please help me solve this problem!!

The number of possibilities for 8 of 37 servers to fail is 38608020

From the question, we have

Total number of servers, n = 37

Numbers to servers that fail, r = 8

The number of ways for 8 serves to fail is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 37 and r = 8

Substitute the known values in the above equation

Total = ³⁷C₈

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 37!/29!8!

Evaluate

Total = 38608020

Hence, the number of ways is 38608020

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Step-by-step explanation:

850 calls

1000:100=10

1%=10

10×85=850

Discount is the reduction in value. The total number of calls not answered this is 150 calls

Given the following

Total number of calls = 1000 calls

If 15% of those calls were not answered, the total calls that were not answered is given as:

Total call not answered . = 0.15 * 1000

Total call not answered = 150 calls

Hence the total number of calls not answered this is 150 calls

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The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

Both the girls have 62 lollipops

Step-by-step explanation:

25+25=50

50+12=62

Answer:

62 lollipops

Step-by-step explanation:

If Angie has 12 more lollipops than Crystal...

25 + 12 = 37 lollipops

Angie has 37 lollipops and Crystal has 25 lollipops. In total, that is...

37 + 25 = 62 lollipops

Using proportions, it is found that the dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Each TB has 1000 GB, hence:

20.6 terabytes = 20,600 Gigabytes.

You have available a 1 Gbps dedicated link for data transfer, hence the time it would take for the transfer through the dedicated link is:

20,600/1 = 20,600 seconds.

Each hour has 3600 seconds, hence the time in hours is:

20600/3600 = 5.72 hours.

The dedicated link would take 5.72 hours, which is significantly less time than the USPS delivery, hence the link should be used.

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Answer:

His overall final score is a 73, which means that that student recieved a letter grade of a C.

Step-by-step explanation:

First, we are finding the mean of the scores to average everything out.

So, start by adding up all the scores given: 60+80+75+78=293.

Then, divide that sum by the number of scores given: 293/5=73.25, or rounded to a whole number is a 73.

In most schools, a 73 is a C, so this students letter grade for this course is a C.

Answer:

a. 1.44

Step-by-step explanation:

We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.

At the null hypothesis, it is tested if the proportion is of at most 40%, that is:

\(H_0: p \leq 0.4\)

At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:

\(H_1: p > 0.4\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \(p = 0.4, \sigma = \sqrt{0.4*0.6}\)

A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.

This means that:

\(n = 200, X = \frac{90}{200} = 0.45\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}\)

\(z = 1.44\)

Thus the correct answer is given by option a.

A graph of the data is shown in the image attached below.

The slope is equal to 0.4.

The y-intercept from the graph is equal to

An equation for the graph in slope-intercept form is y = 0.4x + 2.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the formula, we have;

Slope, m = (10 - 4)/(20 - 5)

Slope, m = 6/15

Slope, m = 2/5 or 0.4

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (5, 4), an equation in slope-intercept form is given by:

y - y₁ = m(x - x₁)

y - 4 = 0.4(x - 5)

y - 4 = 0.4x - 2

y = 0.4x - 2 + 4

y = 0.4x + 2.

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Answer:

y = -x + 11

Step-by-step explanation:

y = mx + b

m is the slope and b is the y-intercept so m = -1

y = -x + b

Now substitute x = 8 and y = 3:

3 = -8 + b

b = 11

Thus the final equation is y = -x + 11.

Answer:

The lines represented by the equations y = -X – 3 and

5y + 5x = -15

Step-by-step explanation:

neither are parallel nor perpendicular

Submit Answer

the same line

parallel

perpendicular

What is the answer?

Answer:

The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:

standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7

To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:

z = (37.4 - 40) / (8 / 7) = -1.225

Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.

give thanks, your welcome <3

Step-by-step explanation:

Answer:A shopkeeper has 2425 boxes of 24 pencils each. How many pencils do all the boxes have in all?​

Step-by-step explanation:

9 directly precede 2, 4 times, in the sequence, 12909296292629.

An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).

In the given sequence,

12909296292629,

there are 4 such 9's that are preceded by 2 immediately.

That means, for the clear representation,

1-29-09-29-6-29-26-29

Therefore, there are 4 such 9's that are preceded by 2.

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Looking at the 4th net, we see it has what seems to be 4 squares in a line. And two of them are each one united into another square.

Then, when we join the left side of the left square and the right side of the right square, we obtain a 3D object with 4 square faces, and 2 empty faces also in the form of a square.

After that, we can fold down the upper square face, and fold up the other one.

We will get the following 3D object, that is a cube:

Therefore, the 4th net makes a cube.

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

Answer: 10

Step-by-step explanation:

If two triangles are congruent, then they will have the exact same sides and angle measures.

AB=3x+1

BC=6

DE=2x

Solve for X by making 2x=6 because DE and BC are corresponding sides, indicating they are equal.

x=3, plug that in

AB=10

The evaluated function values are g(-3) = 11, g(5) = 11, g(a) = 11 and g(a+h) = 11

A composite function is a function that results from combining two or more functions. It is created by using the output of one function as the input of another function.

The function g(x) is defined as g(x) = 11, which means that the output of the function is always 11, no matter what value of x is inputted.

i.e. the function g(x) = 11 always returns the value 11, regardless of the input.

Therefore, we have:

g(-3) = 11

g(5) = 11

g(a) = 11

g(a+h) = 11

So, regardless of the value of a or h, the function g(x) will always return 11.

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The right answer is No solution.

Look at the attached picture

Hope it will help you

The class limit of the given data is the actual values from the data that represents the lower values and the larger values of a data set. While the class boundaries represents the values that eliminate gaps between the classes in the frequency distribution which are one decimal place more accurate than the data.

To determine the class limit, using a class interval of 5.00, the following should be carried out;

The lowest figure from the given data set = 48.6. Therefore, the lower class interval should start from a figure lower than 48.6 such as = 45.0

For the class limits;

= 46.0 - 50.0

50.0 - 54.0

54.0 - 58.0

58.0 - 62.0

62.0 - 66.0

66.0 - 70.0

70.0 - 74.0

74.0 - 78.0

78.0 - 82.0

82.0 - 86.0

86.0 - 90.0

90.0 - 94.0

The class boundaries would be determined below:

45.50 - 50.50

50.50 - 54.50

54.50 - 58.50

58.50 - 62.50

62.50 - 66.50

66.50 - 70.50

70.50 - 74.50

74.50 - 78.50

78.50 - 82.50

82.50 - 86.50

86.50 - 90.50

90.50 - 94.50

94.50 - 99.50

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Answer:

B and E

Step-by-step explanation:

A. -7 ÷ (-4) = -7/-4 = 7/4 = 1.75

B. -(3 ÷ 2) = -(1.5) = -1.5

C. -8/5 * (-5/8) = (8/5) * (5/8) = 1

D. -5/-3 = 5/3 ≈ 1.667

E. -9 ÷ 6 = -9/6 = -1.5

Answer:

3/4n = 5/8

Step-by-step explanation:

your…. welcome……

I don’t trust meself so I might be wrong

The probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

To solve this problem using a normal approximation, we need to calculate the mean (μ) and standard deviation (σ) of the binomial distribution and then use the normal distribution to approximate the probability.

Given:

Probability of an airline flight arriving on time (success): p = 0.84

Number of trials (flights): n = 400

Number of flights arriving on time (successes): x > 240

First, we calculate the mean and standard deviation of the binomial distribution using the following formulas:

Mean (μ) = n * p

Standard Deviation (σ) = √(n * p * (1 - p))

μ = 400 * 0.84 = 336

σ = √(400 * 0.84 * 0.16) = √(53.76) ≈ 7.33

Now, we can use the normal distribution to find the probability that more than 240 flights will arrive on time. Since we're interested in the probability of x > 240, we will calculate the probability of x ≥ 241 and then subtract it from 1.

To use the normal distribution, we need to standardize the value of 240:

z = (x - μ) / σ

z = (240 - 336) / 7.33

z ≈ -13.13

Now, we can find the probability using the standard normal distribution table or a calculator. Since the value of z is extremely low, we can approximate it as:

P(x > 240) ≈ P(z > -13.13)

From the standard normal distribution table or calculator, we find that P(z > -13.13) is essentially 1 (close to 100%).

Therefore, the probability that more than 240 flights in a random sample of 400 commercial airline flights will arrive on time is approximately 1 or 100%.

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Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

The "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.

The total number of certain digits in a measurement plus one estimated or uncertain digit make up the significant figures.

Thus, the "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.

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Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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The surd is rationalized to give √6 - 5√3 + 5√2 - 25/2  + 25

It is important to note that fractions are a part of whole number or element.

The different types of fraction includes;

Given the expression;

√3 - 5/√2 + 5

√3 - 5/ √2 + 5 ×√2 - 5/√2 - 5

Multiply the values

√6 - 5√3 + 5√2 - 25/√4 - 5√2 + 5√2 + 25

Add the like surds and find the square roots, we get

√6 - 5√3 + 5√2 - 25/2  + 25

Hence, the expression is √6 - 5√3 + 5√2 - 25/2  + 25

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Answer:

y = 6

Step-by-step explanation:

   3x + y = 9 ---------------(I)

          y = -4x + 10 -----------------(II)

Substitute y = -4x + 10 in equation (I)

  3x - 4x + 10 = 9

Combine like terms,

        -x + 10  = 9

Subtract 10 from both sides. (subtraction property of equality)

               -x  = 9 - 10

              -x = -1

Divide both sides by (-1).  {Division property of equality}

              \(\sf \dfrac{-x}{-1}=\dfrac{-1}{-1}\\\\ \boxed{x = 1}\)

Now, substitute x = 1 in equation (II) and find the value of y.

        y = -4*1 + 10

          = -4 + 10

       \(\sf \boxed{\bf y = 6}\)