what is the measures in degrees and radians of the angle representing 7-8th of a circle

The [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is 3.2498.

To find the [tex]\( t \)[/tex]-value for a 99% confidence interval estimation based on a sample size of 10, we need to use the [tex]\( t \)[/tex]-distribution table or a calculator. The [tex]\( t \)[/tex]-distribution is used when the sample size is small (typically [tex]\( n < 30 \)[/tex]) and the population standard deviation is unknown.

Given:

- Confidence level: 99%

- Sample size [tex](\( n \)): 10[/tex]

The degrees of freedom [tex](\( df \))[/tex] are calculated as:

[tex]\[ df = n - 1 = 10 - 1 = 9 \][/tex]

To find the critical [tex]\( t \)[/tex]-value for a 99% confidence interval with 9 degrees of freedom, we look for the [tex]\( t \)[/tex]-value that corresponds to the area in the tails of the distribution. For a 99% confidence interval, the area in each tail is:

[tex]\[ \frac{1 - 0.99}{2} = 0.005 \][/tex]

So we need the [tex]\( t \)[/tex]-value such that 0.5% of the distribution is in each tail.

Using a [tex]\( t \)[/tex]-distribution table or a calculator, we find the [tex]\( t \)[/tex]-value for 9 degrees of freedom and a 99% confidence interval (or 0.5% in each tail).

The [tex]\( t \)[/tex]-value for 9 degrees of freedom at the 99% confidence level is approximately:

[tex]\[ t_{0.005, 9} \approx 3.2498 \][/tex]

Thus, the [tex]\( t \)[/tex]-value for a 99% confidence interval based on a sample size of 10 is approximately 3.2498.

The volume of a shape is the amount of space in it.

The volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]

The dimensions of the rectangular prism are:

[tex]\mathbf{l = 5a}[/tex]

[tex]\mathbf{w = 2a}[/tex]

[tex]\mathbf{h = (a^3 - 3a^2 + a)}[/tex]

The volume (v) of the rectangular prism is:

[tex]\mathbf{v = l\cdot w \cdot h}[/tex]

So, we have:

[tex]\mathbf{v = 5a \cdot 2a \cdot (a^3 -3a^2 + a)}[/tex]

[tex]\mathbf{v = 10a^2 \cdot (a^3 -3a^2 + a)}[/tex]

Expand

[tex]\mathbf{v = 10a^5 -30a^4 + 10a^3}[/tex]

Hence, the volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]

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volume of the ball = 4/3 * PI *r^3 =

4/3 * 3.14 * 2.86^3 = 97.99 cubic inches

 this is less than the volume of the box, so yes it will fit

Answer: 12

The value of y= 12.

Step-by-step explanation:

We know that the diagonal of rhombus are perpendicular bisector of each other.

i.e. the angle made at the intersection of diagonal is 90 degrees.

Thus , for the given figure m∠1 = 90°

Since it is given that  m∠1 = 8y-6

Thus , 8y-6= 90

⇒8y=96   [Adding 6 both sides]

⇒ y = 12  [Dividing both sides by 8]

Hence, the value of y= 12.

The student worked for 5 hours and 45 minutes before taking a lunch break, calculated by finding the difference between the clock-in time of 6:45 a.m. and the lunchtime of 12:30 p.m.

The student worked for a certain number of hours before taking a lunch break. To calculate the duration of work before lunch, we subtract the start time from the end time. The student clocks in at 6:45 a.m. and clocks out at 12:30 p.m. for lunch.

First, we convert the time worked to a 24-hour format: 6:45 a.m. remains the same but 12:30 p.m. is 12:30 in 24-hour time. Now, we calculate the time difference:

Adding up the hours and minutes, we get a total of 5 hours and 45 minutes worked before lunch.

since you have the 75, we know that a would equal 105 for line g , since a line = 180 degrees

 so to make line f parallel with g it needs the same angles with line n as line g has

so if a = 105, then angle d would also need to be 105

 The answer is D

The percentage of the class that voted for kayaking is 50%.

Given data:

To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.

Hiking got 17% of the vote.

Fishing got 33% of the vote.

Let x be the percentage of the class that voted for kayaking.

Since the total percentage of votes is 100%:

17% + 33% + x = 100%

On solving for x:

x = 100% - (17% + 33%)

x = 100% - 50%

x = 50%

Hence, 50% of the class voted for kayaking.

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Answer:

The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

Step-by-step explanation:

Given information: The line passes through the point (4,3) and (2,2).

If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The line passes through the point (4,3) and (2,2), so the equation of line is

[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]

[tex]y-3=\frac{-1}{-2}(x-4)[/tex]

[tex]y-3=\frac{1}{2}(x-4)[/tex]

Using distributive property, we get

[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]

[tex]y-3=\frac{1}{2}(x)-2[/tex]

Add 3 on both sides.

[tex]y=\frac{1}{2}(x)-2+3[/tex]

[tex]y=\frac{1}{2}(x)+1[/tex]

Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].

1 foot = 12 inches

12.8 x 12 = 153.6 inches each side

Answer: For 0 ≤Ф≥ 2π (where π= 180°)

∴ Ф = 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, 337.5°

Step-by-step explanation:

sin(3Ф)cos(Ф) - cos(3Ф)sin(Ф) = √2/2

sin(3Ф - Ф) =√2/2

3Ф -Ф = sin∧-1{√2/2}

 2Ф = 45°

∴ Ф = 22.5°

Answer:

x + 1 = 4x + 5

Step-by-step explanation:

To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".

To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Given the probabilities of the different types of soil and the accuracy of the test in each soil type, we can calculate the probability using the law of total probability and Bayes' rule.

To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Bayes' rule states that P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) is the probability of event A happening given that event B has occurred, P(B|A) is the probability of event B happening given that event A has occurred, P(A) is the probability of event A happening, and P(B) is the probability of event B happening. In this case, event A is that the soil is clay and event B is that the test result is positive.

Given that the soil is clay, the test gives a positive result with 48% accuracy. Therefore, P(B|A) = 0.48. The probability of the soil being clay is P(A) = 0.21. To find P(B), we need to consider the probabilities of the test result being positive in each type of soil.

If the soil is rock, the test gives a positive result with 35% accuracy, so the probability of the test result being positive in rock soil is P(B|rock) = 0.35. Similarly, if the soil is sand, the test gives a positive result with 75% accuracy, so the probability of the test result being positive in sand soil is P(B|sand) = 0.75. We can calculate P(B) using the law of total probability: P(B) = P(B|rock) * P(rock) + P(B|clay) * P(clay) + P(B|sand) * P(sand).

Plugging in the given values, we have P(B) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26. Now we can substitute the values into Bayes' rule:

P(clay | positive) = (P(positive | clay) * P(clay)) / P(positive) = (0.48 * 0.21) / P(B).

So the probability that the soil is clay given a positive test result is (0.48 * 0.21) / P(B).

The provided differential equation is a first-order linear differential equation, which can be solved using an integrating factor. After solving, the particular solution satisfying the initial condition y(0)=7 is y=e^(-sin(x))(5sin(x)+7).

The differential equation provided is a first-order linear differential equation, which can be solved using an integrating factor. In this case, dy/dx + ycos(x) = 5cos(x), the integrating factor is e^(∫ cos(x) dx) = e^sin(x). Multiplying everything by the integrating factor, we get (ye^sinx)' = 5cos(x)e^sin(x).

Then we can integrate on both sides to get ye^sin(x) = 5sin(x) + C, where C is the constant of integration. To find the particular solution, we can use the initial condition y(0)=7. By substituting these values, we can solve for C. Substituting x=0 and y=7 yields C=7. Thus, the particular solution is y=e^(-sin(x))(5sin(x)+7).

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Answer:

B.

Step-by-step explanation:

The one-way ANOVA or one – way analysis of variance is used to know whether there are statistically substantial dissimilarities among the averages of three or more independent sets. It compares the means between the sets that is being examined whether any of those means are statistically pointedly dissimilar from each other. If it does have a significant result, then the alternative hypothesis can be accepted and that would mean that two sets are pointedly different from each other. The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign.

Answer:

Probability of tails = 0.51

Step-by-step explanation:

Probability is the ratio of number of favorable outcome to the total number of outcomes.

Total number of outcomes = Total number of heads + Total number of tails

                                              = 165 + 172 = 337

Number of favorable outcome = Total number of tails = 172

[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]