You are asked to advise Alpha Tire Co. on the feasibility of offering a 35,000-mile warranty on their tires. At this time Alpha Tire believes the mean time to failure is 40,000 miles
µ
with standard deviation of miles to failure at 3700 or
. If a free replacement warranty is offered, promising that the tires will last for at least 35,000 miles, what proportion of tires would qualify for the free replacement because they are expected to fail while they were still covered by the warranty? In light of your finding, what advice would you give to Alpha Tires about a warranty for a free tire replacement if the tires fail before 35,000.

The equation that models the given situation is: f(t) = 21e^(-0.000361)t

We can model this situation with an exponential decay function.

f(t) = Pe^(rt)

Where:

f(t) = amount of isotope

P = starting amount

r = growth rate

t = time

Let's assume that there is 1 mg of our isotope. Thus,in 1920 years, we will have 1/2 mg. Thus:

(1/2) = (1)e^(1920r)

Take the natural log of both sides to bring the exponent down and to cancel out the e

ln(1/2) = ln(e^(r(1920))

ln(1/2) = r(1920)

ln(1/2)/1920 = r

r = -0000361

Thus, we have:

f(t) = Pe^(-0.000361)t

Plug in 21 for P to get:

f(t) = 21e^(-0.000361)t

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The triangles represented in the picture attached are acute, obtuse, acute and right triangles respectively.

Acute Triangle is a triangle in which each of the three angles are less than 90°.

In fact all angles in an acute triangle are can be equal and sum to 180°.

Right Triangle is a triangle in which one of the angles is exactly 90°, often denoted as a "square corner".

The side opposite the right angle is called the hypotenuse and it is the longest side.

Obtuse Triangle is a triangle in which one of the angles is greater than 90°.

In other words, one of the angles in an obtuse triangle is "blunt" or greater than a right angle.

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Answer:

Step-by-step explanation:

To solve this expression, we need to first combine the integer part of -2 and -1, which gives us -3. Then, we need to combine the fractional parts of -1 and 3/7.

To do this, we find a common denominator, which is 7, and convert -1 to an equivalent fraction with denominator 7 by multiplying both the numerator and denominator by 7, which gives us -7/7.

Now we can add -7/7 and 3/7 to get -4/7.

Therefore, -2 - 1 3/7 = -3 - 4/7, which can also be written as -3 4/7 or -23/7 in improper fraction form

The appropriate statistic for testing the null hypothesis is given as  D (-2.20/0.07)

Coefficient for slope variable (Exercise time) = -2.20

Standard error of coefficient = 0.07

Therefore, the test statistic value to verify whether or not there is an apparent slope on a population regression line can be estimated as follows.

Test statistic = Coefficient for slope variable/Standard error of coefficient = -2.20/0.07

Therefore its correct answer is D (-2.20/0.07)

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Answer:

X       H(x)=2x+3

-4       -5

0        3

1         5

2        7

3        9

8.69 is the length of the right angle.

Let's call the length you are trying to find x.

Using trigonometry, we know that:

cos(75) = x/9

Solving for x:

x = 9sin(75)

The sine function (sin) is a mathematical function commonly used in trigonometry. It relates the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.

Using a calculator to find the cosine of 75 degrees:

x ≈ 8.69

Therefore, the length you are trying to find is approximately 8.69.

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The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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The expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

The perimeter of a triangle is the sum of the lengths of its sides. Using the given expressions for the side lengths of the triangle, we can write the perimeter as:

(6.1w + 7.8) + (1.4w + 8.1) + (8.7x + 2.5)

Simplifying and combining like terms, we get:

7.5w + 11.2x + 18.4

Therefore, the expression that represents the perimeter of the triangle is 18.4 + 8.7x + 7.5w.

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Answer:

84

Step-by-step explanation:

Trust me

Answer:

84

Step-by-step explanation:

There are 9 pieces of luggage.

We can select the first piece 9 different ways, the second piece 8 different ways, since there are only 8 pieces left.  The third piece can be selected 7 different ways.

9*8*7

504

But order doesn't matter since we are taking 3 pieces.

Divide by (3*2*1)

504/6 = 84

There are 84 different combinations of luggage

Answer:

i think the bag contains $3.56

Step-by-step explanation:

The index forms are simplified to;

1. [tex]5^6^\sqrt{2}[/tex]

2.[tex]3^5\sqrt{3}[/tex]

3.  [tex]2^2^\sqrt{25}[/tex]

It is important to note the following about the rules of index forms;

From the information given, we have that;

[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]

Add the exponents, we have;

[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]

Then, we have;

[tex]5^6^\sqrt{2}[/tex]

2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]

We have;

[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]

Add the exponents

[tex]3^5\sqrt{3}[/tex]

3. [tex]2^2^\sqrt{25}[/tex]

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a) When Nevaeh makes $1,975 in sales for the week, her total earnings, based on her base salary and sales commission rate, are $695.

b) When she makes x in sales for the week, her total earnings are represented by the equation, y = 300 + 0.2x.

The total earnings for the week can be determined using the equation y = 300 + 0.2x, where x represents her total sales for the week while 0.2 represents a 20% sales commission.

The base salary, in this situation, is $300.

Guaranteed (base) salary per week = $300

Sales commission = 20% of sales

Sales for the week = $1,975

a) Total earnings = $695 ($300 + $1,975 x 20%)

Sales for the week = x

b) Total earnings, y = $300 + 0.2x ($300 + 0.2x)

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Answer:

Step-by-step explanation:

(-2-3)-(4-5)+ (−1+6)−(−9+8)

-5-4+5-1+6+9-8

-9+4+15-8

-5+7

2

The whisker plot with the data provided should includes a range that goes from 7 to 49, and a median of 23.

A whisker plot, also known as a box plot, is a graphical representation of a data set that shows the distribution of the data along with some important statistical information, such as the median, quartiles, and outliers. It is particularly useful for comparing the distribution of different data sets or for identifying potential outliers in a data set.

To create a whisker plot, follow these steps:

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Answer:

D

Step-by-step explanation:

- 4( [tex]\frac{3}{2}[/tex] x - [tex]\frac{1}{2}[/tex] ) = - 15 ← distribute parenthesis by - 4

- 6x + 2 = - 15 ( subtract 2 from both sides )

- 6x = - 17 ( divide both sides by - 6 )

x = [tex]\frac{-17}{6}[/tex] , that is

x = [tex]\frac{17}{6}[/tex]

The expression that is equivalent to (4.3x + 4)(−1.8x) is -7.74x² -7.2x (optionC)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.

For example, 2a+6 is equivalent to 2(a+3) and will surely have thesame value when a value is substituted for a.

Similar (4.3x + 4)(−1.8x) can be simplified by multiplying -1.8x with both 4.3x and 4

= -7.74x²-7.2x

therefore the equivalent of (4.3x + 4)(−1.8x) is -7.74x²-7.2x.

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It will take 15.03 years for Bentley's money to triple.

For Bentley:

We have

Principal (P) = $670

Interest rate (r) = 6 7/8% = 0.06875 (compounded quarterly)

Time (t) = unknown

Amount after t years (A) = [tex]P(1 + r/4)^{4t}[/tex]

For Camden:

We have

Principal (P) = $670

Interest rate (r) = 7 3/8% = 0.07375 (compounded annually)

Time (t) = unknown

Amount after t years (A) = [tex]P(1 + r)^t[/tex]

We have to find t such that 3P_Bentley = Camden.

[tex]2010 = 2010(1 + r/4)^{4t} / (1 + r)^t[/tex]

Simplifying, we get:

[tex](1 + r/4)^{4t} / (1 + r)^t = 1/3[/tex]

Taking natural logarithm:

4t ln(1 + r/4) - t ln(1 + r) = ln(1/3)

4 ln(1 + r/4) - ln(1 + r) = ln(1/3) / t

t = (4 ln(3.88356) - 4 ln(16)) / ln(3)

Solving for t, we get:

t = 15.034752564

t = 15.03 years.

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Answer:

35%

(I replaced the 1st digit by a and the second digit by b)

Answer:

(x + 3)(x - 15)

Step-by-step explanation:

To factor the expression x^2 - 12x - 45, we need to find two numbers that multiply to -45 and add to -12. Let's use the method of decomposition to find these two numbers:

x^2 - 12x - 45

We need to find two numbers that multiply to -45 and add to -12. Let's try -15 and 3:

x^2 - 12x - 45 = x^2 - 15x + 3x - 45

Now we can group the first two terms and the last two terms:

x^2 - 15x + 3x - 45 = x(x - 15) + 3(x - 15)

We can see that both terms have a common factor of (x - 15), so we can factor this out:

x(x - 15) + 3(x - 15) = (x + 3)(x - 15)

Therefore, the expression x^2 - 12x - 45 can be factored as (x + 3)(x - 15).

Refer to the attachment ^-^

Hope Helpful ~

The minimum value of the data set is 10.5.

Box plots are an effective graphical tool used to display a summary of a dataset. They provide a visual representation of the minimum and maximum values, quartiles, and outliers of the data. They are commonly used in statistics and can provide valuable insights into a dataset.

Now, let's consider the box plot in question. The box plot is labeled "Volunteer Service Hours" and it has four quartiles, each marked by a horizontal line. The first quartile (Q1) is marked at 13, the second quartile (Q2) is marked at 16.5, the third quartile (Q3) is marked at 20, and the fourth quartile (Q4) is marked at 23, with the end of the box extending to 27.

The minimum value of the data set can be found at the lower whisker of the box plot.

The lower whisker represents the minimum value that is not an outlier.

In this box plot, we do not see any outliers, so the minimum value of the dataset is represented by the lower end of the whisker, which is located at 10.5.

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Answer:

False

Step-by-step explanation:

you have to save at least 20 percent

Answer:

5 (100y -601.39)

3028

Step-by-step explanation:

Answer: The answer is actually 12 pieces of vanilla cake.

Answer:

2,090. because Sarah has long distances and wanted to go home

Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is  4 : 20 which is 1: 5

Therefore, 4 of the next 20 horses that come to board should you expect to be white horses

The probability that Rosie does her homework is: 27/44

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

Thus, we can solve this probability as:

(6/11 * 1/2) + ((1 - (6/11) * 3/4)

= (3/11) + (5/11 * 3/4)

= (3/11) + 15/44

= 27/44

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The measure of x is 36.

We have,

The angle opposite to equal sides is equal.

And,

The sum of the triangle.

27 + 90 + (x + 27)= 180

27 + 90 + x + 27 = 180

x = 180 - 144

x = 36

Thus,

The measure of x is 36.

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The mean age of the U.S. presidents at inauguration is 54.7 years and the population standard deviation is approximately 5.7 years.

To find the mean and population standard deviation of the ages of the U.S. presidents at inauguration, we first need to calculate the sum of the ages and the number of presidents in the data set.

The sum of the ages is:

57 + 61 + 57 + 57 + 58 + 57 + 61 + 54 + 68 + 51 + 49 + 64 + 50 + 48 + 65 + 52 + 56 + 46 + 54 + 49 + 50 + 47 + 55 + 55 + 54 + 42 + 51 + 56 + 55 + 51 + 54 + 51 + 60 + 62 + 43 + 55 + 56 + 61 + 52 + 69 + 64 + 46 + 54 + 47 = 2,405

There are 44 presidents in the data set.

Therefore, the mean age is:

mean = sum of ages / number of presidents = 2,405 / 44 = 54.7

To find the population standard deviation, we first need to calculate the sum of the squared deviations from the mean:

(57 - 54.7)² + (61 - 54.7)² + ... + (47 - 54.7)² = 3,391.5

Then, we divide the sum of squared deviations by the number of presidents and take the square root:

population standard deviation = √(3,391.5 / 44) ≈ 5.7

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