Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22

The total amount he puts towards emergency savings is $74

The correct option is C.

His total weekly deposits are as follows: 219+115+40+20+10+40+15 = 459

Now

that we are aware, his weekly deposits total $459 in total.

His total remuneration is $498 due to an error in his addition of the numbers.

The amount he has each week will be determined by deducting his deposits from his paycheck:

498-459 = 39

He contributes two equal payments of $20 and $15 to his emergency fund.

His entire contribution to emergency savings is = 20 + 15 = 35.

Only need to add the additional $39

To determine how much he can set aside each week for emergency savings, multiply his total emergency savings by 35 dollars:

39+35 = 74

the total per week that he can put towards emergency savings = $74

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I understand that the question you are looking for is:

Mr. Thom makes $25,900/year salary as a document processor. He has made the following chart in order to divide his weekly paycheck into his accounts: Expense type Account Weekly deposits Essential (Fixed) 1st Checking account $219 Essential (Variable) 1st Checking account $115 Non-essential 2nd Checking account $40 Other (Unexpected) Emergency savings account $20 Other (Pictable) Education investment fund $10 Other (Pictable) Retirement investment fund $40 Other (Pictable) Emergency savings account $15 Total paycheck $498 Unfortunately, he has made a mistake in adding the numbers and has not allocated all of the paycheck. If he deposits the difference into the two emergency savings accounts, how much total per week can he then put towards emergency savings?

a. $40

b. $60

c. $74

d. $55

Answer: C. $74

Step-by-step explanation:  C. $74.00

Answer:

31 and 37

Step-by-step explanation:

Those are the only two numbers

Answer:

The two numbers between 30 and 40 which have only 2 factors are -

31 and 37

Hope it helps you.

Answer:

P = 1/3

P = 0.333

Step-by-step explanation:

There are 6 marbles in the pack, two of them are yellow.

[tex]P=\frac{2}{6} =\frac{1}{3}[/tex]

Hope this helps

A trapezoid is a plane figure bounded by four sides. Therefore, the required answers are given below;

a) ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) DE = 5 cm and CF = 5 cm

c) AE = 12 cm

Plane figures are shapes that are formed by straight boundaries referred to as sides. Examples include; square, rectangle, trapezium, etc.

A trapezoid is a family of quadrilaterals., these are figures that have four straight sides.

In the given question, the required answers are:

a) To prove that ΔADE = ΔBCF

Thus,

AE ⊥ DC  (given)

BC ⊥ DC  (given)

<AED = <BFC = [tex]90^{o}[/tex]

AE = BF (height of the trapozoid)

<ADE ≅ <BCF (congruent property of two triangles)

Therefore, it can be concluded that;

ΔADE = ΔBCF (Side-Angle-Side congruent property)

b) Given that AB = 8 cm, and DC = 18 cm.

Then,

CD = DE + EF + FC

18 = DE + 8 + FC   (since EF = AB)

18 - 8 = 2 DE     (since DE = FC)

DE = 5 cm

Thus, DE = 5 cm and CF = 5 cm

c) To determine the value of AE, we have to apply the Pythagoras theorem. So that;

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]13^{2}[/tex] = [tex]AE^{2}[/tex] + [tex]5^{2}[/tex]

169 - 25 =  [tex]AE^{2}[/tex]

[tex]AE^{2}[/tex] = 144

AE = [tex]\sqrt{144}[/tex]

     = 12

AE = 12 cm

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The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

According to the statement

we have to explain all about the APR and tel that why it is important for the consumers.

So, For this purpose,

We know that the

The term annual percentage rate of charge, corresponding sometimes to a nominal APR and sometimes to an effective APR.

It is the interest rate for a whole year, applied on the loan etc. It is a finance charge expressed as an annual rate

APR is the important tool for the consumers because of some reasons which are written below:

APR is important because it can give you a good idea of how much you'll pay to take out a loan.

APR helps a customer determine the true cost of the loan, allowing them to compare many loans and choose the most advantageous one.

So, The option B is correct. APR is important tool because It allows consumers to compare the full cost of loans from different lenders.

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Answer: [tex]\Large\boxed{x=6.5}[/tex]

Step-by-step explanation:

Given equation

-9 - (x + 1) = -2 - (3x - 5)

Expand the parenthesis

-9 - x - 1 = -2 - 3x + 5

Combine like terms

-9 - 1 - x = -2 + 5 - 3x

-10 - x = 3 - 3x

Add 3x on both sides

-10 - x + 3x = 3 - 3x + 3x

-10 + 2x = 3

Add 10 on both sides

-10 + 2x + 10 = 3 + 10

2x = 13

Divide 2 on both sides

2x / 2 = 13 / 2

[tex]\Large\boxed{x=6.5}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Work(W)=7.5*10⁴J

Step-by-step explanation:

Greetings !

[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]

Answer:

Multiply 3 and 4, then subtract that total from 5.

Step-by-step explanation:

You would need to follow P.E.M.D.A.S.

Parentheses, Exponents, Multiply & Divide, Add & Subtract

Hope that helps! Let me know if you need more help. Please mark me as brainliest!

The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.

The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.

On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.

Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.

Graph A has a slope of -1/3 and the shaded part is above the boundary line.

Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.

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Answer: 177

Step-by-step explanation:

1. 4x4=16

(3-16)^2+8

2. 3-16=-13

(-13)^2+8

3. -13x-13=169

169+8

4.169+8=177

177

Answer:

177

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

[tex](3-4^2)^2+8[/tex]

Parentheses

Begin by calculating the part inside the parentheses.

Following PEMDAS, calculate the exponent first:

[tex]\implies (3-4^2)^2+8=(3-16)^2+8[/tex]

Then carry out the subtraction:

[tex]\implies (3-16)^2+8=(-13)^2+8[/tex]

Exponents

[tex]\textsf{Apply the exponent rule}: \quad (-a)^n=a^n, \quad \textsf{if }n \textsf{ is even}[/tex]

[tex]\implies (-13)^2+8=169+8[/tex]

Addition

[tex]\implies 169+8=177[/tex]

Therefore:

[tex]\implies (3-4^2)^2+8=177[/tex]

Option (b) -6 and 7 is the correct option.

The zeroes of the function f and g are x=7 and x=-6 respectively.

The values of x that satisfy the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case. The degree of the equation f(x) = 0 determines how many zeros a polynomial has.

Put x-7=0

X=7

Now, put x+6=0

So, x=-6

The zeroes of the function f and g are 7 and -6 respectively.

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Answer:

$64

Step-by-step explanation:

Equation: 50 + 15x = 1010

x = (1010 - 50) ÷ 15 = 64

Since x is the total amount of money deposited in the bank per week, the answer is $64.

The results of the division of polynomials are given as follows:

Considering that x² - 9 is the subtraction of perfect squares, we have that:

x² - 9 = (x - 3)(x + 3)

Hence the division is:

h(x) = (x - 3)(x + 3)/(x - 3) = x + 3.

Considering that x² - 16 is the subtraction of perfect squares, we have that:

x² - 16 = (x - 4)(x + 4)

Hence the division is:

h(x) = (x - 4)(x + 4)/(x - 4) = x + 4.

Considering that the roots of x² - 4x + 3 are x = 1 and x = 3, we have that:

x² - 4x + 3 = (x - 1)(x - 3).

Hence the division is:

h(x) = (x - 1)(x - 3)/(x - 3) = x - 1.

Considering that the roots of x² + 4x - 5 are x = -5 and x = 1, we have that:

x² + 4x - 3 = (x + 5)(x - 1).

Hence the division is:

h(x) = (x + 5)(x - 1)/(x - 1) = x + 5.

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Answer:

Step-by-step explanation:

9. the set containing all objects or elements and of which all other sets are subsets.

10. complement --> the amount in only one of teh sets

intersection --> the amount in both sets

11. 14 or -14

13. 46 1/2

14. 2 31/120

15. 1100% profit

16. 1200 gm

17. cube root of 7?

18. 6000 per year

Answer: 1223.07

Step-by-step explanation: you don't round up

Answer: 32 is the answer to the expression you provided.

Step-by-step explanation:

[tex]2^3\times2^2\\2\times2\times2\times2\times2\\4\times4\times2\\16\times2\\\rightarrow32[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{E}\textsf{quation:}[/tex]

[tex]\mathsf{2^3 \times 2^2}[/tex]

[tex]\huge\boxed{S}\textsf{olving:}[/tex]

[tex]\mathsf{2^3 \times 2^2}[/tex]

[tex]\mathsf{= 2\times2\times2 \times2\times2}[/tex]

[tex]\mathsf{= 4\times4\times2}[/tex]

[tex]\mathsf{= 16\times2}[/tex]

[tex]\mathsf{= 32}[/tex]

[tex]\huge\boxed{T}\textsf{herefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{32}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

A

Step-by-step explanation:

First, we should put this equation in slope-intercept form by isolating y.

Thus, we have:

[tex]2x-\frac{4}{3}y=4\\ -\frac{4}{3}y=4-2x\\ y=\frac{3}{2}x-3[/tex]

The slope-intercept equation shows that the y-intercept is -3 and the slope is 3/2.

Only answer A meets these requirements.

Step-by-step explanation:

Set A is a subset of set B if all the elements of A are also the elements of Set B.. (common element)

The above set have 0 common elements so.. if there is no common element and are subsets then it means that there arent any elements in both the sets

so, the answer for the question would be "both the Sets A and B are the empty sets"

Answer:

x = 6

Step-by-step explanation:

put '3' in where 'y' is :

7x + 2(3) = 48

7x + 6 = 48              subtract 6 from both sides of the equation

7x = 42                 divide both sides by 7

x = 6

x[x²-25] - [x³+8] = 17

x³- 25x - x³- 8 = 17

-25x = 17 + 8

-25x = 25

x = -1

The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.

The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.

For example:

If we have a*a*a*a, it can be written in exponential form as:

=a^4

where

The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power. 

From the information given:

We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:

[tex]\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }[/tex]

[tex]\mathbf{= 2^8\times (2^6) \times (2^{-8}) }[/tex]

[tex]\mathbf{= 2^{8+6+(-8)}}[/tex]

[tex]\mathbf{= 2^{6}}[/tex]

Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.

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A semicircle is a part of a circle, and it is referred to as half of a given circle. Thud the area of the semi-circle window is 982 [tex]in^{2}[/tex].

A circle is a shape that is bounded by a curved path which is referred to as the circumference. Some parts of a circle are radius, diameter, sector, arc, semi-circle, circumference, etc.

A semicircle is a part of a circle, and it is referred to as half of a given circle.

such that:

Area of a circle = [tex]\pi[/tex] [tex]r^{2}[/tex]

and

area of a semicircle = [tex]\frac{\pi r^{2} }{2}[/tex]

where: r is the radius of the circle, and [tex]\pi[/tex] is a constant with a value of [tex]\frac{22}{7}[/tex].

Thus from the given question, it can be inferred that;

r = [tex]\frac{50}{2}[/tex]

 = 25

r = 25 in

Thus, the area of the semi-circle can be determined as;

area of the semi-circle = [tex]\frac{1}{2}[/tex] * [tex]\frac{22}{7}[/tex] * [tex]25^{2}[/tex]

                                      = 982.1429

area of the semi-circle = 982.14 [tex]in^{2}[/tex]

The area of the semi-circle window is approximately 982 [tex]in^{2}[/tex].

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The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.

According to the statement

we have given that the Sumalee sold 6 pecan cheesecakes and 12 apple

cheesecakes for a total of $270. Julio sold 12 pecan cheesecakes and 9 apple cheesecakes for a

total of $285.

And we have to find that the cost each of one pecan cheesecake and one apple cheesecake.

So, for this purpose,

Let x be the cost of each pecan cheesecake.

and y be the cost of each one apple cheesecake.

Then The equation become

6x + 12y = 270  -(1)

12x + 9y = 285  -(2)

From elimination method

multiply (1) by 12 and (2) by 6 then

72x + 144y = 3240

72x + 54y = 1710

Now eliminate x from them then the equation become

90y = 1530

here y = 17

then the x become

6x + 12y = 270  

6x + 12(17) = 270  

6x = 270-204

6x = 66

and x become 11.

So, The cost of the pecan cheesecake and one apple cheesecake are $11 and $17.

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{Area\text{ ABCD=}\frac{1}{2}\times AC\times BD}[/tex]

▪ [tex] \sf{Area = 72 yd^2}[/tex]

▪ [tex] \sf{BD = 6yd}[/tex]

[tex]\leadsto[/tex] Substitute the values:

[tex]\longrightarrow \sf{72 = \dfrac{1}{2} \times AC \times 16}[/tex]

[tex]\leadsto[/tex] Solve for AC:

[tex]\longrightarrow \sf{72=8\times AC}[/tex]

[tex]\longrightarrow \sf{ \dfrac{72}{8}=\dfrac{8\times AC}{8}}[/tex]

[tex]\longrightarrow \sf{AC=9}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\large \bm{AC= \: 9 yd}[/tex]

BD = 16 yd

Area of ABCD = 72 yd²

AC = ?

Area of rhombus, using diagonal:

[tex] \frac{1}{2} \times d1 \times d2[/tex]

Therefore:

[tex] \frac{1}{2} \times 16 \times ac = 72[/tex]

Then:

[tex] \frac{16ac}{2} = 72[/tex]

Cross multiply the above into:

[tex]16ac \times 1 = 72 \times 2 = 144 \\ 16ac = 144[/tex]

Divide by the coefficient of AC:

[tex] \frac{16ac}{16} = \frac{144}{16} [/tex]

Final answer is 9 yd

Profit decreased by 7.5%

Answer:

Solution Given:

Marked Price= Rs 6,000

discount =20%

Selling Price =M.P- discount% of M.P

=M.P(1-discount%)

=6000(1-20%)

= Rs 4,800

Again

Profit = 20%

Cost Price=(S.P*100)/(100+profit%)

= (4800*100)/(100+20%)

= Rs 4,000

For discount 25%

Marked Price =Rs 6,000

Selling Price =M.P - discount% of M.P

=M.P(1-discount%)

=6000(1-25%)

=Rs 4,500

Profit = S.P- C.P= Rs 4,500- Rs 4,000=Rs 500

Profit %=Profit/C.P* 100%= 500/4000*100 = 12.5%

Profit % decreased from 20% to 12.5%

Profit decreased by 7.5%

Answer:

7.5%

Step-by-step explanation:

Marked Price

Rs 6,000

Discounted Price

If the price is discounted by 20%, then the discounted price is 80% of the marked price:

[tex]\implies \sf Discounted\:Price =80\% \textsf{ of marked price}[/tex]

[tex]\implies \sf Discounted\:Price =0.8 \times 6000[/tex]

[tex]\implies \sf Discounted\:Price = 4800\:Rs[/tex]

Cost Price

If the dealer makes 20% when selling the watch at the discounted price, then the cost price is:

[tex]\implies \sf Cost\:Price=\dfrac{100\%}{120\%} \times 4800[/tex]

[tex]\implies \sf Cost\:Price=\dfrac{4800}{1.2}[/tex]

[tex]\implies \sf Cost\:Price=4000\:Rs[/tex]

Discount of 25%

If the price is discounted by 25%, then the discounted price is 75% of the marked price:

[tex]\implies \sf Discounted\:Price =75\% \textsf{ of marked price}[/tex]

[tex]\implies \sf Discounted\:Price =0.75\times 6000[/tex]

[tex]\implies \sf Discounted\:Price = 4500\:Rs[/tex]

Profit after 25% discount

[tex]\implies \sf Profit=\dfrac{discounted\:price}{cost\:price}-1 \times 100[/tex]

[tex]\implies \sf Profit=\dfrac{4500}{4000}-1 \times 100[/tex]

[tex]\implies \sf Profit=12.5\%[/tex]

Therefore, the profit decreased from 20% to 12.5% which means the profit percent decreased by 7.5%.

Step-by-step explanation:

Answer:

y > 3x + 2

Step-by-step explanation:

The slope is 3.       slope = (-7 - 2)/(-3 - 0) = -9/(-3) = 3

The y-intercept is 2.

The equation of the line is y = 3x + 2

The shading is "above" the line.

Answer: y > 3x + 2

Answer:

if you end up landing on a heads you should walk away with a $1.46

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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