Lucy earns $15.75 per hour. Last week she worked 25 hours. What is her gross pay:
Lance has a yearly salary of $52,300 and pays 21% in taxes. Answer the following
a. How much does he pay in taxes?
b. What is his net pay?
c. If he receives two paychecks a month, how much will each paycheck be?

Least Common Multiple of  3x² + 7x + 2 and 2x² + 3x-2 is  (2x-1)(x+2)(3x+1)

Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers. Finding the LCM of a given collection of numbers can be done in a variety of ways. Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

Given that :  3x² + 7x + 2 and 2x² + 3x-2

3x² + 7x + 2

3x² +6x +x + 2

3x(x +2)+1(x+2)

(3x+1)(x+2)

2x² + 3x-2

2x² + 4x-x -2

2x(x+2)-(x+2)

(2x-1)(x+2)

L.C.M of  3x² + 7x + 2 and 2x² + 3x-2 is

(2x-1)(x+2)(3x+1)

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If the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7.

The given equation is

1/3(2x - 3/7)+(1/6)x = 4/7

First we have to apply the distributive property of subtraction in the equation

1/3(2x - 3/7)+(1/6)x = 4/7

(3/2)x - 1/7 + (1/6)x = 4/7

Here we have to rearrange the terms and group the like terms

Move the 1/7 to right hand side of the equation

(3/2)x + (1/6)x = (4/7)+(1/7)

Addition of like terms

(5/3)x = 5/7

Move the 5/3 to the right hand side of the equation

x = 5/7 ÷ 5/3

x = 5/7 × 3/5

x = 3/7

Hence, if the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7

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Answer:

A. 7:10

B. 10:17

Explanation: The ratio of A. would be 14:20, simplified would be 7:10. The ratio of B. would be 20:34, simplified being half of both numbers. Giving you 10:17.

Answer:

(-5, -3, 1, 2, 3) .... the fourth one

Step-by-step explanation:

the domain is all the x values.

so look at your points and look at the x values ( the number on the X-axis) for those points!

Answer:

26 1/4 miles per gallon

Explanation:

We are told that the car travels 21 miles per 4/5 gallons. Therefore, the rate at which the car uses the gas is

which can also be written as (by taking the reciprocal of the denominator)

If you want to make an annual salary of $31,836, then your sales must be $25,280

Ok, so you want to earn a total of $31,836, and he has a fixed salary of $30,572, so the missing amount is:

$31,836 - $30,572 = $1,264

Now, we know that you make a commission of the 5% of what you sell, so if X is what you sell, then to make the desired salary X must be:

X*0.05 = $1,264

Solving that linear equation for X we get:

X = $1,264/0.05 = $25,280

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The linear equation of the line that passes through point (-4,-2) and has a slope of -3 is y = -3x - 14.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the data in the question;

Point ( -4, -2 )

First we calculate the y-intercept 'b' using the equation of line formula.

y = mx + b

Plug in point ( -4, -2 ) and slope -3.

-2 = -3(-4) + b

-2 = 12 + b

b = -2 - 12

b = -14

Now that we have the values of slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = -3(x) + ( -14 )

y = -3x - 14

Therefore, the equation of the line is y = -3x - 14.

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The equation in slope-intercept form is y = 2x + 6

The equation is given as

6x - 3y = -18

The above equation is a linear function, and it is in its general form

To determine the slope-intercept form of the equation, we simply make y the subject of the formula in the equation

So, we have

6x - 3y = -18

Divide through  the equation by -3

So, we have

-2x + y = 6

Add 2x to both sides

y = 2x + 6

Hence, the slope-intercept form of the equation is y = 2x + 6

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The area of the reservoir in standard form is 1.8 × 10⁴ square miles

The volume of the reservoir in scientific notation is 2.8 × 10⁴ cubic miles

From the question, we are to determine the area of the reservoir in standard form and the volume of the reservoir in scientific notation

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form

Thus,

To write a number in standard form, we will write the number as a product of a number between 1.0 and 10.0 and a power of 10

From the given information,

The area of the reservoir is 1.8 × 10⁴ square miles.

The area of the reservoir is already written in standard form

Now,

To write the volume of the reservoir in scientific notation

NOTE: Standard form is the same as scientific notation

From the given information,

The volume of the reservoir is 28000 cubic miles

28000 = 2.8 × 10⁴

Hence, the volume in scientific notation is 2.8 × 10⁴ cubic miles

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Answer:

90 minutes(1hour 30 minutes)

Step-by-step explanation:

If 1 room=15 minutes

Then 6 rooms= ?

=6×15/1

=90 minutes

=1hour 30 minutes

If you're talking about the lower case m, which sporadically appears before a specific angle, like m ANGLE A-B-C. The m denotes the angle ABC's "measure" (angular measure in degrees).

Here the angle m ∠UVX = [tex]52^{0}[/tex].

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Answer:

9  57/ 100

Step-by-step explanation:o convert the decimal 9.57 to a fraction, just follow these steps:

Step 1: Write down the number as a fraction of one:

9.57 = 9.57/ 1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,

9.57 / 1

= (9.57 × 100)

(1 × 100)

= 9 57/ 100

.

(This fraction is alread reduced, We can't reduce it any further).

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 9 57/ 100

is also equal to 9 57/ 100

when expressed as a mixed numbeR

Answer:

9 3/4

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.

Based on the given task content; the first term of the series whose nth term is 3n-5/4 is -1/2.

nth term = (3n - 5) /4

Where,

First term, a = (3n - 5) / 4

= (3n - 5) / 4

= {3(1) - 5} / 4

= (3 - 5) / 4

= -2/4

= -1/2

The first term of the series whose nth term is 3n-5/4 is -1/2

(3n - 5) / 4

= {3(12) - 5} / 4

= 36 - 5 / 4

= 31/4

= 7.75

Therefore, the 12th term of the series whose nth term is 3n-5/4 is 7.75

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Answer:

Step-by-step explanation:

 Both equations are linear equations with one variable.

Difference:

  Problem1: Linear equation uses discrete variable. Money can be counted.

 Problem 2: Linear equation uses continuous variable. water can be measured.

The biggest problem with the results of this research study is B. Lack of realism.

It should be noted that when an experiment's procedures, participants, or setting are unrealistic. The ability of researchers to apply the findings of an experiment to the situations that hold the most interest may be constrained by a lack of realism.

The study is how how noise impacts student performance on exams is being proposed.

An experiment's subjects, medications, or environment might not accurately replicate the circumstances we truly wish to explore. In that circumstance, we are unable to extrapolate the experiment's findings broadly.

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The options are:

a. Lack of attention to experimental detail

b. Lack of realism

c. Placebo effect

The function modeling given situation, where y represents the total weight of the crates in pounds, has a range described by the inequality 0 ≤ y ≤ 2000. The correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The set that includes all the output values that the function expects is the range of a function.

The following information is provided regarding the input and output for this problem

The number of containers placed inside the vehicle as input.

Total weight of the crates loaded into the truck or output.

The range of this problem is represented by the following inequality:

0 ≤ y ≤ 2000.

The weight of an amount will never assume a negative value, and the maximum weight is 2,000 pounds, as stated in the problem.

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One paint container is enough to paint all the faces of fifty 8 cm cubes.

Given

The paint can cover 20,000 [tex]cm^{2}[/tex]

Side of square  = 8 cm

As the Total surface area of a cube is  [tex]6a^{2}[/tex],

where a is the side of the cube.

The total surface area of one cube =  6 x [tex]8^{2}[/tex]

                                                          =  384 [tex]cm^{2}[/tex]

Since there are fifty such cubes,

384 x 50

Total area to be painted = 19200 [tex]cm^{2}[/tex]

Since 19,200 [tex]cm^{2}[/tex] is less than 20,000 [tex]cm^{2}[/tex] , it is possible to paint all the cubes.

Hence one paint container is enough to paint all cubes.

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Answer:

M∠2 = 37°

M∠3 = 143°

M∠4 = 37°

Step-by-step explanation:

∠3 is the complete opposite of ∠1

143° + 143° = 286°

there is 360° in a full circle or a repeating angle (aka the scissors)

360°-286°=74°

since ∠2 and ∠4 is opposite of each other

74°÷2=37°

Answer:

[tex]m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ 143° + m∠2 = 180°

⇒ m∠2 = 37°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

Answer: The eastbound train is traveling at 65mph while the westbound train travels at 47mph.

Step-by-step explanation:

You would use x as the variable for the speed of the westbound train. The eastbound train would be 18+x. your equation would be 2.5(18+x+x)=280
You would find that x=47 for the westbound train. You would then add 18 to get the speed of the eastbound train which would be 65.

Answer:

b

Step-by-step explanation:

The equation of the line is y = -400x + 800

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Initial number of gallon, c = 800

Constant rate, m = -400 gallons per hour

This means that

Slope = -400

y-intercept = 800

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = -400x + 800

Hence. the equation of the amount of grain is y = -400x + 800

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Answer:

To one decimal place, x = 7.7 cm

Step-by-step explanation:

Let y equal BD.

Since AD is a bisector of angle BAC, angle DAB is 17°.

tan(17°) = y/21, so y = 21 tan(17°)

tan(34°) = (x + 21 tan(17°))/21

21 tan(34°) = x + 21 tan(17°)

x = 21(tan(34°) - tan(17°)) = 7.7 cm

Answer:

there must be 14 students and each one can get 4 pencils and 3 erasers

Step-by-step explanation:

56 goes into 14 4 times. 42 goes into 14 3 times none left over

We have a translation of 3 units to the left and 4 units upwards.

To find the translation, we only need to look at one of the vertices of the triangle.

We can see that the coordinates of B are (4, 1), while the coordinates of the translated point B' are (1, 5)

The translation is given by the difference:

(1, 5) - (4, 1) = (1 - 4, 5 - 1) = (-3, 4)

So the translation is defined by (-3, 4)

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The number of pies that Red Riding Hood's mother made is 25.

Let x represent the number of pies mother baked in the morning.

Pies left after mother ate 1 = x - 1

The number of pies that Red Riding Hood takes to her grandmother: 1/2(x - 1)

0.5(x - 1)

0.5x - 0.5

Pies left after Red Riding Hood ate 2: [(0.5x - 0.5) - 2]

Pie after she gave the wolf 1/3 ; (1 - 1/3) × [(0.5x - 0.5) - 2]

2/3 × [(0.5x - 0.5) - 2]  = 8

In order to determine the value of x, take the following steps:

Multiply both sides of the equation by 3/2.

[(0.5x - 0.5) - 2] = 12

Add 2 to both sides of the equation: 0.5x - 0.5 = 12 + 2

0.5x - 0.5 = 12

Add 0.5 to both sides of the equation

0.5x = 12 + 0.5

0.5x = 12.5

Divide both sides by 0.5

x = 25

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Answer: 5 + 2 = 7

Step-by-step explanation: its easy

1. The rate of the descent of Andy as a unit rate will be -4 feet per minute.

2. If Andy continues descending at this rate, the relation to sea level after 6 minutes is -24 feet.

From the information, the following can be deduced'

1. Distance = -10 feet

Time = 2 1/2 minutes = 2.5 minutes

Speed = Distance / Time

Speed = -10 / 2.5

Speed = -4 feet per minutes

2. When Andy continues descending at this rate, the relation to sea level after 6 minutes will be:

= -4 × 6

= -24

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Andy is scuba diving. He starts at sea level and then descends 10 feet in 212 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet