Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty

Answers

Answer 1

Answer:

You should claim 10.5325 years on your warranty.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 13, \sigma = 1.5[/tex]

Want's to replace no more than 5% of the products.

This means that the warranty should be 5th percentile, that is, the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.645 = \frac{X - 13}{1.5}[/tex]

[tex]X - 13 = -1.645*1.5[/tex]

[tex]X = 10.5325[/tex]

You should claim 10.5325 years on your warranty.


Related Questions

If the area of a circle is 121 pi square units, what is its diameter

Answers

Ffhhbbvgghjjiufdeeedfhjytreetuhh

Answer:22

Step-by-step explanation:

diameter=d

Area=121π

area of circle=π x (d/2)^2

121π=π x d^2/4

121π=πd^2/4

Cross multiplying we get

121π x4=πd^2

484π=πd^2

Divide both sides by π

484π/π=πd^2/π

d^2=484

Taking the square roots of both sides we get

d=√(484)

d=22 diameter=22

The Cartesian coordinates of a point are given.(a) (6, −6)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) = (b) (−1, 3)(i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.(r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π.(r, θ) =

Answers

Final answer:

To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the equations (r, θ) = (√(x² + y²), atan2(y, x)).

Explanation:

To find the polar coordinates (r, θ) of a point given in Cartesian coordinates (x, y), we can use the following equations:

(r, θ) = (√(x² + y²), atan2(y, x))

(a)(i) For the Cartesian coordinates (6, -6),

(r, θ) = (√(6² + (-6)²), atan2(-6, 6))

(r, θ) = (√(36 + 36), atan2(-6, 6))

(r, θ) = (6√2, -45°)

(a)(ii) For the Cartesian coordinates (6, -6),

(r, θ) = (-√(6² + (-6)²), atan2(-6, 6) + π)

(r, θ) = (-6√2, -45° + π)

(b)(i) For the Cartesian coordinates (-1, 3),

(r, θ) = (√((-1)² + 3²), atan2(3, -1))

(r, θ) = (√(1 + 9), atan2(3, -1))

(r, θ) = (√10, 116.57°)

(b)(ii) For the Cartesian coordinates (-1, 3),

(r, θ) = (-√((-1)² + 3²), atan2(3, -1) + π)

(r, θ) = (-√10, 116.57° + π)

Simon walks a total of 45.55 miles in March and 35.7 miles in April.
How many miles does Simon walk in all in March and April?
Enter your answer ​

Answers

Answer:

81.25

Step-by-step explanation:

45.55 + 35.7

Answer:I hope that helps

Step-by-step explanation:

10 percent of what number is 350

Answers

Answer:

3500

Step-by-step explanation:

multiply 10*350

3500

because 350 x 100 / 10 = 3500

the height of the two triangular faces is 5.2 centimeters. the surface area of the triangular prism is ____ square centimeters.

Answers

The surface area of the triangular prism is 171.2 square centimeters.

From the given triangular prism,

Area of base (rectangle) = Length×Breadth

= 8×6=48 square centimeter

So, area of 3 congruent rectangles = 3×48

= 144 square centimeter

Here, area of a triangle = 1/2 × Base × Height

= 1/2 ×6×5.2

= 15.6 square centimeter

So, area of 2 congruent triangles= 2×15.6

= 31.2 square centimeter

Total surface area = 144+31.2

= 171.2 square centimeter

Therefore, the surface area of the triangular prism is 171.2 square centimeters.

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On the Red Trail, the distance between point A and point B is 7.3 kilometers. You walked this distance back and forth. What is the distance you walked in meters?

Answers

Answer:

[tex]d = 14,600\,km[/tex]

Step-by-step explanation:

The distanced travelled is equal to twice the distance between points A and B. The distance that was walked in meters is:

[tex]d = 2\cdot (7.3\,km)\cdot \left(\frac{1000\,m}{1\,km} \right)[/tex]

[tex]d = 14,600\,km[/tex]

Final answer:

The total distance walked on the Red Trail, back and forth, when converted from kilometers to meters, is 14,600 meters.

Explanation:

The question asks for the total distance walked in meters if a person walks from point A to point B and back on the Red Trail, where the distance between point A and point B is 7.3 kilometers.

Firstly, we know that 1 kilometer equals 1,000 meters. Therefore, to find the distance in meters for a single trip from point A to point B, we multiply 7.3 kilometers by 1,000:

7.3 km × 1,000 = 7,300 meters

Since the trip was made back and forth, the total distance covered is twice the distance of a single trip:

Total distance = 2 × 7,300 meters = 14,600 meters

Therefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.

How can you isolate the variable x-3=7

Answers

to get the variable alone you need to add three to both sides

x-3=7

+3  +3

-----------------

x= 10

Answer:

Step 1: Bring like terms together Step 2: Add variable to both sides Step 3: Simplify Step 4: Add the constant to both sides Step 5: Simplify  Step 6: Divide by the coefficient Step 7: Solve Step 8: Test your solution Answer: 10

Step-by-step explanation:

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign​ sedan, you decide to estimate the resale value of this car with a 99​% confidence interval. You manage to obtain data on 17 recently resold​ 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $ 12 comma 260 with a standard deviation of $ 800. Suppose that the interval is calculated to be (11693 comma 12827 ). How could the sample size and the confidence coefficient be altered in order to guarantee a decrease in the width of the​ interval?

Answers

Answer:

If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:

[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The width of the confidence interval is just defined as two times the margin of error:

[tex] Width = 2ME[/tex]

And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%

By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.

Step-by-step explanation:

For this case w ehave the following info given from the problem

[tex] n =17[/tex] represent the sample size for the cars selected

[tex]\bar X = 12260[/tex] represent the average price for the cars sold

[tex] s= 800[/tex] represent the standard deviation for the solds

And we have a 99% confidence interval for the true average price for the cars given:

[tex]11693 \leq \mu \leq 12827[/tex]

And we know that the confidence interval for the true mean is given by this formula:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:

[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The width of the confidence interval is just defined as two times the margin of error:

[tex] Width = 2ME[/tex]

And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%.

By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.

What function do you use to find the angle of a vector, when you know its components?

Answers

Answer:

[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]

Step-by-step explanation:

If we are given components of a vector then we can find the angle between them.

Suppose we are given a vector v

[tex]v = (x, y)[/tex]

Where x is the horizontal component and y is the vertical component.

The angle can be found by using

[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]

The magnitude of the vector v can be found using

[tex]v = \sqrt{x^{2}+y^{2}}[/tex]

Example:

Lets do a quick example:

[tex]v = (2, 4)[/tex]

The angle of the vector is

[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]

The magnitude of the vector is

[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]

How do I write the exponent expression below in numbers

Three to the sixth power all divided by two

Answers

Answer:

(3^6)/2

Step-by-step explanation:

make sure everything as the numerator is in parenthesis

Wich shapes can the the shaded area be divided into to find the area

Answers

Answer:

A. a rectangle and a triangle

Answer:

a) rectangle and triangle, then add both to fin the total area.

Step-by-step explanation:

In a random sample of 125 highway bridges around the country, 75 were in need of repair.
What is the sample proportion (point estimate) of highway bridges that need repaired? (Only type ONE decimal place)

Answers

Answer:

The sample proportion of highway bridges that need repaired is 0.6.

Step-by-step explanation:

The sample proportion of highway bridges that need repaired is the number of bridges in need of repair divided by the number of bridges around the country.

In this question:

75 bridges in need of repair, out of 125. So

75/125 = 0.6

The sample proportion of highway bridges that need repaired is 0.6.

87 1/3% into a fraction

Answers

Final answer:

87 1/3% is approximately 17433/10000 as a fraction after converting 87.33% to a fraction with a denominator of 100 and simplifying.

Explanation:

To convert 87 1/3% into a fraction, we first recognize that 1/3% is equal to 0.33% (approximately), so 87 1/3% is approximately 87.33%. Next, we write this percent as a fraction with a denominator of 100 to represent the percent: 87.33/100.

To simplify further, we can convert the decimal to a fraction, where 0.33 is approximately 33/100, and add this to 87 to get:

8733/10000 + 8700/10000 = 17433/10000

Thus, 87 1/3% is approximately 17433/10000 when expressed as a fraction.

Maria and her friends went on a bike ride. The start and end times are shown below how long did they Ride

Start time: 1:09
End time: 2:05

Answers

Maria and her friends rides for 56 minutes

Duration of timeDuration is defined as the length of time that something lasts. Eg. When a film lasts for two hours, this is an example of a time when the film has a two hour duration

How to solve the problem?Given

Start time = 01:09

End time = 02:05

From start and end time we can see that there is 4 minutes to complete 1 hoursSo to find total time we need to subtract 4 minutes from 1 hours i.e 60 minutes

∴ Ride Time = 60-4

∴ Ride Time = 56 minutes

Therefore the total ride time that Maria and her friend rode is 56 minutes

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Will give brainliest please explain how

Answers

Answer:

x = 5/4

Step-by-step explanation:

√2+√2+√2+√2 = 2^x

4√2 = 2^x

4√2 = [tex]2^{\frac{5}{2} }[/tex] = [tex]2^{x}[/tex]

x = 5/2

Answer:

x = 5/4

Step-by-step explanation:

√2+√2+√2+√2 = 2^x

4√2 = 2^x

4√2 =  =

x = 5/2

What is the value of this expression when a=3 and b=-1?

Answers

Answer:

1/4

Step-by-step explanation:

[tex](\dfrac{3(3)^{-2}(-1)^6}{2(3)^{-1}(-1)^5})^2=[/tex]

[tex](\dfrac{\frac{1}{3}}{-\frac{2}{3}})^2=[/tex]

[tex](-\dfrac{1}{2})^2=[/tex]

[tex]\frac{1}{4}[/tex]

Hope this helps!

One of the more famous anecdotes in the field of statistics is known as the "Lady Tasting Tea" and involves the renowned statistician Sir Ronald Aylmer Fisher. A woman claimed to be able to tell the difference in a cup of tea depending on whether or not the milk or tea was poured first. You have chosen to recreate this experience with a classmate and have fixed 40 cups of tea, of which your classmate correctly identifies 12. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.30 as the value for p. n = 42 n = 81 n = 4116 n = 8068

Answers

Answer:

[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]  

And rounded up we have that n=8068

Step-by-step explanation:

The margin of error for the proportion interval is given by this:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

We want for this case a 95% of confidence desired, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The margin of error for this case is [tex]ME =\pm 0.01[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

The estimated proportion for this case is [tex]\hat p=0.3[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.3(1-0.3)}{(\frac{0.01}{1.96})^2}=8067.36[/tex]  

And rounded up we have that n=8068

"If a method produces a random error for each measurement of 4%, but a percent error of equal to or less than 1% is required for this value for later analysis, what is the minimum number of measurements that must be collected and averaged? You will need to solve equation 1 for the value of n that meets the criterion of a 1% error in the average."

Answers

Answer:

N = 16 measurements

Step-by-step explanation:

A method produces a random error for each measurement of 4%

A percent error of equal to or less than 1% is required.

We want to find out the minimum number of measurements that must be collected.

The standard error is given by

[tex]SE = \frac{S}{\sqrt{N} } \\[/tex]

Where s is the standard deviation and N is the number of measurements.

We are given standard deviation equal to 4% and SE equal to 1%

So re-arranging the above equation for N

[tex]\sqrt{N} = \frac{S}{SE} \\N = (\frac{S}{SE})^{2}\\N = (\frac{0.04}{0.01})^{2}\\N = 16[/tex]

Therefore, a minimum 16 number of measurements are needed.

Translate the triangle left 1 units and up 5 units. What are the coordinates of point C after the translation?


Answers

Answer:

b++nfr

Step-by-step explanation:

jjkiki

Answer: Where is point C?

Explanation:

A major building contractor has 10 new floor plans that she would like to start using in the homes she builds. She wants to know whether her homes will sell for a higher price in the city or the suburbs. She builds two homes—one in the city and one in the suburbs—for each of the 10 floor plans. She uses the same real estate agency to sell all 20 homes and then she calculates the difference in selling price (city – suburb) for each of the floor plans. What is the most appropriate test to analyze her data? a. Two Proportion Z Test b. One Sample T Test c. One Proportion Z Test d. Independent Samples T Test e. Paired T Test

Answers

Answer: d. Independent Samples T Test

Step-by-step explanation: Independent Samples T Test is commonly used when you want to compare the means of two independent groups and determine if there is evidence that the the associated means are significantly different.

For this test, the data must have: continuous dependent variable; independent variable is categorical (two or more groups); cases that have values on both variables; the obervations are independent, i.e. the groups don't interfere on each other; random sample of data for the population; normal distribution of the dependent variable for each group; homogeneity of variances and no outliers.

Each groups should have at least 6 subjects and have the same number of individuals in each group.

The hypothesis in this test can be expressed as:

H₀: μ1 = μ2 or μ1 - μ2 = 0

H₁: μ1 ≠ μ2 or μ1 - μ2 ≠ 0

What percent is 7 out of 40?​

Answers

Answer:

17.5%

Step-by-step explanation:

Convert fraction (ratio) 7 / 40 Answer: 17.5%

Answer:

17.5

Step-by-step explanation:

7/40 = 17.5

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Do political science classes require less writing than history classes? The 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages. The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages. What can be concluded at the α = 0.01 level of significance?

Answers

Answer:

We conclude that political science classes require less writing time than history classes at 0.01 level of significance.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 16.3 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 54 randomly selected history classes assigned an average of 18.9 pages of essay writing for the course. The standard deviation for these 54 classes was 5 pages.

Let [tex]\mu_1[/tex] = average writing time required by political science classes.

[tex]\mu_2[/tex] = average writing time required by history classes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1\geq\mu_2[/tex]      {means that political science classes require more or equal writing time than history classes}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1<\mu_2[/tex]      {means that political science classes require less writing time than history classes}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

                     T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]   ~ [tex]t__n_1_-_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample average pages of essay writing for political science classes = 16.3 pages

[tex]\bar X_2[/tex] = sample average pages of essay writing for history classes = 18.9 pages

[tex]s_1[/tex] = sample standard deviation for political science classes = 4.8 pages

[tex]s_2[/tex] = sample standard deviation for history classes = 5 pages

[tex]n_1[/tex] = sample of political science classes = 55

[tex]n_2[/tex] = sample of history classes = 54

Also,  [tex]s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }[/tex]  =  [tex]\sqrt{\frac{(55-1)\times 4.8^{2}+(54-1)\times 5^{2} }{55+54-2} }[/tex] = 4.90

So, test statistics  =  [tex]\frac{(16.3-18.9)-(0)}{4.9 \sqrt{\frac{1}{55}+\frac{1}{54} } }[/tex]  ~ [tex]t_1_0_7[/tex]

                               =  -2.77

The value of t test statistics is -2.77.

Now, at 0.01 significance level the t table gives critical value of -2.365 at 107 degree of freedom for left-tailed test.

Since our test statistics is less than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that political science classes require less writing time than history classes.

If f(x) = 2x – 1 and g(x) = 3x + 5, then (f o g)(x) is equal to

Answers

Answer:

  (f◦g)(x) = 6x +9

Step-by-step explanation:

Use g(x) as the argument to f(x) and simplify.

  (f◦g)(x) = f(g(x)) = f(3x +5) = 2(3x +5) -1

  (f◦g)(x) = 6x +9

14/10 divided by blank equals seven

Answers

Answer:

14/10=1.4

7/1.4=5

1.4x5=7

Step-by-step explanation:

Final answer:

In the given equation 14/10 divided by a certain number equals seven, the missing number is 0.2

Explanation:

The subject of this question is Mathematics and it appears to be suitable for a Middle School grade level. You're asking for a number that, when 14/10 or 1.4 is divided by it, the result is seven.

To solve it, one can set it up as an equation in the form of 1.4 / x = 7. To find 'x', multiply both sides by 'x' to get rid of 'x' on the denominator of the left side, so the equation becomes 1.4 = 7x. The next step is to isolate 'x' by dividing both sides of the equation by 7. Solving this equation gives x = 1.4/7 = 0.2.

So, 14/10 divided by 0.2 equals seven.

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Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court judges consist of 24 men and 3 women. (Enter your probabilities as fractions.) (a) Find the probability that both appointees are men. (b) Find the probability that one man and one woman are appointed. (c) Find the probability that at least one woman is appointed.

Answers

Answer:

[tex](a)\dfrac{92}{117}[/tex]

[tex](b)\dfrac{8}{39}[/tex]

[tex](c)\dfrac{25}{117}[/tex]

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are without replacement.

(a)Probability that both appointees are men.

[tex]P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}[/tex]

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed)[tex]=P(MW)+P(WM)[/tex]

[tex]=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}[/tex]

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.A woman is appointed first and a man is appointed next.Two women are appointed

P(at least one woman is appointed)[tex]=P(MW)+P(WM)+P(WW)[/tex]

[tex]P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}[/tex]

In Part B, [tex]P(MW)+P(WM)=\frac{8}{39}[/tex]

Therefore:

[tex]P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}[/tex]

(1) Saad had a box that is 15cm by 20cm by 22cm. What is the volume of the box?

(2) jake is redoing her kitchen. It measures 18ft by 19 ft. If wallpaper costs $1.29 per foot, how much will it cost her to wallpaper the kitchen?

Answers

Answer:

Question1:volume=6600cm^3

Question2:cost=$441.18

Step-by-step explanation:

Question 1:

volume=length x width x height

Volume=15 x 20 x 22

Volume=6600cm^3

Question 2:

area of kitchen=length x width

Area of kitchen=18 x 19

Area of kitchen=342ft^2

$1.29 for 1ft^2

$b for 342ft^2

$b=342 x1.29

$b=$441.18

Which of the following is equivalent to tan(x) * csc(x) when simplified?
O
O
O
sec(x)
cos(x)
sin(x)
csc(x)
O
cot(x) + 1

Answers

Answer:

Sec(x)

Step-by-step explanation:

Tan(x) = Sin(x)/Cos(x)

Csc(x) = 1/Sin(x)

Sin(x)        1

--------- . ---------

Cos(x)    Sin(x)

Sin(x) cancel

   1

--------- =

Cos(x)

Sec(x)

The simplified expression is,

⇒ sec x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ tan x × csc x

Now,

We can simplify as;

⇒ tan x × csc x

⇒ ( sin x/ cos x ) × (1 / sin x)

⇒ 1 / cos x

⇒ sec x

Thus, The simplified expression is,

⇒ sec x

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Spanky, Alfalfa, and Buckwheat sit down to take a geography test that has 12 multiple-choice questions. Each question has three possible answers, of which only one is correct. Alfalfa, as usual, has been spending too much time daydreaming about Darla and has not properly studied for the exam. After looking it over, he discovers that he knows the answers to just five of the questions. So, he answers those questions correctly and randomly guesses on the remaining seven. Afterward, as Miss Crabtree is grading Alfalfa’s exam, she selects one question at random and finds that he answered it correctly. What is the exact probability that Alfalfa actually knew the answer to this question? Answer this question by completing the following parts:a. Carefully construct a correct tree diagram using the letters K for the event that he knows the answer to a question, N for the event that he doesn’t know the answer to a question, and C for the event that he answers a question correctly. Also, label each edge with its exact probability (as either a fraction or a whole number).b. Use the definition of conditional probability to compute the exact value of P(K|C), writing your answer as a fraction in simplified form.

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Plot the point (3 comma StartFraction 7 pi Over 4 EndFraction )​, given in polar​ coordinates, and find other polar coordinates (r comma theta )of the point for which the following are true. ​(a) r greater than 0 comma negative 2 pi less than or equals theta less than 0 ​(b) r less than 0 comma 0 less than or equals theta less than 2 pi ​(c) r greater than 0 comma 2 pi less than or equals theta less than 4 pi

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Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the step by step solution of the given problem.

The attached file have the solved problem.

Answer: B

Step-by-step explanation:
just did it

1+2x-3x-4 I need it please

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Answer:

Simplified as -3 - x

Step-by-step explanation:

I know, you want to simplify this answer.

So.

1 + 2x - 3x - 4 = 1 - x - 4  =  -3 - x

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