A man starts his job with a certain monthlysalary and earns a fixed increment every year. If his salary was$7500 after 4 years of service and $9000 after 10 years ofservice, what was his starting salary and what is the annualincrement? Do you consider it a fair increment according to ourpresent cost of life and infletion?

we are asked to determine the probability that a variable x is greater than 119.8. To do that we will assume a normal distribution of probability and use the following relationship:

To determine the probability that x is smaller than 119.8 we need first to find the z-score of the data set using the following formula:

Where

replacing we get:

Now we use this value to look into the chart for probabilities, we get 0.94408. This is the probability that x is smaller than 119.8. Replacing in the initial relationship we get:

Therefore, the probability is 5.6%.

Let:

Replace (1) into (2):

When a positive number x is divided by 7, the remainder is 4. The remainder when x is divided by 4 is 7.

What is a remainder?

The quantity "leftover" after executing a computation in mathematics is referred to as the remainder. The remainder is the integer that remains after dividing two integers to get an integer quotient in mathematics.

The remainder operator (%) returns the amount of one argument that is left over after dividing it by another operand. For instance, when 41 is divided by 7, the remaining is 6 and the quotient is 5.

Solution Explained:

A/Q

x / 7 = 4

Solving this equation

x = 4 X 7 = 28

Now putting the value of x in the equation

x / 4

= 28 / 4 = 7

Therefore, the remainder when x is divided by 4 is 7.

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Remember that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$3,200

r=5 1/2 %=5.5%=0.055

t=6 years

n=2

substitute the given values

Find out the interest

I=A-P

I=4,431.31-3,200

Solution

Step 1:

Write the expression:

Step 2:

Step 3:

Step 4:

Final answer

The slope-intercept form is

→ y = m x + b

→ m is the slope

→ b is the y-intercept

∵ The given equation is

First, multiply the bracket (x + 9) by 1/3

Subtract 10 from both sides

The equation in the slope-intercept form is y = 1/3 x - 7

In a cyclic quadrilateral opposite sides add up to 180:

Therefore:

Answer:

∠x = 98

ANSWER

EXPLANATION

The total number of muffins is 21.

To find out how many muffins each person will receive, you have to divide the total number of muffins by the number of people it is to be shared with;

Each person will receive 2.625 muffins

Given:

The total cost of espresso machine costs $46.95. and the tax rate is 4%.

To find:

Find the sales tax?

Explanation:

Solution:

We will start by converting sales tax percentage into a decimal by moving

the point two spaces to the left.

6%=0.06

Now, we need to multiply the pre-max cost of this item by this value

in order to calculate the sales tax cost

Round to two decimal places

Last, add this value of the pre-tax value of the item to find the total cost.

Hence, these are the required values.

Remember that the equation of the line in slope-intercept form is equal to

y=mx+b

where

m is the slope

b is the y-coordinate of the y-intercept

In this context

we have

C=mt+b

step 1

Find out the slope

we need two points

looking at the graph

we take (0,100) and (1,150)

so

m=(150-100)/(1-0)

m=50 --------> that means $50 per month (monthly fee to remain a member)

the y-intercept is the value of y when the value of x is zero

in this context, the y-intercept is the cost C when the value of t is zero

b=100 ------> that means a one-time fee to join

substitute

so the answer is option #1

These questions can have multiple answers

for instance,

a)

_+_=10.5

8.5 + 2 = 10.5

5.5 + 5 = 10.5

3.5 +7 = 10.5

5.25 + 5.25 = 10.5



b)

_-3.25 =_

7 - 3.25 = 3.75

7.25 - 3.25 = 4

10. 5 - 3.25 = 7.25

c)

if each _ have the same value

x + x = 10.5

2x= 10.5

x= 5.25

d)

if each _ have the same value

_-3.25 =_

x -3.25= x

x-x = 3.25

0= 3.25

In this case, each x cannot be the same, it would have to be a number that you subtract 3. 25 and it remains the same number. That is not possible.

but if i use x= 5.25

5.25- 3.25= 2

Here, we want to select from the options, the two best statements that completes the steps

The two steps are;

Multiply the origi

Answer:

17/24

Explanation:

To add the fractions

we first find their common denominators.

The common multiple of 3 and 8 is 24 because 3 * 8 = 24; therefore,

Adding the numerators gives

Hence,

You first draw two circles when different radii.

When you select two point over the circumference, and you connect a line in between these points and the center of the circle, you will always obtain two sides with the same length. It is because the length of these sides coincides witht the ratio of the circle.

Then, when you connect the points over the circumference between them, you have a side that can have a different length compared with the lengths of the lines connected to the center. Thus, you obtain an isosceles triangle; you have two sides with the same length (remember, it's the same as the radius) and one side with another length.

Answer:

C. -4 ± 2√6

Explanation:

The given equation is

3x² + 24x - 24 = 0

First, add 24 to both sides

3x² + 24x - 24 + 24 = 0 + 24

3x² + 24x = 24

And factorize 3 on the left side

3(x² + 8x) = 24

Then, to complete the square, we need to add and substract (b/2)² to the expression in parenthesis. In this case, b = 8, so

(b/2)² = (8/2)² = 4² = 16

Then, add and subtract 16 as follows

3(x² + 8x + 16 - 16) = 24

3(x² + 8x + 16) - 3(16) = 24

3(x² + 8x + 16) - 48 = 24

Finally, we can factorize and solve for x

3(x + 4)² - 48 = 24

3(x + 4)² - 48 + 48 = 24 + 48

3(x + 4)² = 72

3(x + 4)²/3 = 72/3

(x + 4)² = 24

Solving for x, we get

Therefore, the answer is

C. -4 ± 2√6

Answer:

15.5

Step-by-step explanation:

23-20=3

6x-3=90

3-90=93

93÷6=15.5

Answer:

14.5

Step-by-step explanation:

i got it right on the test

Answer

Step-by-step Explanation

In the expansion of variables in a bracket raised to a particular power, we either use the Binomial theorem or the Pascal's triangle.

The Binomial theorem teaches how to use permutaion and combination to obtain the coefficients of each term while the Pascal's triangle presents the coefficient of each term for different integer powers of the variables in a triangular form where the next line of the triangle can be obtained from the previous line just by starting with a 1 and adding two consecutive terms of that previous line and ending with 1.

The solution of the given equation are; (x + 8)(x − 9)

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

We have been given the quadratic equation as;

x² − x − 72

Solving;

x² − (9-8)x − 72

x² − 9x +8x− 72

The factors are;

(x + 8)(x − 9)

Therefore, the solution of the given equation are; (x + 8)(x − 9)

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Solve the given inequality as shown below

Therefore, any number equal to or greater than 5 is a solution to the given inequality.

The correct answers are 5, 6, and, 7.

Step 1: Write out the formula

By the intersecting secant theorem (interior),

Step 2: Write out the given values and substitute them into the formula

Therefore,

Hence, m<1 = 46 degrees

Since BD bisects ABC, then angles ADB and BDC are congruent. Now that we have that both triangles ABD and CBD have the same two sides and angle, we have that they are congruent (because the side-angle-side postulate)

• You know that the sum of the two numbers must be:

In order to find any pair of numbers whose sum is that number shown above, you can subtract 1 from it:

Now you can set up that:

• To find any pair of numbers whose difference is:

You can add 2 to it:

Then, you can set up that:

• Let be "x" and "y" the numbers that add up to 5.678. and whose difference is 9.876.

Then, you can set up these equations:

• To solve the riddle, you can follow these steps:

- Set up a System of equations using the equations found in the previous part:

- Apply the Elimination Method by adding both equations and solving for "x":

- Substitute the value of "x" into one of the original equations and solve for "y":

Therefore, the answers are:

• Any pair of numbers whose sum is 5.678:

• Any pair of numbers whose difference is 9.876:

• Equations that represents the riddle:

• Solution of the riddle:

The function in the graph is V shaped, this indicates that it corresponds to a function of an absolute value of x:

The V opens downwards, which means that the coefficient that multiplies the module (a) is negative:

→ This means rthat when we calculate the value of "a", this value has to be negative

As you can see in the graph, the vertex of the function is (0,3)

Following the vertex form:

Where xv represents the x-coordinate of the vertex and yv represents the y-coordinate of the vertex. Replace them in the formula and we get that:

Now all we need to do is determine the value of "a", for this we have to use one point of the function and replace it in the formula, this way "a" will be the only unknown.

Lets take for example one of the roots (points where the function crosses the x-axis)

Point (1, 0)→ replace it in the formula

Now that we know the value of a, we can determine the wquation of the function as

Given the function:

The x-intercept iswhen y =0, so:

And

And

Therefore, the x-intercepts are:

(-4, 0), (2, 0) and (1, 0)

Answer:

(-4, 0), (2, 0) and (1, 0)

Tp fint the total area of the figure start by calculating the area of the square and the triangle separately.

Area of the square is calulated by mutiplying the side by the side

Area of the triangle follows the formula:

The base of the triangle is the same as the length of the square's side.

Add both sides to find the total area

Answer:

2012: $950,000

2025: $625,000

Explanation:

Since the scrap value is $0, the amount depreciated each year is equal to the initial worth of the building divided by the number of years, so

It means that each year the worth of the building decreases by $25,000

Then, 2012 is 2 years after 2010, so the book value of the building in 2012 is:

$1,000,000 - 2($25,000) = $950,000

In the same way, 2025 is 15 years after 2010, so the book value is

$1,000,000 - 15($25,000) = $625,000

Therefore, the answers are

2012: $950,000

2025: $625,000

There can be infinite solutions for x and y, this is because if we look at the equation like a slope intercept equation

we can see that this is the equation for a straight line.

if we graph it

All values of x and y that are obtain by the line can be a solution to the equation given.

Triangle GAF is an

Triangle BEC is a

Triangle BFG is an

Triangle CFE is