A woman earned wages of $34,600, received $1500 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. She was entitled to a personal
exemption of $2900 and had deductions totaling $5090. Find her gross income, adjusted gross income, and taxable income.

|u|=c is equivalent to u = c or u = -c.

Given that c > 0.

i.e., c is a positive number.

Then |u| = c. That is, absolute value of u = c, a positive number.

An absolute value function is defined by,

 |u| = { u   ; if u ≥ 0

        { -u   ; if u < 0

The absolute value of any number, Positive or negative, is always a positive number.

So here |u| = c, with c > 0.

Comparing with the definition of absolute value function, c is either u or -u.

More clearly, c = u, when u ≥ 0 or c = -u , when u < 0.

Hence the value of c depends on u.

Thus,  |u|=c is equivalent to u = c or u = -c.

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A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12

B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9

A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;

-1/8j + 2/3 - (5/3j + 9/12)

= -1/8j + 2/3 - 5/3j - 9/12

= -1/8j - 5/3j + (2/3 - 9/12)

= (-3j-40j / 24 + (8-9) / 12

= [-⁴³/₂₄j + (-1)]/12

B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)

Expand the brackets to get;

-13.5b - 6.3 - 6b - 0.6

= -13.5b - 6b - 6.3 - 0.6

= - 19.5b - 6.9

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a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

What is permutation and combination?

In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.

Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations

We are given that license plate allows 2 digits and 4 upper case letters

a) repetition is allowed

hence for 2 numbers we have 10*10=100 choices

Also letter are allowed 26*26*26*26=456976 choices

And Hence total choices are 456976*100=45697600 ways

b) Repetition is not allowed

hence for 2 numbers we have 10*9=90 choices

Also letter are not allowed 26*25*24*23= 358800 choices

And Hence total choices are 456976*100=32292000 ways

Hence

a)Total different number plates will be 45697600

b) Total different number plates will be 32292000

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Answer:

Since AB = BC,

3m + 5 = 4m - 10

m = 15

Answer:y

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

-7/8  /  (- 7/5)     =  - 7/8  *- 5/7  = 5/8  

Answer:

so 50:30

=50-30=20

chocolate and 5are caramel

20:5

5can go into 20 =4

20:5

=4:1

Step-by-step explanation:

bag of candy is 50pieces 30piecesare chocolate and 5arecaramel

step 2 . you will subtract 50from30=20

step 3. 5can go into 20=4times

20:5 is equal to 4:1

Answer:

f(1)= -3

Step-by-step explanation:

what f(1) means is when x is 1 what is y. I dont see the graph labeled so im just assuming that the graph is going by ones. So what i did was i found where x is one and then i checked at what point did the line match with the y axis which was 3 points below 0 on y axis ( disclaimer if the graph isnt going by ones then its going to be a different answer, but you can use the same process to find it.

We are given the following two vectors

We are asked to find the following

First, multiply the vector a with the scaler -2 to get -2a

Now, multiply the vector b with the scaler 5 to get 5b

Finally, add -2a and 5b to get -2a+5b

Therefore, the resultant vector in component form is

Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.

we know that

The formula to calculate the midpoint between two points is equal to

we have

S(2,-1)

(x1,y1)=R(-9,4)

(x2,y2)=T

substitute the given values in the formula

Find the x2 coordinate

2=(-9+x2)/2

-9+x2=4

x2=4+9=13

Find the y2 coordinate

-1=(4+y2)/2

4+y2=-2

y2=-2-4

y2=-6

therefore

The y-intercept of the line graphed by the equation [tex]\frac{1}{2} x+y=7[/tex] is (0,7)

Option (D) is correct.

The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

The given equation is [tex]\frac{1}{2} x+y=7[/tex]

Converting the equation in Slope-intercept form, we get

[tex]y=-\frac{1}{2} x+7[/tex]                   ...(1)

Now, to find the y-intercept, substitute x = 0 in the equation and solve for the value of y

Putting x = 0 in equation (1), we get

[tex]y=-\frac{1}{2} (0)+7[/tex]

[tex]y=7[/tex]

Therefore, the y-intercept of the line will be (0,y) i.e., (0,7)

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Answer:

The five consecutive integers whose sum is 170 are 32, 33, 34, 35, and 36

Step-by-step explanation:

hope it help

have a nice day

There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.

A set of two linear equations with two variables is a system of linear equations.

ax + by = C

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.

Ex: ax+b = 0

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Step-by-step explanation:

Chance to roll even number on one dice is 1/2 so

[tex] \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} [/tex]

The difference in the record temperatures is 58.3° Fahrenheit.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol - , or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

Given Data

The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8.

Difference = High temperature - Low temperature

Difference = 41.5 -(-16.8)

Difference = 41.5 + 16.8

Difference = 58.3

The difference in the record temperatures is 58.3° Fahrenheit.

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Answer:

14.7

Step-by-step explanation:

Let's say the width is x

So volume would be 24 × 2x × x = 10368

24 × 2x² = 10368

2x² = 10368 / 24 = 432

x² = 216 , width can't be negative so

x = 14.6969... ~~ 14.7

Olivia would be able to get 11 toppings.

Steps:

8.00 / .75 = 10.6

Round~

11

You're welcome!!!

The ratio of the new scale that we are to be having is going to be 1/2

we have the ratio to be 1 grid unit / 2 ft

the new scale ratio is given as 1 grid unit / 4 ft

We have to divide the ratio of the original scale to the new scale that we have here

This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)

This can be written as

1/4 * 2/1

when we rewrite it we would have 2/4

= 1/2

This is 1 unit 2 feet

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Given a quadratic equation in vertex form

In our case,

h = -10, and k= 2

Therefore the vertex is (-10, 2)

Answer:

Explanation:

• Car 1 leaves point A at 5:30 p.m., driving due south at an average speed of 35 mph.

• Car 2 leaves point A at 6:30 p.m., driving due north at an average speed of 45 mph.

At 9:30 pm, the time taken by the cars is:

The distance covered by each car is:

Since car 1 drives due South and Car 2 due North of point A:

Therefore, the distance between the drivers at 9:30 p.m. will be:

The two drivers are 275 miles apart at 9:30 pm.

The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is  TL14,467.

A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also,  if the length and width of the cloth decreases, the cost of the cloth decreases.

The equation that represents joint variation is:

y = kab

Where:

TL3848 = k(13 x 8)

k = TL3848 / (13 x 8)

k = $37

The cost of 17 feet by 23 feet cloth :

37 x 17 x 23 = TL14,467

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Robert will paint 310.5 square ft

The side of Robert's barn contains a triangle and a rectangle of which the dimensions are given in the diagram.

If Robert paint one side of the barn, then he needs to paint the triangle as well as the rectangle. So we need to find the area of the triangle and rectangle first.

For the triangle, base = 23 ft

height = 7 ft

Area of the triangle = 1/2 bh

                                 = 1/2 x 7 x 23

                                 = 80.5 square ft.

For the rectangle, length = 23 ft

width = 10 ft

Area of the rectangle = length x width

                                    = 23 x 10

                                    = 230 square ft.

Area Robert needs to paint = Area of the triangle + Area of the rectangel

                                              = 80.5 + 230

                                              = 310.5 square ft.

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Speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.

As given in the question,

Given data:

Jet speed in still air = 240mph

Let x be the speed of the wind.

Speed with tail wind = 240 +x

Distance covered with tail wind = 700miles

Time taken by jet with tail wind

= Distance/ speed

= 700 / (240 +x)  __(1)

Speed against the wind = 240 - x

Distance covered against the wind = 700miles

Time taken by jet against the wind

= Distance/ speed

= 700 / (240 - x)  __(2)

Total time taken is 6 hours

[700 / (240 +x)] + [700 / (240 - x)] = 6

⇒ 700( 240 -x + 240 + x) = 6 (240 +x)(240 - x)

⇒ 700 ( 480) = 6 ( 240² -x²)

⇒ 700 (80) = 57600 -x²

⇒ x² = 57600 - 56000

⇒ x² = 1600

⇒ x = √1600

⇒ x= 40 mph

Therefore, speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.

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Using the binomial distribution, the probability of no one having done a one time fling is of 0.735 = 73.5%.

The mass density formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the formula are given as follows:

In the context of this problem, the values of the parameters are as follows:

The probability that no one has done a one time fling is P(X = 0), hence the probability is calculated as follows:

P(X = 0) = (0.95)^6 = 0.735 = 73.5%.

The problem asks for the probability that no one has done a one time fling.

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We are told that

If we were given the graph of f(x), note that in this equation we add 5 to the value of f(x) to find the value of g(x). So, in terms of the graph, as we are taking the final value of f and adding 5, this means that we are moving the graph of f 5 units up. That is the graph of g(x) is the graph of f(x) shifted 5 units up

Answer:

x + 6.

Step-by-step explanation:

a number which is x and increased by 6 is adding 6

Given data:

The expression for the age of the girl after two year is,

x+2

The age of girl 5 year ago is,

x-5

According to the given statement of the question.

x+2=2(x-5)

x+2=2x-10

x=12

Thus, the present age of the girls is 12 years old.

Answer:

5

Step-by-step explanation:

negetive two minus negative seven equal to five