An automobile battery manufacturer offers a 31/54 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 31 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 31 months but within 54 months, the manufacturer provides a prorated credit toward the purchase of a new battery. The manufacturer assumes that X, the lifetime of its auto batteries, is normally distributed with a mean of 45 months and a standard deviation of 5.6 months.

1. If the manufacturer's assumptions are correct, it would reed to replace _______ of its batteries free.2. The company finds that it is replacing 1.07% of its batteries free of charge. It suspects that its assumption standard deviation of the life of its batteries is incorrect. A standard deviation of ____ results in a 1.07% replacement rate.3. Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't free replacement but do qualify for the prorated credit?

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

d.5/6

Step-by-step explanation:

2/3÷4/5

2/3×5/4

5/6

Answer:

2/3÷ 4/5 is 5/6

.

Step-by-step explanation:

11

Step-by-step explanation:

first you have 6 colors, then you have 22 inches, now multiple 22 × 6=132÷12=11

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

The linear function that models this problem is y = 25x + 25 and the cost for 6 hours is $175

To solve this problem, we have to find the slope and y-intercept of the line.

m = y2 - y1 / x2 - x1

Taking two points from the line;

A = (2, 75)

B = (5, 150)

Substituting the values into the formula;

m = 150 - 75 / 5 - 2

m = 25

Using the slope;

y = mx + c

150 = 25(5) + c

150 = 125 + c

c = 150 - 125

c = 25

The equation of line is ;

y = 25x + 25

The cost for 6 hours will be

y = 25(6) + 25

y = 175

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NO = NM and PO = MN, meaning that all four sides of MNOP are equal. So MNOP is a rhombus.

A rhombus is a quadrilateral with all facets of equal length and each pair of opposite faces parallel, making it an equilateral parallelogram. A rhombus is occasionally referred to as a rhomb, while a rhombus is occasionally referred to as a diamond.

We must demonstrate that MNOP has four equal sides and that the opposite angles are equal in order to establish that it is a rhombus.

Given NOP, NMP, and NOM, PMN, we can infer that:

Because their corresponding angles are equal, the triangles NOP and NMP are comparable.

NOM and PMN have proportional comparable sides since they are equivalent.

The matching sides of NOP and NMP are proportionate since the triangles are comparable. As a result, NP = PM, NO = NM, and NP/NO = PM/NM.

Since NP/PO = PM/PM and NP = PM, we obtain PO = MN because NOM and PMN are equivalent and their respective sides are proportional.

As a result, NO = NM and PO = MN, indicating that MNOP's four sides are equal. Additionally, since corresponding angles of identical triangles are equal and opposite angles of rhombuses are equal, we can infer that MNOP's opposite angles are also equal.

MNOP is therefore a rhombus.

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Answer:

I think its A

Step-by-step explanation:

Answer:

+1 is the answer

Step-by-step explanation:

-19-(-10)

-19+10

+1

Answer:

1,467.6 cm³

Step-by-step explanation:

Volume of the solid = volume of the rectangular prism - volume of the cylinder

= L*W*H - πr²h

L = 12

W = 10

H = 16

r = ½(6) = 3

h = 16

Plug in the values

Volume of the solid = 12*10*16 - π*3²*16

= 1,920 - 452.40

= 1,467.6 cm³

Answer:

C.

Explanation: I hope it's help you

The use of estimates to make the decisions It is important to calculate those estimates to at least six decimal places.

We have given the options that are

A. It is important to always use a 95% confidence level

B. It is important to remember that you will never achieve certainty

C. It is important to calculate those estimates to at least six decimal places.

D. It is important to use a 100% confidence level so as to achieve certainty.

E. All of the above

F. None of the above

We have to determine the correct decision.

Any of numerous procedures used to calculate the value of some property of a population from observations of a sample drawn.

That is we are estimating the value up to 6 decimal places

Therefore option C is correct.

It is important to calculate those estimates to at least six decimal places.

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Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

1/5

Step-by-step explanation:

Chance is also referred to as probability

probability = Number of event/Total samples space

If there are 6 black socks,8 white socks,2 red socks, and 4 blue socks in a drawer, the total number of socks will be the sample space

Sample space = 6 + 8 + 2 + 4

Sample space = 20socks

Total number of blue socks is the event

Number of event = 4 blue socks

Chance that the socks is blue = n(E)/n(S)

Chance that the socks is blue = 4/20

Chance that the socks is blue = 1/5

Answer:

A: 336 km

B: 14 L

Step-by-step explanation:

Use a proportion

210 km / 5 L = x / 8L         Cross multiply

8*210  = 5 x

1680  = 5x

x = 1680 / 5

x = 336 km

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

210 /5 = 588/x                   Cross multiply

210x = 588 * 5

210x = 2940                     Divide by 210

x = 2940/210

x = 14 L

Answer:

Step-by-step explanation:

slope intercept: y = mx + b

where m is the slope and b is the y-intercept

Equation: y = -3x + 4

Since y-intercept is given, then we have the first point of the line as (0,4)

Let's find the value of x when y is 0

y = -3x + 4

0 = -3x + 4

3x = 4

x = 4/3

(4/3,0) ---second point

Since there are two points/coordinates already then we can now plot/graph.

Answer: 180.

Step-by-step explanation:

Appetizers = 5 types

drinks = 3 types

Sandwiches = 4 types.

Solution:

This is a combination problem.

For appetizers

= 5C2

= 10.

For drinks

= 3C2

= 3.

For sandwiches

= 4C2

= 6.

No. Of combinations scot can choose for his party

= 10*6*3

= 180

Scot can choose a total of 180 combinations for his party.

Answer:

-22

Step-by-step explanation:

f(4) = \(2^{4}\) + 8 = 24

f(-2) = \((-2)^{2}\)-48 = -46

24 + -46 = -22

we have

10 colors

and the probability of picking four of the ten possible colors is:

answer: A

Answer:

Hi! The answer to your question is \(x^{2}\)+11x+28

Step-by-step explanation:Answer:

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What are the answers? Also, an equivalent ratio would be multiplying/dividing both the 3 and the 8 by the same number

Answer:

11.25

Step-by-step explanation:

Answer:

108 degrees

Step-by-step explanation:

Since we are not given the radian measure. Let the radian measure be 3π/5 rad;

Using the conversion;

πrad = 180°

3π/5 rad = x

Cross mulriply;

π * x = 180 * 3π/5

x =  180 * 3/5

x = 36 * 3

x = 108 degrees

Hence the degree measure is 108 degrees

Note that the same conversion can be used to convert other values in radians

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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Part 5

Use either loading or unloading methods.

Since the two factors are not significant. So, use either loading or unloading methods.

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference between two levels of method at 5% level of significance.

Against alternative hypothesis,

H_a: There is significant difference between two levels of method at 5% level of significance.

From the ANOVA table, the P-value for factor A is 0.315.

Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between two levels of method of main effect at 5% level of significance.

Part 2

The P-value is 0.315.

There is no significant difference between two levels of method of main effect at 5% level of significance.

Explanation

Since, 0.315 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between two levels of the method of main effect at 5% level of significance.

Step 3/5

(3)

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference between three types of rides at 5% level of significance.

Against alternative hypothesis,

H_a: There is significant difference between three types of rides at 5% level of significance.

From the ANOVA table, the P-value for factor B is 0.687.

Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significance difference between three types of ride at 5% level of significance.

Part 3

The P-value is 0.687.

There is no significance difference between three types of ride at 5% level of significance.

Since, 0.687 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference between three types of ride at 5% level of significance.

Step 4/5

(4)

The null and alternative hypotheses can be defined as follows:

The null hypothesis,

H_0: There is no significance difference of interaction between method and ride at 5% level of significance.

Against alternative hypothesis,

H_a: There is significance difference of interaction between method and ride at 5% level of significance.

From the ANOVA table, the P-value for integration of factor A and factor B is 0.138.

Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Part 4

The P-value is 0.138.

There is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Explanation

Hint for Next Steps

Since, 0.138 is greater than the level of the significance. So, the null hypothesis fails to be rejected.

Therefore, there is no significant difference that the interaction between loading and unloading method and types of ride at 5% level of significance.

Step 5/5

(5)

Since, the two factors are not significant. So, use either loading or unloading methods.

Part 5

Use either loading or unloading methods.

Since the two factors are not significant. So, use either loading or unloading methods.

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to get the y-intercept, we can simply set x = 0 and solve for "y".

\(2x-4y=4\implies 2(\stackrel{x}{0})-4y=4\implies -4y=4\implies y=\cfrac{4}{-4}\implies y=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-1)~\hfill\)

Answer:

62 trees = 100%

62 / 2 = 31 trees

100% / 2 = 50%

31 trees = 50%

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Because Milwaukee's population is smaller than that of Baltimore, the only correct answer would be one that has the population of Baltimore higher than that of Milwaukee, which is only A

Answer:

3 years: $27691.30

7 years: $23359.70

Step-by-step explanation:

3.5% of 30,940 = 1082.9

for each year there is interest, we multiply it by that amount of years.

equation: 1082.9x

3 years: 3248.7  

7 years: 7580.3

since interest is subtracted, we will subtract the multiplied interests from above.

equation: 30940 - 1082.9x = answer

3 years: $27691.3

7 years: $23359.7

Answer:

Step-by-step explanation: