R
On his first three tests Al averaged 76 out of 100.
What score out of 100 must he get on the fourth
test so his average will be 81?

After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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Substituting the value of y = x - 3 we get:-   x - 3 = x²+2x-4

What is Algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for manipulating these symbols in formulas.

In the bottom equation, we need to determine the outcome of substituting for y.

Here is equation (1): y = x - 3

Here is equation (2): y=x²+2x-4

Add the y value from equation (1) to equation (2) in such a way that:

x - 3 = x²+2x-4

The equation above demonstrates that option (4) is the same as the equation above.

Hence, The correct option is D

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the answer is b. x =7

steps

176=(3x+5)+(21x+3)

176=24x+8

168=24x

x=7

Answer:

120

Step-by-step explanation:

We start with the equation:

\(\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40\)

We need to set the fractions into equal denominations so we can sum them all together:

\(\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\\)

Now sum the fractions:

\(\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40\)

Multiple both sides by 24 to eliminate denominator on left side of equation:

\(-8x=-960\)

Divide both sides by -8 to get the value of x:

\(x=120\)

Answer: reject the null hypothesis

Explanation:

If the p-value is smaller than the significance level alpha, then we reject the null. You can think of the p-value being the probability that the null is correct. If the p-value is below a certain threshold (the significance level), then we can be fairly confident that rejecting the null is a good decision.

Your teacher or textbook might have brought up the phrase "If the p-value is low, then the null must go" as a way to help remember this rule. If the alpha level isn't stated, then usually it defaults to 0.05

Given:

There are given the expression:

Explanation:

According to the question:

We need to solve the expression.

Then,

To solve the given expression, we need to use the exponent rule of radical.

So,

From the exponent rule of the radical:

Where

n is the constant number.

So,

Apply the above rule to the given expression;

Final answer:

Hence, the correct option is A.

The range of the function is y ≥ -2 so , correct option is option c

Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.

The graph of the range of the given function is attached below .

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Equation y (1/8 x3 + 7) is rewritten by using a common factor. A literal equation is regarded as having at least two variables.

Given that,

Use a common factor to rewrite one eighth times x cubed times y plus seven eighths times x times y squared.

This is how the equation can be rewritten:

The first equation is written as 1/8 x3y + 7/8 xy2.

It is possible to rewrite the equation 1/8 xy(x2 + y) using the common factor.

Equation two:

1/4x.y.4x2 + 28y

1/4 .4 x³ .y + 28y

x3.y + 28y equation to be solved

Using the formula

y = (x3 + 28).

Third claim:

1/4. x. y. x2 + 7y

Fix the problem.

1/4 . x³ .y + 7y

Write y = (1/4x3 + 7) in a new way.

Fourth assertion:

1/8 x3y2.y + 7 x 1/8 x3y3 + 7 x

After removing the common element x(1/8 x2y3+ 7), rewrite the equation.

Fifth Declaration

1/8 x. y. x² + 7y

1/8 x³. y + 7y

Equation y (1/8 x3 + 7) is rewritten.

Thus, a literal equation is one that contains at least two variables. Solve for one variable in terms of the other variable to rephrase a literal equation.

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Answer:

B.2.5

Step-by-step explanation:

The equation would be

\(-4x +8 = 2x -7\)

I believe that you would know how to solve this.

You could also sub in 2.5 for the x to check.

Good Luck!!!!!

Answer:60 degrees

Step-by-step explanation:

60 degress

43 + 167 + 90 = 300

360 - 300 = 60

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Answer:

171-3=168  168/3=X

Step-by-step explanation:

The number of different arrangements that are there is 72.

If there are 5 people standing with 2 people staying adjacent to each other, hence we can take the 2 people as 1 to have a total of 4.

Hence the number of ways they can be arranged if two people are together is 4! * 2

Hence the number of different arrangements that are there is 72.

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Answer:

104°

Step-by-step explanation:

The principle to apply here is that angle subtended at the center of a circle is twice the angle at circumference.

  Angle subtended at arc  = 52°

  Angle at the center  = 2 x 52°  = 104°

Answer:

104°

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

The member of females before they leave the team is 16. If 4 leave the team, then it is 12. Hence, the current amount of members if 30. 18 divided by 30 equals 0.6, which makes 60%.

Answer:

Rate = 56 gal / 7 min

         = 8 gal / min

Step-by-step explanation:

Hope this helps leave a heart ad maybe brailiest

Answer:

16

Step-by-step explanation:

16

To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

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Answer:

x=1

Step-by-step explanation:

3-√x-2 =0

-√x=2-3

√x=1

x=1²=1

Answer: 43/100

Step-by-step explanation:

43%=

43/100 * 100%=

43/100 * 1=43/100

Answer:

Step-by-step explanation:

Write out the first 4 terms of an infinite geometric series whose sum, S = 2/(4 - 6x ^ 4)

To show that Γ(1) = 1, we substitute z = 1 into the integral representation of the gamma function. Using integration by parts, we can evaluate Γ(2) = 0 + 1 = 1. Using recursive formula for Γ(n), Γ(n) = (n-1)Γ(n-1).

(a) To show that Γ(1) = 1, we substitute z = 1 into the integral representation of the gamma function:

Γ(1) = ∫₀^∞ x^(1−1)e^(−x) dx = ∫₀^∞ e^(−x) dx.

Integrating the exponential function e^(-x) from 0 to infinity gives us the limit as x approaches infinity, which is 0. Therefore, Γ(1) = 0 - 1 = 1.

(b) Using integration by parts, we can evaluate Γ(2):

Γ(2) = ∫₀^∞ x^(2−1)e^(−x) dx.

Let u = x, dv = e^(-x) dx. Then du = dx and v = -e^(-x).

Applying the integration by parts formula: ∫ u dv = uv - ∫ v du, we have:

Γ(2) = [-xe^(-x)]₀^∞ + ∫₀^∞ e^(-x) dx.

The first term on the right-hand side evaluates to 0 - 0 = 0. The second term is the same as the integral in part (a), which we previously determined to be 1.

Therefore, Γ(2) = 0 + 1 = 1.

(c) Using integration by parts again, we can derive the recursive formula for Γ(n):

Γ(n) = ∫₀^∞ x^(n−1)e^(−x) dx.

Let u = x^(n-1), dv = e^(-x) dx. Then du = (n-1)x^(n-2) dx and v = -e^(-x).

Applying the integration by parts formula, we have:

Γ(n) = [-x^(n-1)e^(-x)]₀^∞ + ∫₀^∞ (n-1)x^(n-2) e^(-x) dx.

The first term evaluates to 0 - 0 = 0. The remaining integral is (n-1) times the integral of x^(n-2)e^(-x), which is Γ(n-1).

Therefore, Γ(n) = (n-1)Γ(n-1).

By repeatedly applying this recursive formula, we can express Γ(n) in terms of Γ(n-1), Γ(n-2), and so on, until we reach Γ(1) = 1. This leads to the conclusion that Γ(n) = (n-1)!, demonstrating the connection between the gamma function and the factorial function for counting numbers n.

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Answer:

1,6

Step-by-step explanation:

i just did the test on edge

Answer:

angle 6,2

Step-by-step explanation:

supplementary angles means that the sum of all the angle eqaul 180 degrees, so 6,2 would equal 180 degrees

And i got it correct on e d gu n i t y 2020

Answer:

Step-by-step explanation:

Answer: 1: 14

2: -2

3: 3

4: 2

5: 5

6: 6

7: -1

Step-by-step explanation:

The surface area of the cylindrical food storage container given by the formula SA = 2πrh + 2πr² is 954. 56 inch².

The region is the space taken up by a flat, two-dimensional surface. Its unit of measurement is the square. A three-dimensional object's surface area is the area occupied by its outside surface. It is also measured in square units.

Surface area and volume are calculated for each geometric object in three dimensions. The surface area of an object refers to the space that it takes up.

As, we Know the Surface Area of Cylinder

= 2πr² + 2πrh

Radius of the base = 8 inches

Height of the cylinder = 11 inches.

Now, putting the values we get

= 2πr² + 2πrh

= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11

= 401.92 + 552.64

= 954. 56 inch²

Therefore, the surface area of the cylinder is 954. 56 inch².

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Complete question

Use the formula SA = 2πrh + 2πr2 to find is the surface area of the cylindrical food storage container. Use 3. 14 for π. Round your answer to the nearest hundredth of a square inch

Answer:12220

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

- 7x = - 105 ( divide both sides by - 7 )

x = 15

A line with equation x = c is a vertical line parallel to the y- axis passing through all points with an x- coordinate of c

Thus x = 15 is a vertical line passing through all points with an x- coordinate of 15

Plot (15, 0 ) , (15, 3 ) and (15, - 3) and join a straight line through them for graph

To predict the cost of driving 1800 miles per month, substitute 1800 in the given function C(d) = 0.2d + 280C(1800) = 0.2 (1800) + 280= $640 per month. Therefore, the cost of driving 1800 miles per month is $640.

(b) Graph is shown below:(c)The slope of the graph represents the rate of change of the cost of driving a car per mile. The slope is given by 0.2, which means that for every mile Lynn drives, the cost increases by $0.2.The y-intercept of the graph represents the fixed cost (amount she pays even if she does not drive).

The y-intercept is given by 280, which means that even if Lynn does not drive the car, she has to pay $280 per month.The linear function gives a suitable model in this situation because the monthly cost increases as the number of miles driven increases.

This is shown by the positive slope of the graph. The fixed cost is also included in the function, which is represented by the y-intercept. Therefore, a linear function is a suitable model in this situation.

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Answer:

160 sq units

Step-by-step explanation: multiple 16 times 10 and you get that