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Answer:

The point estimate for the true difference between the population means is 0.13.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Step-by-step explanation:

To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.

This means that:

\(\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325\)

A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.

This means that:

\(\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753\)

Difference between the true mean ages for cars owned by students and faculty.

Distribution s - f. So

\(\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13\)

This is also the point estimate for the true difference between the population means.

\(s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912\)

90% confidence interval for the difference:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = zs = 1.645*0.2912 = 0.48\)

The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years

The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

∑ Hey, claudiavg2000 ⊃

Answer:

No solutions.

Step-by-step explanation:

Given:

-2(x-2)-4x=3(x-1)-9x​

Solve:

-2 ( x - 2 ) - 4x : -6x + 4

3(x - 1) - 9x : -6x - 3

Now we have;

-6x + 4 = -6x - 3

Subtract 4 from both sides:

-6x + 4 - 4 = -6x - 3 - 4

-6x = -6x -7

Add 6x to both sides:

-6x + 6x = -6x - 7 + 6x

Simplifying:

0 = -7

As you can see the sides are not equal.

Hence, This problem has no solution.

xcookiex12

8/18/2022

The number of horse is 1, goat is 2 and sheep is 3 a man has.

The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.

Now w consider x to be the number of sheep, y to be the  number of  goats, and z to be the number of horses the man owns.

the actual equation for the total number of animals he owns  is :

x+ y+ z

according to the first condition:

that all sheep bar three, means

y+ z=3

similarly, for the other condition, it will be

x+ z=4   and x+ y=5

Now we adding the three  equations:

y + z +x +z +x +y=5+4 +3

2(x+y+z)=12

x+y+z=6........equation(1)

As x + y = 5

Put this in equation in (1), we get

x+y+z = 6

5 + z = 6

z = 1

x + z = 4

x + y + z = 6

y + 4 = 6

y = 2

Now we know

x + y + z = 6

x + 1 + 1 = 6

x = 4

So simplifying the other equation  we get, that the number of horse is 1, goat is 2, and sheep is 4.

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Answer::2,075,673,600 batting orders may occur.

Step-by-step explanation: A baseball team has 4 pitchers, who only pitch, and 12 other players, all of whom can play any position other then pitcher.

If one of the roots is \(w=B+2i\), then the other root is its conjugate \(\bar w=B-2i\). So we can factorize the quadratic to

\(z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))\)

Expand the right side and collect all the coefficients.

\(z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4\)

From the \(z\) and constant terms, we have

\(\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}\)

From the second equation we get

\(B^2 = 16 \implies B = \pm4\)

Then

\(4+(A+1)i = \pm8\)

\((A+1)i = 4 \text{ or } (A+1)i = -12\)

Since \(\frac1i=-i\), we have

\(-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12\)

\(A+1 = -4i \text{ or } A+1 = 12i\)

\(\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}\)

Answer:

length TR = 6

Step-by-step explanation:

Length TL = 24

scale ratio = 3:4:5

T-------R--------V----------L

find: TR

24 / (3+4+5) = 2

length TR at 3 x 2 = 6  

length RV at 4 x 2 = 8

length VL at 5 x 2 = 10

a total of 6 + 8 + 10 = 24

therefore,

length TR = 6

Answer:

B. Data are collected about a population.

Step-by-step explanation:

Data collected isn't experimenting. Experimenting is when you modify certain things in the population, not just take data from it. Hence, option b is just observation, not experimenting.

The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

the distance between 1.8 & 9.4=9.2

Answer:

Option D

Step-by-step explanation:

If the bases are the same in a multiplication problem, then you can simply add the exponents. (i.e., a² × a⁶ = a²⁺⁶ = a⁸)

\(\bullet \rightarrow 5^4\times5^7\)

\(\bullet\rightarrow 5^{4 + 7}\)

\(\bullet \rightarrow \boxed{5^{11}}\)

Answer: D

Step-by-step explanation:

5^4 x 5^7

You will add the exponent 4 + 7 = 11

You will keep your base 5^11

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

the answer to your question is

6 2/3 if you were dividing 60 ÷ 9 that is

Answer:

q=0.5 or 1/2

Step-by-step explanation:

5q-21/14=1

add 21/14 to both sides

5q=2.5

divide both sides by 5

q=0.5 or 1/2

Answer:

the first (top) answer option. ... = 129/100

Step-by-step explanation:

the for me qualifying or disqualifying term is the constant term as the product and sum of all the constant parts.

the general form has the constant parts

... + 1 = 0

so, all the constant terms from the squares on the left side minus the constant term on the right side must be 1.

let's start from the bottom : the 4th answer option.

the constant parts are

... + (-1/5)² + ... + (3/2)² = 121/100

... + 1/25 + ... + 9/4 = 121/100

... + 0.04 + ... + 2.25 = 1.21

... + 2.29 - 1.21 = ... + 1.08

and NOT 1. so, this is wrong.

the 3rd answer option.

... + (-1/3)² + ... + (-3/2)² = 221/100

... + 1/9 + ... + 9/4 = 221/100

... + 0.111111... + ... + 2.25 = 2.21

... + 0.111111... + ... + 2.25 - 2.21 = 0

... + 0.111111... + ... + 0.04 = 0

... + 0.111111 + 0.04 = 0.15111111...

and NOT 1. so, this is wrong.

the 2nd answer option.

... + (-1/5)² + ... + (3/2)² = 229/100

... + 1/25 + ... + 9/4 = 229/100

... + 0.04 + ... + 2.25 = 2.29

... + 2.29 - 2.28 = ... + 0

and NOT 1. so, this is wrong.

the first answer option.

... + (-1/5)² + ... + (3/2)² = 129/100

... + 1/25 + ... + 9/4 = 129/100

... + 0.04 + ... + 2.25 = 1.29

... + 2.29 - 1.29 = ... + 1

this IS 1. so, this is correct.

this corresponds now to the original

... + 1 = 0

Answer: Choice A (May vary from test to test)

Step-by-step explanation:

(x-1/5)^2 + (y+3/2)^2 = 129/100

Just an FYI:

We are given:

There were 7 chocolate bars, evenly shared between 4 friends

Number of Bars one person will get:

Number of bars one person will get = Number of Bars / Number of Friends

Number of Bars = 7 / 4

but since this number does NOT match any of the given options, we will convert it to a mixed fraction

The number of bars one person will get will be \(1\frac{3}{4}\), written as a mixed fraction.

Therefore, the correct answer is option D

Answer:

4 friends =7 chocolate

1 friend =7/4 chocolate =1 3/4 part of chocolate.

Using the equivalent decimals, the lake that lost  least amount of water is Lake Partlow

Lake Jensen lost 1/9 of its water

We have to convert the simple fraction to decimal form

1/9 = 0.11

Lake Partlow lost 10% of its water

The percentage is a number or ratio that can be represented as a fraction of 100.

10% = 10/100

= 0.1

Lake Stockton lost 21/200 of its water

Convert the simple fraction to decimal form

21/200 = 0.105

Lake Partlow lost 10% of its water. that is the least amount of water.

Hence, Using the equivalent decimals, the lake that lost  least amount of water is Lake Partlow

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After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.

To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:

Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)

where:

P = the initial loan amount (in this case, $219,000)

r = the monthly interest rate (which is the annual interest rate divided by 12)

n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)

b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)

First, we need to calculate the monthly interest rate:

r = 4.5% / 12 = 0.00375 = 0.375%

Next, we can plug in the values to get:

Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)

= $145052.36

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Answer: 3/2

Step-by-step explanation:

Answer:

3/2 or 1 1/2

Step-by-step explanation:

\(2\frac{1}{4}/1\frac{1}{2} \\\frac{9}{4}/\frac{3}{2} \\(\frac{9}{4})(\frac{2}{3})\\\frac{18}{12} \\\frac{3}{2} or 1\frac{1}{2}\)

The distance between point C and the perpendicular bisector of AB is 2√3.

Given points A(9, 2), B(5,6), and C(-3,-2).

We need to find the distance between point C and the perpendicular bisector of AB.

We first need to find the midpoint of line segment AB using the midpoint formula:

Midpoint of AB

= [(x1 + x2)/2, (y1 + y2)/2]

= [(9+5)/2, (2+6)/2]

= [(14/2), (8/2)]

= (7, 4)

Now, we need to find the slope of the line AB:

Slope of AB= (y2 - y1) / (x2 - x1)

= (6-2) / (5-9)

= 4/-4

= -1

So, the slope of the perpendicular bisector to AB is 1 (negative reciprocal of -1).

Now we need to find the equation of the perpendicular bisector of AB, which passes through (7, 4) with a slope of 1.

Using point-slope form of the line: y - y1 = m(x - x1)y - 4

= 1(x - 7)y - 4

= x - 7y

= x - 3

Now we have the equation of the perpendicular bisector of AB.

Now we can find the distance between C and the line by finding the length of the perpendicular from C to the line.

To do this, we need to find the equation of the line that is perpendicular to the line we found, which passes through point C, and then find the point where the two lines intersect.

This new line has a slope of -1, since it is perpendicular to the line with slope 1.

Using point-slope form of the line:

y - y1 = m(x - x1)y - (-2)

= -1(x - (-3))y + 2

= -x - 3y

= -x - 5

Now we have the equation of the new line.

Now we can find the point of intersection of the two lines:

y = x - 3y

= -x - 5

Adding the two equations:

2y = -8y

= -4

The point of intersection is (-4, -4).

Now we can find the distance between C and (-4, -4) using the distance formula:

Distance between C and (-4, -4) = √(x2 - x1)2 + (y2 - y1)2

= √((-3 - (-4))2 + (-2 - (-4))2)

= √(12)

= 2√3

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Answer:

I think its third answer..24=w*+5w

Therefore, the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83 is 75%, rounded to one decimal place.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It measures how spread out the data is from the mean or average value. A low standard deviation indicates that the data is closely clustered around the mean, while a high standard deviation indicates that the data is more spread out. It is calculated as the square root of the variance, which is the average of the squared differences from the mean.

Here,

Chebyshev's theorem states that for any dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations of the mean, where k is any positive number greater than 1. To find the minimum percentage of stores that sell a gallon of milk for between $3.27 and $3.83, we can first find how many standard deviations away from the mean these prices are:

$3.27 is (3.27 - 3.55)/0.14 = -2 standard deviations from the mean

$3.83 is (3.83 - 3.55)/0.14 = 2 standard deviations from the mean

Thus, the distance between $3.27 and $3.83 is 4 standard deviations (2 in each direction).

Using Chebyshev's theorem with k = 2 (since we want to know the minimum percentage within 2 standard deviations), we have:

=1 - 1/2²

= 1 - 1/4

= 0.75

This means that at least 75% of stores sell a gallon of milk for between $3.27 and $3.83.

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Answer:

0.125%

Step-by-step explanation:

To find the percentage, just move the decimal place two places.

Answer:

Answer is c or 0.0104.

Step-by-step explanation:

12.5/12= 1.04...

1.04/100= 0.0104

KN/NM = KL/LM

4/NM = 8/5

cross-multiply

Divide both-side of the equation by 8

Answer:

2

Step-by-step explanation:

every rectangular prism has 6 faces, 2 will be congruent together and thw other 4 will be congruent to each other

The compound inequality that represents the range of the actual weight of the object is 125.4 ≤ w ≤ 126.2.

Part A: The absolute value inequality that describes the range of the actual weight of the object is:

|w - 125.8| ≤ 0.4

Part B: To solve the absolute value inequality, we can break it down into two separate inequalities:

w - 125.8 ≤ 0.4 and - (w - 125.8) ≤ 0.4

Solving the first inequality:

w - 125.8 ≤ 0.4

Add 125.8 to both sides:

w ≤ 126.2

Solving the second inequality:

-(w - 125.8) ≤ 0.4

Multiply by -1 and distribute the negative sign:

-w + 125.8 ≤ 0.4

Subtract 125.8 from both sides:

-w ≤ -125.4

Divide by -1 (note that the inequality direction flips):

w ≥ 125.4

Combining the solutions, we have:

125.4 ≤ w ≤ 126.2

The object is 125.4 ≤ w ≤ 126.2.

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The polynomial that represents the area of the shaded region is given as follows:

x² - 3x + 36.

The area of a rectangle is given by the multiplication of the width and the length of the triangle, as follows:

A = lw.

For the entire region, the area is given as follows:

A = (x + 1)(x + 1)

A = x² + 2x + 1.

The area of the white region is given as follows:

Aw = 5(x - 7)

Aw = 5x - 35.

Then the area of the shaded region is given as follows:

As = A - Aw

A = x² + 2x + 1 - (5x - 35)

A = x² + 2x + 1 - 5x + 35

A = x² - 3x + 36.

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Answer:

18 meters = 1800 milimeters

Step-by-step explanation:

Hope this helps!      :3

plz mark as brainliest!

Answer:

Just search it up. The answer is 1800

Step-by-step explanation:

Type.

Or there's another way.... you multiply if you want to convert a unit that is greater to smaller, and you divide if you want to convert a smaller unit to a larger one.

For example hours to minutes:

You cross out the word that matches. Here it's hour.

3.15 hours X 60 min/1 hour=189 min

189min X 60 sec/1min=11340 sec

and if it's from smaller to greater you divide, get it?

Answer:

Median

Step-by-step explanation:

i think median would be better than mean. This is because with mean, your adding it together then dividing it(by 3 in this case), making the end number higher. tou dont want a higher number in this case.

ex: your numbers are 50, 55,and 90

median = 55 (as it's the middle number)

mean = 65 ( 90+ 55+ 50 / 3)

so median is the lower number, meaning it would be better in this** case.

Let's start by finding the rates at which the inlet and drain pipes can fill and empty the pool, respectively.

The rate of the inlet pipe is:

1 pool / 26 hours

The rate of the drain pipe is:

-1 pool / 27 hours (note the negative sign, indicating that it is emptying the pool)

When both pipes are open, the net rate of filling the pool is the sum of their rates:

1/26 - 1/27 = 1/702

This means that when both pipes are open, the pool is being filled at a rate of 1/702 of the pool per hour.

If the pool is 2/3 filled, then it still needs to be filled by 1/3 of its volume. Let's assume that the volume of the pool is V, so the amount of water that needs to be added to the 2/3 filled pool is:

(1/3)V

The time it takes to fill this amount of water is:

[(1/3)V] / [(1/702) pool/hour]

Simplifying this expression, we get:

(1/3)V x (702/1) hours/pool

234 hoursV / pool

Rounding this answer to two decimal places, we get:

234.57 hours (rounded to 2 decimal places)

Therefore, it would take approximately 234.57 more hours to fill the pool when both the inlet and drain pipes are open.

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