Convert 60 quarts to gallons. 60 qt = ? gal Will the converted amount have more or fewer units than the original? ​

Complete question is;

A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem?

The Central Limit Theorem tells us that for large sample sizes (in practice n > 30) the sampling distribution of the sample mean will be approximately normal.

A. The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30.

B. The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30.

C. The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30.

D. The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

E. The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30.

Answer:

D. The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.

Step-by-step explanation:

We are told that the Central Limit Theorem tells us that for large sample sizes (in practice n > 30) the sampling distribution of the sample mean will be approximately normal. Thus we can pick the correct option as follows:

Option A: This is not the correct answer because it is the sample size (n) that should be greater than 30 and not the population mean as stated.

Option B: This is not the correct answer because the distribution of the sample should correspond to the population shape for large samples because it's only the sampling distribution that is approximately normal.

Option C: This option is not correct because the sample is not meant to have any impact on the population.

Option D: This option is the correct answer because it fulfills the condition of the central limit theorem earlier described.

Option E: This is not the correct answer because just like in option A, it is the sample size (n) that should be greater than 30 and not the population mean as stated.

Answer:

[tex]m=\frac{7}{8}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-2, -2)

Point (-10, -9)

Step 2: Find slope m

Answer:

1/5, 2/9, 0/4

Answer:

x=1

Step-by-step explanation:

Using quadratic formula

Answer:

Monday: 2 hours

Tuesday: 7 miles

Thursday: 27 miles

Friday: 2 hours

Step-by-step explanation:

Monday: 16 divided by 8 = 2

Tuesday: 21 divided by 3 = 7

Thursday: 9 x 3 = 27

Friday: 16 divided by 8 = 2

I hoped this helped

Answer:

bottom rung 24cm. wide and the top rung

18cm. wide. If the length of the rungs decreases uniformly from bottom to top, how long

should each of the seven intermediate rungs be?

3,Find the first term of the sequence 10, 5, 2.5, 1.25, . . . which is less than 0.0001.

3,In an arithmetic sequence, if the p

th term is q and the q

th term is p, find the (p + q)

th term.

Answer:

-0.296296296296...

Answer:

TRUE/  −0.296296

Step-by-step explanation:

(-2/3)^3 = (-2/3) (-2/3) (-2/3) =

−0.296296=−0.296296

True

Answer:

A= 1.50x+75  B= 2.50x+45

Company A is cheaper than Company B when x > 30 miles.

Step-by-step explanation:

Company A charges$75 for the rental even when driving x=0 miles, and will charge and additional $1.50 per mile driven. Therefore the amount Company A would charge for xx miles is:

A=1.50x+75

Company B charges $45 for the rental even when driving x=0 miles, and will charge and additional $2.50 per mile driven. Therefore the amount Company B would charge for x miles is:

B=2.50x+45

When x takes less than 30 miles, Company A is cheaper than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.

A linear equation is defined as an equation in which the highest power of the variable is always one.

When driving x = 0 miles, Company A charges $75 for the rental and an additional $1.50 for each mile driven. Thus, the price that Company A would charge for x miles is as follows:

⇒ A = 1.50x + 75

When driving x = 0 miles, Company B charges $45 for the rental and an additional $2.50 for each mile driven. Thus, the price that Company B would charge for x miles is as follows:

⇒ B = 2.50x + 45

Hence, when x takes less than 30 miles, Company A is less expensive than Company B. This is the equation of price that companies i.e. A = 1.50x+75 and B= 2.50x + 45.

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Answer:

x > -1

See picture.

Step-by-step explanation:

[tex]-3x-5<-2\\\\-3x-5+5<-2+5\\\\-3x<3\\\\\frac{-3x<3}{-3}\\\\\boxed{x>-1}[/tex]

Hope this helps.

The solution of the given inequality -3x - 5 < -2 is x > -1.

Inequality is comparing of two non-equal expressions or terms.In linear inequality variables have highest degree of 1.It shows that one value is less than, greater than, less than or equal to or greater than or equal to other.

According to the given question we have to find the solution of the given inequality -3x -5 < -2.

-3x - 5 < - 2

-3x < 3

3x > -3          ( Think of moving the terms to other side to make x positive )

x > 3/-3

x > - 1.

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Step-by-step explanation:

5+2•(-3)-10/(-5)

15+2•(-3×2)

15+2•-6

15-12

3

So; the answer is 3

Answer:

M (2,8)= (x1y1)

B(-4,19)= (x2y2)

here,

midpoint = (x1+x2/2) (y1+y2/2)

= ( 2+ (-4)/2) (8 +19/2)

= (-2/2) (27/2)

= -1, 13.5

Step-by-step explanation:

by using midpoint formula

Answer:

20%

Step-by-step explanation:

Answer: They are not perpendicular because their slopes are  not negative reciprocals.

Step-by-step explanation:

For these two lines to be perpendicular, their slopes have to be negative reciprocals.

Slope of FG.

F = (-4, 1)

G = (0, -2)

= (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 1) / (0 + 4)

= -3/4

Slope of HJ

J = (0 , 4)

H = (-4, -2)

Slope =  (Y₂ - Y₁) / (X₂ - X₁)

= (-2 - 4) / (-4 -0)

= 6/4

= 3/2

The slopes of these lines are not negative reciprocals so these lines are not perpendicular.

[tex] - 6 \frac{1}{4} - ( - 2 \frac{1}{8} )[/tex]

[tex] = - 6 \frac{1}{4} + 2 \frac{1}{8} [/tex]

[tex] = \frac{ - 25}{4} + \frac{17}{8} [/tex]

[tex] = \frac{ - 50}{8} + \frac{17}{8} [/tex]

[tex] = \frac{ - 50 + 17}{8} [/tex]

[tex] = \frac{ - 33}{8} [/tex]

[tex] = - 4 \frac{1}{8} [/tex]

Answer:

Wouldnt it be 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Describes pairs are:

This is matching the option B

Answer:

B. (4,4), (9,6), (4,4)

Step-by-step explanation:

:)

Answer:

$28.00

Step-by-step explanation: All you need to do is multiply 7 and 4. Then you get 28.

Answer:

The estimated weight that the airplane can carry is: Option C: 350,000 pounds

Step-by-step explanation:

Given that each individual weighs 205 pounds with baggage and one gallon of fuel weighs 5 pounds.

We will work out the passengers weight first.

For Passengers:

Let w be the total weight of all passengers

[tex]w = weight\ of\ one\ passenger * number\ of\ passengers\\w =205 * 495\\w =101475\ pounds[/tex]

For Fuel:

Let f be the total weight of fuel

Then

[tex]f = Weight\ of\ one\ gallon * Number\ of\ gallons\\f = 5 * 49500\\f =247500[/tex]

Total weight = 101475 + 247500 = 348975 pounds

As 350000 is nearest to the calculated answer, it will be the right answer.

Hence,

The estimated weight that the airplane can carry is: Option C: 350,000 pounds

Answer:

We conclude that the rule will be:

aₙ = 31/12 +  1/6n

Step-by-step explanation:

Answer:

we conclude that the rule will be:

[tex]a_n=\frac{31}{12}+\frac{1}{6}n[/tex]

Step-by-step explanation:

Given

The nth term of Arithmetic Sequence

We know the arithmetic sequence with the common difference is defined as

where a₁ is the first term and d is a common difference.

To Determine:

The Rule of the nth term of Arithmetic Sequence

Steps to solve the problem

The 6th term of the Arithmetic sequence be defined as

a₆ = a₁ + (6-1) d

substituting a₆ = 43/12 and a₁ = 11/4 to determine d

43/12 = 11/4 + 5d

switch sides

11/4 + 5d = 43/12

subtract 11/4 from both sides

11/4 + 5d - 11/4 = 43/12 - 11/4

5d  = 5/6

Divide both sides by 5

5d/5 = [5/6] / [5]

d = 1/6

as

a₁ = 11/4

d = 1/6

Therefore, the nth term of the Arithmetic sequence will be:

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting d = 1/6 and a₁ = 11/4

aₙ = 11/4 + (n-1) × 1/6

    = 11/4 + 1/6n - 1/6

    = 31/12 +  1/6n

Therefore, we conclude that the rule will be:

aₙ = 31/12 +  1/6n

Answer:

11 meters below sea level or -11

Step-by-step explanation:

think of a number line. sea level is 0. if the diver is 3 meters down, he's -3 from 0; then he descends another 8 or -8 for a total of -11.

i'm not sure which way you need to write the answer so i've provided both; hope this helps

Answer:

368/5

Step-by-step explanation:

hope it helps

.........

Answer:

73.6

Step-by-step explanation:

80% = 0.8

0.8 * 92 = 80% of 92

0.8 * 92 = 73.6

80% = 73.6

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Answer:

y=35x+50

Step-by-step explanation:

The 50 is a one-time fee, therefore it is shown as addition

35 per day means that for 3 days, you would pay 105

X represents the number of days

Answer:

We conclude that all the points of the table satisfy the equation y = x²

Hence, the option containing the equation y =  x² is true.

The graph of y =  x² is also attached below.

Step-by-step explanation:

Given the table

x             y

-2           4

-1             1

0            0

1             1

2            4

Let us substitute the x-values of the table in the equation

y = x²

plun in x = -2

y = (-2)² = 4

so the point (2, 4) lies on the graph of y =  x²

y = x²

plun in x = -1

y = (-1)² = 1

so the point (-1, 1) lies on the graph of y =  x²

y = x²

plun in x = 0

y = (0)² = 0

so the point (0, 0) lies on the graph of y =  x²

y = x²

plun in x = 1

y = (1)² = 1

so the point (1, 1) lies on the graph of y =  x²

y = x²

plun in x = 2

y = (2)² = 4

so the point (2, 4) lies on the graph of y =  x²

Therefore, we conclude from the above calculations that all the points of the table satisfy the equation y = x²

Hence, the option containing the equation y =  x² is true.

The graph of y =  x² is also attached below.

Answer:A function should pass the vertical line test.

Graph each of the functions to determine whether it passes the vertical line test.

Set #1  is a function

Set #2 is a function

Set #3 is not a function

Set #4 is not a function

Set #5 is not a function

Set #6 is not a function

Step-by-step explanation:

The ratio is 2 : 5 and the smaller portion is 100

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount be A = $ 350

Now , the ratio is 2 : 5

So , the total ratio is = 2x + 5x

                                 = 7x

And, the value 7x =  total amount

So , 7x = 350

Divide by 7 on both sides of the equation , we get

x = 50

So , the number 350 in the ratio 2 : 5 is 100 : 250

Hence , the smaller portion is 100

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Answer:

Solving the expression [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex] we get [tex]\mathbf{n=-\frac{36}{5} }[/tex]

Step-by-step explanation:

We need to solve the expression: [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex]

Solving:

[tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex]

First we convert mixed fraction into improper fraction

[tex]\frac{3}{4}n=-\frac{7}{4}n-18[/tex]

Now adding 7/4 n on both sides

[tex]\frac{3}{4}n+\frac{7}{4}n=-\frac{7}{4}n-18+\frac{7}{4}n\\\frac{3}{4}n+\frac{7}{4}n=-18[/tex]

Now, taking LCM on left side

LCM of 4 and 4 is 4

[tex]\frac{3}{4}n+\frac{7}{4}n=-18\\\frac{3*1n+7*1n}{4}=-18\\\frac{3n+7n}{4}=-18\\\frac{10n}{4}=-18[/tex]

Now, multiply both sides by 4/10

[tex]\frac{10n}{4}\times \frac{4}{10} =-18\times \frac{4}{10}\\n=-\frac{36}{5}[/tex]

So, solving the expression [tex]\frac{3}{4}n=-1\frac{3}{4}n-18[/tex] we get [tex]\mathbf{n=-\frac{36}{5} }[/tex]

Step-by-step explanation:

b^(-2) / ab^(-3)

= 1/a * [b^(-2)/b^(-3)]

= 1/a * b = b/a.

P.S. Law of Indices: a^m / a^n = a^(m-n)

Answer:  [tex]\frac{b}{a}[/tex]

Step-by-step explanation:

A variable raised to a negative exponent p is equivalent to 1 divided by the variable raised to a positive exponent p.

In this equation, this rule applies to both b variables as follows:

[tex]b^{-2} = \frac{1}{b^2}[/tex]

[tex]\frac{1}{b^{-3}} = \frac{1}{\frac{1}{b^3} } = \frac{b^3}{1}[/tex]

After 'solving' for each negative exponent, you can plug them into the previous negative exponents:

[tex]\frac{1}{b^2} * \frac{b^3}{a} = \frac{b^3}{ab^2}[/tex]

Afterwards, cancel out b^2 from the top and bottom of the equation to get your final answer, as b^2 / b^2 = 1

[tex]\frac{b}{a}[/tex]

Answer:

9.6

Step-by-step explanation:

8/50=x/60

cross multiply

50x=480

x=9.6