24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X

Answer:

y = 10

Step-by-step explanation:

given DEFG = SPQR

QR = FG

=> 2x - 4 = 12

=> 2x = 16

=> x = 8

angle PQR = EFG

=> 6y + x = 68

=> 6y + 8 = 68

=> 6y = 60

=> y = 10

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 678400\\ P=\textit{original amount deposited}\dotfill & \$320000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 678400 = 320000[1+(0.07)(t)] \implies \cfrac{678400}{320000}=1+0.07t\implies \cfrac{53}{25}=1+0.07t \\\\\\ \cfrac{53}{25}-1=0.07t\implies \cfrac{28}{25}=0.07t\implies \cfrac{\frac{23}{25}}{0.07}=t\implies \boxed{16=t}[/tex]

Answer:

The probability is 0.9

Step-by-step explanation:

Suppose that we have a bag with N outcomes (such that these N outcomes have the same probability of being randomly drawn from the bag, we can suppose that the outcomes are given elements, like marbles or something like that.)

Suppose now that there are K of these elements with a given property.

The probability of randomly drawn one of these K elements is equal to the quotient between the number of these elements in the set (K) and the total number of elements in the bag (N)

The probability is: P = K/N

In this case, we know that there are 40 slips of paper, numbered from 1 to 40.

We want to find the probability of NOT choosing a multiple of 10.

The multiples of 10 in that range are:

10*1 = 10

10*2 = 20

10*3 = 30

10*4 = 40

So we have 4 multiples of 10, then we have 36 non-multiples of 10.

The probability of drawing at random a number that is not a multiple of 10, is equal to the quotient between the number of slips of papers with numbers that are not multiples of 10 (36) and the total number of slips of paper (40)

P = 36/40 = 0.9

The probability is 0.9

Answer:

x=8, y=6. (8, 6).

Step-by-step explanation:

x+3y=26

x+y=14

------------

x+3y=26

-(x+y)=-14

-----------------

x+3y=26

-x-y=-14

---------------

2y=12

y=12/2

y=6

x+3(6)=26

x+18=26

x=26-18

x=8

Answer:

a = 12

Step-by-step explanation:

a² + 9² = 15²

a² = 15² - 9²

a² = 225 - 81

a² = 144

take the square root of both sides

a = 12

Answer:

[tex] {a }^{2} + {9}^{2} = {15}^{2} \\ {a}^{2} = - 81 + 225 \\ {a}^{2} = 144 \\ a = \sqrt{144 \: } \\ a = 12[/tex]

The cost of the 4 cartons of grape juice and 8 cartons of apple juice will be $32 and the difference is $12.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jared and Missy are buying refreshments for their class party. Jared is buying a variety case of juice for $20. Missy is buying cartons of grape juice for $2 and cartons of apple juice for $3.

The cost of 4 grapes and 8 apples will be,

Cost = 2g + 3a

Cost = ( 2 x 4 ) + ( 3 x 8 )

Cost = 8 + 24

Cost = $32

The difference in the price  Missy and Jared paid is,

Difference = $32 - $ 20

Difference = $12

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Answer:

We'll use the following identities:

r = √(x2 + y2), from which we also have r2 = x2 + y2

y = r*sinθ

First, let's re-write your equation:

r = 8*sin(θ).  Multiply both sides by r:

r2 = 8r sin(θ)

Now, we'll use substitute using the identities:

x2 + y2 = 8y

Re-arrange and complete the square:

x2 + y2 - 8y = 0

x2 + (y-4)2 - 16 = 0

x2 + (y-4)2 = 16

This represents a circle with center (0,4), and radius 4.

Step-by-step explanation:

sorry if it wrong

Answer:

10x10x10 or 10*3......

The table is given below.

The graph is given below.

The linear model that represents lucky's current weight in pounds as a function of his age in months is

f(x) = 9x - 15.

Lucky's weight in one year is 93 pounds.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Lucky current age and weight = 2 months and 3 pounds.

The growth rate of lucky per month = 9 pounds.

Table of age and weight of lucky.

Age (months)        Weight (pounds)

2                              3

3                              12

4                              21

5                              30

6                              39

7                              48

8                              57

Now,

The coordinates on the graph from the table are:

(2, 3), (3, 12), (4, 21), (5, 30), (6, 39), (7, 48), and (8, 57).

The graph of the table is given below.

Now,

The function for the weight of the lucky in x months.

f(x) = mx + c

m = 9

(2, 3) = (x, f(x))

So,

3 = 9 x 2 + c

c = 3 - 18

c = -15

So,

f(x) = 9x - 15

Where x is the number of months.

Now,

The weight of lucky in one year i.e 12 months.

This means,

x = 12 months

f(12) = 9 x 12 - 15 = 108 - 15 = 93

Thus,

The table is given above.

The graph is given below.

The function for lucky weight in x months is f(x) = 9x - 15.

The weight of lucky in one year is 93 pounds.

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Answer:

Rectangular Prism Volume = [tex]210cm^{3}[/tex]

Total Volume of Composite Figure = [tex]247.68cm^{3}[/tex]

The number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .

What is area ?

Area can be defined as the total space taken by  a 2-dimensional surface or shape of an object.

Given

Jake has a floor that is 64 square feet.

He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet.

The area of 3 feet by 5 feet could be  = 3 * 5 = 15 square meters.

number of tiles required to fill the space could be  = 64 / 15

that is 4.3 (approx )

Hence , the number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .

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Answer:

B

C

E

Step-by-step explanation:

Answer:

Step-by-step explanation:

A person selected by others to run for office is the nominee.

Answer:

No

Step-by-step explanation:

Input the values and see if the equation is true.

2x + 3y = 6

(2, 3) x = 2, y = 3

2(2) + 3(3) = 6

4 + 9 = 6

13 ≠ 6

Answer:

B. a1 = 3

Step-by-step explanation:

Since we have the comon ratio and 12th term, we could just divide the 12th term (6144) by 2 11 times until we get to the 1st term:

[tex]6144 /2/2/2/2/2/2/2/2/2/2/2 = 3[/tex]

For a better understanding of the question, let's use the formula for geometric equations:

a(r)^(n-1)

1. Let's plug in the values we know

a(2)^(12-1)

2. Set equation equal to 6144 (Since we use n = 12) and solve for a

To confirm this, let's use the formula for geometric equations again:

a(r)^(n-1)

a = first term = 3

r = common ratio = 2

3(2)^(12-1) = 6144

Therefore, a1 = 3

The cost of a one mile ride is given as follows:

$6.

The cost per mile is constant, hence a linear function is used to model the situation.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

A taxi driver charges a $2 fee plus an additional $4 per mile, hence the slope and the intercept are given as follows:

m = 4, b = 2.

Thus the function that gives the cost for a x mile ride is:

y = 4x + 2.

The cost for a one mile ride is of:

y = 4(1) + 2 = $6.

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Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

Therefore Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

Therefore this option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

Therefore this option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

This option is always true

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It will it take 56 years for the account value to reach $20,900.

This amount is calculated based on the principal amount of a loan or the first deposit in a savings account. Simple interest does not compound, thus, a creditor will only pay interest on the principal amount and a borrower would never have to pay more interest on the previously accumulated interest.

formula for calculating Simple Interest, S.I:

S.I = P * R * T

            100

Where,

S.I =  Simple Interest

P =Pricipal

R = rate ( in percentage)

T= Time

To how long will it take for the account value to reach $20,900

S.I = $20,900

R = 6.5%

P =$ 5,700

T =?

S.I = P * R * T

            100

$20,900 = $ 5,700 * 6.5 * T

                            100

Cross multiplying and Making Time, T  subject of the formula we have:

$20,900 * 100 = $ 5,700 * 6.5 * T

T=   $20,900 * 100

         $ 5,700 * 6.5

T=  56.41

T ≈  56 years

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Answer:

I don't know

Step-by-step explanation:

i don't know

Answer:

4th term = 0

6th term = -4

13th term = -18

Step-by-step explanation:

a(n) = 6 + -2(n-1)

a(4) = 6 + (-2)(3) which is 6-6

a(6) = 6 + (-2)(5) which is 6-10

a(13) = 6 + (-2)(12) which is 6-24

Answer:

A and B

Step-by-step explanation:

2(-6c + 3) + 4c

According to PEMDAS, we should evaluate the parentheses first.

However, the parentheses are already simplified completely.

Now we look for exponents. However, there are no exponents.

Next is multiplication. We can see there is a 2 directly outside of the parentheses. Distribute the 2 across each term in the parentheses.

-12c + 6 + 4c

Now combine like terms with addition.

-8c + 6

We can see that A. -8c + 6 is an answer choice.

Let's look at B. 3(-4c + 2) + 4c

Following the same steps, we will move on to multiplication.

-12c + 6 + 4c

Combine like terms with addition.

-8c + 6

This is also an answer choice.

Hope this helps!

clothing,fuel,groceries and utility bill

A number between 47 and 53 such that the prime factors are not repeated is:

3*17 = 51

Remember that any number can be written as a product of prime factors.

If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.

For example:

2*3*5*7 = 210

There are no repeated factors, but the number is not in the desired range.

2*5*7 = 70

Still not in the range.

You can try some times until you get for example:

3*17 = 51

This a number in the desired range, such that their prime factors are not repeated.

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Answer:

3.496

Step-by-step explanation:

Multiply these two by getting rid of the decimal:

 38 -decimal is moved one place here.

x092  -decimal is moved two places here.

3496  -move decimal three places over.

Answer: To find the expected amount of money the radio caller should win, you can multiply the prize amount by the probability of winning that prize, and add those products for each prize. The expected value is also known as the mean value.

$500 * 1/8 = $62.50

$750 * 1/8 = $93.75

$1,250 * 1/8 = $156.25

$2,500 * 1/8 = $312.50

$5,000 * 1/8 = $625.00

$10,000 * 1/8 = $1250.00

$25,000 * 1/8 = $3,125.00

Total expected value = $62.50 + $93.75 + $156.25 + $312.50 + $625.00 + $1250.00 + $3,125.00 = $5,050.00

So, the expected amount of money the radio caller should win if the caller gets to spin the wheel once is $5,050.

It's worth to mention that the probability for each prize is the same, but the prizes are not the same so each prize win will be different according to the prize amount.

The expected value doesn't assure that the prize will be won, but it's a good approximation of the prize the caller could win.

Step-by-step explanation:

You can sand 14.4 yd² of wood in 3.2 hours.

A ratio is used to compare two or more like quantities or numbers with the same units. It is often written with a colon, and when used in words, we say the ratio of one quantity "to" the second quantity. A rate is a ratio that compares two different quantities which have different units.

9:2

x:3.2

therefore;

x = (3.2 x 9)/2

x = 28.8/2

x = 14.4 yd² of wood

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Answer:

1.40p+2n=40

Step-by-step explanation: