11. Lucretia, who works part-time as a substance abuse counselor, earns $18.15
per hour and works 20 hours per week. She is single and claims one withholding
allowance. She lives in a state with no state income tax. (2.1)

The inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;  -40°F < x < 140°F

A)  x is the temperature, and the temperature can't go down to -40°F and so x is greater than -40°F so that the gas doesn't freeze. Finally, x can't go higher than 140°F because the gas will evaporate. Thus, the inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;

-40°F < x < 140°F

B) Open interval of the graph would mean that the interval is from -40°F to < 140°F. However, not equal to means that the gas in the truck can't stay liquid and as such means the coordinate is (-40°F, 140°F)

C) The gas will freeze because it has been said in the question the gas freezes at -40°F and as such if it goes -49°F, then it will freeze because the gas is supposed to stay higher than -40°F.

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The equation for the average cost function C   [tex]= \frac{0.00048(x - 200)^{3} + 246840 }{x}[/tex]

When a company creates products or services, it is required to pay production-related expenses. Some of these expenses are cyclical and alter as the output does. Expenditures that alter when production changes include things like raw materials, labor, and utility costs. These are referred to as variables. Other expenses are set, such as rent and insurance payments. These fixed expenses do not alter with changes in output.

The sum of the fixed and variable costs is the total cost.

Total Cost = Variable Cost + Fixed Cost

Now as per the question the cost equation is :

[tex]= \frac{C(x)}{x} = \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]

Therefore,  the equation for the average cost function :[tex]= \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]

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The correct option regarding individuals and variables is given by:

An individual is the population of interest. A variable is an aspect of an individual subject or object being measured.

Hence the correct option is:

An individual is the population of interest. A variable is an aspect of an individual subject or object being measured.

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Step-by-step explanation:

10.

the various sides and line segments have been marked as equal already.

so, SSS proves that both triangles are congruent.

but to reprove things with the midpoint theorem :

remember

the line segment in a triangle connecting the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.

so,

D, F are the midpoints of BA and BC.

so, AC is parallel to DF and twice as long as DF.

D, E are the midpoints of BA and AC.

so, BC is parallel to DE and twice as long as DE.

E, F are the midpoints of AC and BC.

so, BA is parallel to EF and twice as long as EF.

so, DF = AE = EC

DE = BF = FC

EF = BD = DA

so, the EF of DEF corresponds to DA of ADE.

DF corresponds to AE.

and DE is shared between both triangles.

so, again, all 3 sides correspond 1:1 to sides in the other triangle. and SSS proves they are congruent.

11.

equilateral means all 3 sides are equal :

PS = PT = ST

TSR can only be isoceles (both legs are equal) when

ST = SR

because PM = MQ, M is the midpoint of PQ.

and because of MS || QR, S is the midpoint of PR.

that means PS = SR.

and because PS = ST, ST = SR

therefore, TSR is isoceles.

Answer:

918 , bc it is the answer

Step-by-step explanation:

i used a source

Answer:

18.84

Step-by-step explanation:

The number of students whose best subject is Maths  is 78.

A pie chart is a graph that displays information in a circle. The circle is divided into sections which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees. A pie chart is equal to 100%.

The first step is to determine the percentage of the section allocated to mathematics: 100% - (8% + 15% + 8% + 32% + 11%)

100% - 74% = 26%

Number of students whose best subject is Maths = (26/100) x 300 = 78

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Answer:

76

Step-by-step explanation:

76 occurs multiple times in the set, thus deviating from it.

Answer:

1/4 of the dozen is broken

Step-by-step explanation:

Answer:

[tex] \sf \large \: x=15[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

2x/5+1=7

Step 1: Simplify both sides of the equation.

2/5x+1=7

Step 2: Subtract 1 from both sides.

2/5x+1−1=7−1

2/5x=6

Step 3: Multiply both sides by 5/2.

(5/2)*(2/5x)=(5/2)*(6)

x=15

If we are borrowing $10840 to buy a car and repaying it in 6 years (or 72 months) , our monthly payment will be $150.55 or rounded of $200.

As per the question statement, we are borrowing $10840 to buy a car and repaying it in 6 years (or 72 months) , what will be the estimate monthly payment by rounding off to the nearest hundred dollars

First we are supposed to find the monthly payment then we can round it off to the nearest hundred dollars.

Total loan borrowed = $10840

Time taken to pay it off = 6 years or 72 months,

Payment to be made per month = [tex]\frac{10840}{72} \\ 150.5556[/tex]

Therefore [tex]150.5556[/tex] dollars is to be paid every month for 72 months.

After rounding off to the nearest hundred dollars we will get $200.

Hence we are supposed to pay approximately $200 every month for 72 months.

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Answer:

Forty-four and two-hundred fifty-nine thousandths.

Answer: x = -14, y = -13

Step-by-step explanation:

As stated by the question, we can use a system of equations to help us solve.

First, the difference between two numbers (x and y) is -1. The difference represents subtraction.

     x - y = -1

Next, the sum of the numbers (x and y) is -27. The sum represents addition.

     x + y = -27

Now, we can solve this system. We will graph both of the equations. The point of intersection is the solution, see attached. This gives us an answer of x = -14 and y = -13.

     x - y = -1

     x + y = -27

Answer: 0.1111111111

The number of cars should be 100 and that of bus be 0.

x is the number of cars and y is the number of buses.

Area: 6x + 30y <= 600 simplifies to x + 5y <= 100

Total money collected: 2.50x + 7.50 y …..this is what you want to maximize

OR you want to maximize 2.50 (x+ 3 y)

OR you want to maximize (x+3y)

Replacing the value of x from the Area equation in the above price, we get

100 - 5y + 3y is the maximum amount you can collect

So you want to maximize 100 - 2y. This happens when y is 0.

When y is 0; x will be 100 and you will collect 250.

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If initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.

Given that the initial deposit is GBP 3000 and the rate is 3.5%.

We are required to find the number of years after which the amount will reach to GBP 9000.

Compound interest is basically the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Amount after compounding=P[tex](1+r)^{n}[/tex], where P is principal ,r is rate of interest and n is number of years.

The number of years can be calculated as under:

9000=3000[tex](1+0.035)^{n}[/tex]

3=[tex](1.035)^{n}[/tex]

[tex](1.035)^{32}[/tex]=[tex](1.035)^{n}[/tex]

By comparing both sides,we will get n=32.

Hence if initial deposit is GBP 3000 and the rate is 3.5%,then after 32 years it will reach to GBP 9000.

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The algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.

We are given the inequality;

3x – 2 > –4

Step 2;

Using Addition Property of Equality, add 2 to both sides;

3x – 2 + 2 > –4 + 2

3x > –2

Step 3;

Using Division Property of Equality, divide both sides by 3 to get;

3x/3 > –2/3

x > –2/3

Thus, we conclude that the algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.

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If the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)

Given,

The vertices of the triangle = J(-3,-5), K(-2,2) and L(1,-4)

We know,

In reflection in y axis (x,y)  will become (-x,y)

Then the vertices of the reflection in y axis = J(3,-5), K(2,2) and L(-1,-4)

Draw the triangle using the vertices.

Hence, if the vertices of the triangle are J(-3,-5), K(-2,2) and L(1,-4) then its reflection in y axis are J(3,-5), K(2,2) and L(-1,-4)

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Answer: 103. h<=2 or h>=12

105. No solution

107. -6<x<1

Step-by-step explanation:

103. |h-7|>=5

h-7>=5

h>=12

h-7<=-5

h<=2

h<=2 or h>=12

105. |2x-8|<-10 ==> No solution since absolute value functions are always positive.

107. |10+4x|<14

10+4x<14

4x<4

x<1

10+4x>-14

4x>-24

x>-6

-6<x<1

The equation of the tangent line to the graph is equal to y = 0.

A line is tangent to a function if and only if the function meets the curve only in one point. The slope of the tangent line can be found by using the first derivative of the curve and the y-intercept is determined from the slope-intercept form of the equation of the line. First, determine the slope of the tangent line:

f'(x) = 12 · x

f'(0) = 12 · 0

f'(0) = 0

Second, find the intercept of the equation of the line:

y = 6 · 0²

y = 0

b = y - m · x

b = 0 - 0 · 0

b = 0

Then, the equation of the tangent line to the graph is equal to y = 0.

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hope it help ya..

☘☘☘...

spellings are incorect

Answer: 24, 26, 28

Step-by-step explanation:

a=even integer one.

b=even integer two.

c=even integer three.

a=b-2

b=c-2

a=c-2-2

a=c-4

a+b+c=50+c

c-4+c-2+c=50+c

c+c+c-4-2=50+c

3c-6=c+50

2c-6=50

2c=56

c=28

b=c-2

b=28-2

b=26

a=26-2

a=24

24, 26, 28

From the given absolute value function, we have that:

The absolute function is defined by:

It measures the distance of a point x to the origin.

For this problem, the function is:

d(t) = 1/3|t - 60|.

The d-intercept is given by:

d(0) = 1/3|-60| = 20.

Hence: The cyclist starts 20 kilometers from the station.

The t-intercept is found as follows:

1/3|t - 60| = 0

t - 60 = 0

t = 60.

Hence: The cyclist reaches the station in 60 minutes.

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The correct option regarding the standard deviation of the data-set adding observation 55 is:

The standard deviation would be about the same, perhaps a little smaller.

For this problem, we have that an observation of 55 has a difference squared of 1 with the mean, which is less than the variance of 7² = 49, hence the mean of the differences squared would suffer a small decay(small due to the sample size), and would the standard deviation, hence the correct option is given by:

The standard deviation would be about the same, perhaps a little smaller.

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Answer:

No, its A: The standard deviation would be noticeably larger. I swearrr, these "verified" accounts are so useless bru

Answer:

  2·2·3 or {1, 2, 3, 4, 6, 12} depending on what you mean

Step-by-step explanation:

You want the factors of 12.

The prime factors of 12 are ...

  12 = 2·2·3 = 2²·3

The product of exponents of the prime factors, each increased by 1, is the number of divisors of 12:

  (2+1)(1+1) = 3·2 = 6 . . . . number of divisors of 12.

Those are ...

  1, 2, 3, 4, 6, 12

__

Additional comment

The word "factors" is often used when "divisors" is intended. An expression is factored when it is expressed as a product of prime factors.

Answer:

-4/9 * 8/5 = (- 4/9) x

-32/45= - 4x /9

-288 = 180x

-8/5

Scale factor back to original size = 1/7

        7x and 7 years.

This means the original size will be;

Length = 7x × 1/7

Width = 7y × 1/7

Hence, the scale factor will be 1/7 back to the original size.

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Answer:

26

Step-by-step explanation:

First, split the figure into 3 rectangles and label the sides so that it is easier to work with.

Then you have to find the unknown values: HG and AH.

HG: Since AB=7 and AB is the longest horizontal side; we know that HG+EF+CD=AB=7. Plugging in the known values: HG+3+1=7 => HG+4=7. Therefore, HG=3 because 3+4=7.

AH: BC and FG are the corresponding sides to AH so AH+FG=BC. Plugging in the known values: AH+1=3. Therefore, AH is 2 because 2+1=3.

Now you have to use the perimeter of rectangle formula which is P=2(L+w) for the 3 rectangles.

Rectangle 1: 2(3+2)=10

Rectangle 2: 2(3+1)=8

Rectangle 3: 2(3+1)=8

Add them all up to find the total perimeter: 10+8+8=26.