Answer:
We conclude that the null hypothesis is rejected which means the proportion of men with elevated cholesterol levels is greater than the proportion of women.
Step-by-step explanation:
We are given that an article in the Archives of Internal Medicine reported that in a sample of 244 men, 73 had elevated total cholesterol levels.
In a sample of 232 women, 44 had elevated cholesterol levels.
Let [tex]p_M[/tex] = population proportion of men with elevated cholesterol levels.
[tex]p_W[/tex] = population proportion of women with elevated cholesterol levels.
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]p_M \leq p_W[/tex] {means that the proportion of men with elevated cholesterol levels is smaller than or equal to the proportion of women}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_M > p_W[/tex] {means that the proportion of men with elevated cholesterol levels is greater than the proportion of women}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = [tex]\frac{(\hat p_M-\hat p_W)-(p_M-p_W)}{\sqrt{\frac{\hat p_M(1-\hat p_M)}{n_M} +\frac{\hat p_W(1-\hat p_W)}{n_W}} }[/tex] ~ N(0,1)
where, [tex]\hat p_M[/tex] = sample proportion of men with elevated cholesterol levels = [tex]\frac{73}{244}[/tex] = 0.299
[tex]\hat p_W[/tex] = sample proportion of women with elevated cholesterol levels = [tex]\frac{44}{232}[/tex] = 0.189
[tex]n_M[/tex] = sample of men = 244
[tex]n_W[/tex] = sample of women = 232
(b) The difference in sample proportions between groups is given by = [tex]\hat p_M-\hat p_W[/tex] = 0.299 - 0.189 = 0.11
(c) So, the test statistics = [tex]\frac{(0.299-0.189)-(0)}{\sqrt{\frac{0.299(1-0.299)}{244} +\frac{0.189(1-0.189)}{232}} }[/tex]
= 2.82
The value of z test statistics is 2.82.
Now, the P-value of the test statistics is given by;
P-value = P(Z > 2.82) = 1 - P(Z < 2.82)
= 1 - 0.9976 = 0.0024
(d) If there is difference between the proportions of high cholesterol, then there is a 95% chance that there is a 11% percentage point difference between the high cholesterol rates.
(e) Since, in the question we are not given with the level of significance so we assume it to be 5%.
As the P-value of the test statistics is less than the level of significance as 0.0024 < 0.05, 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 the proportion of men with elevated cholesterol levels is greater than the proportion of women.
Final answer:
To test if the proportion of men with high cholesterol is greater than the proportion of women, we need to define hypotheses, calculate the difference in sample proportions, determine the P-value, interpret the P-value, and make a decision about the null hypothesis.
Explanation:
(a) The hypotheses for the test are:
H0: M ≤ W
Ha: M > W
(b) To calculate the difference in sample proportions between groups, subtract the proportion of women with elevated cholesterol levels from the proportion of men with elevated cholesterol levels:
Difference = M - W = 73/244 - 44/232
(c) To calculate the P-value using the 2PropZTest, you need the sample proportions, sample sizes, and the alternative hypothesis. The P-value would provide the probability of observing a difference as extreme as the one calculated, assuming the null hypothesis is true.
(d) The P-value represents the probability of observing a difference as extreme as the one calculated, assuming the null hypothesis is true. Therefore, if there is a low P-value, it indicates that there is strong evidence to reject the null hypothesis and conclude that the proportions of high cholesterol are different between men and women, with a certain percentage point difference between the rates.
(e) The decision about the null hypothesis would be based on the P-value. If the P-value is less than the level of significance (alpha), which is not provided in the question, we would reject the null hypothesis. However, the given solution does not provide the P-value or the level of significance, so a specific decision cannot be determined.
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
Answer:
81.25
Step-by-step explanation:
45.55 + 35.7
Answer:I hope that helps
Step-by-step explanation:
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.
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 appointedP(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+2x-3x-4 I need it please
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
What percent is 7 out of 40?
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
Hope this helps! Please mark brainliest :)
Wich shapes can the the shaded area be divided into to find the area
Answer:
A. a rectangle and a triangle
Answer:
a) rectangle and triangle, then add both to fin the total area.
Step-by-step explanation:
10 percent of what number is 350
Answer:
3500
Step-by-step explanation:
multiply 10*350
UPOOD
The area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square,
If the side length of a square is 4 inches, its area is
16.6 square inches and its perimeter is
074 Inches.
Reset
Next
Answer:
If the side length of a square is 4 inches, it's Area is 16 inches, and Perimeter is 16 inches.
Step-by-step explanation:
Given that the Area = s²
Perimeter = 4s
Side length of the square = s
If the length of a square is 4 inches, then applying the above formulas, we have
s = 4 inches
Area = 4² = 16 inches
Perimeter = 4s = 4×4 = 16 inches
Final answer:
The area of a square with a side length of 4 inches is 16 square inches and its perimeter is 16 inches. Doubling the side length to 8 inches yields an area that is four times greater, 64 square inches, due to the squared relationship between side length and area.
Explanation:
Understanding Square Area and Perimeter
A student has posed a question about the properties of squares. We are given that the side length of a square is 4 inches. From this, we can calculate the square's area and perimeter. The area of a square is found by squaring the length of its side (s2), which in this case would be 4 inches × 4 inches = 16 square inches. The perimeter is the length around the square, calculated by multiplying the side's length by 4, yielding 4 inches × 4 = 16 inches.
By understanding the formulas for area (s2) and perimeter (4s), students can solve many geometrical problems related to squares. For instance, if the dimensions of a square are to be doubled, the new side length would be 4 inches × 2 = 8 inches, resulting in an area of 8 inches × 8 inches = 64 square inches, which is four times the original area, demonstrating that the area scales with the square of the linear dimensions.
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?
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.
How do I write the exponent expression below in numbers
Three to the sixth power all divided by two
Answer:
(3^6)/2
Step-by-step explanation:
make sure everything as the numerator is in parenthesis
Rachel bought two coloring books.
One had 134 pictures and the other
had 309. After one week she had
already colored 145 of the pictures,
How many pictures does she still have
to color?
Answer:
298 pictures
Step-by-step explanation:
One coloring book has 134 pictures, and other one has 309 pictures. The total will be addition:
134 + 309 = 443 pictures
Rachel colored 145 of them all, so subtract 145 from 443:
443 - 145 = 298
She still has 298 pictures left.
Answer:
298
Step-by-step explanation:
Total pictures:
134 + 309
443
Already coloured: 145
To be coloured: 443 - 145
= 298
87 1/3% into a fraction
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 = 17433/10000Thus, 87 1/3% is approximately 17433/10000 when expressed as a fraction.
How can you isolate the variable x-3=7
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:
Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $70,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $2900 per performance, and your jazz ensemble is charging $800 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.) C(x, y)
Answer:
The monthly cost function for the scenario C(x,y) is;
C(x,y) = 70,000 + 2900x + 800y
Step-by-step explanation:
Let C represent the monthly cost in dollars.
x represent the number of performances by the cabaret artist per month
and y represent the number of hours of jazz per month
Given;
monthly costs of $70,000
regular cabaret artist is charging you $2900 per performance.
Per month = $2900x
your jazz ensemble is charging $800 per hour.
Per month = $800y
The monthly cost function for the scenario C(x,y) is the sum of all the costs;
C(x,y) = 70,000 + 2900x + 800y
If f(x) = 2x – 1 and g(x) = 3x + 5, then (f o g)(x) is equal to
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
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
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
If the area of a circle is 121 pi square units, what is its diameter
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
(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?
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
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
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 durationHow to solve the problem?GivenStart 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
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
If f[6} = x ^ -2x , find: f [6} =
Answer:
1/ 6^12
Step-by-step explanation:
f[x} = x ^ (-2x)
f(6) = 6 ^ (-2*6)
= 6 ^ -12
We know the negative exponent moves it to the denominator
= 1/ 6^12
What function do you use to find the angle of a vector, when you know its components?
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]
382
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x-3)2 + (y – 5)2 = 6
(x - 3)2 + (x - 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
(x+3)^2 + (y+5)^2 = 36
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--3)^2 + (y--5)^2 = 6^2
(x+3)^2 + (y+5)^2 = 36
What is the domain of the function Y equals cube root x
Final answer:
The domain of the function y = x^(1/3) (cube root of x) is all real numbers, which is expressed as (-∞, +∞).
Explanation:
The domain of a function describes all the possible values of 'x' for which the function is defined. In the case of the function y = cubic root of x, which is written as y = x^(1/3), the function is defined for all real numbers because you can take the cubic root of any real number, negative, positive, or zero. Hence, the domain of the function y = x^(1/3) is all real numbers, which mathematically is expressed as (-∞, +∞). This is different from the function y = x^2, where the domain must often be restricted to nonnegative numbers to have a well-defined real inverse function.
Which expression is the result of
10x2 + 50x = ?
Step-by-step explanation:
10x2 + 50x
10x ( x +5)
Is the result
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
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
What is the value of this expression when a=3 and b=-1?
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!
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?
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 metersSince 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 metersTherefore, the total distance walked back and forth on the Red Trail, in meters, is 14,600 meters.
"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."
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.
the height of the two triangular faces is 5.2 centimeters. the surface area of the triangular prism is ____ square centimeters.
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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Solve: tan(x)-cos^2(x)=sin^2(x)
Answer:
x = 45 degrees +180 n where n is an integer
Step-by-step explanation:
tan(x)-cos^2(x)=sin^2(x)
Add cos^2(x) to each side
tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)
tan(x)=sin^2(x)+ cos^2(x)
We know that sin^2(x)+ cos^2(x) = 1
tan (x) =1
Take the inverse tan of each side
tan ^-1 ( tan x) = tan ^-1 (1)
x = 45 degrees +180 n where n is an integer
Answer:
Pi/4+kpi
Step-by-step explanation:
X= 45 degrees and on unit circle that is pi/4