16. Fill in the left side of the two-column proof (4 points).
Given:
32 = 2x + 4y; x = 2
y = 7
Prove:
32 = 2x + 4y; x = 2
Given
Substitution Property
Subtraction Property of Equality
Division Property of Equality
Symmetric Property of Equality

x represents the amount of gas in the tank, has a domain described by which inequality

[tex]0 \leq x \leq 3[/tex]

This is further explained below.

Generally, A typical 3-gallon lawnmower requires 0.6 gallons of petrol per hour.

This circumstance is modeled by a function, where x is the volume of gas in the tank.

The lawnmower's gas tank has a maximum capacity of gallons and may be completely empty (having 0 gallons of gas).

In conclusion, a function's domain is

[tex]0 \leq x \leq 3[/tex]

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The Compound Interest would be $1104.895

What is Compound Interest ?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.

Number of quarters in 5years =5×4=20

Quarterly rate of compound interest

r=24=0.5%

Initial amount

P=$1000

hence the total amount after 5years

=  P(1+r/100)n

=1000(1+0.5/100)^20

=1000(1.005)^20

=$1104.895

Hence, The Interest will be $1104.895

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Hi :)

[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]

    - we just insert the number for slope before x in the y=mx+b formula and then write the y-intercept

[tex]\star\sim\star\sim\star\sim\star\sim\star\sim[/tex]

Answer:

we need more info than this

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Set x equal to the amount of money Jim has

2. Create equations of the amount of money the other people have based on x

3. Now, we set all of these equations as equal to 68

4. Combine the like terms, which means that the previous equation will simplify to:

5. Add 8 to both sides

6. Divide 76 by 4

7. Plug the value of x into the previous equations:

Final Answer:

Answer:

Step-by-step explanation:

5 over 12 is 5/17

Answer:

$500

Step-by-step explanation:

Startup cost: $200

Cost of 1 car: $3

Cost of 100 cars: $3 × 100 = $300

$200 + $300 = $500

Answer:

x=1/3k-y-z

Step-by-step explanation:

3x+3y+3z=k

Move the variables to the right

3x= -3y-3z+k

Divide both sides of the equation by 3

x=1/3k-y+z

Answer:

I think this is correct.

Step-by-step explanation:

y=-3x+10

John holds 26 percent of the debt from discover bank in its total debt obligation.

The Total debt represents the obligations being taken by a company in the form of debt and yet to be repaid by them to the lender.

Given that the Debt hold in discover bank is $10,000

Total debt: $26,000

Computation of ratio of debt in discover bank:

Debt proportion = Debt hold in discover bank / Total debt

Debt proportion = 10,000/ 26,000

Debt proportion = 26%

Therefore, John holds 26 percent of the debt from discover bank in its total debt obligation.

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For this problem, we are given the zeros of a polynomial, we need to determine its expression.

The zeros are:

Therefore we can write:

The correct answer is option A.

Answer:

[tex]\sqrt{8}[/tex]

We use the process of elimination to solve:

When we solve [tex](\sqrt{10})^{2}[/tex] we get 10 and we know that 10 is a integer and we know all integers are rational numbers, therefore, this is rational.

When we solve [tex]\sqrt{196}[/tex] we get 14 and we know its a rational number because it can be expressed as the quotient of two integers: 14 ÷ 1. Therefore this one is, rational.

0.63, The decimal 0.6 is a rational number. It is the decimal form of the fraction 6/10. A rational number is, by definition, any number that results when one integer is divided by another. Since both 6 and 10 are integers, or whole numbers, 0.6 is a rational number.

And lastly this leaves is with [tex]\sqrt{8}[/tex]  and It is a non-terminating decimal with non-repeating digits. The number 2.828427125... can't be written in p/q form. Hence, the square root of 8 is a irrational number.

The number of customers surveyed is 499.

UESTION A

ehe age ranges that fall within the required one for this question are 20-29, 30-39, and 40-49.

The number of people in these groups in total will be:

Therefore, the probability of this occurring is calculated to be:

he probability is 0.4449.

QUESTION B

he age ranges for this question are >≥60, <20, and 20-29.

The number of people in these groups in total will be:

he probability is 0.4850.

QUESTION C

is ≥60.

The number of people in this group is 84.

m = -19 is the solution to the equation -2(m - 2) = -3(m + 5).

Given the data in the question;

To determine the numerical value of m, remove the parenthesis and simplify.

-2(m - 2) = -3(m + 5)

Apply distributive property

-2(m - 2) = -3(m + 5)

m(-2) - 2(-2) = m(-3) + 5(-3)

-2m + 4 = -3m - 15

Now, collect like terms by bring all values containing variable m to the left and all constant to the right side of the equation.

-2m + 3m = -15 - 4

m = -15 - 4

m = -19

Therefore, the numerical value of m is -19.

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a) An equation to model the problem of determining the birth year when the average life expectancy will be 71 years is y = 55 + 0.2x.

b) From the equation above, from 1980 or in the 80th birth, the average life expectancy will be 71 years.

The average life expectancy refers to the average time in years that a person is expected to live after birth.

The average life expectancy has been a statistical tool for understanding a person's lifespan on earth based on some demographics.

An equation is a mathematical statement that equates two or more variables, numbers, or values or regards them as equivalent or equal.

For this situation, we can use the formed equation to predict a person's life expectancy average in the future, given the current years and increasing rate of life expectancy.

Life expectancy in 1900 = 55 years

Life expectancy increase for each birth year after 1900 = 0.2

Life expectancy = y

Year = x

y = 55 + 0.2x ... Equation

71 = 55 + 0.2x

0.2x = 16

x = 16/0.2

= 80 birth year

1980 = (1900 + 80)

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The number of elements in the complement of a set A is the total number of elements in the universal set minus the number of elements in the set A.

It is given that A={volleyball players who are younger than 8 years old}.

From the table, volleyball players who are younger than the age of 8, are players who are 7 years old.

Hence, the number of players in A is 5.

Add the number of players for each age to get the total number of players:

It follows that the number of players in the complement of A is:

Hence, the number of players in the comp

P( A and B) is [tex]\frac{1}{15}[/tex].

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is accurate. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given Data

P(A) = [tex]\frac{1}{3}[/tex]

P(B) = [tex]\frac{1}{5}[/tex]

P (A or B) = [tex]\frac{1}{2}[/tex]

1) No, events are not mutually exclusive. as P(A) + p(B) is not equal to P(A or B)

2) P( A and B) = P(A) × P (B)

P( A and B) = [tex]\frac{1}{3}[/tex] ×[tex]\frac{1}{5}[/tex]

P( A and B) = [tex]\frac{1}{15}[/tex]

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Answer: The Y intercept is B) 3.

Step-by-step explanation:

you just have to see where the line crosses the y axis which in this case is it crosses the y axis on 3

Answer:

(-6, -5).

Step-by-step explanation:

f(x)+3 represents the graph of f(x) shifted up 3 units, meaning we add 3 to the y-coordinate

Answer:

Step 6: Subtraction Property of =

Step-by-step explanation:

According to the given information, the sum of the calories of a bag of popcorn and a juice box is 518. Taking x as the number of calories of a bag of popcorn and y as the number of calories of a juice box, we have that:

Then, 2 bags of popcorn (it means 2x) and 6 juice boxes (it means 6y) have a total of 1456 calories, this is:

Use this system of equations and solve the problem, this way:

Solve the first equation for x:

Use this expression and replace for x in the second equation:

Use this value to find the value of x:

It means that there are 413 calories in each bag of popcorn and 105 calories in each juice box.

Unit analysis is a helpful tool we can use to convert units.

All we have to do is multiply the original value by a fraction, to cancel out the units that we don't want.

We're given:

There are a couple things we need to know before we tackle this question:

Step 1 ⇒ Multiply [tex]\dfrac{20\hspace{4}miles}{hour}[/tex] by [tex]\dfrac{5280\hspace{4}feet}{mile}[/tex] to change miles to feet:

[tex]\dfrac{20\hspace{4}miles}{hour}\times\dfrac{5280\hspace{4}feet}{mile}\\\\= \dfrac{20\times5280\hspace{4}feet}{hour}\\\\= \dfrac{105600\hspace{4}feet}{hour}[/tex]

Step 2 ⇒ Multiply [tex]\dfrac{105600\hspace{4}feet}{hour}[/tex] by [tex]\dfrac{hour}{60\hspace{4}minutes}[/tex] to change hours to minutes:

[tex]\dfrac{105600\hspace{4}feet}{hour}\times\dfrac{hour}{60\hspace{4}minutes}\\\\=\dfrac{105600\hspace{4}feet}{60 minutes}\\\\=\dfrac{1760\hspace{4}feet}{minute}[/tex]

Step 2 ⇒ Multiply [tex]\dfrac{1760\hspace{4}feet}{minute}[/tex] by [tex]\dfrac{minute}{60\hspace{4}seconds}[/tex] to change minutes to seconds:

[tex]\dfrac{1760\hspace{4}feet}{minute}\times\dfrac{minute}{60\hspace{4}seconds}\\\\= \dfrac{1760\hspace{4}feet}{60\hspace{4}seconds}\\\\= \dfrac{29.3\hspace{4}feet}{second}[/tex]

[tex]\dfrac{29.3\hspace{4}feet}{second}[/tex]

The ratio value of multiplication problems to division problems is 1:2.

The ratio value compares two quantities or values.

The ratio value shows the quantity of one variable contained in another.

Ratios are depicted by the ratio sign (:) or in fractions, decimals, or percentages.

The number of multiplications problems in the math test = 12

The number of division problems in the math test = 24

The ratio value of their relationship = 12:24 or 1:2

Thus, the math test shows that there are twice as many division problems as multiplication problems.

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Solution:

Thus;

Given;

FINAL ANSWER: Associative Property.

Evaluate (-2) (-2) . 2

The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.

From the information, I have have $100 in a savings accoun and save an additional $40 each week.

Let the number of weeks be represented by w. The expression to represent this will be:

= 100 + 40w

My friend has $80 in a savings account and saves and addtional $10 each week. This will be:

= 80 + 10w

The sum will be:

= 100 + 40w + 80 + 10w

= 180 + 50w

The difference in the amount will be:

= 100 + 40w - (80 + 10w)

= 20 + 30w

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Answer:

side length = 5cm

Step-by-step explanation:

The volume of the prism is:

V = l × w × h

But we only know the width and height which are both 3cm. See image.

We put it in the calibrated container (container with markings on it) We find out the volume is 45. Because 115 - 70 is 45.

Divide to find the missing length. See image.

Vol

= 3 × 3 × sidelength

V = 9s

45 = 9s

5 = s

see image.

If y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)

Given,

y = -3 cos (2x)

We have to find derivative d²y / dx²

d²y / dx² = -3 (d² cos x / dx²) = -3 d/dx (d cos 2x / dx)

According to the concept:

d cos x / dx = - sin x

Here,

d cox 2x / dx = - sin 2x

So,

d²y / dx² = (- 3 × 2) d/dx (- sin 2x)

d²y / dx² = -6 (d sin 2x / dx)

d²y / dx² = 2 × 6 cos 2x

d²y / dx² = 12 cos (2x)

That is, if y = -3 cos (2x), then derivative d²y / dx² is 12 cos (2x)

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Answer:

============================

This is an absolute value function and is the translation of f(x) = |x| down by 5 units.

We know that f(x) = |x| is never negative as per definition of absolute value. So its range is zero or positive numbers:

The given function (|x| - 5) can get values 5 less than the parent function (|x|), so its range is:

This is option B.