What is the surface of the prism ​

The first derivative of the implicit function given by x^(2/3) + y^(2/3) = 14 can be found using implicit differentiation. We take the derivative of both sides with respect to x and use the chain rule to differentiate the terms involving y:(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0Then, we solve for dy/dx:dy/dx = -(x/y)^(1/3)This is the first derivative of the implicit function. To evaluate it at a specific point, we need to substitute the coordinates of that point into the equation above.

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The continuous compound rate of decay of this isotope is approximately 1.41%.

In order to find the continuous compound rate of decay of the radioactive isotope, we can use the formula:

N(t) = N0 * e^(-λt)

Where N(t) is the amount of the isotope present at time t, N0 is the initial amount of the isotope, λ is the continuous decay constant, and t is the time elapsed (in this case, 6 years).

We are given that 91.9% of the isotope is still present after 6 years, so:

0.919 = e^(-λ * 6)

To solve for λ, we can take the natural logarithm of both sides:

ln(0.919) = -6λ

Now, we can solve for the decay constant:

λ = -ln(0.919) / 6 ≈ 0.0141

So, the continuous compound rate of decay of this isotope is approximately 1.41%.

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61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.

A national grocery chain is considering expanding their selection of prepared meals, and they believe that 67 percent of households purchase at least one meal per week from the grocery store. In a survey conducted in Maryland, 641 out of 1,035 households purchase at least one meal per week at the store.
To determine the percentage of Maryland households purchasing at least one prepared meal per week, follow these steps:
Divide the number of households purchasing at least one meal per week (641) by the total number of households surveyed (1,035).
Multiply the result by 100 to get the percentage.
Here's the calculation: (641 / 1,035) x 100 = 61.93%
So, 61.93% of the surveyed Maryland households purchase at least one prepared meal per week from the grocery store.

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It will take the population 10.5 years to reach 25,000

From the question, we have the following parameters that can be used in our computation:

Inital population, a = 15000

Rate of increase, r = 5%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

So, we have

f(x) = 15000 * (1 + 5%)ˣ

When it reaches 25000, we have

15000 * (1 + 5%)ˣ = 25000

Divide both sides by 15000

(1 + 5%)ˣ = 1.67

Take the logarithm of both sides

x = log(1.67)/log(1 + 5%)

Evaluate

x = 10.5

Hence, the number of years is 10.5

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If he put 40 red balls, 55 purple balls, 45 yellow balls, and 60 green balls into the ball pit. while his sister is playing, one ball rolls out of the pit. Therefore, the probability that the ball that rolled out of the pit is red is 0.2.

The probability of selecting a red ball from the ball pit can be found by dividing the number of red balls by the total number of balls in the pit.

Total number of balls = 40 + 55 + 45 + 60 = 200

Probability of selecting a red ball = Number of red balls / Total number of balls

Probability of selecting a red ball = 40 / 200

Probability of selecting a red ball = 0.2

Therefore, the probability that the ball that rolled out of the pit is red is 0.2.

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The correct answers are:True, True, False.

The first statement is true. The initial investment is represented in the formula as the coefficient of the growth factor[tex](1+0.05)^t[/tex].

The second statement is true. The growth factor in the formula is (1+0.05), which represents a 5% increase or a multiplier of 1.05.

The third statement is false. The annual interest rate is not 50%. The growth factor (1+0.05) represents a 5% increase, but the actual annual interest rate is 5%, not 50%.

Therefore, the correct answers are:

True

True

False

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Laptop- 44, Tablet- 94, Desktop- 62, Percentage of tablets- 47%.

To calculate the percentage of devices that are tablets, we need to find the proportion of tablets among all devices. In this case, there are 94 tablets out of a total of 200 devices (44 laptops + 94 tablets + 62 desktops).

To find the proportion, we divide the number of tablets by the total number of devices: 94/200 = 0.47.

To convert this proportion to a percentage, we multiply by 100: 0.47 * 100 = 47%.

47% of the devices owned by the local company are tablets.

This means that nearly half of the devices fall into the tablet category, making it a significant portion of their device inventory.

It's important to note that this calculation assumes the given numbers accurately represent the actual device distribution and that there are no missing or unaccounted devices.

By determining the percentage of tablets, we gain insight into the composition of the device inventory, which can be useful for decision-making and resource allocation within the local company.

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The measure of angle PQR is 90 degrees.

Since PR is the diameter of the circle, it follows that angle POR is a right angle, i.e., it measures 90 degrees.

By the inscribed angle theorem, the measure of angle PQR is half the measure of angle POR. Thus,

angle PQR = 1/2 * angle POR

= 1/2 * 90

= 45 degrees.

However, this is not the final answer since angle PQR is not a stand-alone angle, but rather a part of a right-angled triangle PQR.

Since the three angles in a triangle add up to 180 degrees, and we already know that angle PQR is 45 degrees, it follows that:

angle PRQ + angle PQR + angle QPR = 180 degrees

Since angle PQR = 45 degrees, we have:

angle PRQ + 45 + angle QPR = 180 degrees

Rearranging, we get:

angle PRQ + angle QPR = 135 degrees

Since angles PRQ and QPR are complementary angles (together they form a right angle), their sum is 90 degrees. Therefore,

angle PRQ + angle QPR = 90 degrees

Substituting this into the previous equation, we get:

90 degrees = 135 degrees

This is a contradiction, and hence our assumption that angle PQR measures 45 degrees is false.

Therefore, we conclude that angle PQR must measure 90 degrees, since it is the only angle that can satisfy the given conditions.

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The analogy that best represents the bold letters for each question is related to relationships and cross-sections.

Some analogies are given below:

Explanation: The relationship between happy and sad is that they are opposite emotions.

Similarly, up and down are opposite directions, so the analogy holds.

Explanation: The relationship between a cat and a kitten is that a kitten is a young cat.

Similarly, a puppy is a young dog, so the analogy holds.

Explanation: The relationship between circle and sphere is that a circle is a two-dimensional shape, while a sphere is a three-dimensional shape that has a circular cross-section.

Similarly, a square is a two-dimensional shape, while a cube is a three-dimensional shape that has a square cross-section, so the analogy holds.

Explanation: The relationship between the oven and baking is that an oven is a tool used to bake food.

Similarly, a grill is a tool used to grill food, so the analogy holds.

Explanation: The relationship between mother and father is that they are the parents of a child.

Similarly, a daughter and a son are the children of their parents, so the analogy holds.

Explanation: The relationship between a book and a chapter is that a book is divided into chapters.

Similarly, a play is divided into acts, so the analogy holds.

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Based on these calculations, option 1 gives you the cheaper price per square inch of pizza.

To determine which option will give you a cheaper price per square inch of pizza, you will need to compare the prices of the two options and calculate their respective prices per square inch.

Let's say option 1 is a large pizza with a diameter of 18 inches and costs $20, while option 2 is a medium pizza with a diameter of 14 inches and costs $15.

To calculate the area of each pizza, you need to use the formula for the area of a circle:

A = πr^2

For option 1, the radius is 9 inches (half of the diameter), so the area is:

A = π(9)^2 = 81π square inches

For option 2, the radius is 7 inches (half of the diameter), so the area is:

A = π(7)^2 = 49π square inches

Now you can calculate the price per square inch for each option by dividing the cost by the area:

Option 1:

Price per square inch = $20 / (81π) = $0.078/square inch

Option 2:

Price per square inch = $15 / (49π) = $0.098/square inch

Based on these calculations, option 1 gives you the cheaper price per square inch of pizza.

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In the scenario you mentioned, the part of the Federal Reserve's congressional mandate that is triggered is both price stability and maximum sustainable employment.

The Federal Reserve has a dual mandate from Congress which consists of:

1. Price stability: This objective aims to maintain a stable inflation rate, ensuring that the purchasing power of money remains relatively constant over time. Price stability helps households and businesses make informed decisions regarding investments and consumption.

2. Maximum sustainable employment: This objective focuses on maintaining a high level of employment while avoiding unsustainable economic growth that could lead to high inflation. Achieving maximum sustainable employment involves minimizing unemployment while not causing inflation to rise significantly.

In the scenario you mentioned, the Federal Reserve would need to carefully balance its monetary policy to ensure that both objectives, price stability and maximum sustainable employment, are achieved. This might involve adjusting interest rates or using other monetary policy tools to influence economic activity, employment levels, and inflation.

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Answer 1 inch per hour

Step-by-step explanation:

Answer:

1 inch per hour

Step-by-step explanation:

Let x represent inches burned per hour

The equation to finding the rate of the candle burning:

3x=3

For those who dont know, whenever you have a variable with a term, its basically multiplying, and we want to do the opposite to get x by itself, so we divide

x=3/3

Which can be simplified as:

x=1

Where x is the inches burned per hour, which equal 1

It seems that the question provided is not clear and has some typos or formatting issues, making it difficult to understand the exact problem you need help with. Please rephrase or clarify the question, and I'll be more than happy to help you!

To find W,(1,0), we need to use the formula for the partial derivative of F with respect to u at (6,7) and (6,-7) and plug in the given values:

F_u(6,7) = 6,0(6,7) = -5
F_u(6,-7) = 6,0(6,-7) = -7

Now we can use these values to solve for W,(1,0) using the formula:

W,(1,0) = F(6,t) - F_u(6,7)(1-6) - F_u(6,-7)(1-6)

Plugging in the given values, we get:

W,(1,0) = F(6,t) - (-5)(-5) - (-7)(-5)
W,(1,0) = F(6,t) + 30

We still need to find F(6,t). To do this, we use the formula for the partial derivative of F with respect to s at (1,0) and plug in the given values:

F_s(1,0) = 1,0(6,0) - 7,0(1,0) - 9,0(1,0)
F_s(1,0) = -7

Now we can use F_u(6,7), F_u(6,-7), and F_s(1,0) to solve for F(6,t) using the formula:

F(6,t) = F_u(6,7)(6,t-7) + F_u(6,-7)(6,t+7) + F_s(1,0)(t)

Plugging in the given values, we get:

F(6,t) = (-5)(6,t-7) + (-7)(6,t+7) + (-7)(t)
F(6,t) = -77t - 188

Now we can substitute this value of F(6,t) into our formula for W,(1,0) to get the final answer:

W,(1,0) = -77t - 188 + 30
W,(1,0) = -77t - 158

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Answer:

Step-by-step explanation:

Find area of all shapes and add

A(biggest rectangle) = Lw =  6*3 =18   there are 2 of those A=36

A(long skinny rectangle = Lw = 2*6 =12  there are 2 of those A=24

A(smallest) = Lw = 2*3=6 there are 2 of those A=12

Add it all up

A=36+24+12 = 72

I checked it 5 times.  I keep getting 72

If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.

To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:

-1 and 9 add up to 8

-3 and 3 add up to 0

-9 and 1 add up to -8

3 and -3 add up to 0

1 and -9 add up to -8

9 and -1 add up to 8

Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.

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By  null hypothesis there is sufficient evidence at the 5% significance level to purchase the proposed panels.

To determine if there is sufficient evidence to purchase the proposed panels, we can perform a hypothesis test. Let's define the following:

- p: the proportion of all panels that produce an efficiency rating greater than 20%

- p0: the proportion specified in the proposal, which is p0 = 0.18

- n: the sample size, which is n = 140

- x: the number of panels in the sample that produce an efficiency rating greater than 20%, which is x = 32

We want to test the null hypothesis H0: p <= p0 against the alternative hypothesis Ha: p > p0. The significance level is alpha = 0.05.

We can use the normal approximation to the binomial distribution since both np0 and n(1-p0) are greater than 10, where np0 is the expected number of panels that produce an efficiency rating greater than 20% under the null hypothesis.

Under the null hypothesis, the test statistic z is approximately:

z = (x - np0) / sqrt(np0(1-p0))

Plugging in the values, we get:

z = (32 - 140*0.18) / sqrt(140*0.18*0.82) ≈ 1.96

The critical value of z at alpha = 0.05 with a one-tailed test is 1.645. Since our calculated z value is greater than the critical value, we reject the null hypothesis.

Therefore, there is sufficient evidence at the 5% significance level to purchase the proposed panels.

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The original number was 17 to which when Angad adds 20, then doubles it and gets an answer of 53.

To solve this problem, we need to work backwards from the final answer. If Angad added 20 to the original number, we can subtract 20 from 53 to get 33. This means that after Angad doubled the number, he had 33.

To find the original number, we need to undo the doubling process. If Angad had 33 after doubling the number, we can divide 33 by 2 to get the original number.

33 divided by 2 equals 16.5. However, we know that the original number must be a whole number since we cannot add 20 to a decimal. Therefore, we can round up to the nearest whole number to get 17.

So, the original number was 17.

In summary, to find the original number, we worked backwards from the final answer and undid the steps that Angad took. We subtracted 20 to undo the addition, then divided by 2 to undo the doubling. We rounded up to the nearest whole number since the original number must be a whole number.

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If Jesse can mow 3 yards in 8 hours. Jackson can mow twice as many yards per hour the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

To find the constant of proportionality between the number of yards Jackson can mow and the number of hours, we can use the formula:

k = y/x

where k is the constant of proportionality, y is the number of yards, and x is the number of hours.

We know that Jesse can mow 3 yards in 8 hours, which means his rate of mowing is: 3 yards/8 hours = 3/8 yards per hour

We also know that Jackson can mow twice as many yards per hour as Jesse, which means his rate of mowing is:

2 * (3/8) yards per hour = 3/4 yards per hour

Now we can use the formula to find the constant of proportionality for Jackson:

k = y/x = (3/4) yards per hour / 1 hour = 3/4

Therefore, the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

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We have evidence to suggest that the true percentage of college degrees in mathematics is different from 1%.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.

To test the claim that the percentage of college degrees in mathematics is not 1%, we can use a hypothesis test. Let's assume the null hypothesis is that the true percentage of college degrees in mathematics is 1%, and the alternative hypothesis is that it is different from 1%.

- Null hypothesis: The percentage of college degrees in mathematics is 1%.

- Alternative hypothesis: The percentage of college degrees in mathematics is different from 1%.

We can use a binomial distribution to model the number of graduates with math degrees in a sample of 12,317. Under the null hypothesis, the expected number of graduates with math degrees is:

Expected value = sample size * probability of math degrees = 12,317 * 0.01 = 123.17

Since we are testing at a 0.10 level of significance, the critical values for a two-tailed test are ±1.645 (using a standard normal distribution table).

The test statistic can be calculated as:

z = (observed value - expected value) / standard deviation

The standard deviation of the binomial distribution can be calculated as:

√(sample size * probability of success * (1 - probability of success))

So,

standard deviation = √(123.17 * 0.01 * 0.99) = 1.109

The observed value is 148.

The test statistic is:

z = (148 - 123.17) / 1.109 = 22.38

Since the absolute value of the test statistic is greater than 1.645, we can reject the null hypothesis at the 0.10 level of significance.

Therefore, we have evidence to suggest that the true percentage of college degrees in mathematics is different from 1%.

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The diameter of the circle whose circumference equals 172.7 cm is approximately 55 cm, as found using the formula c = πd with the given value of π as 3.14. The answer is option A.

The formula for the circumference of a circle is c = πd, where c is the circumference and d is the diameter. We are given that the circumference of the circle is 172.7 cm, and π is approximately 3.14. So we can solve for the diameter as

d = c/π = 172.7/3.14 ≈ 55

Therefore, the diameter of the circle is approximately 55 cm.

The correct answer is option A: 55 cm.

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The horizontal distance between (16, -24) and (-3, -24) is 19 units.

Explanation:

We can calculate the horizontal distance by finding the difference between the x-coordinates of the two points.

Horizontal distance = difference in x-coordinates = (-3) - 16 = -19

However, the distance is negative, which doesn't make sense as distance is always positive. So we take the absolute value of the difference to get the actual distance.

|Horizontal distance| = |-19| = 19

Therefore, the horizontal distance between the two points is 19 units.

To find the length of border needed to put around a rectangular room, you can follow these steps:

Measure the length and width of the room using a tape measure or ruler. Let's say the length is L and the width is W.

Determine the type and width of the border you want to put around the room. Let's say you want to use a wallpaper border that is 6 inches wide.

Calculate the length of the border needed for the top and bottom of the room.

This can be done by adding the width of the room to twice the width of the border. So the length of the top and bottom borders would be:

Length of top/bottom borders = 2(W + 6 inches)

Calculate the length of the border needed for the left and right sides of the room. This can be done by adding the length of the room to twice the width of the border. So the length of the left and right borders would be:

Length of left/right borders = 2(L + 6 inches)

Add up the length of all four borders to get the total length of border needed to put around the room:

Total length of border = 2(W + 6 inches) + 2(L + 6 inches)

Simplifying the above equation, we get:

Total length of border = 2L + 2W + 24 inches

So the total length of border needed to put around the room is 2L + 2W + 24 inches.

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Answer:

Step-by-step explanation:

Using cosine rule, the largest angle In the triangle is

The angle is found first using cosine rule by the formula

cos A = (b² + c² - a²) ÷ 2bc

Solving for the largest angle

substituting the values

cos γ = (2² + 1.5² - 3²) ÷ 2 * 1.5 * 2

< γ = arc cos ( -0.4583 )

< γ = 117.28 degrees

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The approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.

To find the approximate probability that someone might answer E.J.'s next call, we'll use the information provided and follow these steps:

1. Calculate the total number of calls made: answered calls (40) + unanswered calls (120).
2. Find the proportion of answered calls to the total calls.
3. Express the proportion as a probability (as a percentage or fraction).

Let's do the calculations:

1. Total calls = 40 (answered) + 120 (unanswered) = 160 calls
2. Proportion of answered calls = 40 answered calls / 160 total calls = 1/4
3. Probability = 1/4 = 0.25 (as a decimal) or 25% (as a percentage)

So, the approximate probability that someone might answer the next call E.J. makes is 0.25 or 25%. The correct answer is C. 0.25.

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The E is enclosed by the planes z = 0 and z = x + y + 5

Why will E is enclosed by the planes z = 0?

The evaluate the triple integral ∫∫∫_E eˣ dV, where E is enclosed by the planes z = 0 and z = x + y + 5, and by the cylinders x² + y² = 4 and x² + y² = 9,

Follow these steps:

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Answer: The probability of getting heads on a fair coin is 1/2, and the probability of rolling an even number on an eight-sided fair die is 4/8 = 1/2. Therefore, the probability of getting both heads and an even number is:

P(heads and even number) = P(heads) x P(even number) = (1/2) x (1/2) = 1/4

The probability of getting tails on a fair coin is also 1/2, and the prime numbers less than 4 are 2 and 3. The probability of rolling a 2 or a 3 on an eight-sided fair die is 2/8 = 1/4. Therefore, the probability of getting tails and a prime number less than 4 is:

P(tails and prime number less than 4) = P(tails) x P(prime number less than 4) = (1/2) x (1/4) = 1/8

So the probability that Oscar gets heads and an even number is 1/4, and the probability that Oscar gets tails and a prime number less than 4 is 1/8.

Step-by-step explanation: can i get brianliest :D

Answer:

x^9√x

Step-by-step explanation:

Answer: The given polynomial is -2x³.

a) To write the polynomial in standard form, we arrange the terms in descending order of degrees:

-2x³

b) The degree of a polynomial is the highest exponent of the variable in the polynomial. In this case, the degree of the polynomial is 3.

c) The lead coefficient is the coefficient of the term with the highest degree. In this case, the lead coefficient is -2.

Step-by-step explanation:

The velocity with which a ball reaches the ground when it is dropped

from a height of 64 m is 35.44m/sec

From the information given, we have that the equation representing the velocity of the ball is expressed as;

V = 4.43√h

Given that the parameters of the formula are;

Since the height of the ball from the ground is 64m, we have to substitute the value, we have;

V = 4.43√64

Find the square root of the value

V= 4.43(8)

Now, multiply both the values to determine the velocity, we get;

V = 35.44m/sec

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