what is equilivent to 28/2

The area of the shaded region is given as follows:

298.3 units².

The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:

A = πr²

The larger circle has a radius of 7 + 5 = 12 units, hence it's area is given as follows:

A = 3.14 x 12²

A = 452.16 units².

The smaller circle has a radius of 7 units, hence it's area is given as follows:

A = 3.14 x 7²

A = 153.86 units².

Hence the area of the shaded region is given as follows:

452.16 - 153.86 = 298.3 units².

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As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.

However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.

One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:

7+37 = 7(1+3)

Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:

7 x (1+3) or 7 x 4

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Note that given the factors above, Orr should replace the above plant. This has to do with depreciation and book value.

We need to first compute the current total cost of keeping the old plant.

Book value = $4,500,000 - $1,000,000/year x 4 years

= $500,000

Thi smean that the current total cost of keeping the old plan tfor the reamining 10 year is

Total cost of keeping old plant = $1,000,000/year x 10 years - $500,000 + $150,000

= $9 650 000

Now lets calculate the total cost of purchasing the new plant for 10 years.

$600,000 - $150,000

= $450,000 per year.

The salvage value after 10 years is $0.

Total cost of new plant = $3,500,000 + $450,000/year x 10 years = $8,000,000

Since the cost of keeping is higher than the new one, then Orr should get a new plant.

$9 650 000 > $8,000,000

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The sum of both sides is 2x² + 4. The length of the third side is 5x³ - 4x² + 3x - 12

A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, right angled, scalene, equilateral.

Given that the perimeter of the triangle is 5x³ - 2x² + 3x - 8. The length of side one is 3x² - 4x - 1 and that of side two is -x² + 4x + 5

The sum of side one and side two is:

Sum = side 1 + side 2 = (3x² - 4x - 1) + (-x² + 4x + 5) = 2x² + 4

The sum of both sides is 2x² + 4

The third side is:

Third side = Perimeter - Sum of two sides = (5x³ - 2x² + 3x - 8) - (2x² + 4) = 5x³ - 4x² + 3x - 12

The length of the third side is 5x³ - 4x² + 3x - 12

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Part A) The vertex of the graph of the function, (t, h(t)) is (2, 68).

Part B) The t-coordinate of the vertex represent is the time it takes for the ball to reach its maximum height (option b)

Part C) The h(t)-coordinate of the vertex represent is the ball's maximum height (option a).

Part A asks for the vertex of the graph of the function, which is the point where the function reaches its maximum or minimum value. To find the vertex of a quadratic function like

=> h(t) = 4 + 64t – 16t²,

we can use the formula

=>  t = -b/2a,

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c and t is the input variable (in this case, the time).

The t-coordinate of the vertex is simply the value we get when we plug this formula into our equation.

So, for

=> h(t) = 4 + 64t – 16t²,

we have a = -16, b = 64, and c = 4.

Plugging these values into the formula

=> t = -b/2a,

we get

=> t = -64/(2*(-16)) = 2.

The t-coordinate of the vertex is therefore 2.

To find the h(t)-coordinate of the vertex, we can simply plug t = 2 into the function h(t) = 4 + 64t – 16t² and evaluate it.

This gives us

=> h(2) = 4 + 64(2) – 16(2²) = 68.

Therefore, the vertex of the graph of h(t) is (2, 68).

Part B asks what the t-coordinate of the vertex represents. We know that the t-coordinate is the time at which the ball reaches its maximum height.

Therefore, the correct answer is B: the time it takes for the ball to reach its maximum height.

Part C asks what the h(t)-coordinate of the vertex represents. We just found that the h(t)-coordinate of the vertex is the maximum height of the ball.

Therefore, the correct answer is A: the ball's maximum height.

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Answer:

so first off if its six grandchildren and 3 children then that means 9 people but if the children get double the amount distributed then lets treat it like 12 people so 25,000 each meaning each child of the police officer gets 50 thousand and each grandchild gets 25 thousand

Step-by-step explanation:

hope this helps !

Answer:

$12,276.24

Step-by-step explanation:

22000 / (1 + 0.105/12)^4*12

12276.24

She earn fοr each year frοm 2014 thrοugh 2016 is 80628.40. The average οf her last five years οf wοrking $78,302.80. His annual retirement benefit was $28,423.92.

a) Salary οf 2014 : $76000

Salary in 2014 is the salary in 2015 increased by 3% οf the salary

= $76,000+3%

Salary οf 2015 = $78,280

Salary in 2015 is the salary in 2016 increased by 3% οf the salary

=$78,280+3%

Salary οf 2016 = $80,628.40

Hence, she earn fοr each year frοm 2014 thrοugh 2016 is 80628.40

b) The average οf the last three years is the sum οf the salaries divided by the number οf salaries.

= $76,000+$78,280+$80,628.40 / 3

= $78,302.80

Hence, the average οf her last five years οf wοrking $78,302.80

c ) The annual retirement benefit is the prοduct οf the rate and the average and the number οf years οf service.

= 1.65%×$78,302.80×22

=$28,423.92

Hence,  his annual retirement benefit was $28,423.92.

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The functions f(x) = cos 2x + 1 and g(x) = sin x + 2 intersect at x = pi/6, pi/2, 5pi/6, and 3pi/2 in the interval [0, 2π).

To find the intersection points, we set f(x) equal to g(x) and solve for x.

cos 2x + 1 = sin x + 2

Rearranging, we get:

cos 2x = sin x + 1

Using the identity cos 2x = 1 - 2sin²x, we can rewrite this as:

1 - 2sin²x = sin x + 1

Simplifying and factoring, we get:

2sin²x + sin x = 0

sin x(2sin x + 1) = 0

Therefore, sin x = 0 or sin x = -1/2. Solving for x in the interval [0, 2π), we get x = pi/6, pi/2, 5pi/6, and 3pi/2. These are the values at which f(x) and g(x) intersect.

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Answer:

2 (x + 1)(x + 9)

Step-by-step explanation:

The given expression is
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right)[/tex]

and we are asked to factor it

Step 1
Remove parentheses
[tex]\left(2x^2\:+\:23x\right) = 2x^2 + 23x\\\\-\:\left(3x\:-\:18\right) = - (3x) - (-18) = -3x + 18\\\\[/tex]

Step 2
Add the individual terms to correspond to the original expression:
[tex]\left(2x^2\:+\:23x\right)\:-\:\left(3x\:-\:18\right) \\\\= 2x^2 + 23x -3x + 18\\\\= 2x^2 + 20x + 18[/tex]

Step 3
Factor out common term 2

[tex]2x^2+20x+18 \\\\= 2\left(x^2+10x+9\right)[/tex]

Step 4
Factor [tex]x^2+10x+9[/tex]

To do this find two numbers such that their sum = 10 and product = 9
We can easily see that these two numbers are 1 and 9 because 1 + 9 = 10 and 1 x 9 = 9

Therefore, splitting the expression into groups we get
[tex]x^2 + 10x + 9 = x^2 + 1x + 9x + 9\\\\[/tex]

Step 5

Factor:

[tex]x^2 + 1x = x(x+ 1)\\9x + 9 = 9(x + 1)\\\\[/tex]

Therefore
[tex]x^2 + 1x + 9x + 9 = x(x + 1) + 9(x + 1)\\\\[/tex]

Step 6

Factor common term (x + 1) from the expression
[tex]x(x + 1) + 9(x + 1) = (x + 1)(x + 9)[/tex]

Step 7
Putting it all together
Remember we factored out the 2 in step 3 so we got to put it back into the factored expression giving the final factored expression as

[tex]2 (x + 1)(x + 9)[/tex]

If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23.  the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

The formula for a confidence interval for the population mean is:

CI = X- bar ± z* (σ/√n)

where:

X- bar  = sample mean

z* = z-score for the desired level of confidence (99% in this case)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 113 ± 2.576 * (23/√100)

Calculating the standard error:

SE = σ/√n = 23/√100 = 2.3

Now we can substitute this value into the formula:

CI = 113 ± 2.576 * 2.3

CI = 113 ± 5.92

So,

Lower limit: 107.1

Upper limit: 118.9

Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

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the correct expression which can also be used to determine the total time needed to cook x batches of boiled cornbread is,

B) 10x + 10x + 20 - 5.

Given that;

The expression 20x + 15 represents the total time needed to cook x batches of boiled cornbread.

We can simplify this expression by factoring out the common factor of 5: = 20x + 15

= 5(4x + 3)

Therefore, the expression that can also be used to determine the total time needed to cook x batches of boiled cornbread must have a factor of 5 in it.

Option A:

18x + 4x + 6 + 7 does not have a factor of 5,

so it cannot be the correct answer.

Option B:

10x + 10x + 20 - 5

= 20x + 15,

which is the same as the original expression.

Therefore, Option B is equivalent to the original expression and can also be used to determine the total time needed to cook x batches of boiled cornbread.

Option C:

6(5x + 5) - 10x + 15 = 30x + 15 - 10x + 15 = 20x + 30,

which does not have a factor of 5.

Therefore, Option C is not correct.

Option D:

3(x + x + x + 3) + 2x + 15 = 9x + 6 + 2x + 15 = 11x + 21,

which does not have a factor of 5.

Therefore, Option D is not correct.

Therefore, the correct answer is,

B) 10x + 10x + 20 - 5.

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Answer: 1; 520/9 number 2: 9/2 number 3: d number 4:d number 5: 151.7

Step-by-step explanation:

Answer:

-3 3/8

Step-by-step explanation:

The critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data.

To find the critical value for an 80% confidence interval, we need to determine the z-score corresponding to the level of confidence. We can use a standard normal distribution table or a calculator to find this value.

Using a standard normal distribution table, we can find the z-score that corresponds to an 80% confidence level by finding the area between the mean and the upper tail of 10%, which is (100% - 80%)/2 = 10%.

The area between the mean and 10% is 0.5 - 0.10 = 0.40. Using the standard normal distribution table, the z-score that corresponds to an area of 0.40 is approximately 1.28.

Hence, the critical value for an 80% confidence interval is 1.28 (rounded to three decimal places).

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In the triangles given the analysis for same is given below

1) the corresponding vertices are

R ~ C and

E ~ 0

2) The corresponding angle are

∠E ~∠O  and

∠ R ~ ∠C

3)

The corresponding sides are;

ER ~ CO;
MO ~ EM
CM ~ RM

4)  the congruent angles are:

∠REM ≅ ∠MOC
∠ERM ≅ ∠MCO
∠CMO ≅ EMR

5) the congruent sides are:

ER ≅ CO;
MO ≅ EM
CM ≅ RM

6) the congruent triangles are;

ΔMER ≅ ΔMOC

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Answer:

Step-by-step explanation:

4x - 5 = 7

4x = 7 + 5

4x = 12

x = 12/4

x = 3

Answer:

Step-by-step explanation:

Observation of the real life and way of life of the peoples of Oceania are intertwined in them with local myths.

If the number 48700 is written in scientific notation, it will be in form 4.87×10ⁿ, and the value of n is 4.

Scientific notation describes the shorthand way of writing very large or very small numbers in standard forms.

Writing in scientific notation, a number between 1 and 10 is multiplied by a power of 10.

48700 = 4.87×10ⁿ = 4.87×10⁴

Thus, the n represents the exponent of power 10 to which the number is reduced.

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The confidence interval is 0.52±0.067.(option c)

What is confidence interval?

In statistics,  confidence interval means that the probability in which a population parameter will fall between a set of values for a certain proportion of times.

A political pollster wants to know what proportion of voters are planning to

vote for the incumbent candidate in an upcoming election. A poll of 150

randomly selected voters is taken from the more than 2,000 voters in the

population, and 78 of those selected plan to vote for the incumbent

candidate.

The formula for confidence interval(CI) is given by:

                      CI=  p ± z √{p(1-p)/n} ----------------(1)

Here from the given data p= 78/150= 0.52

                                          n= 150

For 90% confidence interval the value of z= 1.645.

Putting all the values in equation (1) we get,

                         CI= 0.52± 1.645√{(0.52×0.48)/150}

                             = 0.52±1.645×0.04

                             = 0.52±0.067

Hence, the confidence interval is 0.52±0.067.

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Using the data given such as the margin of error, sample size and z-score, the maximum sample size required is 499

To solve this problem, we need to know the minimum sample size required. The formula for this is given as;

n = (z² * p(1 - p))/ E²

Substituting the values into the formula;

n = (1.645² * 0.21(1 - 0.21))/ 0.03²

n = 498.8

The sample size should be at least approximately 499

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The function to describe the number of new wheels Boyd has left is f(x) = 92 - 4x

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

After assembling x skateboards, we have

f(x) = Shipmnet - Rate * x

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

f(x) = 92 - 4 * x

Evaluate

f(x) = 92 - 4x

Hence, the function is f(x) = 92 - 4x

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To find out how many visitors Jackson's Ice Cream Shop needs on Saturday to make a profit for the week, we need to first calculate the total number of visitors for the six days already given in the table. Then we can find out the number of visitors needed on Saturday to reach the required mean of 110 visitors per day for the week.

Total number of visitors for the six days = 63 + 77 + 121 + 96 + 137 + 154 = 648

To make a profit for the week, the total number of visitors for the entire week needs to be:

110 visitors/day × 7 days/week = 770 visitors/week

We already have 648 visitors for the six days, so the number of visitors needed on Saturday to make a profit can be found by subtracting the total number of visitors already counted from the total number of visitors needed for the week:

770 - 648 = 122

Therefore, the answer is (C) 122 visitors on Saturday are needed to make a profit for the week.

Answer:

the answer for this question is x=8

Answer: the increase in price from $25 to $25.25 would result in a small increase in annual pass revenue of $178.50 or about 0.3%.

Step-by-step explanation: we can calculate the modern yearly pass income by increasing the modern amount requested by the unused cost of $25.25:

Unused yearly pass income = Modern cost x Modern amount requested

Unused yearly pass income = $25.25 x 2482 = $62,678.50

We as of now know that the ancient yearly pass income is $62,500 (since 2500 passes were sold at $25 each), so ready to calculate the alter in yearly pass income:

Alter in yearly pass income = Unused yearly pass income - Ancient yearly pass income

Alter in yearly pass income = $62,678.50 - $62,500 = $178.50

The community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms.

Now, The evaluation of community response to women and children in the context of Bill of Rights, Discrimination, and Human Rights Violations can be done as follows:

Bill of Rights:

The Bill of Rights guarantees certain rights and freedoms to all individuals regardless of their gender or age. Therefore, any discrimination or violation of women and children's rights would be a direct violation of the Bill of Rights. The community must ensure that women and children are not denied their right to life, dignity, equality, and freedom from all forms of violence and exploitation.

Discrimination:

Discrimination against women and children is a prevalent issue in many societies. Women and children are often subjected to discrimination on the basis of their gender, age, race, religion, or socio-economic status. The community should work towards eliminating all forms of discrimination against women and children and provide them with equal opportunities in all spheres of life.

Human Rights Violations:

The community must also ensure that the human rights of women and children are protected. Human rights violations against women and children can include physical and emotional abuse, sexual harassment and assault, child labor, child marriage, and human trafficking, among others. The community must take a strong stance against such violations and work towards preventing and punishing the perpetrators.

In conclusion, the community's response to women and children in light of the Bill of Rights, Discrimination, and Human Rights Violations should prioritize the protection and promotion of their rights and freedoms. Any form of discrimination or violation of their rights should be condemned and punished to ensure that women and children are safe and empowered members of society.

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Answer:

12.5 is the answer

Step-by-step explanation:

7 × 60 ( 7 being the minutes, 60 being the hour )

= 420

+ 30

= 450

450 ÷ 3600 × 100

45000 ÷ 3600

450 ÷ 30

= 12.5

12.5 being the answer

read the paragraph and then you’d have all the information that you need

Answer:

First braclets coast 3$ and necklaces coast 6$ so now in the box you can put 3in the first one then 6 in the next and keep going its like multiples of 3 and 6 :) Hope this helps.

Step-by-step explanation:

Answer: you could reflect the points (2, 4) to both axisis to find the inverse, add a negative in front of both numbers, or multiply the function by -1.

Step-by-step explanation:

Have a great night.