Find two values of Θ, 0< Θ < 2 pi, that satisfy the following equationsin Θ = negative square root 2 over 2

Answer: 22 minutes

Step-by-step explanation: m + 2m + m + 7 = 4m + 7

4m + 7 = 50

4m = 44

m = 11

2m = 11 x 2 = 22 minutes

a) The null hypothesis is that there is no difference in the proportion of homeowners using water filters among the three communities. The alternative hypothesis is that at least one community has a different proportion of homeowners using water filters than the other communities.

b) To calculate the expected count for the bottom right cell, we can use the formula:

Expected count = (row total x column total) / grand total

The row total for Community C and the column total for No are both 100, and the grand total is 300. Therefore:

Expected count = (100 x 100) / 300 = 33.33

The expected count of 33.33 for the bottom right cell means that if there were no difference in the proportions of homeowners using water filters among the three communities, we would expect 33.33 of the 100 homeowners in Community C to answer 'No' to the question about water filters.

c) To determine what we can conclude from the Chi-square statistic of 13.22, we need to compare it to the critical value for a Chi-square distribution with (3-1) x (2-1) = 2 degrees of freedom at the desired level of significance. Let's assume a level of significance of 0.05. From a Chi-square distribution table, the critical value with 2 degrees of freedom at 0.05 level of significance is 5.99.

Since 13.22 is greater than 5.99, we can reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners using water filters among the three communities. However, we cannot determine from this test alone which communities have different proportions of homeowners using water filters. We would need to conduct further tests, such as post-hoc tests, to investigate the specific differences among the communities.

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

3.04

Step-by-step explanation:

Let x be the cost of each pair

42 - 8x = 17.68

-8x = -24.32

8x = 24.32

x = 3.04

The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Answer:

D. (bottom right)

Step-by-step explanation:

If there is a line where y = x, that means that y and x can both equal 1, 2, 3, -1, -2, -3, etc. They are just always the same. This line, then, would pass through (just for example) (-4, -4) and (4, 4). If you reflect the pink figure across that line, you will get the blue figure. Hope this helps!

Answer: y + 3 = 1 ⋅ (x + 2)

Step-by-step explanation:

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer:

Yes

Step-by-step explanation:

Yes.  They did exponents and grouping symbols first, then multiplication and division left to right.  Addition came before multiplication and division because it was inside a grouping symbol.

Answer:

A

Step-by-step explanation:

From the information given:

To create the required stochastic matrix, we need to take parents who are shown to be vegetarian or nonvegetarian in the column and the children who are vegetarian or nonvegetarian into the row section.

So;

Vegetarian V → 70% →            nonvegetarian NV → 30%

nonvegetarian NV → 40%             vegetarian    V →  60%

                                                           V     NV

The 2x2 stochastic matrix  =     \(\left \Big { {{V} \atop {NV}} \right.} \left [\begin{array} {cc}0.7&0.4\\0.3&0.6\\\end{array}\right]\)

instantaneous rate of change of the search length 0.1667 seconds per

We need to take the derivative of the function S(n) with respect to n and evaluate it at n=12 in order to determine the instantaneous rate of change of the search length for a set of 12 articles.

Taking the derivative of S(n) with respect to n using the chain rule, we get:

S'(n) = 1.6 * (1/(0.8n)) * 0.8 = 2/n

Evaluating this expression at n=12, we get:

S'(12) = 2/12 = 0.1667 seconds per article

This indicates that the search time will increase by approximately 0.1667 seconds per article if the set contains 12 articles by one unit. Alternately, the search time per article will decrease by approximately 0.1667 seconds if the set's number of articles decreases by one unit from 12.

Therefore, the units for the instantaneous rate of change are "seconds per article", indicating the change in search time for each additional or fewer article in the set.

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Answer:

First, let's find how many students there are in total:

11 girls + 9 boys

= 20 students.

Out of those 20 students, we are trying to find the probability if Natalia will be selected first.

There is only one Natalia.

So, out of those students, the probability of selecting Natalia is a:

1/20 probability

(if wanted to convert into a percentage):

1/20 x 100

= 5% probability

Since we already know there are 28 given pens in total and 4 of them are red pens, there is a:

4/28 chance of selecting a red pen which can be simplified to a 1/7 probability.

(if wanted to convert into a percentage):

1/7 x 100

= 14% probability

Since we already know there are 24 jelly beans in total and 9 of them are cherry beans, there is a:

9/24 chance/probability of selecting a cherry jelly bean.

(if wanted to convert into a percentage):

9/24 x 100

= 37.5% probability

Let's first figure out how many marbles there are in total.

2 + 3 + 7

= 12 marbles in total.

Now let's exclude the marbles that are blue and yellow, leaving us with 7 orange marbles.

So the probability of selecting a marble that isn't blue/yellow is a:

7/12 probability

(if wanted to convert into a percentage)

7/12 x 100

= 58% probability

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

The congruence theorem required for each figure are

1. AAS

2. ASA

3. ASA

4. ASA

5. ASA

6. ASA

ASA (Angle-Side-Angle) congruence theorem states that if two triangles have two angles and the included side in common, then they are congruent.

That is to say, if two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the two triangles are congruent.

AAS (Angle-Angle-Side) congruence theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding angles and non-included side of another triangle, then the two triangles are congruent.

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Answer:d

Step-by-step explanation:

The translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The parallelogram ABCD is shifted to the right by 2 units and shifted up by 1 unit to get parallelogram A'B'C'D'.

Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph.

The graphs can be translated or moved about the xy-plane.

This transformation rule is represented as:

(x,y) -> (x + 2,y + 1)

This transformation rule can be rewritten as:

T2, 1(x, y)

Hence, the translation from the pre-image, Parallelogram ABCD, to the image, Parallelogram A'B'C'D' is T2, 1(x, y)

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The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

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

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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The results of operations between vectors are, respectively:

Case A: u + w = <- 3, - 1>

Case B: - 6 · v = <6, 6>

Case C: 3 · v - 6 · w = <- 21, - 15>

Case D: 4 · w + 3 · v - 5 · u = <39, 4>

Case E: |w - v| = √(4² + 3²) = 5

In this problem we must determine the operations between vectors, this can be done by following definitions:

Vector addition

v + u = (x, y) + (x', y') = (x + x', y + y')

Scalar multiplication

α · v = α · (x, y) = (α · x, α · y)

Norm of a vector

|u| = √(x² + y²)

Now we proceed to determine the result of each operation:

Case A:

u + w = <- 6, - 3> + <3, 2>

u + w = <- 3, - 1>

Case B:

- 6 · v = - 6 · <- 1, - 1>

- 6 · v = <6, 6>

Case C:

3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>

3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>

3 · v - 6 · w = <- 21, - 15>

Case D:

4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>

4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>

4 · w + 3 · v - 5 · u = <39, 4>

Case E:

|w - v| = |<3, 2> - <- 1, - 1>|

|w - v| = |<4, 3>|

|w - v| = √(4² + 3²) = 5

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Answer:

Answer A

Step-by-step explanation:

The vertices of the feasible region is (4, 3)

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

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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Answer:

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.95}{2} = 0.025\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.025 = 0.975\), so \(z = 1.96\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1\)

The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds

The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.

The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.

Answer:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

Step-by-step explanation:

Information given

\(\bar X=2.9\) represent the sample mean

\(\mu\) population mean

\(\sigma =1.4\) represent the population standard deviation

n=2092 represent the sample size  

Confidence interval

The confidence interval is given by:

\(\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\)   (1)

Since the Confidence interval is 0.95 or 95%, the significance is \(\alpha=0.05\) and \(\alpha/2 =0.025\), and the critical value would be \(z_{\alpha/2}=1.96\)

Replacing the info we got:

\(2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84\)    

\(2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96\)    

The confidence interval is given by \(2.84 \leq \mu \leq 2.96\)

187.6miles

Step-by-step explanation:

blue ridge parkway is 469miles

sam drove 2/5 of the parkway

2/5×469

=469×2/5

938/5

187.6miles

Answer:

the answer is c the one above d

Step-by-step explanation:

Answer: y+-1m -1

Step-by-step explanation:

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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