solve for brainliest

Answer:

To determine Martha's monthly pension, we need to use the formula provided by the Merrick Oaks School District for calculating the annual pension benefit:

Annual Pension Benefit = (Years of Service x Average of Last Three Annual Salaries) / 55

where 55 is the "pension factor" used by the district.

Using this formula, we can calculate Martha's annual pension benefit as follows:

Annual Pension Benefit = (18 x $100,000) / 55

Annual Pension Benefit = $32,727.27

Therefore, Martha's annual pension benefit is $32,727.27.

To calculate her monthly pension, we simply divide the annual pension benefit by 12:

Monthly Pension Benefit = $32,727.27 / 12

Monthly Pension Benefit ≈ $2,727.27

Therefore, Martha's monthly pension benefit would be approximately $2,727.27 if she retires after 18 years of service.

Step-by-step explanation:

The probability that all three wires will meet the specifications is approximately 0.173 .

Expected value (mean) of wire resistance = 0.13 ohms Standard deviation of wire resistance = 0.005 ohms

the probability for each wire, we need to standardize the range of resistance values using the expected value and standard deviation. We can use the Z-score formula:

Z = (X - μ) / σ

Z is the standard score (Z-score) X is the observed value (resistance) μ is the mean (expected value) σ is the standard deviation

For the lower specification of 0.10 ohms

Z1 = (0.10 - 0.13) / 0.005

For the upper specification of 0.17 ohms

Z2 = (0.17 - 0.13) / 0.005

Using a standard normal distribution table , we can find the probability associated with each Z-score.

Lower bound of standardized range = (0.10 - 0.13) / 0.005 = -0.06

Upper bound of standardized range = (0.17 - 0.13) / 0.005 = 0.80

Let's calculate the probabilities for each wire

P(z < -0.60) ≈ 0.2743

P(z < 0.80) ≈ 0.7881

Since we want the probability that all three wires meet the specifications, we need to multiply these probabilities together since the wires are selected independently.

P(all three wires meet specifications) = P(z < -0.60) × P(z < 0.80) × P(z < 0.80)

P(all three wires meet specifications) ≈ 0.2743 × 0.7881 × 0.7881 ≈ 0.1703

Therefore, the probability that all three wires will meet the specifications is approximately 0.173, or 17.3% .

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The number of triangles is (a) 1 triangle

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

m/A = 51°, a = 22,b = 27

There is only one triangle that can be created using the given parameters

This is so because the given information provides the angle measure of one angle of the triangle and the lengths of the two sides adjacent to that angle.

These three pieces of information (angle measure and two side lengths) are enough to determine the unique triangle.

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Sigma notation is a shorthand way of writing the sum of a series of terms.

The given expression can be written using sigma notation as:

∞

Σ (2/n)

n=1

This is an infinite series that starts with the term 2/1, then adds the term 2/2, then adds the term 2/3, and so on. The nth term in the series is 2/n.

what is series?

In mathematics, a series is the sum of the terms of a sequence. More formally, a series is an expression obtained by adding up the terms of a sequence. Series are used in many areas of mathematics, including calculus, analysis, and number theory.

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Answer:

I think you would be right.

The required choice is given as, " A scatter plot is best when the data are positively correlated."

Here,
A scatterplot is a graph that displays the correlation between two variables. They are a very effective type of chart because they enable viewers to see relationships or trends that would be nearly impossible to see in any other form right away.
A positive correlation is best suited for the scatter plot.

Thus, the required choice is given as, " A scatter plot is best when the data are positively correlated.

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Answer:

396

Step-by-step explanation:

circumference of a circle is 2 x pi x r = 2 x 63 x (22/7) = 396

The solution to the given system of linear equations is x = 4, y = 20

From the question, we are to determine solution to the given system of equations

The given system of equations is

x+y=6x=y+4

Thus, we can write that

x + y = 6x ----------- (1)

and

6x = y + 4 ------------(2)

Solve the two equations simultaneously

From equation (1)

x + y = 6x

y = 6x - x

y = 5x --------- (3)

Substitute into equation (2)

6x = y + 4

6x = 5x + 4

6x - 5x = 4

x = 4

Substitute the value of x into equation (3)

y = 5x

y = 5(4)

y = 20

Hence, the solution to the given system of linear equations is x = 4, y = 20

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Answer:

x < -8, third from top option in the picture.

Step-by-step explanation:

5(2x - 4) < -100

10x - 20 < -100

10x < -80

x < -8

Answer:

3rd option from the top (open circle arrow going left)

Step-by-step explanation:

5(2x-4) is less than - 100

5 times 2x is 10x and 5 times - 4 is - 20 so,

10x - 20 is less than - 100

now do inverse operations to isolate x, add 20

- 20 plus 20 is 0 and -100 plus 20 is - 80

10x is less than -80

divide both sides by 10 and you get,

x is less than - 8

Answer: 1,176 miles

Step-by-step explanation:

490 / 5 = 98 miles

98 mph X 12 hours is 1,176

Using  all the techniques, we can factored the polynomial f(x) = x^4 - x^3 - 7x^2 + x + 6 into its simple factors f(x) = (x + 1)(x - 1)(x^2 + 2x - 5)

To factorize the fourth-order polynomial f(x) = x^4 - x^3 - 7x^2 + x + 6, we can use various techniques such as factoring by grouping, synthetic division, and trial and error. Let's go through the different methods to factorize the polynomial:

Factoring by grouping:

Group the terms in pairs and look for common factors:

x^4 - x^3 - 7x^2 + x + 6

= (x^4 - x^3) + (-7x^2 + x) + 6

= x^3(x - 1) - x(7x - 1) + 6

Now, we can factor out common terms from each group:

= x^3(x - 1) - x(7x - 1) + 6

= x^3(x - 1) - x(7x - 1) + 6

= x(x - 1)(x^2 - 7) - (7x - 1) + 6

The polynomial can be factored as: f(x) = x(x - 1)(x^2 - 7) - (7x - 1) + 6.

Synthetic division:

Using synthetic division, we can find the possible rational roots of the polynomial. By trying different values, we find that x = -1 is a root of the polynomial.

Performing synthetic division with x = -1:

-1 | 1 -1 -7 1 6

-1 2 5 -6

The result is: x^3 + 2x^2 + 5x - 6

Now, we have a cubic polynomial x^3 + 2x^2 + 5x - 6. We can continue factoring this polynomial using the same methods mentioned above.

Trial and error:

We can try different values for x to find additional roots. By trying x = 1, we find that it is also a root of the polynomial.

Performing synthetic division with x = 1:

1 | 1 1 -7 1 6

1 2 -5 -4

The result is: x^2 + 2x - 5

Now, we have a quadratic polynomial x^2 + 2x - 5. We can further factorize this quadratic polynomial using factoring by grouping, quadratic formula, or completing the square.

By applying these techniques, we have factored the polynomial f(x) = x^4 - x^3 - 7x^2 + x + 6 into its simple factors:

f(x) = (x + 1)(x - 1)(x^2 + 2x - 5)

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Answer: 40 cm

Step-by-step explanation: 2/5 x 100 =

200/5 = 40

Answer:

\( \frac{1}{2} \)

Step-by-step explanation:

Given line is passing through the points (8, 0) & (0, - 4)

\(slope \: of \: line = \frac{ - 4 - 0}{0 - 8} = \frac{ - 4}{ - 8} = \frac{1}{2} \\ \)

Answer:

log (2/5)

Step-by-step explanation:

The rule/law you have in mind is as follows:  log a - log b = log (a/b).

Thus, your log 2 - log 5 = log (2/5).

Answer:

Step-by-step explanation:

The answer is the last one because it does not have a relation of increase or decrease of pens or books.

Answer: The 4th one

Step-by-step explanation:

The points keep jumping up and down, so there is no relationship.

Answer:

y > 7x

Step-by-step explanation:

(5xy)/7        [5 x y over 7]

["what value of y would make a product greater than 5 ?​"] can be written as:

(5xy)/7 > 5

Rearrange to find y:  

 (5xy)/7 > 5

  (5xy) > 35

   y > 35/5x

y > 7x

Answer:

Carlos accounts for more than 25% of the total strikeouts

Step-by-step explanation:  Carlos scored 13 points so divide 13 by 37 to get the score Carlos makes up of the 6 people

13/37 = 0.35 or 35%

(The total number of points for all 6 people is 37)

Answer:

8.

Step-by-step explanation:

(8+4)=12. 12 x 1/2 = 6.

Answer:

B

Step-by-step explanation:

Integers cannot contain any decimals. Since 4/3 equals 1.33333, it is not an integer. The other fractions like 12/4 can be simplified to 3 which is an integer.

Answer: $1,652.

Step-by-step explanation:

To calculate Jen's net worth, we need to subtract her liabilities from her total assets:

Net worth = Total assets - Liabilities

In this case, Jen's total assets are $6,964, and her liabilities are $1,670 for credit card debt and $3,642 for a student loan. So:

Net worth = $6,964 - $1,670 - $3,642

Net worth = $1,652

Therefore, Jen's net worth is $1,652. Answer: $1,652.

Answer:

A e f

Step-by-step explanation:

Hope this was helpful!!!

Simplifying 5.5m(3m + 1.2) using the distributive property is A. 16.5m² + 6.6m.

When you multiply a value by a sum, the distributive property of multiplication over addition is used. Say you want to multiply 5 by the product of 10 plus 3. When two terms are similar, we typically add the two numbers before multiplying by 5. However, the property states that you should first multiply each addend by 5.

In this case, 5.5m(3m + 1.2) will be:

= 5.5m(3m + 1.2)

= 16.5m² + 6.6m

In conclusion, it is A.

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

4p^2-8p-5

Step-by-step explanation:

Answer:

4p^2-8p-5

Step-by-step explanation:

Hope this helps :)

In 3 hours Tom drives 243 miles.

So, to find how many miles Tom can drive in 3 hours:

Given: Tom drives 81/2 miles every 1/30 hour.

So, in 30 minutesTom drives 40.5 miles.

Therefore, Tom drives 243 miles in 3 hours.

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Answer:

Okay so x greater then or equal to 7

To plot ask yourself:

Open or Closed Circle:

Open->, <

Closed-Greater then or equal to or less then or equal to

Also ask:

am i ploting to the left or to the right

Step-by-step explanation:

It is going to be a closed circle, since it is greater then or equal too

And you cand use the sign so it is going to go to the left <------ (that way)

You can use the sign to guied you ex: x>5 you are going to the right ---->

Also, for this topic just know if the equation is like this: 3>x

MAKE SURE TO SWICH IT TO THIS:

x<3

YOU HAVE TO SWITCH THE EQUATION AROUND AND THE SIGN

I hope this helped! :D

The units for da/dx are pounds per foot squared.

The units for da/dx would be pounds per foot squared. This is because da/dx represents the rate of change of the function a(x), which has units of pounds per foot, with respect to x, which has units of feet. When we take the derivative of a(x), we essential do division of the change in a(x) by the change in x.  

The change in a(x) has units of pounds, and the change in x has units of feet. Therefore, the units for da/dx are pounds per foot squared.

To further explain this, imagine that a(x) represents the weight of a beam that is x feet long. The units for a(x) would be pounds per foot, as it gives us the weight of the beam per unit of length. The derivative of a(x), or da/dx, would give us the rate at which the weight of the beam changes as we increase its length by one foot.

This rate of change would be in units of pounds per foot squared, as we are dividing the change in weight (pounds) by the change in length (feet squared).

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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Answer:

Step-by-step explanation:

Remark

Moving 6 points left is not going to alter the slope (or it shouldn't).

The x value has to have 6 subtracted from it. Leave the y value alone.

Givens

C: (-5-6,8) = (- 11,8)

D: (2-6,5) =  (-4,5)

Formula

m = (y2 - y1)/(x2 - x1)

Solution

m = (8 - 5)/(-11 - - 4)

m = 3 / - 7

m = - 0.429

Check

Let's find the slope of the original points.

(8 -5)/(-5 - 2) = 3/-7 which is the same thing.