The given curve is rotated about the y-axis. Find the area of the resulting surface.
x²/³ + y²/³ = 4, 0 ≤ y ≤ 8

Answer:

\((A)\frac 1 {cosx} \frac 1 {sin x} - \frac {cosx} {sin x} = \frac {sin x} {cosx} \\\\(B)\frac{1-cos^2 x }{cos x sin x} = \frac {sin x} {cosx} \\\\(C) \frac{(sin^2x + cos^2x)-cos^2 x }{cos x sin x} = \frac {sin x} {cosx} \\\\(D) \frac{sin^2x }{cos x sin x} = \frac {sin x} {cosx}\\\\(E)\frac {sin x}{cos x} = \frac {sin x}{cos x}\)

In step A, you replace all trigonometric functions with their definitions in terms of sine and cosine.

In step B, you add the two together as you add fractions.

In step C, you replace 1 with the sum of the squares of sine and cosine.
In step D, you add the cosine terms together so they disappear.

In step E, finally, you divide numerator and denominator by \(sin x\).

There are many assumption that must be met for independent samples t-tests and anovas, but not for single sample z or t tests

The assumption that must be met for testing independent samples from t-test or anovas are :

1. Takes into account the normal distribution of the dependent variable.

2. Makes the supposition that the variance of the two groups is equal to that of the dependent variable.

3. Pretends that the two samples are unrelated to one another.

4. Random selection is used to select samples from the population.

5. All observations in a t-test with an independent sample must be unrelated to one another.

6. To use the independent sample t-test, dependent variables must be measured on an interval or ratio scale.

Where For single Sample t-test ,

Data should be randomly selected and normally distributed

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Answer:

Step-by-step explanation:

-2x^6-9

please give me the brainliest

Answer:

−12

Step-by-step explanation:

To solve this expression, we need to use the order of operations. The order of operations is a set of rules that dictate the sequence in which operations should be performed in a mathematical expression. The order of operations is often abbreviated using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Answer:

f(x) = x + 2

Step-by-step explanation:

If we graph x + 2, we can see that it passes the Vertical Line Test. Each x-value only has 1 y-value.

Step-by-step explanation:

Apples cost four times as much as oranges per pound.

If the cost of orange =x

then, cost of apples =4x

But,

the costs of apples =2.80$

So,4x=2.80

\(\tt{ x=\dfrac{2.80}{4} }\) ⠀

\(\tt{ x=0.70\$ }\) ⠀

so,oranges costs for per pound =0.70$

Step-by-step explanation:

you can see this either as projection or as 2 similar triangles.

in any case we know that the scale factor is the same for every line and side.

midsegment means that B and D are in the middle of CA and CE. so, the scale factor from CB to CA is 2.

the same scaling factor applies to BD to AE.

AE = 56×2 = 112

Answer:

(12,1)

Step-by-step explanation:

We know that ordered pairs are in the format of (x,y).

This means in that (12, __) 12 is our x coordinate. Plugging 12 into the equation as x we get:

\(12-3y=9\\-3y=9-12\\-3y=-3\\y=1\)

Therefore our answer is (12,1) as we plug y back into our coordinate (x,y).

Answer:

(12,1)

Step-by-step explanation:

In the ordered pair, x=12

plug 12 back in the equation

12-3y=9

-3y=-3

3y=3

y=1

it will take approximately 29.823 seconds to produce 1.0 g of silver metal by the electrolysis of an AgNO3 solution using a current of 30 amps.

To determine how many seconds will be required to produce 1.0 g of silver metal by the electrolysis of an AgNO3 solution using a current of 30 amps, we need to follow these steps:

1. Calculate the number of moles of silver (Ag) in 1.0 g:
1.0 g / 107.87 g/mol (molar mass of Ag) = 0.00927 mol of Ag

2. Use Faraday's law of electrolysis to find the total charge needed:
Total charge (Q) = n × F
where n is the number of moles of Ag (0.00927 mol) and F is the Faraday constant (96,485 C/mol).
Q = 0.00927 mol × 96,485 C/mol = 894.7 C (Coulombs)

3. Determine the time (t) required to pass the total charge at a current of 30 amps:
t = Q / I
where Q is the total charge (894.7 C) and I is the current (30 A).
t = 894.7 C / 30 A = 29.823 seconds

So, it will take approximately 29.823 seconds to produce 1.0 g of silver metal by the electrolysis of an AgNO3 solution using a current of 30 amps.

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Answer:

9 3/4 cubic units

Step-by-step explanation:

The formula for the volume of a rectangular prism =

Length × Width × Height

From the question:

Length = 3 units

Height = 3 1/4 units

Width = 1 unit.

Volume of the prism =

3 units × 3 1/4 units × 1 unit

= (3 × 13/4 × 1 )cubic units

= 39/4 cubic units

= 9 3/4 cubic units

The total volume of the rectangular prism = 9 3/4 cubic units

Answer:

✔ 9

whole-unit cubes fit inside the prism.

✔ 3

quarter-cubic units fit inside the prism.

The total volume of the prism is  

✔ 9 3/4  units3.

Answer:  the bigger is one is 0.24 which means the symbol is >

Answer:no one doin that

Step-by-step explanation:

The slope of a line perpendicular to  y=-4x + 16 is (1/4), so the correct option is the first one (counting from the top).

The general linear equation in the slope-intercept form is:

y = a*x + b

Where a is the slope and b is the y-intercept.

Let's say that we have another line:

y = c*x + d

These two lines are perpendicular if and only if the slope of one of the lines is equal to the inverse of the opposite of the other line.

So, the two lines:

y = a*x + b

y = c*x + d

Are perpendicular only if c = -(1/a).

Now, we want to find a line perpendicular to:

y=-4x + 16

Then the slope of that perpendicular line must be:

-(1/-4) = (1/4)

So the slope of a line perpendicular to  y=-4x + 16 is (1/4).

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Answer:

The answer is 15 cm.

Step-by-step explanation:

y= k/x

x= width

y= length

So there for;

x= 5

y= 12

Which means that;

12= k/5

k= 60

And then;

y= 60/x

Which then finally means that;

y= 60/4

60/4= 15 cm

False. If E and F are independent events, then Pr(E|F) is not necessarily equal to Pr(E).

The probability of an event E given event F, denoted as Pr(E|F), represents the probability of event E occurring given that event F has already occurred. In the case of independent events, the occurrence of one event does not affect the probability of the other event occurring.

By definition, two events E and F are independent if and only if Pr(E ∩ F) = Pr(E) × Pr(F), where Pr(E ∩ F) represents the probability of both events E and F occurring.

Now, let's consider the statement that Pr(E|F) = Pr(E) when E and F are independent events. This implies that the probability of event E occurring given that event F has occurred is the same as the probability of event E occurring without any knowledge of event F.

However, this is not necessarily true. The conditional probability Pr(E|F) takes into account the occurrence of event F, which may affect the probability of event E. Even if events E and F are independent, the value of Pr(E|F) may differ from Pr(E) if the occurrence of event F provides additional information or changes the probability distribution of event E.

The statement "Pr(E|F) = Pr(E)" when E and F are independent events is false. While independence between events E and F ensures that the occurrence of one event does not affect the probability of the other event, it does not guarantee that the conditional probability Pr(E|F) will be equal to the unconditional probability Pr(E).

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A. The expected value for Jeremy's initial distribution is:

E(X) = (18/38)$20 + (18/38)(-$20) + (2/38)(-$20) = -$0.53

B. This means that on average, Jeremy can expect to lose $0.53 per round played in the long run.

C. The expected value for Jeremy's new distribution, where he bets $40 per round, is:

E(X) = (18/38)$40 + (18/38)(-$40) + (2/38)(-$40) = -$1.05

D. Doubling his bet does not increase Jeremy's odds of winning money, as his expected value is still negative.

The expected value for Jeremy's initial distribution is calculated by multiplying the net win for each event by its probability of occurring and summing the results. The expected value for Jeremy's new distribution is calculated in the same way, but with a net win of $40 instead of $20.

The negative expected value in both cases means that, on average, Jeremy can expect to lose money over time. Doubling his bet does not increase his odds of winning money, as his expected value is still negative. In fact, increasing his bet actually increases his expected loss per round, as seen in the comparison of the expected values for the two distributions.

This is due to the fact that the increased bet size does not change the underlying probabilities of the game. Roulette is a game of pure chance, and the odds of winning or losing a given round are always the same, regardless of the size of the bet.

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Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.

First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.

In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.

Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.

Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.

Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.

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The value of the slope between each pair of points are,

9) - 1/3

10) 1

11) 3/4

We have to given that;

Points are,

9. (4, 6) and (-2, 8)

10. (-1, 3) and (5,9)

11. (5, -1) and (-3,-7)

Now, We know that;

Slope of line passing through the points  (x₁ , y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

Hence, We get;

9) Points are,

(4, 6) and (-2, 8)

So, Slope is,

m = (8 - 6) / (- 2 - 4)

m = 2/ - 6

m = - 1/3

10) Points are,

(-1, 3) and (5,9)

So, Slope is,

m = (9 - 3) / (5 + 1)

m = 6/ 6

m = 1

11) Points are,

(5, -1) and (-3,-7)

So, Slope is,

m = (- 7 + 1) / (- 3 - 5)

m = - 6/- 8

m = 3/4

Thus, The value of the slope between each pair of points are,

9) - 1/3

10) 1

11) 3/4

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Step-by-step explanation:

maybe it's helpful for you

Answer:

x = 2 or 3

Step-by-step explanation:

Diagonal of a rhombus bisects the vertex angles. So,

\(x^{2} =5x-6\)

\(=> x^{2} -5x + 6 = 0\)

Lets factorise the eqn.

\(=> x^{2} - 2x - 3x + 6 = 0\)

\(=> x (x - 2) -3(x-2)\)

\(=> (x-2)(x-3) = 0\)

Here x will have 2 values.

1) \(x-2=0\)

\(=> x =2\)

2) \(x - 3 = 0\)

\(=> x = 3\)

Answer:

answer is [(-5)+6]+6]+(-3)=4

Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.

According to the question,

They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.

In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.

\(\frac{252}{350} = 0.72\)

To convert decimal into Percentage multiply 0.72 into 100.

0.72*100 = 72%.

Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.

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Using compound interest and continuous compounding, it is found that it would take 2.61 years longer for Carter's money to triple.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

For Carter, we have that the rate of interest and the number of compoundings are, respectively, r = 0.04875 and n = 12. The time to triple is t for which A(t) = 3P, hence:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(3P = P\left(1 + \frac{0.04875}{12}\right)^{12t}\)

\((1.0040625)^{12t} = 3\)

\(\log{(1.0040625)^{12t}} = \log{3}\)

\(12t\log{(1.0040625)} = \log{3}\)

\(t = \frac{\log{3}}{12\log{(1.0040625)}}\)

t = 22.58.

The amount of money is given by:

\(A(t) = Pe^{kt}\)

For Jack, we have that the rate of interest is of k = 0.055, hence:

\(A(t) = Pe^{kt}\)

\(3P = Pe^{0.055t}\)

\(e^{0.055t} = 3\)

\(\ln{e^{0.055t}} = \ln{3}\)

\(0.055t = \ln{3}\)

\(t = \frac{\ln{3}}{0.055}\)

t = 19.97.

The difference is given by:

22.58 - 19.97 = 2.61

It would take 2.61 years longer for Carter's money to triple.

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Answer:

34 = 22 + x

x = 12

Step-by-step explanation:

alternatively, you could say (10x3)+(1x4) = (10x2) + (1x2) + x

Answer: C) \(f^{-1}(x)=3-7x\)

Step-by-step explanation:

When solving for an inverse of a function replace f(x) with x and replace the original x with y.

\(f(x) = \frac{3-x}{7} \\x=\frac{3-y}{7}\)

Now solve for y

\(x=\frac{3-y}{7} \\(7)x=(\frac{3-y}{7}) (7)\\7x=3-y\\7x+y=3-y+y\\7x+y=3\\7x-7x+y=3-7x\\y=3-7x\)

Replace y with the \(f^{-1}(x)\)

Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

Answer:

19

Step-by-step explanation:

You will need expand so you can plug in the givens

Quotient rule: log(b^7)-[log(a^5c^6)]

Product rule: log(b^7)-[log(a^5)+log(c^6)]

Distribute: log(b^7)-log(a^5)-log(c^6)

Power rule: 7log(b)-5log(a)-6log(c)

Plug in: 7(4)-5(3)-6(-1)

Simplify: 28-15+6

Simplify: 13+6

Simplify: 19

Answer:

every hour is $8.15 if 4.5hours her mows is $33.15

Answer:

$36.68

Step-by-step explanation:

If she mows for 4.5 hours, you multiply that by how much she makes an hour. each hour she makes $8.15 each hour.

4.5 * 8.15= 36.675

you'd round up to the 100ths place because of the 5