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 41 months and a standard deviation of 5 months. Using the empirical rule (as presented in class), what is the approximate percentage of cars that remain in service between 46 and 51 months

Answer:

35 is the 'is' and 40 is the 'of'

Step-by-step explanation:

is/of = %/100

35/40 = x/100

cross-multiply to get:

40x = 3500

x = 3500/40

x = 87.5

Answer:

Ok, we can define a function as a relation that maps elements from a set (the domain) into elements from another set (the range), such that each element in the domain can be mapped into only one element of the range.

2) Here you choose the autographed poster, and we know that each one of these costs $10.

So, if the artist sold x posters, then he/she would earn x times $10:

earnings =  $10*x

So we can create a function:

f(x)

such that f(x) represents the total earnings of the artist for selling x posters.

And we already know the equation for the earnings, so the function will be:

f(x) = $10*x

3) Now, it asks us if the values:

-2, -1, 0, and 1

be appropiate for the domain of the function.

Remember that x represents the number of posters that the artist sold.

Then, if we take x = -2 or x = -1 (like the first two given values) this would mean that the artist sold a negative number of posters, which has no real sense in the situation given. So we can conclude that these values should not be in the domain of the function.

For the other two cases, 0 and 1, these two can be in the domain, because these represent the case where the artist sold only one poster and the case where the artist did not sell any poster (that are two possible cases)

Answer: [tex]x=3.0206[/tex]

Step-by-step explanation:

Given

[tex]3(2^{2x}+3)-5(2^x+2)-156=0[/tex]

Replace [tex]2^x[/tex] by [tex]y[/tex]

We can write

[tex]\Rightarrow 3(y^2+3)-5(y+2)-156=0\\\Rightarrow 3y^2+9-5y-10-156=0\\\Rightarrow 3y^2-5y-157=0\\\\\Rightarrow y=\dfrac{5\pm \sqrt{25-4(3)(-157)}}{2\times 3}\\\\\Rightarrow y=\dfrac{5+43.69}{6}\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206[/tex]

The number of coloured papers as per the given problem is 18.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The ratio of coloured papers to white papers is 3/8.

And, the number of white papers is 48.

Suppose, the number of coloured papers be x.

Then, as per the question the following equation can be obtained,

3/8 = x/48

=> x = 3/8 × 48

=> x = 18

Hence, the number of coloured papers is 18.

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Area of this trapezoid is 264 unit²

Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides.

Given perpendicular distance as 12 and parallel sides as 20,24 units respectively.

Thus Area is (20+24 /2) ×12=264 units²

Hence, the Area of trapezoid is 264 unit²

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Answer:

Total Number of students taking Math and History and not music are 68.

Number of students who took both math and history at the same time is 6.

Step-by-step explanation:

History = 30

Math = 32

Music= 33

Math and Music= 9

History and Music= 13

History and Music and Math = 2

History but not math = 14

We have to find students taking history and math but not music.

Total number of students = 125

From the figure  number of students taking Math and History and not music are

=30+6+32= 68

Number of students who took both math and history at the same time is 6.

Answer:

50 cups

Step-by-step explanation:

ratio of water to juice = 10 : 6 = 5 : 3

amount of cup = (5 x 30) / 3 = 50

Answer:

5 x 4 = 20, 20 divided by 2 ( x 1/2 ) = 10

Step-by-step explanation:

Formula area of a Triangle:

B(base) x H(height) x 1/2(basically just dividing by 2)

Answer:

x=18

Step-by-step explanation:

Both angles are supplementary angles and form 180

Set your formula up as following

(x-6) + (8x+24) = 180

x+8x-6+24=180

9x=180+6-24

9x=162

x=162/9

x=18

Now substitute 18 for x to get your angles and check your work .

~Refer to the attachment for the solution.

[tex] \to \bf { Sum = 3500 } [/tex]

Answer:

[tex]16m^{10} -25m^{12}[/tex]

Step-by-step explanation:

hope this helps :)

The expand and combination like terms (4m^5) – 5m^6) (4m^5 + 5m^6) is -9m^12 + (16)m^10.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

The equation=(4m^5) – 5m^6) (4m^5 + 5m^6)

Now,

To expand the expression, we need to multiply each term inside the first parentheses by each term inside the second parentheses. This gives us:

(4m^5 - 5m^6) (4m^5 + 5m^6) = 4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6

To simplify the expression, we need to use the exponent rule that a^b * a^c = a^(b + c) and combine the terms that have the same base and exponent. This gives us:

4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6 = 16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6)

To further simplify the expression, we need to add the exponents and simplify the coefficients. This gives us:

16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6) = 16m^10 + 20m^11 - 20m^11 - 25m^12

To combine like terms, we need to add or subtract the coefficients of the terms that have the same base and exponent. This gives us:

16m^10 + 20m^11 - 20m^11 - 25m^12 = (16 - 25)m^12 + (20 - 20)m^11 + (16)m^10

= -9m^12 + (0)m^11 + (16)m^10

= -9m^12 + (16)m^10

Therefore, the equation will be equal to -9m^12 + (16)m^10.

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Answer:

-7

Step-by-step explanation:

answer: the answer is c

Answer:

33464.25

Step-by-step explanation:

Using BODMAS : brackets, division, multiplication, addition

[tex]177\times ((177+(9-4+7)) +\frac{90}{8}\\\\177\times (177+12) +\frac{90}{8}\\\\177\times 189 +\frac{90}{8}\\\\\\177 \times 189 + 11.25\\\\33453 + 11.25\\\\33464.25[/tex]

Answer:

35444.25

Step-by-step explanation:

OFC by computing them

Answer:

Simplify.

Rewrite the expression in the form z”. Z5 • Z6Simplify.

Rewrite the expression in the form z”. Z5 • Z6

Answer:

Simplify.

Rewrite the expression in the form z”. Z5 • Z6Simplify.

Rewrite the expression in the form z”. Z5 • Z6

Answer:

See below

Step-by-step explanation:

This is a piece-wise function.

         4, -4≤ x ≤ -2

f(x) =  2,  -2 ≤ x < 2

        -3,  2 ≤ x ≤ 4

Answer:

6/5t + 4/15s - 3

Step-by-step explanation:

(-4/5t + 5/3s) + (-3 -7/5s + 2t)

You can only add like terms together so convert like terms to have the same denominator:

(-4/5t + 25/15s) + (-3 - 21/15s + 10/5t)

Get rid of the parentheses:

-4/5t + 25/15s - 3 - 21/15s + 10/5t

Combine like terms:

6/5t + 4/15s - 3

Answer:

20

Step-by-step explanation:

Answer:

First, when we have a function f(x), an horizontal dilation of scale factor k, is written as:

g(x) = f(x/k)

Then f((2/3)*x) is an horizontal dilation of scale factor 3/2 of the function f(x).

(The graph will be a little bit wider than the graph of f(x))

Also, knowing that f(x) = x^3 + 3

Then:

f((2/3)*x) = ( (2/3)*x)^3 + 3

              = (8/27)*x^3 + 3

And the graph of this function is shown below:

Answer:

8.

[tex]8. - 1. - 44 [/tex]

9

Answer: The function described in this scenario above is a “Growth Function”

Have a nice day!

Answer:

2

Step-by-step explanation:

Answer:

2t

Step-by-step explanation:

3t-t is the same as 3-1, so it equals 2t

Answer:

52 degrees

Step-by-step explanation:

a line is 180 degrees so just subtract 128 from 180 which is 52

Answer:

[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.

Step-by-step explanation:

Uniform distribution:

An uniform distribution has two bounds, a and b.

The probability of getting a value lower than x is:

[tex]P(X < x) = \frac{x - a}{x - b}[/tex]

The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m.

6 minutes, so [tex]a = 0, b = 6[/tex]

You arrive at 7:33, so if x < 3, you lose the express bus:

[tex]P_E = P(X < 3) = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2}[/tex]

The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m.

10 minutes, so [tex]a = 0, b = 10[/tex]

[tex]P_B = P(X < 3) = \frac{3 - 0}{10 - 0} = \frac{3}{10}[/tex]

Find the probability that you missed both the express bus and the local bus.

[tex]p = P_E*P_B = \frac{1}{2}*\frac{3}{10} = \frac{3}{20}[/tex]

[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.

The probability that you missed both the express bus and the local bus is 3/20

The individual probability of a uniform distribution is calculated as:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

For the express bus

At 7:30 am, a = 0

At 7:36 am, b = 6

You arrived at 7:33 am; this means that:

x = 3

For you to miss the express bus, it means that the express bus left before 7:33 am.

i.e. x < 3

So, the probability that you miss the express bus is:

[tex]P(X < 3) = \frac{3 - 0}{6 - 0}[/tex]

[tex]P(X < 3) = \frac{3}{6}[/tex]

[tex]P(X_E < 3) = \frac{1}{2}[/tex]

For the local bus

At 7:30 am, a = 0

At 7:40 am, b = 10

You arrived at 7:33 am; this means that:

x = 3

For you to miss the local bus, it means that the local bus left before 7:33 am.

i.e. x < 3

So, the probability that you miss the local bus is:

[tex]P(X < 3) = \frac{3 - 0}{10 - 0}[/tex]

[tex]P(X_L < 3) = \frac{3}{10}[/tex]

So, the probability that you miss both bus is:

[tex]P(Both) = P(X_E < 3) * P(X_L < 3)[/tex]

This gives

[tex]P(Both) = \frac 12 * \frac 3{10}[/tex]

[tex]P(Both) = \frac 3{20}[/tex]

Hence, the probability that you missed both the express bus and the local bus is 3/20

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Answer:

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