A mechanic buys 1 gallon of oil. She uses of the oil and then equally divides the rest into 4 smaller bottles. How much does the mechanic put into each bottle? ​

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Answer:

9\(\sqrt{2}\)

Step-by-step explanation:

9^2 = 81

81 + 81 = 162 = 9\(\sqrt{2}\)

Answer:

mean: 220

median: 219

mode: 195

lower extreme: 157

upper extreme: 270

range: 113

lower quartile: 200.5

upper quartile: 241

interquartile range: 40.5

Step-by-step explanation:

(for the box and whisker plot look up examples and list the quartile ranges)

We have shown that there exists an element r in R (namely -1) such that there is no x in R satisfying f(x) = r. This means that f is not onto.

To prove that a function is not onto, also known as not surjective, we need to find at least one element in the codomain that doesn't have a preimage in the domain.

In this case, we chose the element r = -1 in the codomain R. We then showed that there is no real number x in the domain R such that f(x) = -1. This means that the element -1 does not have a preimage under f, and hence f is not onto.

Another way to look at it is that the range of the function f is the set of non-negative real numbers. Since -1 is not a non-negative real number, it is not in the range of f. Therefore, f is not onto.

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Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

5:7

5/7

5 to 7

10:14 --> 10x2=20 14x2=28

20:28 --> 20x2=40 28x2=56

40:56

Answer:

? = -36

Step-by-step explanation:

When you raise an exponent to an exponent, the resulting power is a product of the two exponents.

For this problem, you can solve for the missing value by writing:

\(?*1/3=-12\)

Divide both sides by 1/3 to isolate the missing value.

\(?=\frac{-12}{1/3}\)

Solve for ?.

\(?=-36\)

Answer:

3 1/12

Step-by-step explanation:

To solve the given system of congruences using the Chinese Remainder Theorem (CRT), the following steps need to be followed.

Step 1: First, we need to write the given system of congruences in the form of X ≡ a1(mod m1), X ≡ a2(mod m2), and X ≡ a3(mod m3).X = 1 (mod 5) --- (1)X = 2 (mod 6) --- (2)X = 3 (mod 7) --- (3)Here, a1, a2, a3 are 1, 2, 3, respectively, and m1, m2, m3 are 5, 6, and 7, respectively.Step 2: Then, we need to find the values of M1, M2, and M3, which are the products of the two remaining moduli (i.e., M1 = m2m3 = 6×7 = 42, M2 = m1m3 = 5×7 = 35, and M3 = m1m2 = 5×6 = 30).Step 3: After this, we need to calculate the values of N1, N2, and N3, which are the modular inverses of M1, M2, and M3, respectively, with respect to m1, m2, and m3, respectively, using the following formulas:N1M1 ≡ 1 (mod m1), N2M2 ≡ 1 (mod m2), N3M3 ≡ 1 (mod m3)The values of N1, N2, and N3 can be found using the Extended Euclidean Algorithm (EEA).M1 = 42, m1 = 5, 42 = 8(5) + 2, 2 = 42 - 8(5)N1 ≡ 2 (mod 5)M2 = 35, m2 = 6, 35 = 5(6) + 5, 5 = 35 - 5(6)N2 ≡ 5 (mod 6)M3 = 30, m3 = 7, 30 = 4(7) + 2, 2 = 30 - 4(7)N3 ≡ 4 (mod 7)Step 4: Finally, we need to find the value of X by substituting the values of a1, a2, and a3, M1, M2, and M3, and N1, N2, and N3, respectively, in the following formula:X = a1M1N1 + a2M2N2 + a3M3N3X ≡ 1(42)(2) + 2(35)(5) + 3(30)(4)≡ 84 + 350 + 360≡ 794(mod 210)Therefore, the solution of the given system of congruences using the Chinese Remainder Theorem is X ≡ 794(mod 210).

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The correct answer by Using The Chinese Remainder Theorem to solve the given system of equations is 135.

The Remainder Theorem is used to calculate the remainder that occurs when one polynomial is divided by another of the form x-a.

Given the system:

X = 1 (Mod 5)X = 2 (Mod 6)X = 3 (Mod 7)

Let us solve the given system using the Chinese Remainder Theorem.

First, we'll need to find the value of N.  N = 5*6*7 = 210

Since we have:

x ≡ 1 mod 5x ≡ 2 mod 6x ≡ 3 mod 7

We can find the values of Y1, Y2, and Y3 as follows:

Since 6 * 7 = 42 ≡ 1 (mod 5), we know that: 2 * 42 ≡ 2 (mod 5)

Therefore, we have: Y1 = 2 * 42 ≡ 84 ≡ -1 (mod 5)

Similarly, since 5 * 7 = 35 ≡ 1 (mod 6), we know that: 1 * 35 ≡ 1 (mod 6)

Therefore, we have: Y2 = 1 * 35 ≡ 35 ≡ -1 (mod 6)

Since 5 * 6 = 30 ≡ 2 (mod 7), we know that: 4 * 30 ≡ 1 (mod 7)

Therefore, we have: Y3 = 4 * 30 ≡ 120 ≡ 3 (mod 7)

Therefore, we can calculate the solution using the Chinese Remainder Theorem as follows:

x = [1(-1)Y1 + 2(-1)Y2 + 3(3)Y3] mod 210

x = (-1)(84) + (-1)(35) + (3)(120) mod 210

x = 135 mod 210

Therefore, x = 135 satisfies the given system.

Thus, the solution is x = 135.

Therefore, the Chinese Remainder Theorem is used to solve the given system of equations.

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Answer:

-2

Step-by-step explanation:

The piece of pasta he started with was 34 inches long.

Defining a problem, identifying its underlying cause, locating, ranking, and selecting potential solutions, as well as putting those ideas into practice, are all steps in the issue-solving process. Diagnose the circumstance to keep your attention on the issue and not merely its symptoms.

Let x be the length of the original piece of pasta.

After taking bites, he has (x - 3) pieces of pasta, each 17/10 inches long.

So, the total length of all pieces of pasta is (x - 3) * 17/10 = 17 inches.

Therefore, x = 10 * 17/7 + 3 = 34 inches.

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Reasoning:

g(x) = 4*ln(x)

g(x) = 2*2ln(x)

g(x) = 2*f(x)

Whatever the output f(x) is, it is doubled to get g(x). Recall that y = f(x), so we're really doubling the y values to visually stretch it vertically by a factor of 2. In short, g(x) is twice as tall compared to f(x).

Answer:

C. g(x) stretches f(x) vertically by a factor of 2.

Step-by-step explanation:

a p e x

Answer:

3217.00

Step-by-step explanation:

V=πr^2h=π·8^2·16≈3216.99088

Answer:

804.2 or 803.8

Step-by-step explanation:

volume = π · r2 · h

π · \(4^{2}\) · 16 = 804.2

3.14 · \(4^{2}\) · 16 = 803.8

To determine how many pieces of the press must be purchased, we need to consider the production rate, operating hours, efficiency, and scrap rate.

Number of units processed per day = 10,000

Machine efficiency = 95%

Punching operation time = 10 seconds

Number of shifts per day = 2

Number of hours per shift = 8

To calculate the required number of presses, we can use the following formula:

Number of presses = (Number of units processed per day / (Machine efficiency * Number of shifts * Number of hours)) * (Punching operation time / 3600)

Number of presses = (10,000 / (0.95 * 2 * 8)) * (10 / 3600) = 52.08

Therefore, approximately 52 presses would be needed to meet the production requirements.

If the press has a scrap rate of 10%, we need to consider the effect of scrapped units on the required number of presses.

Number of scrapped units per day = 10,000 * 0.10 = 1,000

Number of units that can be reworked = 1,000 * 0.70 = 700

To modify the formula for the new scenario, we subtract the reworked units from the total units processed per day:

Number of units processed per day (after rework) = 10,000 - 700 = 9,300

Number of presses (after considering scrap and rework) = (9,300 / (0.95 * 2 * 8)) * (10 / 3600) = 48.48

Therefore, approximately 48 presses would be needed when considering the scrap rate and rework capability.

The new answer is different from Exercise 11 because the scrap rate reduces the effective production rate, resulting in a lower requirement for punch presses. By accounting for scrap and rework, the company can optimize its resource allocation and production planning to meet the desired output while considering the potential loss due to scrap.

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A small freezer costs $100,000 in cash and $139,360 by hire purchase.

Hire purchase refers to a payment system by which the purchaser of an item makes regular installment payments, which include finance charges.

Retailers require a downpayment or initial deposit to offer customers hire purchases.

The cash price of a small freezer = $100,000

Hire purchase costs:

Deposit (downpayment) = $62,560

Installment period = 24 months

Installment amount = $3,200

Total installment payments = $76,800 ($3,200 x 24)

The total cost under hire purchase = $139,360 ($62,560 + $76,800)

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It can be brought on hire purchase by depositing $62,560 and 24 monthly installments of $3,200.

Answer: m = 4/7

Step-by-step explanation:

x = m

y = 2m+1

so

x+3y = 7

or, m+3(2m+1) = 7

or, m + 6m+3 = 7

or, 7m = 4

so m = 4/7

Answer:a

Step-by-step explanation:hhehenndherndur

Answer:

n=9

Step-by-step explanation:

You use reverse PEMDAS.

First you would divide by 3 on both sides. This should give you:

n²=81

Then you would find \(\sqrt{81}\). Which is 9.

Answer:

Minor Arc AC = 360 - 235 = 125°

\(mABC = \frac{Major \ arc - Minor \ arc}{2} = \frac{235 - 125}{2} = \frac{110}{2} = 55\)

Given :

B is between A and C

AB= x²-6x

BC= x²+20x

AC= 60-12x

B divide into 2 equal parts

AB and AC are equal

AC = AB +BC

60-12x = x²-6x + x²+20x

\(60= 2x^{2} -6x +20x +12x\)

\(60 = 2x^{2} -6x +32x\\\)

\(60= 2x^{2} +26x\)

\(30 = x^{2} +13x\\\\\)

\(x^{2} +13x -30 = 0\\x^{2} +15x-2x-30 =0\)

\(x(x+15) -2 (x+15) =0\)

\((x-2) (x+15) =0\\\)

x=2 , x=-15

x never be negative the x is 2

BC =  x²+20x

BC = 2*2 +20*2

BC = 4 +40

BC = 44

length of BC =44

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The formula of time is time: distance/speed

Time is an important concept in physics, and it can be expressed in a variety of ways. The most common way to describe time is with the equation t = d/s, where t is time, d is the change in position of an object, and s is the speed of the object. This equation is known as the time-distance formula.  The time-distance formula can be used to calculate the time it takes for an object to travel a certain distance., also the time-distance formula can also be used to calculate the distance an object travels in a certain amount of time.

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Answer: Where is the picture?

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.1 hours is 126 minutes. he drove 125 miles in 126 minutes. now we need to find out how much joseph can drive per a steady amount of time. in 6 minutes, he will drive about 5.95 miles. there are 360 minutes in 6 hours. 360/6 is 60 (just doing this again). 60 times 5.95 is 357.

The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.

We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.

The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.

The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.

Therefore, the probability that neither Betty is first in line nor Mary is last in line is

[(n-2)! / n!] = 1/n(n-1)

The probability we want is

1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)

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The given question is incomplete, the complete question is:

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.

What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.

The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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m = 1/4 = slope

b = 3/4 = y intercept

===================================================

Explanation:

The goal is to solve for y.

Divide both sides by 4 and simplify like so

4y = x+3

4y/4 = (x+3)/4

y = (x+3)/4

y = x/4 + 3/4

y = (1/4)x + 3/4

This equation is in slope intercept form y = mx+b

m = 1/4 is the slope

b = 3/4 is the y intercept

The graph is a straight line that goes through (1,1) and (5,2)

Answer:

3/8

Step-by-step explanation:

= (1/4 + 1/2 )/2

= 3/4 ÷ 2

= 3/(4×2)

= 3/8 (final answer)

Answer:

3/8

Step-by-step explanation:

Answer:

y = -4

Step-by-step explanation:

All you need to do is substitute -2 in for the x's in the equation. This gives you

y = -2(2) + 2 -2

y = -4

The equation x^2 - 5x + 7 = 0 has no real roots.

We know that the general form of a quadratic equation is:

ax^2 + bx + c =0

The equation we have is:

x^2 - 5x + 7 = 0

On comparing the given equation with the general form of a quadratic equation, we get that:

a = 1, b= -5, and c = 7

If D = b^2 - 4ac < 0, then the roots of the quadratic equation are imaginary or there are no real roots.

Therefore, b^2 - 4ac = (-5)^2 - 4x1x7 = -3<0.

Hence, we conclude that the nature of the roots of the give equationis imaginary, thus it has no real roots.

The question is incomplete, the complete question is x^2 - 5x + 7 = 0

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