(y + 4 / 2y) + (y-2 / 3) = (3y^2 + 10 / 6y) for y
{-2, 1}
{-2, 3}
{}

Answer:

C

I took the same assignment, have a nice day.

To solve for the volume of a rectangular prism, we could use the following formula:

\(V=l*w*h\)

Although we typically use this formula to solve for the volume, we could also use it to determine any of the variables above. All we have to do is rearrange the equation to isolate what we need to find.

We're given:

First, rearrange the volume formula to isolate width (w):

\(V=l*w*h\)

⇒ Divide both sides by \(l*h\):

\(\dfrac{V}{l*h}=\dfrac{l*w*h}{l*h}\\\\\dfrac{V}{l*h}=w\\\\w=\dfrac{V}{l*h}\)

⇒ Plug in the given values for V, l and h:

\(w=\dfrac{1144}{8*13}\\\\w=11\)

Therefore, the box is 11 ft wide.

The box is 11 ft wide.

Answer:

(A) 11 ft.

Step-by-step explanation:

got it right

The scale factor of the dilation is k = 5/4

Given data ,

A figure with an area of 25 square units is dilated from a figure with an area of 16 square units

Let the dilation scale factor be k

Now , Given that the original area (A) is 16 square units and the target area (B) is 25 square units, we can write the equation as:

B = k² A

k² = 25/16

Taking square roots on both sides , we get

k = 5/4

Hence , the dilation factor is 5/4

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Answer:

16.25 mL

Step-by-step explanation:

Since we are mixing from the syrup in the inventory, we can say that the syrup in the inventory must be equal to that in the final solution. Thus, we will use the dilution equation to solve for the Initial volume;

Dilution equation is;

V₁C₁ = V₂C₂

Where;

V₁ is initial volume

C₁ is initial concentration or initial molarity

V₂ is final volume

C₂ is final concentration of final molarity

We are given;

C₁ = 80% = 0.8

C₂ = 60% = 0.6

V₂ = 65 mL

Making V₁ the subject in the dilution equation, we have;

V₁ = (V₂C₂)/C₁

V₁ = (65 × 0.6)/0.8

V₁ = 48.75 mL of inventory syrup

Since we have 48.75 mL of inventory syrup and the dilute solution is 65 ml, then the volume of soda solution required = 65mL - 48.75 mL = 16.25 mL

Answer:

The speed of Todd's snowmobile was 22 miles an hour

Step-by-step explanation:

:))

The speed of Todd's automobile is 31 miles per hour.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that It took Todd 11 hours to travel over pack ice from one town in the Arctic to another town 330 miles away. During the return journey, it took him 15 hours.

For the first journey,

v₁ + v₂ = 330 / 11    ......................( 1 )

For the return journey,

v₂ - v₁ = 330 / 15 .........................( 2 )

From equation ( 1 ) and equation ( 2 ),

2v₂ = ( 330 / 11 ) + ( 330 / 15 )

2v₂ = ( 330 ) ( 31 / 165 )

v₂ = 165 ( 31 / 165 )

v₂ = 31 miles per hour

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Answer:

there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

Step-by-step explanation:

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

In this case, we want to determine how many ways we can select 3 batteries out of 6. Using the counting principle, we can break down the selection process into three steps:

Select the first battery. There are 6 choices for the first battery.

Select the second battery. There are 5 choices left for the second battery, since we've already selected one.

Select the third battery. There are 4 choices left for the third battery.

Using the counting principle, we can multiply the number of choices for each step to get the total number of ways to select 3 batteries:

6 x 5 x 4 = 120

Therefore, there are 120 possible points in the sample space if we select 3 batteries at random from a bag containing 6 batteries of different brands.

The csc(theta) = 1/sin(theta) = 1/(-2/√13) = -√13/2. So, the cosecant of theta is -√13/2.

To find the cosecant (csc) of theta when a point (-3, -2) lies on its terminal side, we need to determine the hypotenuse (r) of the right triangle formed by this point.

Using the Pythagorean theorem, r^2 = (-3)^2 + (-2)^2. So, r^2 = 9 + 4 = 13, and r = √13.

The csc(theta) is the reciprocal of sin(theta). Sin(theta) is calculated as the ratio of the opposite side (y-coordinate) to the hypotenuse, or sin(theta) = -2/√13.

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Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

Step-by-step explanation:

given,

alex = x

bella = 3x

cara = x - 10

and also given,

\(x + 3x + (x - 10) = 90 \\ x + 3x + x - 10 = 90 \\ 5x - 10 = 90 \\ 5x = 90 + 10 \\ 5x = 100 \\ x = 100 \div 5 \\ = 20\)

Given x = £20,

Alex = £x = £20

Bella = £3x = £3x20 = £60

Cara = £(x-10) =£(20-10) =£10

Answer:

3 small boxes and 6 large ones

Step-by-step explanation:

3 times 100 equals 300 and 6 times 350 is 2100 and 2100 plus 300 is 2400.

Answer:

The missing number is:

22

Step-by-step explanation:

There are 3 numbers and one more

4 numbers and your average is 17

then:

17*4 = 68

then:

11 + 17 + 18 + a = 68

46 + a = 68

a = 68 - 46

a = 22

Check:

(22 + 11 + 17 + 18)/4 = 17

68/4 = 17

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer:

option B

polynomial cannot have negative power

hope it helps

Answer:

-4

Step-by-step explanation: An integer is a number that can be negative and positive, is a whole number not a fraction so a loss of 4 with an integer would be -4 going back 4 on the number line.

So

Hence

2in line represents

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

9 multiples

Step-by-step explanation:

16,24,32,40,48,56,64,72,80

9

Answer:

decagon (10-sided polygon)

Step-by-step explanation:

A regular polygon has a minimum rotation of 360/n degrees about its center, where n is the number of sides in the polygon.

Therefore, the regular polygon with a minimum rotation of 36 degrees about its center is a polygon with 360/36 = 10 sides, or a decagon.

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Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 4x - 22 = -14

Now the value of x will be,

→ 4x - 22 = -14

→ 4x = -14 + 22

→ 4x = 8

→ x = 8/4

→ [ x = 2 ]

Hence, the value of x is 2.

The formula for the geometric sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In geometric sequence, the general formula of geometric sequence is:

Tₙ= ar⁽ⁿ⁻¹⁾

Information:

Tₙ = the n-th term

a = first term

r = ratio

n = the number of terms

In the question above,

a= 5

r= T2/T1=-15/5=-3 (This is the ratio)

Substitute the value of a and r to the formula of Tₙ:

Tₙ= ar⁽ⁿ⁻¹⁾

Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

So the formula of Tₙ for the sequence above is Tₙ= 5. (-3⁽ⁿ⁻¹⁾)

In the above formula there is a ratio of geometric sequences. In a geometric sequence, two successive terms have the same ratio. Comparisons to geometric sequences are referred to as ratios (r). This is where the quotient of adjacent terms will be obtained.

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Answer:

1st one is 6.9 X 10^6

2nd one is 2 x 10^5

Step-by-step explanation:

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

The standard error of the distribution of sample proportions is of 0.014.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Consider random samples of size 1200 from a population with proportion 0.65 .

This means that \(n = 1200, p = 0.65\)

Find the standard error of the distribution of sample proportions.

This is s. So

\(s = \sqrt{\frac{0.65*0.35}{1200}} = 0.014\)

The standard error of the distribution of sample proportions is of 0.014.

Answer:

2.5

Step-by-step explanation:

you cut the diameter in half and it's 5 so do the math

Answer:

x = 6, x = -4

Step-by-step explanation:

The player made 38 foul shots.

Let's indicate the player's total number of field goals made by F and foul shots attempted by S. Based on the data in the problem, we may construct an equation system:

F + S = 55 (the player made a total of 55 baskets) (the player made a total of 55 baskets)

2F + S = 89 (the player scored a total of 89 points) (the player scored a total of 89 points)

The substitution approach can be used to find the values of F and S. We start by resolving the initial S equation:

S = 55 - F

Next, we change S in the second equation to the following expression:

2F + (55 - F) = 89

When we simplify and find F, we obtain:

F = 17

Hence, the player connected on 17 field goals. We may change this value of F into the first equation and then solve for S to determine the total number of foul shots:

17 + S = 55

S = 38

The player so scored 38 fouls.

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Given:

The line BD and EG are parallel lines.

To find: The measure of an angle,

Explanation:

We know that,

Vertical angles are angles opposite each other where two lines cross.

The vertically opposite angles are always equal in measure.

Hence, the angle of GFC must be equal to the angle of EFH.

Therefore,

Final answer: The measure of angle,