Given the point (7,11,7) in the cylindrical coordinates. When we change to rectangular, it is (-7,0,7).

Answer:

53°

Step-by-step explanation:

\(sin^{-1}(\frac{56}{70})\)=53.13010235° or 53°

Answer:

a₄ = 320

Step-by-step explanation:

To obtain a term in a geometric sequence , multiply the previous term by the common ratio r

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{20}{5}\) = 4 , then

a₄ = 4 × a₃ = 4 × 80 = 320

The correct option of the given question is option(c) becomes narrower.

Based on the given information, when the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes narrower. So, the correct answer is option c. becomes narrower.

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When the confidence level is lowered from 98% to 97%, the confidence interval for the population mean μ becomes wider.

This is because a higher confidence level implies a narrower interval to provide a higher level of certainty in capturing the true population mean. Conversely, when the confidence level is decreased, the interval needs to be wider to allow for a larger margin of error and account for the reduced confidence requirement.

Widening the interval ensures that the estimate is more conservative and includes a broader range of possible values for the population mean. Therefore, the confidence interval for μ becomes wider as the confidence level is lowered.

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Answer: the number can be 9

Step-by-step explanation:

we want that

n + n - 1 + n-2 + .... + 2 + 1 = X

X must be a perfect square.

And the last number, 1, must be said by player 1, so n must be an odd number.

n + (n - 1) + (n -2) + ... + (n - n + 1) = n*n - (1 + 2 + 3 + .... + n)

and we know that:

(1 + 2 + 3 + 4 + ... + n) = n*(n + 1)/2

So we have:

x = n*n - n*(n + 1)/2 = n*n - n*n/2 - n/2 = n*n/2 - n/2 = n*(n + 1)/2

Now we want to find X such that is a perfect square and n must be an odd integer.

You can start giving different values for n until you reach a value of X that is a perfect square, for example, if you take n = 9, we have X = 36.

and 36 = 6*6

So if player 9, he will win always.

Answer:

2839.4 meters

Step-by-step explanation:

Given that:

Altitude = 1200 m

Using trigonometry :

The distance from point P to the airplane :

Using trigonometric relation :

Sin θ = opposite / hypotenus

Sin θ = altitude / x

Sin θ = 1200 m / x

Sin 25 = 1200 / x

0.4226182 = 1200 / x

x = 1200 / 0.4226182

x = 2839.4423

Distance from P to airplane = 2839.4 meters

No, p(x=5) = f(5) = 1/10 is not correct.

If x is a continuous random variable on the interval [0, 10], then the probability of x taking on any specific value (such as 5) is zero.

This is because there are infinitely many possible values that x can take on within the interval, and the probability of x taking on any one specific value is vanishingly small.

Instead, the probability of x falling within a certain range of values is what is meaningful.

This is typically represented by the probability density function (PDF) of the random variable, denoted as f(x). The probability of x falling within a range [a, b] is then given by the integral of the PDF over that range:

P(a <= x <= b) = integral from a to b of f(x) dx

For a continuous uniform distribution over the interval [0, 10], the PDF is a constant function:

f(x) = 1/10 for 0 <= x <= 10

f(x) = 0 otherwise

Using this PDF, we can find the probability of x falling within a specific range, but the probability of x taking on any one specific value is always zero:

P(x = 5) = 0

So, the statement "p(x=5) = f(5) = 1/10" is not correct for a continuous random variable.

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6 is value of x would prove these lines parallel ​.

Describe a parallel line?

Lines that are always the same distance apart in a plane are said to be parallel. Nothing can cross a parallel line. No matter how far in either direction they may be extended, parallel lines are ones that are equally spaced apart from one another and never cross. For instance, parallel lines are represented by a rectangle's opposing sides.

8x + 6 = 2x + 42

8x - 2x = 42 - 6

 6x = 36

    x = 36/6

     x = 6

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Step-by-step explanation:

230m...................

Answer: so the answer would actually b

Step-by-step explanation:

We estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

True, True, True, False, True, True.

The formula for the t-distribution is given by:

t = (x-μ)/(s/√n)

Where x is the mean of the sample, μ is the mean of the population, s is the sample standard deviation, and n is the sample size.

The t-distribution approaches the standard normal distribution as n increases because the denominator, s/√n, gets smaller, making the t-distribution smaller. As n increases, the tails in the t-distribution become "fatter" because the denominator in the formula gets smaller and the resulting t-distribution has a wider range of values.

The shape of the t-distribution depends on its degrees of freedom, which is the number of values in the sample minus one. The more degrees of freedom, the more the t-distribution resembles the standard normal curve.

We use the Student's t-distribution when we estimate the mean of a population that is normally distributed, has an unknown standard deviation, and small n, because it allows us to make better predictions about the population mean than the standard normal curve.

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the inequality on the graph is:

6y + 2x < 9

On the grid we can see a dashed linear equation with a negative slope (because it goes downwards) and we also can see that the shaded region is below the line.

Then we have something like:

y  < ax + b

On the diagram we can see that the y-intercept is 3/2, then:

y < a*x + 3/2

We also can see the point (1.5, 1)

Replacing that we will get:

1 = a*1.5 + 1.5

1 - 1.5 = a*1.5

-0.5 = a*1.5

-(1/2)*(2/3) = a

-1/3 = a

Then the inequality is:

y < (-1/3)x + 3/2

Now we can rewrite this as:

y + (1/3)x < 3/2

2y + (2/3)*x < 3

6y + 2x < 9

That is the correct option, D.

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(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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Answer:

Step-by-step explanation:

The engineer measuring the western rod with a sample size of 20 is expected to have a more precise (narrower) confidence interval compared to the engineer measuring the eastern rod with a sample size of 25.

The engineer who measures the length of the western rod 20 times and calculates the average is expected to have a more precise (narrower) confidence interval compared to the engineer who measures the length of the eastern rod 25 times.

In statistical terms, the precision of a confidence interval is influenced by the sample size. The larger the sample size, the more precise the estimate tends to be. In this case, the engineer measuring the western rod has a sample size of 20, while the engineer measuring the eastern rod has a sample size of 25. Since the sample size of the western rod is smaller, it is expected to have a narrower confidence interval and therefore a more precise estimate of the true length of the rod.

A larger sample size provides more information and reduces the variability in the estimates. It allows for a more accurate estimation of the population parameter. Therefore, the engineer with a larger sample size is likely to have a more precise interval.

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Answer:

Not really,maybe he just went in to find something,just that he didn't that's why maybe he didn't steal anything

Step-by-step explanation:

Answer:

Not necessarily. The robbers might've seen something or someone in your house and ran. They also could've heard something and thought you were home. So, if a robber breaks into your house but runs almost immediately you migt want to get your house checked out. Or, the robbers did think you were poor. Sorry.

Step-by-step explanation:

To find next year's population in one step, the current population should be multiplied by 0.962. This value is obtained by subtracting 3.8% from 100% (1) and converting it to a decimal form (0.962).

1. Multiplying the current population by this factor accounts for the decrease of 3.8% and gives an estimate of the population for the next year.

2. To calculate next year's population in one step, we need to consider the decrease of 3.8% per year. When a population decreases by a certain percentage, we can express it as a decimal value by subtracting that percentage from 100%. In this case, subtracting 3.8% from 100% gives us 96.2%. To convert this to a decimal form, we divide it by 100, resulting in 0.962.

3.By multiplying the current population by 0.962, we take into account the decrease of 3.8% and estimate the population for the next year. This approach assumes a consistent decrease rate over time. For example, if the current population is 100, multiplying it by 0.962 would yield an estimated next year's population of 96.2.

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Answer:

Son is 20

Step-by-step explanation:

*3 - 10 y ago

20 y age diff

The partial derivatives of the original function f(x,y) = 6x3 − 9xy3 with respect to x and y can be found by taking the derivative of the original function with respect to one variable while holding the other variable constant.

The original function is given as f(x,y) = 6x3 − 9xy3. The partial derivatives with respect to x and y can be found by taking the derivative of the original function with respect to one variable while holding the other variable constant.

The partial derivative with respect to x is found by taking the derivative of the original function with respect to x while holding y constant:

∂f/∂x = 18x2 - 9y3

The partial derivative with respect to y is found by taking the derivative of the original function with respect to y while holding x constant:

∂f/∂y = -27xy2

Therefore, the partial derivatives of the original function f(x,y) = 6x3 − 9xy3 with respect to x and y are ∂f/∂x = 18x2 - 9y3 and ∂f/∂y = -27xy2, respectively.

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Answer:

b, c, d

Step-by-step explanation:

Answer:

i = 0.06

n = 108

Step-by-step explanation:

Rate per period:

This is the interest rate, as a decimal.

In this question, the interest rate is 6%. As a decimal, this is 0.06.

So i = 0.06

Number of periods:

The compounding happens monthly.

So 1 period is 1 month.

The payments are made for 9 years, and each year has 12 months.

9*12 = 108

So n = 108R

Answer:

7.5

Step-by-step explanation:

2x+12=6x-18

2x=6x-30

-4x=-30

x=7.5

Answer:

The answer is in the picture, good luck :)

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

sense you have the line in the triangle you would add that to the 16 (length) and multiply that by the 6 (hight) and that would be the area (144)

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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If John has 10 years experience and earns $50,000 and bonus of $9,500 using Regression Equation, then the statement that the residual for John is unusual is True .

Number of workers in the sample is = 80 workers

John has 10 years experience, amount earned is = $50000

Bonus amount is = $9500

The standard deviation of all 80 residuals is $100

The regression equation is given as

Bonus = 2,000 + 257×Experience + 0.046×Salary

From the above data

The residual is = actual value - predicted value

= 9500 - (2000 + 257×10 + 0.046×50000)

= 2630

Since the residual is more than 3 times of standard deviation, therefore, the given statement is True.

-- The given question is incomplete, the complete question is

"For a certain firm, a multiple regression using a sample of 80 workers (including John) gives: Bonus = 2,000 + 257 Experience + 0.046 Salary. John has 10 years' experience, earns $50,000, and gets a bonus of $9,500. Suppose the standard deviation of all the 80 residuals is $100. Then the residual for John is unusual.

The given statement is True or False?" --

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The value of the test statistic used to test the claim is -2.00.

And, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

Now, If a two-sided test of hypothesis is conducted at a 0.05 level of significance and the test statistic resulting from the analysis was 1.23, the potential type of statistical error is Type II error.

A Type II error occurs when we fail to reject a false null hypothesis, meaning that we conclude there is no significant difference or effect when there actually is one.

To answer the second question, we can perform a one-sample t-test to test the claim that the mean GPA for Psychology students at a certain college is less than 3.2.

The hypotheses are:

H₀: μ = 3.2

Ha: μ < 3.2

where μ is the population mean GPA.

We can use the t-statistic formula to calculate the test statistic:

t = (x - μ) / (s / √n)

where, x is the sample mean GPA, s is the sample standard deviation, n is the sample size, and μ is the hypothesized population mean.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

Therefore, the value of the test statistic used to test the claim is -2.00.

Since this is a one-tailed test with a significance level of 0.05, we compare the t-statistic to the critical t-value from a t-table with 48 degrees of freedom.

At a significance level of 0.05 and 48 degrees of freedom, the critical t-value is -1.677.

Since the calculated t-statistic (-2.00) is less than the critical t-value (-1.677), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean GPA for Psychology students at the college is less than 3.2.

To calculate the p-value of the test, we can perform a one-sample t-test using the formula:

t = (x - μ) / (s / √n)

where x is the sample mean GPA, μ is the hypothesized population mean GPA, s is the sample standard deviation, and n is the sample size.

Substituting the given values, we get:

t = (3.1 - 3.2) / (0.35 / √49)

t = -0.10 / 0.05

t = -2.00

The degrees of freedom for this test is 49 - 1 = 48.

Using a t-distribution table or calculator, we can find the probability of getting a t-value as extreme as -2.00 or more extreme under the null hypothesis.

Since this is a two-sided test, we need to find the area in both tails beyond |t| = 2.00. The p-value is the sum of these two areas.

Looking up the t-distribution table with 48 degrees of freedom, we find that the area beyond -2.00 is 0.0257, and the area beyond 2.00 is also 0.0257. So the p-value is:

p-value = 0.0257 + 0.0257

p-value = 0.0514

Rounding to three decimal places, the p-value of the test is 0.051.

Therefore, at a significance level of 0.05, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence to support the claim that the mean GPA for Psychology students at the college is equal to 3.2.

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Answer:16% x 64

Step-by-step explanation:

Answer:10.24

Step-by-step explanation: