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Answer: 151

Step-by-step

you need to first find the area of each piece of the tent

the 2 rectangular flaps would be 6*8= 48 each

the bottom would be 4*8=32

to find the area of the triangular pieces we need to know the height of each triangle, right now we only know sides. To find the height (the altitude) you draw a line straight down to make a 90 degree angle.

that will also cut your base in half (2 instead of 4) and make 6 your hypotenuse

now use the Pythagorean theorem to find the height of the triangle

Area of a triangle is

the area of one triangle is 11.31

so together it is 48+48+32+11.31+11.31= 150.6

round up to 151

=Answer:

Step-by-step explanation:

f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21

Final answer:

Using the chi-square distribution and given data, a 93% confidence interval for the standard deviation is found to be (0.525, 1.095). Therefore, the correct answer is option (c).

Explanation:

To construct a confidence interval to estimate the true standard deviation of the filling process for the boxes of cereal, we will use the chi-square distribution as it is used when dealing with standard deviation and variance.

The formula for the confidence interval in this case is: (sqrt((n-1)*s^2/chi2(upper)), sqrt((n-1)*s^2/chi2(lower))), where n is the sample size, s is the sample standard deviation and chi2 is the chi-square value for the corresponding degrees of freedom and confidence level.

In this case, we have n=31, s=0.81. The degrees of freedom are one less than the sample size, so df = 31 - 1 = 30. For a 93% confidence level, the chi-square values are X2(0.035, 30) = 21.92 and X2(0.965, 30) = 41.34.

Substituting these values into the formula, we get: (sqrt((31-1)*(0.81)^2/41.34), sqrt((31-1)*(0.81)^2/21.92)) = (0.525, 1.095). Hence, the correct answer is (c) (0.525, 1.095).

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Final answer:

The 93% confidence interval for the standard deviation of the filling process for the boxes of cereal is (0.658,1.058), which is choice (b). The solution is determined using chi-square distribution and the formula for constructing a confidence interval specifically for standard deviations.

Explanation:

To answer this question, we will use chi-square distribution which is commonly used to construct a confidence interval for standard deviations.

The formula for a confidence interval in this case is ( √((n-1)s² / χ²_(1 - α/2)), √((n-1)s² / χ²_(α/2)) ). Here, n is the sample size, s is the sample standard deviation, α is the significance level (1 - confidence level). χ² represents chi-square values, where α/2 and 1 - α/2 are the confidence levels for a two-tailed test.

Using the chi-square table, for n - 1 = 30 degrees of freedom, we find the chi-square value for (1 - α/2)=0.935 is 17.708 and the chi-square value for α/2=0.065 is 46.194. Substituting n = 31, s = 0.81 into the formula, we get the 93% confidence interval for the standard deviation of the filling process for the boxes of cereal as ( √((30*0.81²) / 46.194), √((30*0.81²) / 17.708) ) = (0.658, 1.058).

So, the correct answer is (b) (0.658,1.058).

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Answer:

The probability is 0.02275

Step-by-step explanation:

We shall first find the z-score here

z-score = (x -mean)/SD

from the question;

x = 4,000

mean = 3,000

SD = 500

z-score = (4,000-3,000)/500 = 1000/500 = 2

So the probability we want to calculate is;

P(z > 2) = 0.02275

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please refer to the attached figure.

So, we can see that our angle θ is in QII.

Recall All Students Take Calculus. Since this is QII, we use the Students. In other words, only sine (and cosecant) is positive. So, cosine and tangent are negative.

Now, we also know that a point is (-4,5). Referring to our figure, this means that our adjacent side is 4 (technically -4, but we can ignore this) and our opposite side is 5. So, to find the other ratios, let's find the hypotenuse.

Use the Pythagorean Theorem:

Substitute 4 for a and b for 5. Solve for c. So:

Square:

Add:

Take the square root:

So, our side lengths are: Opposite=5; Adjacent=4; and Hypotenuse=√41.

Now, we can find our side lengths.

Sine and Cosecant:

Substitute 5 for Opp and √41 for Hyp. So:

Rationalize:

Since our angle is in QII, sine stays positive.

Cosecant is the reciprocal of sine. So:

Cosine and Secant:

Substitute 4 for Adj and √41 for Hyp:

Rationalize:

Since our angle is in QII, cosine is negative. So:

Secant is the reciprocal of cosine. So:

Tangent and Cotangent:

Substitute 5 for Opp and 4 for Adj. So:

Since our angle is in QII, tangent is negative. So:

Cotangent is the reciprocal of tangent:

And we are finished!

Final answer:

Using the given point (-4,5) in standard position, first calculate the radius using the Pythagorean theorem. Then, calculate each of the six trigonometric functions using the coordinates and the calculated radius.

Explanation:

The given point is (-4,5). In the standard position, the x-coordinate represents the cosine of the angle, while the y-coordinate represents the sin of the angle. However, we need to find the radius (r), which can be found using Pythagorean theorem:

r = sqrt(x

2

+ y

2

)

meaning, r = sqrt((-4)

2

+ 5

2

) = sqrt(41).  

Now, each of the six trigonometric functions can be calculated as follows:

• Sine (Sin θ = y/r): Sin θ = 5/sqrt(41),
• Cosine (Cos θ = x/r): Cos θ = -4/sqrt(41),
• Tangent (Tan θ = y/x): Tan θ = -5/4,
• Cosecant (Csc θ = r/y): Csc θ = sqrt(41)/5,
• Secant (Sec θ = r/x): Sec θ = -sqrt(41)/4,
• Cotangent (Cot θ = x/y): Cot θ = 4/5.

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