Suppose the height of the pyramid is 20 yards. What is the pyramid's volume?
A)50 cubic yards
B)1,500 cubic yards
C)1,850 cubic yards
D)4,500 cubic yards
PLEASE HELP WHOEVER ANSWER CORRECT FIRST GETS BRAINLIEST

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.

There could be several reasons why the total annual hours of work are much greater in Alpha than in Omega, even though both countries have identically sized working-age populations. Here are two possible reasons:

Differences in labor force participation: It is possible that a larger proportion of the working-age population in Alpha is participating in the labor force than in Omega. Labor force participation refers to the percentage of the working-age population that is either employed or actively seeking employment. If more people in Alpha are working or looking for work, then the total annual hours of work would be higher in Alpha than in Omega.

Differences in productivity: Another possible reason for the difference in total annual hours of work is differences in productivity levels between Alpha and Omega. Even if both countries have the same number of people in their working-age population, the productivity of those workers can vary significantly. If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.

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Answer:13

Step-by-step explanation:

Answer:

Y=5\4x

Step-by-step explanation:

gradient is given by ∆y/∆x

g=5/4

Y=MX+C

15=5/4(12)+c

15=15+c

C=0

y=mx+c

y=5\4x

According to the given series, the correct answer is :

C. The series converges because it is the sum of two geometric series, each with |r| < 1.

The sum of the series is 59/60.

To see why, note that we can write the series as:

∑ (4^n / 10^n) + ∑ (7^n / 10^n)

The first sum is a geometric series with first term 1 and common ratio 4/10 = 2/5, which converges to 5/3.

The second sum is a geometric series with first term 1 and common ratio 7/10, which converges to 10/3.

Therefore, the original series converges to (5/3) + (10/3) = 59/60.

The sum of the series is (4/6)+(7/10)=59/60.

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Answer: 4:3

Step-by-step explanation:

The side length of the triangle is 48/3 = 16.

The side length of the square is 48/4 = 12.

So, the ratio is 16:12 = 4:3.

Answer:

Step-by-step explanation:

I used a site it won't let me mention... for this graph

This is if "vertical compression by a factor of 1/3, vertical shift up 5 units" translates to...

\(f(x)=\frac{1}{3} (x^2+5)\)

The equation that has vertical compression by a factor of 1/3, vertical shift up 5 units will be y = (1/3)x² + 5.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The equation of a quadratic function, of vertex (h, k), is given by:

y = a(x – h)² + k

where a is the leading coefficient.

The vertical compression by a factor of 1/3, vertical shift up 5 units.

a = 3

(h, k) = (0, 5)

Then the equation will be

y = 1/3(x – 0)² + 5

y = (1/3)x² + 5

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Answer:

70 mm

Step-by-step explanation:

Use PYTHAGOREAN THEOREM: a^2+b^2=c^2

42^2 + 56^2 = c^2

1764 + 3136 = c^2

4900=c^2

square root of 4900 is 70

so, the final answer is 70 mm

Jupiter is 5,751.51 times more massive than Mercury.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The mass of the planet Jupiter is given below.

1,898,000,000,000,000,000,000,000,000 kg.

The scientific notation is:- 2 x 10²⁷ kg.

The mass of the planet Mercury is given below.

330,000,000,000,000,000,000,000 kg.

The scientific notation is:- 3.30 x 10²³ kg.

Divide the mass of the planet Jupiter by the mass of the planet Mercury. Then we have

Jupiter / Mercury =  2 x 10²⁷  / 3.30 x 10²³

Jupiter / Mercury = 5,751.51

Your question was incomplete, but the complete question was given below.

The most massive planet in the solar system, Jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.

The least massive planet is Mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.

Use your estimates to find out how many times more massive Jupiter is than Mercury. Express your answer in standard form (without using a power of 10).

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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we need 27 ounces of the 11% alcohol solution and 9 ounces of the 23% alcohol solution to obtain 36 ounces of a 14% solution.

Let x be the number of ounces of the 11% alcohol solution, and y be the number of ounces of the 23% alcohol solution. Then we have:

x + y = 36 (total amount of solution)

0.11x + 0.23y = 0.14(36) (total amount of alcohol)

Simplifying the second equation, we get:

0.11x + 0.23y = 5.04

Multiplying the first equation by 0.11 and subtracting from the second equation, we get:

0.12y = 1.08

y = 9

Substituting y = 9 into the first equation, we get:

x + 9 = 36

x = 27

what is numbers?

In mathematics, numbers are abstract concepts used for counting, measuring, and comparing quantities. There are several types of numbers, including natural numbers, integers, rational numbers, irrational numbers, and real numbers. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division, and are a fundamental concept in mathematics.

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Hi!

I'm assuming the question means what integers, so let's figure it out.

Starting from 12, 12 squared is 144, or the square root of 144 is 12.

13 squared is 169, or the square root of 169 is 13.

14 squared is 196, or the square root of 196 is 14.

15 squared is 225, or the square root of 225 is 15.

Based on that list of numbers, we can determine that the square root of 199 lies between the square root of 196 and the square root of 225 -- aka 14 and 15.

Step-by-step explanation:

there is explanation in the answer

Answer:

-16°C

Step-by-step explanation:

Given that:

Average afternoon temperature = 1/4 average morning temperature

Average afternoon temperature = - 4°C

Average morning temperature, x will be :

-4°C = 1/4 * x

-4°C = x / 4

x = - 4 * 4 = - 16°C

Average morning temperature = - 16°C

Answer:

Im pretty sure ur answers would be

x= -32/27 and X=  -46/27

Step-by-step explanation:

So srry if im wrong tho

Answer:

Yes

Step-by-step explanation:

I see no mathematical reason this could not happen. It has three sides which is what makes a triangle.

The area around the given curve according to the green theorem is \(F. dr = 0\).

According to the statement

we have to find the area enclosed by the simple closed curve that encloses the origin.

So, We know that the

The given equation is

\(f(x,y) = \frac{2xyi + (y^{2} - x^{2} ) j}{(x^{2} + y^{2} )^{2} }\)

and

If function is in form of,

\(F = Pi + Qj\)

and C is any positively oriented simple closed curve that encloses the origin.

Then,by use of Green's theorem

Do the partial differentiation of the given function

Then

\(\frac{dQ}{dx} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}\)

and

\(\frac{dP}{dy} = \frac{2x^{3} - 6xy^{2}}{(x^{2} + y^{2} )^{3}}\)

On substitution in Green's theorem,

We get the value

\(F. dr = 0\)

From this it is clear that the area around the given curve is zero.

So, The area around the given curve according to the green theorem is \(F. dr = 0\).

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Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to The Sun.

Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is frequently used metaphorically to refer to a measurement of the difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize the majority of these ideas of distance, both literal and figurative.

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Answer: 11,244,000

Step-by-step explanation:

From the question, we are informed that In 2013 the population of New York state was approximately 19.65 million and the population of New York City was 8,406,000.

To know the number of people in New York State did not live in New York City, we subtract 8,406,000 from 19.65 million. This will be:

= 19,650,000 - 8,406,000

= 11,244,000

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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Answer:

b.) y=3x+2

Step-by-step explanation: The linear equation is y= mx + b

m is the slope and b is the y-intercept

Answer b is the linear equation!

Step-by-step explanation:

Step-by-step explanation:

The general equation for a circle is

\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \)

where (h, k) is the coordinates of the center of the circle and r is the radius. Since the circle passes through (4, 4) and (-4, -4), its center is located at the origin, which means its equation becomes

\( {x}^{2} + {y}^{2} = {( \sqrt{ {4}^{2} + {4}^{2} } )}^{2} = 32\)

Students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific Experiment.

The probability is a measure of the possibility of an event happening. It is expressed as a fraction or decimal between 0 and 1, or as a percentage between 0% and 100%. Probability can be used to determine the likelihood of an event happening or not happening.

Data analysis is the process of analyzing data to extract valuable insights from it. It involves examining data sets to uncover trends, patterns, and relationships that can be used to make informed decisions. Data analysis is an important tool in many fields, including business, finance, and science.

The data analysis and probability unit test assesses students' understanding of these concepts and their ability to apply them in real-world situations.

The test typically includes questions that require students to use probability to determine the likelihood of an event happening or not happening, as well as questions that ask students to analyze data sets to extract valuable insights.In order to prepare for the data analysis and probability unit test, students should review the key concepts and formulas related to probability, such as the addition rule, the multiplication rule, and the complementary rule.

They should also practice analyzing data sets using tools like histograms, scatter plots, and box plots, and should be familiar with key concepts like mean, median, and mode.

Finally, students should be able to apply these concepts and tools in real-world situations, such as calculating the probability of winning a game or analyzing data from a scientific experiment.

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Answer:

\(adjacent = \frac{ 14 }{\sin(60 \degree)} \\ = 16.2 \\ x = \frac{adjacent}{ \cos(45 \degree) } \\ x = \frac{16.2}{ \cos(45 \degree)} \\ x = 22.9 \\ x \approx23\)

The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.

In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.

The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.

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The reliability of the parallel components at 100 hours is approximately 0.670352, or about 67.04%.

To calculate the reliability of the parallel components at 100 hours, we need to use the failure rates (λ) and the time (t).

The reliability function R(t) gives the probability that a component will operate without failure until time t.

The reliability of parallel components can be calculated using the formula:

R_parallel(t) = 1 - [1 - R1(t)] × [1 - R2(t)]

Where R1(t) and R2(t) are the individual reliabilities of the components.

To find the reliabilities at 100 hours, we can use the exponential distribution formula,

R(t) = e^(-λt)

Let's calculate the reliabilities of the individual components first,

R1(100) = e^(-λ1 × 100) = e^(-0.0034 × 100) ≈ 0.670320

R2(100) = e^(-λ2 × 100) = e^(-0.105 × 100) ≈ 0.000045

Now, we can calculate the reliability of the parallel components at 100 hours

R_parallel(100) = 1 - [1 - R1(100)] × [1 - R2(100)]

               = 1 - [1 - 0.670320] × [1 - 0.000045]

               ≈ 1 - (0.329680 × 0.999955)

               ≈ 1 - 0.329648

               ≈ 0.670352

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Answer:

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow (y-5)2-(y-3)2=12 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 2y-10-2y-6=12\)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow 2y-2y-10-6=12 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow -16=12 \)

\(\\\qquad\quad\displaystyle\sf {:}\longrightarrow y's\:value\:is\:undefined \)

Answer:

\( {(y - 5)}^{2} - {(y - 3)}^{2} = 12 \\ = ( {y}^{2} - 10y + 25) - ( {y}^{2} - 6y + 9) = 12 \\ = {y}^{2} - 10y+ 25 - {y}^{2} + 6y - 9 = 12 \\ = - 4y + 16 = 12 \\ = - 4y = 12 - 16 \\ = - 4y = - 4 \\ = y = \frac{ - 4}{ - 4} \\ = \boxed{y = 1}\)

The consumer expenditure for a certain item at a price of $18 is approximately $8.72 million dollars.

The demand function for a certain item is given by:

D(P) = 28e^(-0.25P)

where P is the price per unit, in dollars. The consumer expenditure is the amount of money spent by the consumers to buy a certain quantity of the item at a certain price. It is equal to the product of the quantity demanded and the price per unit: CE = P × Q

where CE is the consumer expenditure, P is the price per unit, and Q is the quantity demanded.

To find the consumer expenditure at a price of $18, we need to first find the quantity demanded at that price by substituting P = 18 into the demand function: D(18) = 28e^(-0.25×18)D(18) ≈ 12.42 million units

Next, we can compute the consumer expenditure at a price of $18 by multiplying the price per unit by the quantity demanded: CE = P × QCE = 18 × 12.42CE ≈ 221.56 million dollars

However, the question asks us to give the answer in million dollars, so we need to divide by 1000 to get the answer in million dollars: CE ≈ 221.56/1000CE ≈ 8.72 million dollars.

Therefore, the consumer expenditure at a price of $18 is approximately $8.72 million dollars.

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Answer:

\(largest = x + 4 \\ smallest = x \\ range = (x + 4) - (x) \\ = 4\)

Por lo tanto, la respuesta es correcta. La empresa tenía 95 kilogramos de materia prima disponible.

Para resolver este problema, debemos utilizar una ecuación matemática. Si llamamos "x" a la cantidad de materia prima disponible, podemos escribir:

0.4x + 57 = x

La primera parte de la ecuación representa el 40% de la materia prima consumida por la empresa (0.4x), mientras que la segunda parte representa la cantidad de materia prima que le queda después de consumir ese 40% (x). Si resolvemos esta ecuación, encontraremos el valor de "x":

0.6x = 57
x = 95

Por lo tanto, la empresa tenía 95 kilogramos de materia prima disponible. Podemos comprobar esto sustituyendo el valor de "x" en la ecuación original:

0.4(95) + 57 = 95
38 + 57 = 95
95 = 95

Por lo tanto, la respuesta es correcta. La empresa tenía 95 kilogramos de materia prima disponible.

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