A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 51 months and a standard deviation of 11 months. Using the Empirical Rule rule, what is the approximate percentage of cars that remain in service between 73 and 84 months

Answer:

Step-by-step explanation:

Let P be the population of the community

So the population of a community increase at a rate proportional to the number of people present at a time

That is

[tex]\frac{dp}{dt} \propto p\\\\\frac{dp}{dt} =kp\\\\ [k \texttt {is constant}]\\\\\frac{dp}{dt} -kp =0[/tex]

Solve this equation we get

[tex]p(t)=p_0e^{kt}---(1)[/tex]

where p is the present population

p₀ is the initial population

If the  initial population as doubled in 5 years

that is time t = 5 years

We get

[tex]2p_o=p_oe^{5k}\\\\e^{5k}=2[/tex]

Apply In on both side to get

[tex]Ine^{5k}=In2\\\\5k=In2\\\\k=\frac{In2}{5} \\\\\therefore k=\frac{In2}{5}[/tex]

Substitute [tex]k=\frac{In2}{5}[/tex]  in [tex]p(t)=p_oe^{kt}[/tex] to get

[tex]\large \boxed {p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

Given that population of a community is 9000 at 3 years

substitute t = 3 in [tex]{p(t)=p_oe^{\frac{In2}{5}t }}[/tex]

[tex]p(3)=p_oe^{3 (\frac{In2}{5}) }\\\\9000=p_oe^{3 (\frac{In2}{5}) }\\\\p_o=\frac{9000}{e^{3(\frac{In2}{5} )}} \\\\=5937.8[/tex]

Answer:

X

Step-by-step explanation:

X and Y make up a graph

Answer:

what's the question?

it's not showing

Answer:

C.

Step-by-step explanation:

To find the perimeter, we'll use the distance formula

Distance Formula = √(x₂-x₁)²+(y₂-y₁)²

Finding Distance of AB

|AB| = √(-2+5)²+(3+1)²

|AB| = √25

|AB| = 5

Now For BC

|BC| = √(6+2)²+(-3-3)²

|BC| = √(8)²+(-6)²

|BC| = √100

|BC| = 10

FOR CA:

|CA| = √(-5-6)²+(-3+1)²

|CA| = √125

Perimeter of Triangle = 10 + 5 + √125

= 15 + √125

Answer:

y = (-1/3)x + 2

Step-by-step explanation:

Equation of line in slope-intercept form is given by

y = mx +c

where m is the slope of line

c is y intercept

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

_________________________________________________

let the equation of required line be y = mx +c

Since points given are  (3,1) and (-6,4)

Then, its slope is

m = 4-1/-6-3 = 3/-9 = -1/3

Thus, slope of line is m = -1/3

lets use m = -1/3 in place of m in equation y = mx +c

y = (-1/3)x + c

Since points   (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.

hence lets plug 3 in place of x and 1 in place of y

1 =  (-1/3)3 + c

=> 1 = -1 + c

=> c = 1 +1 = 2

Thus, intercept is 2.

Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.

Answer:

26 mm

Step-by-step explanation:

Δcda ≅  Δxyz

If cd=26 mm then xy=cd= 26 mm

Answer:

8x10^13

Step-by-step explanation:

Answer:

The answer is 36 hours.

Step-by-step explanation:

As the month increases, the number of hours will be increased by 4 hours.

March = 4 hours

April = 4+4 = 8 hours

May = 8+4 = 12 hours

June = 12+4 = 16 hours

July = 16+4 = 20 hours

August = 20+6 = 24 hours

September = 24+4 = 28 hours

October = 28+4 = 32 hours

November = 32+4 = 36 hours

Answer:

9 + 10 = 21 higkjiitbughu

Answer:

LMK  Let me know. KM  Kilometer's

Step-by-step explanation:

Answer:

Step-by-step explanation:

total number of digits= 10 (from 0 to 9)

total number of letters = 6 (from A to F)

probability of numbers = 10/(10+6)

= 0.625

this is a case of binomial distribution with fixed number trials

n = 32 and probability p = 0.625

we have to find probability of at least 20 numbers

Use the BINOM.DIST function in Excel to find the cumulative probability.

P(at least 20 numbers) = 1 - BINOMDIST(numbers, trials, probability,true)

setting numbers = 20-1, trials = 32 and probability = 0.625

we get

[tex]P(X \geq 20)=1 - BINOMDIST(20- 1, 32, 0.625, true) \\\\=1 -0.4219 \\\\=0.5781[/tex]

Alternatively,

The probability that there are exactly r letters can be found with binomial probability.

P = nCr pʳ qⁿ⁻ʳ

Given that n = 32, p = 5/8, and q = 3/8, you can use Excel to find each probability from r=20 to r=32, then add them all up.

P = ₃₂C₂₀ (⅝)²⁰ (⅜)³²⁻²⁰ + ₃₂C₂₁ (⅝)²¹ (⅜)³²⁻²¹ + ... + ₃₂C₃₂ (⅝)³² (⅜)³²⁻³²

P = 0.578

Answer: 72.

Step-by-step explanation:

You can solve this by representing the number in an equation that models the problem given. I will use the variable x to represent the number:

[tex]x + \frac{1}{3}x = 96[/tex]

In the equation, I listed the number and added one-third of the same number to it to equal 96.

Now, solve:

[tex]\frac{4}{3}x = 96\\ \\x = 96 / \frac{3}{4} \\\\x = 96 * \frac{3}{4} \\\\x = 72[/tex]

The number is 72.

Answer: -13.37

Explanation: I did it in decimals because I didn’t know if your assignment required fraction or decimal. 5 4/7= 5x7=35+4=39/7 so this means 5 4/7 is equal to 39/7. -2 2/5= -2x5=-10+2=-8/5. So it comes out to 39/7x-8/5.

Answer:

16

Step-by-step explanation:

[tex]16x^0= \\\\16(-3)^0= \\\\16(1)= \\\\16[/tex]

Hope this helps!

x = -3

[tex]A = 16.(-3)^{0} \\ x^{0} = 1\\A = 16.1 \\A = 16[/tex]

Remember that [tex]x^{0} = 1[/tex] ∀ [tex]x[/tex]

Answer:

The perimeter is 26 yards

Step-by-step explanation:

Area of rectangle = A= l x w

1st rectangle = 6 x 5 = 30 yards squared

2nd rectangle= 10 x 3 = 30 yards squared

perimeter of rectangle = 2l+2w= 10 + 10 + 3 + 3= 26

Answer:

Step-by-step explanation:

The  histogram shown in the attached file show that the distribution of differences is approximately normal.

So, we can assume that the distribution is normal.

.

b)

The 95% confidence level for [tex]\mu _D=\mu_1-\mu_2[/tex] is found

[tex]\bar d \pm t_{0.025,11}\frac{S_D}{\sqrt{n} }[/tex]

[tex]=0.666667 \pm 2.201\frac{(2.964436)}{\sqrt{12} } \\\\0.666667 \pm 2.201(0.85576)\\\\=0.666667+ 1.883525474=2.5502\\\\=0.666667- 1.883525474=-1.2169\\\\=(-1.2169,2.5502)[/tex]

since 0  is in the confidence interval. we do not reject the null hypothesis.

No, there is no indication of one design language is available.

Answer:

Step-by-step explanation:

The monthly interest rate is ...

  [tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]

a) The monthly payment is given by the amortization formula:

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate on a loan of amount P for n months.

  A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95

The monthly payment is $1214.95.

__

b) The amount to interest is the product of the remaining principal and the monthly interest rate.

 first month's interest = $140,000·0.0070833 = $991.67

__

c) The balance after the first payment is ...

  new balance = $140,000 +991.67 -1214.95 = $139,776.72

__

d) The amount to interest for the second payment is computed the same way:

  second month's interest = $139,776.72·0.00708333 = $990.09

__

e) The balance after the second payment is computed the same way:

  new balance = $139,776.72 +990.09 -1214.95 = $139,551.86

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 1100

A = 1900

n = 4 because it was compounded 3 times in a year and n = 12/3 = 4

t = 10 years

Therefore,.

1900 = 1100(1 + r/4)^4 × 10

1900/1100 = (1+ r/4)^40

1.73 = (1+ r/4)^40

Taking log to base 10 of both sides, it becomes

Log 1.73 = 40log(1 + 0.25r)

0.238 = 40log(1 + 0.25r)

Log(1 + 0.25r) = 0.238/40 = 0.00595

Take exponent of both sides, it becomes

10^log(1 + 0.25r) = 10^0.00595

1 + 0.25r = 1.0138

0.25r = 1.0138 - 1 = 0.0138

r = 0.0138/0.25

r = 0.0552

The The required annual interest rate is

0.0552 × 100 = 5.5%

Answer:

StartFraction 4 over 2 EndFraction = StartFraction 5 over x EndFraction

Solve the proportion for x.

After using cross products, the proportion becomes the equation

✔ 4x = 10

.

Isolate the variable by dividing both sides of the equation by

✔ 4

.

x = ✔ 2.5

.

The value of x is 2.5 for the given proportion.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

The proportion is given in the question, as follows:

4/2 = 5/x

Using cross-product, the proportion becomes the equation as:

4x = 2 × 5

4x = 10

Divide by 4 into both sides of the above equation,

x = 10/4

x = 2.5

Thus, the value of x is 2.5 for the given proportion.

Learn more about the proportion here:

brainly.com/question/1504221

#SPJ3

Answer:

Step-by-step explanation:

The answer is 54.5 on edg

For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

In a right angle triangle ratio of adjacent side to the hypotenuse side is equal the cosine angle between them.

[tex]\rm \cos=\dfrac{ adjacent}{hypotenuse}[/tex]

Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.

The traingle is not provided in the image. Let the triangle for the given problem is similar to the attached image below.

Here the hypontenuse side is AC and adjacent side of triangle is 14.1 units. Thus by the property of right angle triangle,

[tex]\cos75=\dfrac{AB}{AC}\\\cos75=\dfrac{14.1}{x}[/tex]

Now if we compare the above equation with the given statement __(75*)=14.1/x. The term cos is filled in the blank.

For the second part, we need to find the value of x. Thus solve the above equation further as,

[tex]\cos75=\dfrac{14.1}{x}\\x=\dfrac{14.1}{\cos75}\\x=\dfrac{14.1}{0.25882}\\x\approx54.5^o[/tex]

Hence, For the triangle shown on the right, the term cos is used to complete the statement and the value of x is 54.5 degree for the triangle.

Learn more about the right angle triangle property here;

https://brainly.com/question/22790996

Answer:

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Step-by-step explanation:

Given points end  Points are p(-3,-2) and q( 1,6)

The distance of two points formula

P Q = [tex]\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }[/tex]

P Q = [tex]\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }[/tex]

P Q = [tex]\sqrt{16+64} = \sqrt{80}[/tex]

The diameter 'd' = 2 r

                       2 r = √80

                            = [tex]\sqrt{16 X 5}[/tex]

                           = [tex]4 \sqrt{5}[/tex]

                      r =  2√5

Mid-point of two end points

                       [tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )[/tex]

                                              = (-1 ,2)

Mid-point of two end points = center of the circle

                                    (h,k) = (-1 , 2)

The equation of the circle

           (x -h )² +(y-k)² = r²

         (x -(-1) )² +(y-(2))² = (2(√5))²

        x² + 2 x + 1 + y² - 4 y + 4 = 20

         x² + 2 x + y² - 4 y  = 20 -5

          x² + 2 x + y² - 4 y  = 15

Final answer:-

The equation of the circle   (x +1) )² +(y-(2))² = (2(√5))²

  or

The equation of the circle    x² + 2 x + y² - 4 y  = 15

Answer:

Step-by-step explanation:

Answer: D

Step-by-step explanation:

The key to finding the line perpendicular to the one given is teh slope. The slope is the opposite reciprocal of the original line.

m=3

perpendicular m=-1/3

Now that we know the slope, we can see which of our answer choices have -1/3 as the slope. We can see D is the only option that has -1/3 for slope.

Answer:

D) y = -1/3x - 4

Step-by-step explanation:

Perpendicular lines have negative reciprocal slopes. This means that since the slope of this line is 3, the slope of a line perpendicular to it would be -1/3 because:

Original slope: 3 (3/1)

Reciprocal (flipped): 1/3

Negative reciprocal (opposite sign): -1/3

The only equation with a slope of -1/3 is D. Therefore, that is the correct answer.

Hope this helps!

Answer:

[tex]\pi =\frac{C}{d}[/tex]

Step-by-step explanation:

[tex]C=\pi d[/tex]

[tex]\pi =\frac{C}{d}[/tex]

Answer:

I'm not 100%sure but i'm think that it is c

Step-by-step explanation:

Hope this helps! May have gotten it wrong really sorry if I did

Answer:

s+(2s+3)+12

Step-by-step explanation:

Answer:

[tex]\frac{47}{10}[/tex]

Step-by-step explanation:

Given the mixed fraction, [tex]4\dfrac{7}{10}[/tex], to convert it to proper fraction simply means removing all traces of whole number in the fraction.

To convert will will add [tex]4[/tex] to [tex]\dfrac{7}{10}[/tex] as shown;

[tex]= 4 + \frac{7}{10}\\ = \frac{4}{1} + \frac{7}{10}\\= \frac{40+7}{10}\\ = \frac{47}{10}[/tex]

The improper form of the fraction [tex]4\frac{7}{10}[/tex] is [tex]\frac{47}{10}[/tex]

Answer:

28/10 ez

Step-by-step explanation:

in khan

Answer:

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 185

Standard deviation = 26

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?

133 = 185 - 2*26

So 133 is two standard deviations below the mean.

By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133

p = 0.05*0.5 = 0.025

2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages

Answer:

  3.06×10^-6

Step-by-step explanation:

0.00000306 = 3.06×0.000001 = 3.06×10^-6

__

Your calculator or spreadsheet can display numbers in scientific notation.

Answer:

  $18,862.91

Step-by-step explanation:

The appropriate formula is ...

 A = P(1 +r/n)^(nt)

where P is the amount invested (14,000), r is the APR (.05), n is the number of times per year interest is compounded (4), and t is the number of years (6).

Filling in the numbers and doing the arithmetic, we get ...

  A = 14,000(1 +.05/4)^(4·6) = 14,000·1.0125^24 ≈ 18,862.91

The balance after 6 years will be $18,862.91.

Answer:

Only the question 2 is a statistical question.

Step-by-step explanation:

Questions

2. How much time do the students in my school spend on the Internet each  night?

3. What is the height of the tallest waterslide at Wild Rides Water Park?

4. What are the cabin rental prices for each of the state parks in Kentucky?

The question 2 is a statistical question.

Is the only question that can be answered with a parameter of a population (mean number of hours spent on the internet by the students).

The other two ask for individual values: the height of the tallest waterslide at Wild Rides Water Park, and the cabin rental prices for each of the state parks in Kentucky. This need specific values that are not statistical, but deterministic.

Answer:

A. Yes. Each subject is randomly assigned to a treatment

Step-by-step explanation:

In an experimental study design, subjects are usually grouped into one or more groups in a random manner or by chance, in order to study and ascertain the effect of a treatment.

In the study cited in the question above, students were grouped by chance it randomly into a treatment group or the other. This is typical of an experimental study where subjects are usually categorised and placed randomly in control and treatment groups.