Tom is a supermarket manager. He reviewed transaction time when a customer paid by credit card. The
transaction time is normally distribution with mean of 20 seconds and standard deviation of 5 seconds.
(a) For a group of 6 customers, find the probability that 5 customers can finish the transaction within 20
seconds. (Assume that the transaction times of customers are independent.)
After discussion with the network provider, he will upgrade the network so that it is promised that each
transaction time can be reduced by 15%.
(b) Use Y to denote the transaction time after network upgrade. Find the mean and standard deviation of Y.
(c) Calculate the 97th percentile of Y. (i.e. find the value of t such that P(Y (d) Compare with the transaction time before upgrade, is it (I) a higher proportion, (II) a lower proportion,
or (III) the same proportion of all customers can finish the transaction within 20 seconds? (Just state
your answer, no calculation is needed.)

Answer:

1,2, and 4

Step-by-step explanation:

vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.

Answer:

113

Step-by-step explanation:

please mark me as brainlest

Answer:

34 yd²

Step-by-step explanation:

Area of the shaded region = area of the outer rectangle - area of the inner rectangle

Area of outer rectangle = L*W = 13*6 = 78 yd²

Area of inner rectangle = L*W = 11*4 = 44 yd²

Area of the shaded region = 78 - 44 = 34 yd²

The lowest term of the fraction 9/24 is 3/8.

To find the lowest term of a fraction, we need to simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD). In the case of 9/24, we can see that both numbers are divisible by 3. By dividing both 9 and 24 by 3, we get the simplified fraction 3/8.

Simplifying fractions to their lowest terms is important because it gives us the simplest and most compact representation of the ratio between the numerator and the denominator. It provides a clearer understanding of the relationship between the parts of the fraction.

In this example, by simplifying 9/24 to 3/8, we can see that the fraction represents a ratio of 3 parts to 8 parts, indicating that for every 3 units, there are 8 units. This simplified form allows for easier comparisons and calculations.

It's worth noting that simplifying fractions is not just about dividing by the GCD. It involves finding the common factors and dividing them out until no further simplification is possible. This process ensures that the fraction is in its lowest terms, providing a more concise and meaningful representation.

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9514 1404 393

Answer:

  C)  83°

Step-by-step explanation:

The angle marked 97° and b form a linear pair, so are supplementary.

  b = 180° -97° = 83°

Answer:

C .) 83 °

Step-by-step explanation:

Angle b and 99° are on straight line so it's supplementary angles and we know that sum of all angles of supplementary angles is 180 °.

➛ b + 97 ° = 180 °.

subtract each side by 97 °

➛ b + 97° - 97° = 180° - 97°

➛ b = 83°

Evaluating the function in the values of the domain we will get some coordinate pairs. The graph of these is in the image at the end.

Here we have the function:

3x - y = 1

And we want to graph this in the domain (-3, -1, 0, 4)

To do so, we need to evaluate the function (the values of x) in the values of the domain.

Solving the equation for y we get:

y = 3x - 1

Now, when x = -3

y = 3*-3 - 1 = -10

when x = -1

y = 3*-1 - 1 = -4

when x = 0

y = 3*0 - 1 = -1

When x = 4

y = 3*4 - 1 = 11

So we have the points (-3, -10), (-1, -4),  (0, -1), (4, 11)

The graph of these points is on the image below.

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Answer:

−t+24

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The question has 2 + (-8), and in the timeline, your starting point has to be in positive 2. As for the -8, the negative goes to the left, and therefore your answer is D, as that is the only timeline that follows the instructions of the question,

Answer:

\(\Huge \boxed{\mathrm{D}}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

2 + ( -8 )

2 is on the number line.

When -8 is added to 2, the value decreases, and it moves 8 units to the left side.

The result is -6.

\(\rule[225]{225}{2}\)

Using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

So, we know that:

The median monthly rent in 1987 was $399.

The median monthly rent in 1995 was $523.

Percentage increase formula: C = x2 - x1/x1 * 100

Where c is the relative change, x1 is the initial value and x2 is the final value.

Now, insert the values in the formula as follows:

C = x2 - x1/x1 * 100

C = 523 - 399/399 *  100

C = 124/399 *  100

C = 31.07

Round off: 31%

Therefore, using the percentage increase formula, we know that the median monthly rent increase from 1987 to 1995 is 31%.

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The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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Answer:

the solution to the equation is m = 28/3, or approximately 9.3333

Step-by-step explanation:

To solve this equation, you need to get the variable, in this case "m," by itself on one side of the equation. To do this, you can start by isolating the fraction on the left side of the equation. You can do this by multiplying both sides of the equation by 2/3, which will cancel out the 2/3 on the left side:

3m/2/3 = 7

(2/3) * (3m/2/3) = (2/3) * 7

3m/2 = 7 * (2/3)

3m/2 = 14/3

Next, you can multiply both sides of the equation by 2 to get rid of the fraction on the left side:

(2) * (3m/2) = (2) * (14/3)

3m = 28/3

Finally, you can simplify the right side of the equation by dividing both sides by 3 to get the final solution:

(3m) / 3 = (28/3) / 3

m = 28/3

Therefore, the solution to the equation is m = 28/3, or approximately 9.3333.

Answer:

Maybe m = 14/9

Maybe m = 14

Step-by-step explanation:

It is not clear what you mean by the fraction on the left side.

Do you mean

3m/(2/3) = 7  ?

If so:

3m = 7 × 2/3

3m = 14/3

m = 14/9

Do you mean

(3m/2)/3 = 7   ?

If so:

3m/2 = 21

m = 21 × 2/3

m = 14

Do you mean something else?

Answer:

x=32

Step-by-step explanation:

Given:

The triangles  ΔKRO and ΔKCO are right triangles with common leg and congruent hypotenuse. It is sufficient for HL (Hypotenuse - leg) congruence. RK and KC are hypotenuse and OK is common leg.

     Statement                                       Reason                

Given:

To prove FG ≅ AG, we'll first prove the triangles are congruent by AAS as we have one congruent angle pair, one side is common to both triangles, another pair of congruent angles is formed by the angle bisector. The common side is adjacent to one of the congruent angles but not included.

     Statement                                       Reason                

The number of Jim's model car is 48

From the question, we have the following parameters that can be used in our computation:

Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6

This means that

Jim : Terrence = 8 : 6

Also from the question, we have

Terrence owns 36 models cars

This means that

Terrence = 36

Substitute the known values in the above equation, so, we have the following representation

Jim : 36 = 8 : 6

Multiply by 6

Jim : 36 = 48 : 36

So, we have

Jim = 48

Hence, the number of car is 48

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Answer:

2

Step-by-step explanation:

Let x represent the total number of people. Let C represent those that like cake and let I represent those that like ice cream. Given:

C = (1/4)x = 0.25x, I = 0.5x, (C ∪ I)' = 12, C' = 20

Therefore:

C ∩ I' = C' - (C ∪ I)' = 20 - 12 = 8

C ∩ I = C - C ∩ I' = 0.25x - 8

C' ∩ I = I - C ∩ I = 0.5x - (0.25x - 8) = 0.25x + 8

The total students = (C ∩ I) + (C' ∩ I) + (C ∩ I') + (C ∪ I)'

x = 0.25x - 8 + 0.25x + 8 + 8 + 12

x = 0.5x + 8 + 12

x = 0.5x + 20

0.5x = 20

x = 40

Students that liked both = C ∩ I = 0.25(40) - 8 = 2

Check the picture below.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ A=900\\ b=2a\\ h=40 \end{cases}\implies 900=\cfrac{40(a+2a)}{2} \\\\\\ 1800=40(3a)\implies 1800=120a\implies \cfrac{1800}{120}=a\implies \boxed{15=a}~\hfill \boxed{b=30}\)

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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After regrouping 1 tenth into 10 hundredths; we have; 1 whole, 5 tenths, and 10 hundredths, After crossing out 3 tenths and 2 hundredths,; what we have left is; 1 whole, 2 tenths, and 8 hundredths. the result is; 1.28

Given data :

The model can be used as follows;

The model shows a total of 1 whole and 6

tenths. After regrouping 1 tenth into 10

hundredths, there is 1 whole, 5 tenths, and

10 hundredths. After crossing out 3 tenths

and 2 hundredths, there is 1 whole, 2 tenths, and 8 hundredths.

According to the question;

After regrouping 1 tenth into 10 hundredths; we have; 1 whole, 5 tenths, and 10 hundredths

After crossing out 3 tenths

and 2 hundredths,; what we have left is; 1 whole, 2 tenths, and 8 hundredths.

Ultimately, the result is; 1.28

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Answer:

C.

Step-by-step explanation:

(1,000)(0.05)(7)

I = $350

1,000 + 350

=$1,350

Step-by-step explanation:

The ONE  solution to this system of two lines is the point where the two lines cross   at   (1,4)

Answer:

39 ib or pounds

Step-by-step explanation:

easy

Answer:

The slope is 0

Step-by-step explanation:

Given

\((x_1,y_1) = (-8,0)\)

\((x_2,y_2) = (4,0)\)

Required

The slope (m)

This is calculated as"

\(m=\frac{y_2-y_1}{x_2 - x_1}\)

\(m=\frac{0-0}{4 -(-8)}\)

\(m=0\)

The slope is 0

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Setting c=8620 we get:

Now, notice that:

Then:

Therefore:

Since x=-90 does not have real meaning, we get that x=95.

Answer: There are 95 units manufactured at a cost of $8620.

Answer:

Eight hundred and one thousandsths

Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

Answer:

$9.68

Step-by-step explanation:

The total cost before tax is $75.50 + $12.50 = $88

11% of $88 = 0.11 * $88 = $9.68

Answer: $9.68

Answer:

Step-by-step explanation:

$75.50 (bike) + $12.50 (helmet) = $88 (this is the amount shawn will pay before tax

next $88 (total before tax) multiplied by 0.11 (11% tax) to get $9.68 tax. that should be the answer

edit: answer was wrong before, im really sorry if you already submitted the answer and i got it wrong for you.

Using the arithmetic operation of division, the value for 3.12 / 6.5 is obtained as 0.48.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To divide 3.12 by 6.5, we need to use the following steps -

We can align the decimal point by multiplying both the numerator and denominator by a power of 10 to get rid of the decimal in the numerator.

So, we can multiply both 3.12 and 6.5 by 100 to get -

312 / 650

We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF).

In this case, the GCF is 26.

So, we can divide both 312 and 650 by 26 to get -

12 / 25

Use the arithmetic operation of division -

12 / 25 = 0.48

Therefore, 3.12 divided by 6.5 is equal to 12/25 or 0.48 when rounded to two decimal places.

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