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Answer:

1 qrt Equals to 2 pints

1 gallon Equal 4 qrts

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Answer:

Step-by-step explanation:

The volume of water in a pool can be calculated using the following formula:

Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5

For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:

20 x 15 x 5 x 7.5 = 5625 gallons

Note: If you prefer metric units, the formula for volume in liters would be:

Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000

It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.

The photon's energy (E) is equal to its frequency (f) multiplied by the Planck constant (h).

Planck's constant is the elementary quantum of action. Its unit  is the metre-kilogram-second or Joule second. It is denoted by h and has a value of 6.62607015 × 10⁻³⁴ joule second.

The photon's energy (E) is equal to its frequency (f) multiplied by the Planck constant (h). It is given by:

E = hf

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Answer:

Planck's constant is used to relate the energy in one quantum of electromagnetic radiation to the frequency of that radiation.

Step-by-step explanation:

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The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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Answer:

4,000 is that answer to 3,623 to the nearest thousands.

Step-by-step explanation:

We have: \(\frac{4}{3}=\frac{4.2}{3.2}= \frac{8}{6}\)

Answer: Yes

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Answer:

owner withdrawal

1.225000

2.3300

Step-by-step explanation:

\(2\frac{2}{3}(x)=1/3\\x=(1/3)/2\frac{2}{3}\\x=\frac{1}{8}\)

Answer:

(a) P(A ∩ E) = 0.03

(b) P(A) = 0.39

(c) P(A | E) = 0.1

Step-by-step explanation:

The first level of the tree gives the following probabilities

P(E) = 0.1

P(E') = 1 - P(E) = 0.9

The second level gives conditional probabilities

P(A|E) = 0.3  this is the top most branch from the root

P(A ∩ E) = P(A|E) P(E) = 0.3 x 0.1 = 0.03      Answer(a)

To find P(A) we find all routes that will end in A, compute each probability and add up the individual probabilities

For event E happening, P(A ∩ E) = 0.03 which is computed in A

However A can also happen when the complement event E' happens
P(A ∩ E') = P(A | E') P(E') = 0.4 x 0.9 = 0.36

Add these two together to get 0.03 + 0.36 = 0.39 Answer (b)

P(A|E) is nothing but the probability value when we follow the E branch first followed by the A branch

This is 0.1   answer (c)

Answer:

length of unknown side is 59

Partial derivative with respect to\(X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ\)

Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)

The first partial derivatives of the function F(X,Y) = X2Y - 3Y2 + X/(X + Y)2 + XY2e-XZ can be found by taking the partial derivative with respect to each of the variables X and Y separately.
For the partial derivative with respect to X, we have:
Partial derivative with respect to X = dF/dX = 2XY - (X + Y)2-2 + Y2e-XZ
For the partial derivative with respect to Y, we have:
Partial derivative with respect to \(Y = dF/dY = X2 - 6Y + (X + Y)2-2XYe-XZ\)
This completes the calculation of the first partial derivatives of the function F(X,Y).
The first partial derivatives of the functions are given below:

\(F(x, y) = x^2y - 3y^2\)

The first partial derivative with respect to x,

Fx (x, y) = 2xy

The first partial derivative with respect to y,\(Fy (x, y) = x^2 - 6yW = xy^2 e^-xz\)

The first partial derivative with respect to x,

\(Wx (x, y, z) = y^2e^-xz - x^2y^2e^-xz\)

The first partial derivative with respect to y, Wy (x, y, z) = 2xye^-xz

The first partial derivative with respect to z, \(Wz (x, y, z) = -xy^2e^-xz\)

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The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Answer: Part A. Olivia- y=x+4 Camille- idr.k but it increases by 1/2 ever time

Part B. The slope represents the rate of change and the y-intercept indicates the value of y when x is 0.

Part C. Olivia's puppy weighed the most. It weighed 5 pounds.

Part D. Camille's puppy only gained 1/2 a pound each week.

Step-by-step explanation:

The profit-maximizing price and quantity for the monopolist are $350 and 150 units, respectively ,The expected return is greater than the initial investment And the producer surplus is $33,750, consumer surplus is $31,875, and firm profit is $37,500.

Ignoring the time value of money and discounting, the expected value of the lottery winnings each year is 2% × $1 million = $20,000, and this goes on for 10 years.

Thus, the expected value of the investment is 10 × $20,000 = $200,000.

Hence, the expected return is greater than the initial investment, and there is a condition under which the investment can be made.

The monopolist’s total cost can be represented as:

TC = 300 + 200Q + 3Q².

The demand function for the monopolist is given as:

Q = 500 - P,

which can be rearranged to derive the price function as:

P = 500 - Q.

From the total cost function, we can obtain the marginal cost (MC) as the derivative of TC with respect to Q, and it can be represented as follows:

MC = dTC/dQ = 200 + 6Q.

From the marginal cost, we can set the marginal revenue (MR) equal to MC to get the profit-maximising quantity as follows:

MR = dTR/dQ = P + Q(500 - P) = 500 - Q + 500Q - Q² = 1000Q - Q² - 500 = MC = 200 + 6Q.

Substituting P = 500 - Q in the above expression and rearranging yields the following:

Q = 150, and hence, P = $350.

Therefore, the profit-maximising price is $350, and the quantity is 150. We can verify that the solution is a maximum by computing the second-order condition, which is negative.

To calculate the producer surplus, we first need to obtain the area above the marginal cost and below the price.

Thus, we have:

PS = ∫ MC to QdQ

= ∫ (200 + 6Q) dQ from 0 to 150

= [200Q + 3Q²] from 0 to 150

= $33,750.

Similarly, the consumer surplus can be computed as the difference between the market value of the product and what the consumers paid for it. The area below the price line and above the demand curve yields the consumer surplus.

Thus, we have:

CS = ∫ P to QdQ

= ∫ (500 - Q) dQ from 0 to 150

= [(500 × Q) - (Q²/2)] from 0 to 150

= $31,875.

Finally, the firm profit can be obtained by multiplying the profit-maximizing quantity by the profit-maximizing price and subtracting the total cost.

Thus, we have:

Profit = TR - TC = Q × P - TC = (150 × $350) - (300 + 200 × 150 + 3 × 150²) = $37,500.

Hence, the producer surplus, consumer surplus, and firm profit are $33,750, $31,875, and $37,500, respectively.

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The solutions to the trigonometric equation:

cos(x)*(cos(x) - 1) = 0

Are the ones in option B;

x = ± n*π , π/2 ±  2πn,  3π/2 ±  2πn

Where n is a natural number.

Here we have the trigonometric equation:

cos(x)*(cos(x) - 1) = 0

Remember that a product A*B = 0 either if A or B (or both) are equal to zero, so the solutions of the given equation are the values of x such that:

cos(x)=  0

cos(x) - 1 = 0

The solution of the first one is trivial, it is just π/2 and  3π/2

And for the second one:

cos(x) - 1 = 0

cos(x) =1

The solutions are x = 0 and x =  π

Now we can extend that tho the whole range by writting:

x = ± n*π for the second equation.

x = π/2 ±  2πn   and   3π/2 ±  2πn  for the first equation.

That is what we can see in option B.

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Answer:

Isaac worked 12 hours

Ruby worked 18 hours

Svetlana worked 72 hours

Step-by-step explanation:

Here in this question, we are interested in knowing the number of hours each person worked.

We proceed as follows;

Let the number of hours Isaac worked be x hours.

From the question, we are told that Ruby worked 6 hours more than Isaac

So the number of hours Ruby worked will be;

(x + 6) hours

Also;

Svetlana worked 4 times as many as Ruby:

This means that we have to multiply the number of hours Ruby worked by 4 to get the number of hours that Svetlana worked;

So the number of hours Svetlana worked will be : 4(x + 6) hours

Since the three worked a total of 102 hours, to get the number of hours each worked, we need to add together the number of hours each individual put in to work and equate to 102;

Mathematically, that would be;

x + x + 6 + 4(x + 6) = 102

2x + 6 + 4x + 24 = 102

6x + 30 = 102

6x = 102-30

6x = 72

x = 72/6

x = 12 hours

So Isaac worked x hours = 12 hours

Ruby worked (x + 6) hours = 12 + 6 = 18 hours

Svetlana worked 4(x + 6) hours = 4(18) = 72 hours

Answer:

b) 2 was not multiplied by 5

Step-by-step explanation:

Correct answer: 2x + 10

Answer:

-10 vertically and -1 horizontally

Explanation:

shifts -1 horizontally, -10 vertically

note: vertically is up ↑ and bottom ↓ , horizontal is right → and left ←

Given:

Aisha has 3 pizzas.

She is serving each person at a party 1/4 of a pizza.

To find:

The number of people she can serve at the party.

Solution:

Let the number of people be x.

Number of pizzas is 3. So, each person get \(\dfrac{3}{x}\) part of pizza.

It is given that each person get 1/4 of a pizza.

\(\dfrac{1}{4}=\dfrac{3}{x}\)

Using cross multiplication, we get

\(1\times x=3\times 4\)

\(x=12\)

Therefore, the number of persons in 12.

Now, divide the number line in four equal parts between each pair of consecutive integers.

Then, count the marked points from 0 to 3 excluding 0. These points represent number of persons.

Answer:

10,12

Step-by-step explanation:

let the two numbers be x and y

difference between x and y is 2

but y is ½x + 4

x -(½x+4) = 2

x - ½x - 4 = 2

½x = 6

x = 12

y = ½x + 4

y = 10

Answer:

A & C

Step-by-step explanation:

AB is the shortest segment in ABC

AC = 2AB

Answer:

C

Step-by-step explanation:

The middle of the plot falls at 9, making this statement true. None of the others make sense. Good luck!

The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).

To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:

Confidence interval = sample proportion ± z * standard error

Calculate the sample proportion

In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):

Sample proportion = 361/424 ≈ 0.852

Calculate the standard error

The standard error of the proportion is calculated using the formula:

Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)

Using the given values, we have:

Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014

Determine the confidence interval

To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.

Substituting the values into the confidence interval formula, we have:

Confidence interval = 0.852 ± 2.33 * 0.014

Confidence interval ≈ (0.811, 0.892)

Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).

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Answer:  y-intercept is -6

Step-by-step explanation:  Calculate the slope of the line between the two given points:

Rise/Run = slope, m in the standard form of  a straight line:  y=mx+b, with b the y-intercept (the value of y when x=0).

Rise = 1 - (-6) = 7

Run = 4 - (-3) = 7

Slope = Rise/Run, 7/7, or 1

y=mx+b

y = 1x+ b

Find b by entering one of the two given points.  I'll pick (4,1).

y = 1x+ b

What's important now is the next step.  The equation "that is parallel" must have the same slope as the reference equation, 1 in this case.

[If, out of curiosity, you want the full equation of the reference line, we can find b in this way:

Enter one of the two given points and solve for b.  I'll pick (4,1):

y = 1x+ b

1 = 1*(4)+ b

b = -3

y = 1x - 3 is the first equation.]

All we really needed from the first, or reference, equation is the slope, 1 in this case.  Parallel lines have the same slope, so we want an equation in the form:

y=1x+b

This equation will be parallel, regardless of the value of b.  But we want it to go through a specific point, (7,1).  So use that point and solve for b:

y=1x+b

1=1*7+b

b=-6

The equation is y=1x-6

Answer:

4

Step-by-step explanation:

To solve for x in the equation:

√(2x - 7) = 1

We can start by isolating the square root by squaring both sides of the equation:

(√(2x - 7))^2 = 1^2

2x - 7 = 1

Next, we can isolate the variable by adding 7 to both sides of the equation:

2x = 8

Finally, we can solve for x by dividing both sides by 2:

x = 4

Therefore, the solution to the equation √(2x - 7) = 1 is x = 4.

Answer:

125

Step-by-step explanation:

360-70-60-65-40

= 125

Answered by GAUTHMATH