Explain how you can find the side length of a rectangular prism if you are given the volume and the 2 other measurements. Does this process change if one of the measurements is a fraction?

The volume of the soup in the hemispherical bowl is approximately 303.49 cubic centimeters.

To find the volume of the soup, we need to find the volume of the hemispherical bowl first.

The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.

We know that the diameter of the bowl is 10.5 cm, so the radius is half of that, which is 5.25 cm.

Now we can substitute the value of r into the formula and calculate the volume of the hemisphere:

V = (2/3)π(5.25)^3
V ≈ 485.62 cm³

Since the bowl is completely filled with soup, the volume of the soup is the same as the volume of the hemisphere, which is approximately 485.62 cm³.

Therefore, the volume of the soup is 303.49 cubic centimeters.

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Answer:

m=1/7

Step-by-step explanation:

Labeled the points and used Slope of a line formula.

Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

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The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The area of the surface generated by revolving the curve about the x-axis is 243π square units, and the area of the surface generated by revolving the curve about the y-axis is 1152π square units.

We are given the curve x = 8t, y = 9t, and the range of t is 0 ≤ t ≤ 3. We need to find the area of the surface generated by revolving this curve about the x-axis and the y-axis.

(a) To find the area of the surface generated by revolving the curve about the x-axis, we can use the formula for the surface area of revolution: S = 2π∫[a,b] y √(1 + (dy/dx)²) dx. In this case, a = 0 and b = 3, and the curve is given by x = 8t, y = 9t. We can differentiate y = 9t with respect to x to find dy/dx = 9. Plugging these values into the formula, we have S = 2π∫[0,3] 9t √(1 + 9²) dt = 162π ∫[0,3] t dt = 162π (t²/2)∣[0,3] = 243π.

(b) To find the area of the surface generated by revolving the curve about the y-axis, we use the same formula but with x as the variable. The curve is still given by x = 8t, y = 9t, and we differentiate x = 8t with respect to y to find dx/dy = 8/9. Plugging these values into the formula, we have S = 2π∫[c,d] x √(1 + (dx/dy)²) dy. The range of y is determined by the range of t, so c = 0 and d = 27. Evaluating the integral, we get S = 2π∫[0,27] (8/9)y √(1 + (8/9)²) dy = 2π(64/9) ∫[0,27] y dy = 1152π.

Therefore, the area of the surface generated by revolving the curve about the x-axis is 243π square units, and the area of the surface generated by revolving the curve about the y-axis is 1152π square units.

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Answer:

O1

Step-by-step explanation:

Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

We are given a point: (0,-2) and a slope; -3.

we can substitute the numbers into the equation above, with what we know, to find b.

-2=-3(0)+b

multiply

-2=0+b

-2=b

so the y intercept is -2.

Since we know that the slope is -3, and the y intercept is -2, the equation is y=-3x-2

Therefore O1 is your answer

Hope this helps!

Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

The required probability is 1/16.

Given that a campus program evenly enrolls undergraduate and graduate students. A random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast-food outlet on the ground floor of the campus building. We have to find the probability that all 4 students selected are undergraduate students.

The probability that all 4 students selected are undergraduate students is given by: P(Undergraduate) = Number of undergraduate students / Total number of students Given that the program evenly enrolls undergraduate and graduate students. Number of undergraduate students = Total number of graduate students Therefore, P(Undergraduate) = Number of undergraduate students / Total number of students = Number of graduate students / Total number of students Let the total number of students be n, then Number of undergraduate students = Number of graduate students = n/2∴ P(Undergraduate) = Number of undergraduate students / Total number of students= n/2 / n = 1/2

Therefore, the probability that all 4 students selected are undergraduate students is: P(4 undergraduate students) = P(Undergraduate) × P(Undergraduate) × P(Undergraduate) × P(Undergraduate) = (1/2) × (1/2) × (1/2) × (1/2) = 1/16

Hence, the required probability is 1/16.

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Answer:

14 spotted socks

Step-by-step explanation:

Sam has 3 units of striped socks and 6 of them.

Find one unit.

3 units = 6

1 unit = 6 ÷ 3 = 2

Sam has 7 units of spotted socks.

7 units = 2 x 7 = 14

Answer:

15

Step-by-step explanation:

[3(9)-(-3)]/2

30/2=15

Answer:

Your answer should be 15.

Step-by-step explanation:

3 times 9 is 27. When you subtract a negative number they combine to sign to be a + so you would get 30 since you would be adding 3. You would then divide 30 by two to get 15! <3

The slope of the regression line infers that "For every 1 inch increase in tail length, the predicted weight increases by 3 pounds."

The slope gives change in the value of y variable for every change in the x variable. Here, the value of the slope for the regression line is 3.

This means that for every 1 inch increase in the x variable , the value of the y variable increases by 3.

Therefore, For every 1 inch increase in tail length, the predicted weight increases by 3 pounds.

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Independent events are the ones whose occurrence is unrelated to any other event.

Dependent events include those that are dependent on previous events.

If the probability of an event A occurring is not impacted by the occurring of some other event B, then A & B are referred to as independent events.

Consider the example of a die roll. If A is the event 'the number appearing is odd' and B is the event 'the number showing up is a multiple of 3,'

P(A) = 3/6 = 1/2

P(B) = 2/6 = 1/3

A and B are also the events 'the number showing up is odd & a multiple of 3', implying that;

P(A ∩ B) = 1/6

P(A│B) = P(A ∩ B)/ P(B) = 1/2

Then P(A) = P(AB) = 1/2, implying that the happening of event B has had no effect on the probability of occurring of event A.

Dependent events include those that are dependent on previous events. The outcomes of previous events have an impact on these events. Dependent events are two or maybe more events that are dependent on one another.

When two events, A and B, are interdependent, the probability of their occurrence is:

P(A and B) = P(A) · P(B|A)

Assume we desire to have a queen.

The chances of obtaining a queen on the first draw are 4 from out 52 cards. If we receive a queen in the first draw, we have a 3 out of 51 chance of obtaining a queen in the second draw.

As a result, these are referred to as dependent events because the probability of a second event is determined by the results of the first draw.

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Answer:

Step-by-step explanation:

1. -(5/x^6)

2. 4398046511104

3. 65536

4. 1/100

5. 1/5764801

Answer:

5) = 3/4

12) = 1

Step-by-step explanation:

The total change in the consumed quantity of x₁ as per given price and income  is equal to 213.

x₁ = (21/7)P₁

x₂ = (51/7)P₂

P₁ = 10

P₂ = 5

P₁' = 81

To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',

The difference between the quantities consumed at the original price and the new price.

Let's calculate the quantity consumed at the original price,

x₁ orig

= (21/7)P₁

= (21/7) × 10

= 30

x₂ orig

= (51/7)P₂

= (51/7) × 5

= 36.4286 (approximated to 4 decimal places)

Now, let's calculate the quantity consumed at the new price,

x₁ new

= (21/7)P1'

= (21/7) × 81

= 243

x₂ new

= (51/7)P2

= (51/7) × 5

= 36.4286

The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,

Change in x₁

= x₁ new - x₁ original

= 243 - 30

= 213

Therefore, the total change in the quantity consumed of x₁ is 213.

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The above question is incomplete, the complete question is:

The optimal amount of x1, x2, P1, P2 and income are given by the following:

x1= 21/ 7p1 x2= 51 / 7p2

The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?

Please answer step by step

Answer:

multiply the original price ($299) by the first markup percentage (150%)

299*1.50= $448.50

that is markup price!

then you have to do the sale % (25%)

so you'll multiply your (25%) by your new price ($448.50)

448.50*.25= $112. 125

then you will subtract the sale price ($112.125) by the upcharged price ($448.50)

448.50-112.125= 336. 375

= $336. 38(round off)

The probability that they're both home is 1/12.

In the given question,

Probability of Maya at home P(A) = 1/3

And probability of Jim at home P(B) = 1/4

The probability that Jim is home given that maya is home P(A∪B) = 1/2

We have to find the probability when they both are at home P(A ∩ B).

As we can see that the probability of both the events are independent

So, we can use

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

Therefore,

1/2 = 1/3 +1/4 – P(A ∩ B)

P(A ∩ B) = 7/12 – 1/2

P(A ∩ B) = 1/12

Hence, the probability that they're both home is 1/12.

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Answer:

150 mi3

Step-by-step explanation:

volumebox = width x length x height

Answer:

1)  See attachment.

2a)  Initial Amount = 3600.
      Growth/Decay factor = ³/₂.

2b)  Growth function.

\(\textsf{3)}\;\;\; f(x)=1*2^x\)

4)  69 lions.

Step-by-step explanation:

General form of an exponential function

\(\boxed{y=ab^x}\)

where:

If b > 1 then it is an increasing function.

If 0 < b < 1 then it is a decreasing function.

Given function:

\(f(x)=\left(\dfrac{1}{2}\right)^x\)

Complete the table of ordered pairs by substituting the values of x into the given function:

\(\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}-3&8\\\cline{1-2}-2&4\\\cline{1-2}-1&2\\\cline{1-2}0&1\\\cline{1-2}1&0.5\\ \cline{1-2}\end{array}\)

Plot the ordered pairs on the given coordinate plane (see attached graph) and draw a curve through them.

This exponential function has a horizonal asymptote at y = 0.  

As the value of x approaches infinity, the function gets closer and closer to y = 0 (x-axis) but doesn't actually touch it.

Given exponential function:

\(f(x)=3600\left(\dfrac{3}{2}\right)^x\)

Part 2a

To find the initial amount "a" and growth/decay factor "b", simply compare the given function with the general exponential function.  

Therefore:

Part 2b

As  b = ³/₂ and ³/₂ > 1, this is a growth function (increasing).

"a" is the initial value (y-intercept) of an exponential function.

The y-intercept of a function is the y-value when x = 0.  

Therefore, from inspection of the given table, the y-intercept of the given function is 1.

Therefore, a = 1.

"b" is the base (growth/decay factor) of an exponential function.

To find the base (growth/decay factor) of the given function, divide a value of y by its preceding value of y:

\(\implies b=\dfrac{4}{2}=\dfrac{2}{1}=\dfrac{1}{\frac{1}{2}}=...=2\)

Therefore, b = 2.

So the exponential function for the given table is:

\(f(x)=\boxed{1}*\boxed{2}\;^x\)

If the population of lions started at 80, then the initial value "a" of the exponential function is 80.

If the population has been decreasing by 3.5% per year, then the population each year is 96.5% of the previous year since:

Therefore, the base "b" of the exponential function is 0.965 (in decimal form).

Substitute the found values of a and b into the exponential function formula to create an exponential function for the given scenario:

\(\boxed{f(t)=80(0.965)^t}\)

where:

To find how many lions will there be in four years, substitute t = 4 into the found exponential equation:

\(\implies f(4)=80(0.965)^4=69.37440005\)

Therefore, there will be 69 lions in four years.

After dilation the new dimensions of the rectangle is drawn and shown in the image attached below.

Dilation simply refers to the enlargement or reduction of the size of an image.

When an image is enlarge, the original size of the image increases, while when it is reduced, the new image formed will have a size that is smaller than the original image.

To dilate an image, a scale factor is used. If the scale factor is less than 0, it is a reduction, if it is more than 0, it is an enlargement.

To get the length of the sides of the new image, multiply the length of each side of the original image by the scale factor.

In the diagram given, we have the following:

Length of original image = 12 units

Width of original image = 9 units

To create a third of the rectangle given, it means the scale factor for the dilation is 1/3.

Length of new rectangle = 12 units × 1/3 = 4 units

Width of new rectangle = 9 units × 1/3 = 3 units

Thus, after dilation the new dimensions of the rectangle is drawn and shown in the image attached below.

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No

A point is on a line if that point satisfies the equation.

Testing Points

To test if the point (2,7) is on the line y = 2x + 7, we need to plug the point into the equation. For the coordinate pair (2,7), the x-value is 2 and the y-value is 7. So, plug 2 in for x and 7 in for y.

Then, simplify.

As you can see, 7 does not equal 11. Thus, point (2,7) cannot be a point on the given line.

Other Points

We can do this same test with other points such as (1,9). The x-value is 1 and the y-value is 9, so now we can plug them in.

Since 9 equals 9 is a true statement, the point (1,9) is a point on the given line.

Answer:

-20

Step-by-step explanation:

Answer:If p and q vary inversely, it means that their product remains constant. So we can set up the equation:

p * q = k

where k is the constant of variation.

Given that p is 29 when q is 25, we can substitute these values into the equation:

29 * 25 = k

725 = k

Now, let's determine the value of q when p is equal to 5:

p * q = k

5 * q = 725

Dividing both sides of the equation by 5:

q = 725 / 5

q = 145

Therefore, when p is equal to 5, q is equal to 145.

Step-by-step explanation:

Answer:p1q1=p2q2

q1=25,p1=29;

p2=5,q2=?;

q2=p1q1/p2;

q2=25*29/5;

q2=29*5;

q2=145.

Step-by-step explanation:

Using this probability, he would have to make 42.18% or 42 free throws, thus avoiding 27 free throws.

Averaged over 3 out of 4 free throws, the probability of a successful free throw is 0.75 and the probability of a missed free throw is 0.25.

There are several ways to score 3 of the 4 free throws.

Miss Hit Hit Hit

Hit Miss Hit Hit

Hit Hit Hit Hit Hit

So to calculate this probability we need to multiply the probability of each shot. Because when it comes to multiplication, the order of multiplication doesn't matter, it's just the numbers that matter, only her 4-day probability that the shot will be taken. be the same.

So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875

Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18% shot will be taken.

So 0.75 x 0.75 x 0.75 x 0.25 = 0.10546875

Since there are 4 ways to take a 3/4 shot, we have to multiply this by 4, so 4 x 0.10546875 = 0.4218 = 42.18%.

Hence, Eve had to make 42 free throws for getting 27 throws are mied.

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Answer:

hence the required midpoint of the given line is (9,5)

Answer:

\(( \frac{6 + 2}{2} +\frac{12 + 8}{2}) = ( \frac{8}{2} + \frac{20}{2} ) = (4 \: comma10)\)

The answer is :(4, 10)

Answer:

x° = 50°

y° = 70°

z°  = 60°

p° = 50°

(p + 10)° = 60°

(p + 20)° =70°

Step-by-step explanation:

Angles with measurements (p + 20), p and (p + 10) degrees are all on the same line. Therefore these three angles are supplementary angles. In other words the sum of these angles = 180°

Plugging in the expressions for these angles we get

(p + 20 ) + p + (p + 10) = 180°

3p + 30 = 180

Subtracting 150 from both sides,
3p = 180 - 30  = 150

p = 150/3 = 50

x is a vertically opposite angle to p.

Therefor x = p = 50°

y is vertically opposite and equal to p + 20
y = p + 20 = 50 + 20 = 70°

z is vertically opposite and equal to p + 10
z = p + 10 = 50 + 10 = 60°

Answer:

The point of intersection is located at approximately (1.75,7.75), which means both planes will be at an altitude of about 7,750 feet after approximately 1.75 minutes, or 1 minute, 45 seconds.

This is what the graph looks like:

Step-by-step explanation:

The intersection of the lines will be (1.692, 7.769). Then the graph of the lines is drawn below.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Plane A is plummeting toward the neighborhood air terminal at a pace of 2,500 feet/minute. It is right now at an elevation of 12,000 feet. Plane B is climbing from a similar air terminal at a pace of 4,000 feet/minute. It is at present at an elevation of 1,000 feet. This arrangement of conditions models what is happening, where x addresses the time in minutes and y addresses the elevation in a large number of feet:

y = 12 − 2.5x              ...1

y = 1 + 4x                  ...2

From equations 1 and 2, we have

1 + 4x = 12 - 2.5x

6.5x = 11

x = 1.692

Then the value of 'y' will be given as,

y = 12 - 2.5 (1.692)

y = 7.769

The intersection of the lines will be (1.692, 7.769). Then the graph of the lines is drawn below.

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Answer:

70

Step-by-step explanation: