How are exponents related to taking the root of a number

The equation that represents the scenario is P + 1.2x + 0.25 = y. Euclid's weight is 10.625 pounds, and Riemann's weight is 21.25 pounds.

(a) Let us assume that the current weight of Euclid is x and the current weight of Pythagoras is P. Let us also assume that the weight of Pythagoras in January is y. The expression that represents the given scenario will be written as;

when Pythagoras lost 13 pounds in 5 months : P =  y - 13

when Pythagoras gains 1.2 times Euclid's weight: = P + 1.2x

when Pythagoras' weight is 1/4 pound less than their weight in January:

(b) Solving the given equation,

P + 1.2x + 0.25 = y

y- 13 + 1.2x + 0.25 = y

1.2x - 12.75 = 0

(c) Euclid's weight is calculated as follows;

1.2x = 12.75

x = 12.75/1.2

x = 10.625 pounds

(d) The weight of Riemann is calculated as follows;

2(Euclid's weight)

2(10.625)

21.25 pounds

weight of Pythagoras = 60.5-(21.25 + 10.62)

= 28.7

The weight of Pythagoras is 28.7 pounds.

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The complete question is "Jake has two dogs, Euclid and Pythagoras. Euclid is a smaller dog and Pythagoras is larger. Jake found that Pythagoras lost 13 pounds from January to June. If Pythagoras gains 1.2 times Euclid's weight, Pythagoras's weight would still be 1/4 pound less than he did in January. What is Euclid's weight? (a) Write an equation that represents the scenario. Begin by defining your variable (b) Solve the equation. Show your work. (c) What is Euclid's weight? (d) Jake adopts a third dog, Riemann. Riemann weighs exactly twice what Euclid weighs. The combined 60.5 pounds. What is Riemann's weight, and what is Pythagoras's weight? weight of the three dogs is Show your work.​"

Answer:

f(x)=2x-3, substitute the expression for g(x) in f(x)

f(x) = 2(x^2 + 1) - 3

f(x) = 2x^2 + 2 - 3

f(x) = 2x^2 - 1

Answer:

135

285

300

Step-by-step explanation:

The correct option is option (c)-"The distribution is skewed right."

The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.

A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.

The distribution seems to be centered at around 42-43.

The age distribution ranges from about 30 to about 75, without taking into account an outlier.

It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.

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Answer:

y=2x-7

Step-by-step explanation:

so here's my work

I just plugged stuff in so:

y+1=2(x-3)

y+1=2x-6

y=2x-7

Given that 'y' is directly proportional to 'x',

Let 'k' be the constant of proportionality.

Then the equation becomes,

Given that 'y' is 14 when 'x' is 12,

Substitute the values in the equation,

Substitute the value of 'k' in the equation,

Thus, the required equation that relates 'x' and 'y' is,

1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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a. the equation for the hyperbola is x^2 / 4 - y^2 / 12 = 1. b. the equation for the hyperbola is [(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.

A) To find the equation for the hyperbola with vertices (±2, 0) and foci (±4, 0), we can use the standard form equation for a hyperbola:

[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,

where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and c is the distance from the center to the foci.

In this case, the center is at (0, 0) since the vertices are symmetric with respect to the y-axis. The distance from the center to the vertices is a = 2, and the distance from the center to the foci is c = 4.

Using the formula c^2 = a^2 + b^2, we can solve for b^2:

b^2 = c^2 - a^2 = 4^2 - 2^2 = 16 - 4 = 12.

Now we have all the necessary values to write the equation:

[(x - 0)^2 / 2^2] - [(y - 0)^2 / √12^2] = 1.

Simplifying further, we get:

x^2 / 4 - y^2 / 12 = 1.

Therefore, the equation for the hyperbola is:

x^2 / 4 - y^2 / 12 = 1.

B) To find the equation for the hyperbola with foci (4, 0) and (4, 6) and asymptotes y = 1 + (1/2)x and y = 5 - (1/2)x, we can use the standard form equation for a hyperbola:

[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,

where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the foci.

From the given information, we can determine that the center of the hyperbola is (4, 3), which is the midpoint between the two foci.

The distance between the center and each focus is c, and in this case, it is c = 4 since both foci have the same x-coordinate.

The distance from the center to the vertices is a, which can be calculated using the distance formula:

a = (1/2) * sqrt((4-4)^2 + (6-0)^2) = (1/2) * sqrt(0 + 36) = 3.

Now we have all the necessary values to write the equation:

[(x - 4)^2 / 3^2] - [(y - 3)^2 / b^2] = 1.

To find b^2, we can use the relationship between a, b, and c:

c^2 = a^2 + b^2.

Since c = 4 and a = 3, we can solve for b^2:

4^2 = 3^2 + b^2,

16 = 9 + b^2,

b^2 = 16 - 9 = 7.

Plugging in the values, the equation for the hyperbola is:

[(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.

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To visualize this transformation, imagine a rectangle with vertices at and (0,2). Applying the transformation (x,y) →  \((3x,3y)\) to each vertex, we get a new rectangle with vertices at   \((0,0), (3,0), (3,6),\) and \((0,6)\), which is three times the size of the original rectangle.

Algebraic representations can take many forms, including equations, inequalities, functions, and matrices. These representations provide a powerful tool for analysing complex systems and deriving meaningful insights from them.

The algebraic representation \((x,y) (3x,3y)\) describes a dilation transformation, specifically an enlargement or stretch by a scale factor of 3 in both the x and y directions.

This means that every point in the original figure is multiplied by 3 in both the x and y directions, resulting in a larger, similar figure.

To visualize this transformation, imagine a rectangle with vertices at  \((0,0), (1,0), (1,2),\)  and   \((0,2).\) Applying the transformation (x,y) → (3x,3y) to each vertex, we get a new rectangle with vertices at \((0,0), (3,0), (3,6),\)  and (0,6), which is three times the size of the original rectangle.

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Answer:

b

Step-by-step explanation:

Answer:

Independent

Step-by-step explanation:

The reliance of an event on the outcine of another event gives rise to a dependent event. For any two or more event, whereby the outcome of event A has no effect on the possible outcome of event B, then such scenario is termed as being Independent. In the scenario described above, the outcome oof Sam's pick does not depend on the outcine of Steve's pick. This is because, once Steve makes his selection, the marble is returned into the box before Sam makes his own selection.Therefore, no matter the color of marble picked by Steven, it will have no bearing on the outcome of Sam's pick.

The match can be scheduled in 900 different ways with the help of permutations and combinations.

Given,

Number of players from each school = 3.

Let, the players of the first school be A, B, and C.

Let, the players of the second school be X, Y, and Z.

The problem can be solved in two cases,

Case-1

According to the question,

Each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

Round 1 : AX BY CZ

Round 2 : AX BZ CY

Round 3 : AY BX CZ

Round 4 : AY BZ CX

Round 5 : AZ BX CY

Round 6 : AZ BY CX

In other words, we have to permutate these 6 rounds, i.e., 6! = 720 ways.

Case-2

Given,

Three rounds are played simultaneously in each round.

(a)

Round 1 : AX BZ CY

Round 2 : AX BZ CY

Round 3 : AY BX CZ

Round 4 : AY BX CZ

Round 5 : AZ BY CX

Round 6 : AZ BY CX

(b)

Round 1 : AX BY CZ

Round 2 : AX BY CZ

Round 3 : AY BZ CX

Round 4 : AY BZ CX

Round 5 : AZ BX CY

Round 6 : AZ BX CY

The total number of permutations for Case-2 will be twice of 6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Thus, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

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Geraldine receives $14,730.

Geraldine's Stafford student loan is for $15,000, but she must pay a loan fee of 1.8%.

To determine the amount of money she will actually receive, we need to subtract the loan fee from the total loan amount.

First, let's calculate the loan fee.

To find 1.8% of $15,000, we can multiply the loan amount by 0.018 (which is the decimal representation of 1.8%).

Loan fee = $15,000 \(\times\) 0.018 = $270

Now, we subtract the loan fee from the total loan amount:

Amount received = Total loan amount - Loan fee

Amount received = $15,000 - $270 = $14,730

Therefore, Geraldine will receive $14,730 from the Stafford student loan. It's important to note that the loan fee is deducted upfront, so the actual amount disbursed to the student is reduced by that fee.

This ensures that the lender receives a portion of the loan upfront to cover administrative costs and mitigate potential risk.

The remaining amount is what the student receives to use for educational expenses or other approved purposes.

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The percentage of the discount is b) 75%.

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the original price of picture = 120.00

Sale price after discount = 29.99 ≅ 30

Now using discount percent formula,

=> Discount percentage = (original price- sale price)/(original price)*100

=> Discount percentage = \(\frac{120-30}{120}\times 100=\frac{90}{120}\times100 = 75\%\)

Hence the percentage of the discount is b)75%.

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The required correct values for A, B, and C is 9, 52, and 130 respectively.

Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Since a standard piano has a ratio of white to black keys is given as,
= 91/63
= 13/9

Now,
13/A =91/63
A = 9

Similarly,
B = 52

C = 130

Thus, the required correction values for A, B, and C is 9, 52, and 130 respectively.

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the answer is 12.6 :)

Answer:

Step-by-step explanation:

#1, top left

#2, top right

#3, bottom left

#4, bottom right

Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

The time it takes to coat a donut hole is directly proportional to the surface area of the donut hole.

The surface area of a sphere is given by the formula:

Surface Area = 4πr²

Here, r is the radius of the sphere.

Comparing the surface areas of the donut holes:

Niraek's donut hole: Surface Area = 4π(6²)

Theo's donut hole: Surface Area = 4π(8²)

Akshaj's donut hole: Surface Area = 4π(10²)

Now, let's find the LCM of the surface areas to determine the time it takes for all workers to finish:

LCM(144π, 256π, 400π) = 57600π mm²

This means that it will take the same amount of time for all three workers to finish their current donut holes when they have covered a total surface area of 57600π mm².

Number of donut holes = (Total surface area) / (Surface area of Niraek's donut hole)

= (57600π mm²) / (144π mm²)

= 57600 / 144

= 400

Therefore, Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.

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Answer:

320cm³ (option C)

Step-by-step explanation:

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Volume of bird house = volume of a cuboid + volume of a triangular prism

Volume of a cuboid = length × breadth × height

= 8cm × 5cm × 6cm = 240cm³

Volume of triangular prism = ½ base ×height ×length

= ½ × 8×4×5 = 80cm³

Volume of bird house = 240+80

Volume of bird house = 320cm³

Amount of birdseed that will it take to fill the birdhouse = Volume of bird house = 320cm³

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer: 30 kids.

Step-by-step explanation:

Since Mrs. Cunningham's ratio from boys to girls is 2:3 ( with girls being 3) you just need to multiply 6 to 3 to get 18. But you also need to multiply 6 and 2 then add both numbers together, which gets you to 12.

Answer:

30

Step-by-step explanation:

because if ratio 3 is girls and there are 18 of them if you divide that by 3 you get 6 than multiply 6 time the ratio of boys 2 to get 12  then add 18+12

Answer:

(- 4, 4 )

Step-by-step explanation:

y = - 7x - 24 → (1)

y = - 2x - 4 → (2)

substitute y = - 2x - 4 into (1)

- 2x - 4 = - 7x - 24 ( add 7x to both sides )

5x - 4 = - 24 ( add 4 to both sides )

5x = - 20 ( divide both sides by 5 )

x = - 4

substitute x = - 4 into either of the 2 equations and evaluate for y

substituting into (1)

y = - 7(- 4) - 24 = 28 - 24 = 4

solution is (- 4, 4 )

Answer: x = 5, y = 6

Step-by-step explanation: took the quiz.

\(\qquad\qquad\huge\underline{{\sf Answer}}☂\)

Let's evaluate the equation using the coordinates of point (-7 , 4) to check if it's a solution for the given function.

\(\qquad \sf  \dashrightarrow \: 4x + 5y = - 13\)

\(\qquad \sf  \dashrightarrow \: 4( - 7) + 5(4) = - 13\)

\(\qquad \sf  \dashrightarrow \: - 28 + 20 = - 13\)

\(\qquad \sf  \dashrightarrow \: - 8 \not = - 13\)

Therefore, we can conclude that it's not a solution for the given function ~

Answer:

No

Step-by-step explanation:

Given that:

-7, 4

 Thus,

4(-7) + 5(4)

-28 + 20 = -8

- 8 ≠ -13

Doesn't equal  x

Hence, Answer =   No -7,4 is not a solution to 4x+5y = -13

~Lenvy~

Answer:

b or 1.2*10⁻1

Step-by-step explanation:

10^8=one hundred million and that *3=three hundred million

10^7=ten million*3.6=36 million.

it has to be about 0.1 seconds so b

Answer:

1.2 × \(10^{-1}\) of a second

Step-by-step explanation:

d = vt , t = d / v

t = ( 3.6 × \(10^{7}\) )( 3 × \(10^{8}\) ) = (3.6 ÷ 3) × ( \(10^{7}\) ÷ \(10^{8}\) ) = 1.2 × \(10^{7 - 8}\) = 0.12 of second

t = 1.2 × \(10^{-1}\) of a second

Answer:

according to the rules of math and echo the answer is csgo globaloffense with the ration 12.10

Step-by-step explanation:

Answer:

If I know I will defiantly answer .but where is the question