This figure represents a garden box that is to be filled with soil.

How much soil will it take to fill the garden box?

Enter your answer in the box.

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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Answer:

1/2 of the cup.

3/4 is half of 1 1/2.

The probability that event B occurs is 1/4

The probability that event A occurs given that event B occurs is 1/3

What is the probability that events A and B both occur?

Recall that the conditional probability is given by

Re-writing the above formula for P(A and B)

So, the probability that events A and B both occur is

Therefore, the probability that events A and B both occur is 1/12

Answer:

(15.23,41.016)

Step-by-step explanation:

WE must determine the mean of the data set: Which is the sum of the set divided by the number in the set.
\(= (21 + 24 + 25 + 32 + 35 + 31 + 29 + 28)/8 = 225/8 = 28.125\)
We must also determine the standard deviation: Which is the square root of the variance and the variance is the sum of squares of the sample number minus the mean divided by the number if the set data:
\(= ((21 - 28.125)^{2} + (24 - 28.125)^{2} +(25 - 28.125)^{2} + (32 - 28.125)^{2} + (35 - 28.125)^{2} + (31 - 28.125)^{2} + (29 - 28.125)^{2} (28 - 28.125)^{2}\)
\(= 148.877/8 = 18.6\)
The 95% confidence interval is defined as: The mean ± 1.96*standard deviation divided by the sqaure root of the number of data in the set:
\(= 28.125 + (1.96 *18.6)/(\sqrt{8} )\)
\(= 41.016\)
\(= 28.125 - (1.96 * 18.6)/(\sqrt{8}) = 15.23\)
The confidence interval for this data set is (15.23,41.016)

Answer:

32.7 ± 2.262(1.19)

Step-by-step explanation:

See attached pictures

Answer:

No

Step-by-step explanation:

For ratios to be equivalent, they need to have something in common like 2:4

4:8. Those are common because ":2:4" is the simplified version of 4:8. (I mean it could be simplified to 1:2 but this is used as an example) (mark brainliest plas)

Roselyn can drive a distance until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.Roselyn can travel 120 km before running out

Distance travelled with 20 l of petrol in solution and final answer.

Roselyn's average speed is 60 kilometers per hour, and she needs to travel 150 kilometers to reach her family's place. Therefore, she will require a total of 150/60 = 2.5 hours to complete the journey.

The car's fuel efficiency is 6 kilometers per liter, meaning it consumes 1/6 liters of fuel per kilometer. To determine the total fuel required, we multiply the fuel consumption rate by the total distance: 150 * (1/6) = 25 liters of fuel.

Since the car's tank has 20 liters of fuel at the beginning of the drive, Roselyn will need an additional 25 - 20 = 5 liters of fuel to complete the journey.

As fuel costs 0.60 dollars per liter, Roselyn will need to spend a total of 5 * 0.60 = 3 dollars to purchase the necessary fuel.

Therefore, Roselyn can drive until she runs out of fuel for a time of 2.5 hours or until she spends all the fuel, whichever comes first.

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Answer:

about 390

Step-by-step explanation:

you multiply 41% by the 950 and that's what you get

Answer:

Option (1).

Step-by-step explanation:

Amount of water hold by both the pitchers (Large + small) = 12 cups

Let the small pitcher holds the water = S cups

If the water hold by the large pitcher is twice the size of the small pitcher, then the amount of water hold by large pitcher = 2S

Total amount water hold by both = S + 2S

Equation for this situation will be,

S + 2S = 12

Therefore, Option (1) will be the answer.

Answer:

Option 2

Step-by-step explanation:

Using cosine rule for this triangle

=> \(a^2= b^2+c^2-2bc(Cos A)\)

Where b = 2, c = 1 and A = 25

=> \(a^2 = 2^2+1^2 -2(2)(1)(Cos 25)\)

=> \(a^2 = 4+1 - 4(0.906)\)

=> \(a^2 = 5 - 3.6\)

=> \(a^2 = 1.4\)

Taking sqrt on both sides

=> a = 1.2

Answer:

x=685

Good Luck!!!

Answer:

try 685

Step-by-step explanation:

Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:

1.) 3.075 gallons.

To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.

We have that:

Hence the remaining amount is:

15 - 11.925 = 3.075 gallons.

Which means that option 1 is correct.

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Answer: 3.075 gallons

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 Section on the spinner and three spins:

4^3=64

The number of individual outcomes when spinning the wheel three times is 64 times

In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.

A power exists as the product of multiplying a number by itself. Usually, power is illustrated with a base number and an exponent. The base number tells what number exists being multiplied. The exponent, a small number written beyond and to the right of the base number, tells how many times the base number exists being multiplied.

Given

Sections = 4

no. of spinners per player = 3

no. of spinners per player per game = 4 ³ = 4 * 4 * 4 = 64

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Answer:

Part A: The maximum of the graph is the highest point which is at (2.5, 2531.25). Since xx is the decrease in price and yy is the profit, the maximum of (2.5, 2531.25) means that the maximum profit is $2531.25 and occurs when the price of the t-shirts is decreased by $2.50.

Part B: The yy-intercept is when the graph intersects the yy-axis which occurs at about (0, 2500). The yy-intercept then means that the profit is $2500 if the price of the t-shirts does not decrease.

Part C: The solution of a graph is its xx-intercept(s). The graph crosses the xx-axis at (25,0) so this point is the solution. The solution means that the profit will be $0 if the price is decreased by $25.

Step-by-step explanation:

Answer:

76%

Step-by-step explanation:

First, we know that 6 tables of 6 are already seated. We can go ahead and multiply 6 by 6, which is 36.

This means that 36 of the 150 seats are already taken.

But, we want to find the amount of seats that are still empty. So, we subtract 36 from 150 to get 114 seats.

The question is asking for the percentage, so we can divide 114 by 150 seats to get 0.76. Then, we have to move the decimal to the right 2 spaces to get 76%

Answer:

76% of the restaurant is still empty

Step-by-step explanation:

6 tables of 6 seated means there are currently 36 people seated. If the restaurant can seat 150 people, 76% of the restaurant is still empty.

\(6\times6=36\text{ | there are 36 guests}\\36\div150=0.24\text{ | 24\% of the restaurant is filled}\\1-0.24=0.76\text{ | 76\% of the restaurant is not filled}\)

Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.

In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.

For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.

To find the image of point E under this translation, you can apply the same translation to point E:

Point E is located at (5, 5).

The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).

You can follow the same process to find the images of the other points under the translation.

Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.

In this case, the translation vector is given by the displacement from point D to point D′:

Point D is located at (2, 5).

Point D′ is located at (-6, -2).

The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).

To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:

Point E is located at (5, 5).

The translation vector is (-8, -7).

The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).

You can follow the same process to find the images of the other points under the translation.

Step-by-step explanation:

Answer: A. H0: Mean= 5 and Ha: Mean is not equal to 5.

Step-by-step explanation:

Definitions:

Given: The diameter of a spindle in a small motor is supposed to be 5.8 millimeters.

If the spindle is either too small or too large, the motor will not work properly. so, Mean diameter ≠ 5.8 to work correctly.

i.e. \(H_a: \text{Mean}\neq 5.8\)

So, \(H_a: \text{Mean =5.8}\)

The required null and alternative hypotheses:

H0: Mean= 5 and Ha: Mean is not equal to 5.

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

The domain of function f(x) is given as follows:

{x | 1 ≤ x < 5}.

The values of x of the function given at the end of the answer are as follows:

Hence the domain is given as follows:

{x | 1 ≤ x < 5}.

The function is given by the image presented at the end of the answer.

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Answer:

A - {x | 1 < x < 5}

Step-by-step explanation:

took the Quiz

Answer:

d> -5/2

Step-by-step explanation:

-2d<5

divide both sides by -2

d>-5/2

Answer:

d > - \(\frac{5}{2}\)

Step-by-step explanation:

- 2d < 5

divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

d > \(\frac{5}{2}\) or d > 2.5

Answer:

a. 0.5 = 50% probability that the driver is selected as a medium-risk driver.

b. 0.3 = 30% probability that he has been classified as high-risk

c. 0.51 = 51% probability that at least one of them has been classified as high-risk.

Step-by-step explanation:

To solve this question, we need to understand conditional probability, for items a and b, and the binomial distribution, for item c.

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

a. If a driver had an accident during the year, find the probability that the driver is selected as a medium-risk driver.

Event A: Had an accident

Event B: Medium-risk driver

Probability of having an accident:

0.01 of 0.6(low risk)

0.05 of 0.3(medium risk)

0.09 of 0.1(high risk)

So

\(P(A) = 0.01*0.6 + 0.05*0.3 + 0.09*0.1 = 0.03\)

Probability of having an accident and being a medium risk driver:

0.05 of 0.3. So

\(P(A \cap B) = 0.05*0.3 = 0.015\)

Desired probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.03} = 0.5\)

0.5 = 50% probability that the driver is selected as a medium-risk driver.

b. If a driver who had an accident during the I-year period is selected, what is the probability that he has been classified as high-risk?

Event A: Had an accident

Event B: High risk driver.

From the previous item, we already know that P(A) = 0.03.

Probability of having an accident and being a high risk driver is 0.09 of 0.1. So

\(P(A \cap B) = 0.1*0.09 = 0.009\)

The probability is

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.009}{0.03} = 0.3\)

0.3 = 30% probability that he has been classified as high-risk

c. If two drivers who had an accident during the I -year period are selected, what is the probability that at least one of them has been classified as high-risk?

0.3 are classified as high risk, which means that \(p = 0.3\)

Two accidents mean that \(n = 2\)

This probability is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{2,0}.(0.3)^{0}.(0.7)^{2} = 0.49\)

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.49 = 0.51\)

0.51 = 51% probability that at least one of them has been classified as high-risk.

Answer:

11%

Step-by-step explanation:

If you assume this is out of 100 you can do 98/100 - 87/100, or 98% - 87%, which equals 11%

The composite result function (f o g) and (g o f ) the given functions f(x) = x/(x-7) and g(x) = 5/x are 5/(5 - 7x ) and (5(x - 7))/x respectively.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, set up the composite result function ( f o g ).

( f o g ) = f( g(x) )

( f o g ) = f( g(x) )  = 5/x / ( (5/x) - 7 )

Simplify

( f o g ) = 5/x / ( (5/x) - 7 )

( f o g ) = 5/x × 1/( (5/x) - 7 )

( f o g ) = 5/x × x/(5 - 7x )

( f o g ) = 5/(5 - 7x )

Next, we find ( g o f ).

( g o f ) = g( f(x) ) = 5 / ( x/ (x - 7) )

Simplify

( g o f ) = 5 / ( x/ (x - 7) )

( g o f ) = 5 × (x - 7)/x

( g o f ) = (5(x - 7))/x

Therefore, the composite result function ( f o g ) equals 5/(5 - 7x ) and ( g o f ) equals (5(x - 7))/x.

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Answer:

225 square cm.

Step-by-step explanation:

The maximum possible area of Kyle's quadrilateral occurs when it is a square with side length equal to half the perimeter, which is 30/2 = 15 cm. The area of a square with side length 15 cm is 15 x 15 = 225 square cm.

Step-by-step explanation:

(a)(i) The average rate of change is:

(895 − 455) / (250 − 150)

4.4

(a)(ii) Since the profit is linear, the slope of the line is equal to the average rate of change.  Using point-slope form:

y − 455 = 4.4 (x − 150)

Simplifying to slope-intercept form:

y − 455 = 4.4x − 660

y = 4.4x − 205

(a)(iii) The break-even point is when the profit is 0.

0 = 4.4x − 205

4.4x = 205

x = 46.6

(b)(i) The "demand function" is the selling pice of the compasses:

p = 40 − 4q²

where p is the price in dollars and q is the quantity in millions of units.

Profit is revenue minus cost.

P = R − C

P = pq − 15q

P = (p − 15) q

P = (25 − 4q²) q

P = 25q − 4q³

where P is the profit in millions of dollars and q is the quantity in millions of units.

(b)(ii) Find values of q when P = 18.

18 = 25q − 4q³

4q³ − 25q + 18 = 0

We know that q=2 is a root of this equation.  Using grouping:

4q³ − 8q² + 8q² − 25q + 18 = 0

4q² (q − 2) + (q − 2) (8q − 9) = 0

(q − 2) (4q² + 8q − 9) = 0

4q² + 8q − 9 = 0

Solve with quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

q = [ -8 ± √(8² − 4(4)(-9)) ] / 2(4)

q = (-8 ± √208) / 8

q = (-8 ± 4√13) / 8

q = (-2 ± √13) / 2

Since q is positive, q = (-2 + √13) / 2, or approximately 0.803.

Answer:

I think the answer was 190,000 people that can fit comfortably in 25 feet square. Moreover, 30 x 5280x 2=316,000 so take that times 0.6 and get the answer.

Not sure if this is exactly what you are wanting but is it 15:25??

If the selling price of a toy is x . The selling price that will give him the maximum revenue is $20 and the amount of the maximum revenue is 400.

Given quadratic equation:

R=−x2+40x

Now let use the quadratic equation  to find the selling price that will give the maximum revenue

R(x) =−x2+40x

R(x) =-x²+40x-400+400

R(x) =-(x-20)²+400

x = 20

R(x) max=400

Therefore If the selling price of a toy is x . The selling price that will give him the maximum revenue is $20 and the amount of the maximum revenue is 400.

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Answer:

$9.52

Step-by-step explanation:

1.09 x 3 = 3.27

2.68 x 2 = 5.36

3.27+5.36+.89=9.52

Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)