What’s the area of the sector=

you would need to calculate the z-scores and look up the cumulative probabilities using a standard normal distribution table or a calculator to obtain the final probabilities.

To find the probability that a single randomly selected value is between 178.7 and 198.2, we can use the z-score formula and the standard normal distribution.

Step 1: Calculate the z-scores for the given values using the formula:

z = (x(bar) - μ) / σ

For 178.7:

z1 = (178.7 - 208.5) / 94.8

For 198.2:

z2 = (198.2 - 208.5) / 94.8

Step 2: Look up the corresponding cumulative probabilities associated with the z-scores using a standard normal distribution table or a calculator.

Let's assume the cumulative probabilities for the z-scores are P1 and P2, respectively.

Step 3: Calculate the probability using the cumulative probabilities:

P(178.7 < X < 198.2) = P2 - P1

To find the probability that a sample of size n=85 is randomly selected with a mean between 178.7 and 198.2, we need to use the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases.

Since the sample size is large (n=85), we can approximate the distribution of sample means as a normal distribution with the same mean (μ) as the population but with a standard deviation (σ/√n).

Step 4: Calculate the standard deviation of the sample mean (σ/√n):

σ_sample = σ / √n

Step 5: Calculate the z-scores for the sample mean using the formula:

z_sample = (x(bar) - μ) / σ_sample

Here, x(bar) represents the sample mean.

Step 6: Look up the corresponding cumulative probabilities associated with the z-scores using a standard normal distribution table or a calculator.

Let's assume the cumulative probabilities for the z-scores of the sample mean are P_sample1 and P_sample2, respectively.

Step 7: Calculate the probability using the cumulative probabilities:

P(178.7 < ¯x < 198.2) = P_sample2 - P_sample1

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Answer:

incorrect addition

Step-by-step explanation:

graph of the linear function y = 5 is attached below. which is true for all the values of x.

a function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given a linear function y = 5 here

The graph of that linear function will be a straight line that is attached below.

this function will be the same for all the values of x. since it is not dependent on the variable x

it will pass through points (0, 5),  (1, 5),  (-6, 5),  (5, 5),  (-9, 5),.... and so on.

therefore, Below is a graph of the linear function at y = 5. This holds true regardless of x's value.

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Answer:

5/8

Step-by-step explanation:

This means 0.625 as a fraction can be written as 5/8.

Answer: 5/8

Step-by-step explanation:

125 times 5 is 625

125 times 8 is 1000

625/1000 is equivalent to 5/8

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

49

Step-by-step explanation:

Go by PEMDAS. there arent any parentheses so we skip that and move on to exponents. there is 5 squared. 5 squared is 25 which makes the equation now-   1+13x2+25-3  after that we move on to multiplication. 13x2 equals 26 which makes the equation-     1+26+25-3 now we just add and subtract from right to left.

Answer:

8.003 x 10^6

Step-by-step explanation:

The limit is simply 14/9, or approximately 1.56.
\(lim (x -> pi/2) [tan(14x) / tan(9x)]\)

First, we need to apply L'Hopital's rule, which states that if the limit of the ratio of two functions is in the indeterminate form \((0/0 or ∞/∞)\),

then the limit of their derivatives can be considered instead:
\(lim (x -> pi/2) [d(tan(14x))/dx / d(tan(9x))/dx]\)
Now, we can find the derivatives of both the numerator and the denominator:
\(d(tan(14x))/dx = 14 * sec^2(14x)\)
\(d(tan(9x))/dx = 9 * sec^2(9x)\)
Thus, the limit becomes:
\(lim (x -> pi/2) [14 * sec^2(14x) / 9 * sec^2(9x)]\)
We can now cancel the common factor sec^2:
\(lim (x -> pi/2) [14/9]\)
Since 14/9 is a constant

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Answer:

J. 50x < 330 + 30x

Step-by-step explanation:

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

<95141404393>

Step-by-step explanation:

Hope this helped and the answer is correct!

Answer: 18. B(5,-2) 19. C(4,10).

Step-by-step explanation:

18.

\(Let\ the\ midpoint\ of\ \overline {AB}\ is\ F\ and\ coordinates\ of \ B\ is\ (x,y).\\Hence,\\F_x=1\\\displaystyle\\F_x=\frac{A_x+B_x}{2} \\1=\frac{-3+x}{2} \\\)

Multiply both sides of the equation by 2:

\(G_y=2.\\\displaystyle\\2=\frac{12+y}{2}\)

\(4=6+y\\4-6=6-6+y\\-2=y.\\Hence, \ B(5,-2).\)

19.

\(Let\ the\ midpoint\ of\ \overline {CD}\ is\ G\ and\ coordinates\ of \ C\ is\ (x,y).\\Hence,\\G_x=4\\\displaystyle\\G_x=\frac{C_x+D_x}{2} \\4=\frac{x+4}{2} \\\)

Multiply both sides of the equation by 2:

\(8=x+4\\8-4=x+4-4\\4=x.\)

\(G_y=11.\\\displaystyle\\11=\frac{y+12}{2}\)

Multiply both sides of the equation by 2:

\(22=y+12\\22-12=y+12-12\\10=y.\\Hence, \ C(4,10).\)

The probability that there are at least two people with the same birthday in a class of 95 students is about 0.9156 or 91.56%. This is a high probability due to the large number of students in the class.

To calculate the probability of at least two people having the same birthday in a class of 95 students, we can use the formula:
P(at least 2 people have the same birthday) = 1 - P(all 95 students have different birthdays)
The probability that the first student has a unique birthday is 1 (since there are no other students to share a birthday with yet). The probability that the second student has a unique birthday is 364/365 (since there is now one day taken up by the first student's birthday). The probability that the third student has a unique birthday is 363/365, and so on. We can multiply all of these probabilities together to get the probability that all 95 students have different birthdays:
P(all 95 students have different birthdays) = 1 x 364/365 x 363/365 x ... x 272/365
Using a calculator, we can find that this probability is approximately 0.0844.
Therefore, the probability that at least two people have the same birthday is:
P(at least 2 people have the same birthday) = 1 - 0.0844
P(at least 2 people have the same birthday) ≈ 0.9156
So the probability that there are at least two people with the same birthday in a class of 95 students is about 0.9156 or 91.56%. This is a high probability due to the large number of students in the class.

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The equivalence classes of the given equivalence relation are: {1, 4}, {2, 5}, and {3}. To determine the equivalence classes of the equivalence relation given by {(1, 1), (1, 4), (2, 2), (2, 5), (3, 3), (4,1), (4, 4), (5, 2), (5, 5)}, we need to identify all the pairs of elements that are related to each other.

Two elements are related if there is a pair (a, b) in the relation such that a is related to b. In this case, we can see that:

- 1 is related to 1 and 4
- 2 is related to 2 and 5
- 3 is related to 3
- 4 is related to 1 and 4
- 5 is related to 2 and 5

We can use these relationships to group the elements into equivalence classes. An equivalence class is a set of elements that are related to each other. In this case, we have the following equivalence classes:

- {[1, 4]}: This equivalence class contains the elements 1 and 4, which are related to each other.
- {[2, 5]}: This equivalence class contains the elements 2 and 5, which are related to each other.
- {[3]}: This equivalence class contains the element 3, which is related to itself.
- {[1, 4], [2, 5]}: This equivalence class contains the elements 1, 4, 2, and 5, which are all related to each other.
- {[1, 4], [2, 5], [3]}: This equivalence class contains all the elements, since they are all related to each other.

Each equivalence class contains elements that are related to each other, and no element in one equivalence class is related to any element in another equivalence class. These equivalence classes form a partition of the set of elements, since every element is contained in exactly one equivalence class.

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The break-even point, measured in sales dollars, can be calculated by dividing the fixed costs by the contribution margin ratio.

The contribution margin ratio is the difference between the selling price and the variable cost per unit, expressed as a percentage of the selling price. In this case, the contribution margin per unit is calculated as $23 (selling price) - $15 (variable cost) = $8 per unit. The contribution margin ratio is then $8 / $23 = 0.348, or 34.8%.

To find the break-even point in sales dollars, we divide the fixed costs by the contribution margin ratio. In this scenario, the fixed costs are $56,000. Therefore, the break-even point in sales dollars is calculated as $56,000 / 0.348 = $160,920. This means that the company needs to generate sales of $160,920 to cover all its fixed costs and reach the break-even point. Any sales above this amount would result in a profit, while sales below this amount would lead to a loss.

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Answer:

1) 31.41593

2) 26.38938

Step-by-step explanation:

Circumference = 2πr

2 · π · 5 ≈ 31.41593

2 · π · 4.2 ≈ 26.38938

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Answer:

it’s A

Step-by-step explanation:

I graphed it out

Answer:

3

Step-by-step explanation:

here is explain.

2*3+3 = 9

number 3 from the replacement set makes the equation

To find the probability of either event occurring, we can use the formula for the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Given that P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.25, we can substitute these values into the formula.

\(P(A or B) = P(A) + P(B) - P(A and B)\)
\(P(A or B) = 0.6 + 0.5 - 0.25\)
\(P(A or B) = 0.85 - 0.25\)
\(P(A or B) = 0.60\)
The probability of either event occurring is 0.60 or 60%.

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The probability of either event occurring can be found by adding the probabilities of the individual events and subtracting the probability of both events happening together. In this case, the probability of either event A or event B occurring is 0.6.

The probability of either event occurring can be calculated using the principle of addition. To find the probability of either event happening, we need to sum the individual probabilities of the events and subtract the probability of both events happening together.

Given:

p(a) = 0.6 (probability of event A occurring)
p(b) = 0.5 (probability of event B occurring)
p(a and b) = 0.25 (probability of both events happening together)

To calculate the probability of either event occurring, we can use the formula:

p(a or b) = p(a) + p(b) - p(a and b)

Substituting the given values into the formula:

p(a or b) = 0.6 + 0.5 - 0.25

p(a or b) = 0.85 - 0.25

p(a or b) = 0.6

Therefore, the probability of either event A or event B occurring is 0.6.

To understand this concept better, let's consider an example. Suppose event A represents rolling a fair six-sided die and getting an even number (2, 4, or 6). The probability of event A occurring would be 0.5. Now, let event B represent flipping a fair coin and getting heads. The probability of event B occurring would be 0.5.

If we want to find the probability of either rolling an even number or flipping heads, we can use the formula mentioned earlier. The probability of rolling an even number is 0.5, the probability of flipping heads is 0.5, and the probability of both happening together is 0.25. Plugging these values into the formula, we get:

p(A or B) = 0.5 + 0.5 - 0.25

              = 0.75

Therefore, the probability of either rolling an even number or flipping heads is 0.75.

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Variables:

S: number of small candles sold

L: number of large candles sold

The store sold a total of 20 candles then:

S + L = 20

Small candles sell for $10.98 and large candles sell for $27.98, and the store received $355.60, then:

10.98S + 27.98L = 355.60

Isolating s from the first equation:

S = 20 - L

Substituting the last equation into the second one:

10.98(20 - L) + 27.98L = 355.60

10.98*20 - 10.98L + 27.98L = 355.60

219.6 + 17L = 355.60

17L = 355.60 - 219.6

L = 136/17

L = 8

And the value of S is:

S = 20 - 8

S = 12

The store sold 12 small and 8 large candles.

Based on the dimensions of the triangular flower bed, the cost of the border will be $70.

First, you need to find the total length of the triangular flower bed to find out how much thin metal border is needed.

This length is:

= 7 feet + 6 feet + 9 feet

= 22 feet

Then convert these to yards because the cost of the thin metal border wall is in yards. Every yard is about 3 feet so 3 feet is 1/3 yeards.

If you have 22 feet therefore, the number of yards is:
= 22 x 1/3

= 22 / 3

= 7.33 yards

Only whole numbers of yards can be bought so we round this up to 8 yards.

The cost of the border would be:

= Number of yards x Cost per yard

= 8 x 8.75

=  $70

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Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

You turn the fractions improper, 9/2 x 8/3. Multiply the top numbers and then multiply the bottom. Simplify to get 12.

Answer:

4 days

Step-by-step explanation:

first, figure out how many cars are produced in a day. since there are 7 days in a week, and 1400 cars are produced in a week, divide 1400 by 7. 1400/7 equals 200. so, if 200 cars produced each day, then:

200x= 800 (x = days)

200x/200 = 800/200

So, 4 days.

The mean of the sample is affected by the outlier. The mean is non-resistant. That means, it's affected by outliers.

More specifically, the mean will want to move towards the outlier.

Say we have some information

1\s,2 \s, \s3 \s. This has a mean of 2 in it. However, if we include a 94-point outlier in the data set, the mean will change to 25. The mean shifted toward the outlier, as you can see.

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

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The maximum probability of Type I error that can be tolerated is referred to as the level of significance.

What is Type I error? Type I error is the probability of rejecting a true null hypothesis. A type I error occurs when an experimenter rejects a null hypothesis that is actually true. This happens because of the chance that a sampling error can produce results that seem to reject a null hypothesis but are not statistically significant. Type I error is sometimes known as the error of alpha or alpha error. It is a measure of the likelihood of falsely rejecting a null hypothesis. This error is often referred to as a false positive. The probability of making a type I error is represented by α. Alpha is generally set at 0.05 or 0.01.

This implies that there is a 5 percent or 1 percent probability of rejecting the null hypothesis when it is actually true. The maximum probability of type I error that can be tolerated is referred to as the level of significance. The level of significance is usually set at 0.05 or 0.01. It represents the likelihood of incorrectly rejecting the null hypothesis.

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The square root of 4761 is equal to 21√(7).

To find the square root of 4761, we can use a method called prime factorization to simplify the number and then extract the square root of its factors. Here's how we can do it:

First, we need to find the prime factors of 4761. We can do this by dividing the number by the smallest prime factors and working our way up. We find that 4761 is divisible by 3, so we can start with that:

4761 ÷ 3 = 1587

Next, we can see that 1587 is not divisible by 3, but it is divisible by 7:

1587 ÷ 7 = 227

We can stop here because 227 is a prime number. Therefore, we can express 4761 as the product of its prime factors:

4761 = 3 × 3 × 7 × 7 × 7

Now, we can simplify the square root of 4761 by breaking it down into the square roots of its factors:

√(4761) = √(3 × 3 × 7 × 7 × 7)

We can group the factors into pairs of identical numbers, as follows:

√(3 × 3 × 7 × 7 × 7) = √(3 × 3) × √(7 × 7) × √(7)

We can simplify the square roots of the pairs:

√(3 × 3) × √(7 × 7) × √(7) = 3 × 7 × √(7)

Therefore, the square root of 4761 is equal to 21√(7). This is the exact, simplified form of the square root of 4761.

Note that if we want an approximate decimal value for the square root of 4761, we can use a calculator or estimation methods to get an answer of about 69.062.

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Using the normal distribution, we have that the desired information is given as follows:

a) X ~ N(3,1.8).

b) 3 days.

c) Z = 0.5556.

d) 0.33 = 33%.

e) 0.2048 = 20.48%.

f) 5.3 days.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given, respectively, by:

\(\mu = 3, \sigma = 1.8\)

Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.

The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:

Z = (4 - 3)/1.8 = 0.5556.

The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:

Z = (3.8 - 3)/1.8 = 0.44.

Z = 0.44 has a p-value of 0.67.

1 - 0.67 = 0.33.

The probability is of 0.33 = 33%.

The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:

X = 4.2:

Z = (4.2 - 3)/1.8

Z = 0.67.

Z = 0.67 has a p-value of 0.7486.

X = 3.2:

Z = (3.2 - 3)/1.8

Z = 0.11.

Z = 0.11 has a p-value of 0.5438.

0.7486 - 0.5438 = 0.2048 = 20.48%.

The 90th percentile is X when Z = 1.28, hence:

1.28 = (X - 3)/1.8

X - 3 = 1.8 x 1.28

X = 5.3 days.

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If the can's combined lips measure 38 inches and the adhesive overlaps by around 12 inches, the label's surface area will be 50 square inches.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

Given data;

Height of can,\(\rm H=5 \frac{3}{8} \ inch\)

Height of label,

\(\rm h=5\frac{3}{8} -\frac{3}{8} \\\\ h= 5 \ inch\)

Diameter,\(\rm d= 3 \ inch\)

The area of the label is;

A = ( overlap area  + circumfereence ) h

\(\rm A = [\frac{1}{2} + 2 \pi \times \frac{3}{2} ] \\\\ A =[ \frac{1+6\pi}{2} ] \times 5 \\\\ A = 49.6 \ inch^2\)

Hence, the label's surface area will be 50 square inches.

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Step-by-step explanation:

According to the Alternate Exterior Angles Theorem, when a transversal cuts two parallel lines, the alternate exterior angles are congruent.

In this scenario, angle ZCXP is an alternate exterior angle with respect to angles ZRYD and ZSYD. Since angle ZRYD is congruent to angle ZSYD, angle ZCXP is also congruent to angle ZRYD.

Therefore, the correct answer is A. ZRYD.

The given function f(x) = x² - 8x can be rewritten in vertex form using the process of completing the square. The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The process of completing the square involves adding and subtracting a constant term to the expression in such a way that it becomes a perfect square trinomial.

So, f(x) = x² - 8x = (x² - 8x + 16) - 16 = (x - 4)² - 16. Therefore, the function f(x) = x² - 8x is equivalent to f(x) = (x - 4)² - 16 in vertex form. Now, we need to check which function in vertex form is equivalent to f(x) = x² - 8x from the given options:Option A: f(x) = (x - 8)² - 56Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = 8, which is not equal to -4. So, this function is not equivalent to f(x) = x² - 8x.

Option B: f(x) = (x - 4)² + 0Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = 4, which is equal to -(-4). So, this function is equivalent to f(x) = x² - 8x.Option C: f(x) = (x + 8)² - 72Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = -8, which is not equal to -4. So, this function is not equivalent to f(x) = x² - 8x.Option D: f(x) = (x + 4)² - 32Comparing it with the vertex form f(x) = a(x - h)² + k, we can see that h = -4, which is equal to -(-4). So, this function is equivalent to f(x) = x² - 8x.Therefore, the function in vertex form equivalent to f(x) = x² - 8x is f(x) = (x - 4)² - 16.

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