorize the equation to find the roots

x²+4x+2x+8

x(x+4)+2(x+4)

(x+2)(x+4)

x=-2 and x=-4 are the roots

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The expression that gives Angela the total amount of money she will make per hour is y = 10x + 25.

In equation y = 10x + 25, x represents the number of hours she babysits, and y represents the total amount of money she will make, which is equal to the flat rate of $25 plus $10 per hour.

So, for example, if she babysits for 3 hours, the total amount of money she will make is:

y = 10(3) + 25 = 30 + 25 = $55

Therefore, the correct answer is A, y = 10x + 25.

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Answer:24,000 pounds

Step-by-step explanation: a ton is 2,000 pounds so 12 times 2,000 is 24,000

Answer: figure ii

Step-by-step explanation:

The answers to the quadratic equations are as follows:

13. Option A. f(x) = x² - 4x + 5

14. Option A. fx = x 2 4x + 7

15. Option B. (-3, 2)

13. f(x) = x² - 4x + 5

Identify the coefficients

a = 1, b = -4

Substitute the coefficients into the expression

X = – (- 4)/2×1

Solve the equation

x = 2

Evaluate the function for x = 2

f(x) = x² - 4x + 5, x = 2

Calculate the function value

f(2) = 1

The vertex is at (2,1)

14. Option A. fx = x 2 4x + 7

Identify the coefficients

a = 1, b = -4

Substitute the coefficients into the expression

X = – (-4)/2×1

Solve the equation

x = 2

Evaluate the function for x = 2

X:

f(x) = x² - 4x + 7, x = 2

Calculate the function value

f(2) = 3

The vertex is at (2,3)

15. Option B. (-3, 2)

f(x) = x+x-6

Identify the coefficients

a = 1, b = 1

Substitute the coefficients into the expression

-1/ 2×1

Solve the equation

X = -1 /2

Evaluate the function for x = - ½

f(x) = x²+x-6, x = - ½

Calculate the function value

f (-½) = - 25/4

(-½, -25/4)

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Answer:

First, we need to move the constant term to the other side of the equation:

y + x^2 - 16x = -100

Next, we need to "complete the square" by adding and subtracting a constant term that will allow us to write the left-hand side of the equation as a perfect square. To do this, we need to take half of the coefficient of the x-term (-16), square it, and add that to both sides of the equation:

y + x^2 - 16x + 64 = -36 + 64

Now, we can simplify the left-hand side by factoring it as a perfect square:

(y + (x - 8)^2) = 28

So the equation, in completed square form, is:

y + (x - 8)^2 = 28

Step-by-step explanation:

gg

The slope and y-intercepts of each line, respectively, are:

5. m = -2; b = 6       6. m = 5/3; b = 10/3       7. m = -1/4; b = 4

Slope of a line is calculated as, m = change in y / change in x.

5. Given (2, 2) and (3, 0):

Slope of the line (m) = change in y / change in x = 2 - 0 / 2 - 3

m = 2/-1

m = -2

To find the y-intercept (b), substitute m = -2 and (x, y) = (2, 2) into y = mx + b:

2 = -2(2) + b

2 = -4 + b

2 + 4 = b

b = 6

6. Given (1,5) and (4, 10):

Slope of the line (m) = change in y / change in x = 10 - 5 / 4 - 1

m = 5/3

To find the y-intercept (b), substitute m = 5/3 and (x, y) = (1, 5) into y = mx + b:

5 = 5/3(1) + b

5 - 5/3 = b

b = (15 - 5)/3

b = 10/3

7. Given (8, 2) and (-8, 6):

Slope of the line (m) = change in y / change in x = 6 - 2 / -8 - 8

m = 4/-16

m = -1/4

To find the y-intercept (b), substitute m = -1/4 and (x, y) = (8, 2) into y = mx + b:

2 = -1/4(8) + b

2 = -2 + b

2 + 2 = b

b = 4

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The total number of students on the honor roll increased by approximately 19.3%.

What is percenatge?

Percentage is a way of expressing a fraction or a portion of a whole number as a portion of 100. It is often denoted by the symbol %. For example, 50% represents 50 parts out of 100, or 50/100, which simplifies to 1/2.

Let's first find the total number of students on the honor roll last year:

Total number of students on the honor roll last year = 100 (boys) + 50 (girls) = 150

This year, the number of boys on the honor roll increased by 19%, which means the new number of boys on the honor roll is:

New number of boys on the honor roll = 100 + 0.19(100) = 119

Similarly, the new number of girls on the honor roll is:

New number of girls on the honor roll = 50 + 0.20(50) = 60

Therefore, the total number of students on the honor roll this year is:

Total number of students on the honor roll this year = 119 (boys) + 60 (girls) = 179

The percentage increase in the total number of students on the honor roll is:

Percentage increase = [(Total number of students on the honor roll this year - Total number of students on the honor roll last year) / Total number of students on the honor roll last year] x 100%

Percentage increase = [(179 - 150) / 150] x 100% = 19.3%

Therefore, the total number of students on the honor roll increased by approximately 19.3%.

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The equation of the line that passes through (-2, -11) that is perpendicular to the given line is: y = 2x - 7.

Recall that the slope of a line is the change in y over the change in x along the line, and also, the slope of two lines that are perpendicular to each other will be negative reciprocals to each other.

Therefore, find the slope between (1, 1) and (5, -1):

Slope (m) = change in y / change in x = -1 - 1 / 5 - 1

m = -2/4

m = -1/2.

The line that is perpendicular to it will have a slope that is negative reciprocal to -1/2, which is 2.

Substitute m = 2 and (a, b) = (-2, -11) into y - b = m(x - a)

y - (-11) = 2(x - (-2))

y + 11 = 2(x + 2)

y + 11 = 2x + 4

y = 2x + 4 - 11

y = 2x - 7 (equation of perpendicular line)

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The value of a diagonal through the interior of the cube is, BG.

We have to given that;

A cube is shown in figure.

Now, By the given cube, We get;

The value of a diagonal through the interior of the cube is,

⇒ BG.

Thus, The value of a diagonal through the interior of the cube is, BG.

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