Why is π = 3.14... instead of 6.28...?

A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

B. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

C.  The sampling distribution of p is approximately normal.

D. We find that the probability is 0.0912 or about 9.12%.

E. We get:z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

a. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.

b. The sample proportion, p, is a random variable because it varies from sample to sample. The source of the variability is due to chance or sampling error, which arises from taking a sample instead of surveying the entire population.

c. The sampling distribution of p is approximately normal if the sample size is sufficiently large and if np ≥ 10 and n(1-p) ≥ 10, where n is the sample size and p is the population proportion. In this case, we have:

Sample size (n) = 100

Population proportion (p) = 0.82 Thus, np = 82 and n(1-p) = 18, both of which are greater than 10. Therefore, the sampling distribution of p is approximately normal.

d. To calculate the probability that the proportion who are satisfied with the way things are going in their life exceeds 0.85, we need to find the z-score and then look up the corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.85 - 0.82) / sqrt[0.82(1-0.82)/100] = 1.33

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0912 or about 9.12%.

e. Yes, it would be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfied with the way things are going in their life. To check if it is unusual or not, we need to calculate the z-score and find its corresponding probability from the standard normal distribution table. The formula for the z-score is:

z = (p - P) / sqrt[P(1-P)/n]

where p is the sample proportion, P is the population proportion, and n is the sample size. Substituting the given values, we get:

z = (0.75 - 0.82) / sqrt[0.82(1-0.82)/100] = -2.29

Looking up the corresponding probability from the standard normal distribution table, we find that the probability is 0.0106 or about 1.06%. Since this probability is less than 5%, it would be considered unusual to observe 75 or fewer Americans being satisfied with the way things are going in their life.

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Step-by-step explanation:

or,(-6)=3(3-2x)

or,(-6)=9-6x

or,-6-9=-6x

or,-15=-6x

or,-15+6=x

or,-9=x

x=-9

Answer:

2 1/4

Step-by-step explanation:

Answer:

8.9 lb

Step-by-step explanation:

I divided 47.17 by 5.3

47.17÷5.3= 8.9

then to check my answer I multiplied 8.9 by 5.3 and got 47.17

hope this helps <3

Answer:

8.9 lb

Step-by-step explanation:

took test

The answer to this probability Question is 0.35

What is addition theorem in Probability?

Its a theorem which helps in calculating probability associated with different events at a time

Lets discuss proper solution to it this problem is based on Addition theorem in Probability which is given as

P(AUB) = P(A) + P(B) - P(A∩B)

here P(A) = 0.24

P(B) = 0.13

P(A∩B) = 0.02

we need to find P(AUB) = 0.24 + 0.13 - 0.02

P(AUB) = 0.35

which is required answer

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Answer:

the first option

Step-by-step explanation:

The value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.

To find the value of k, we need to consider the relationship between the area y of the patio and the number of paving stones x used to make the patio.

Since the top surface of each paving stone is a square with side length k feet, the area of each paving stone is \(k^2\) square feet.

Now, let's consider the relationship between the area of the patio and the number of paving stones. We know that there will be no gaps between the paving stones, and they will not overlap. This implies that the area of the patio will be equal to the sum of the areas of all the paving stones used.

Let's assume that each paving stone covers an equal area of the patio. In this case, the area y of the patio will be directly proportional to the number of paving stones x used, and the constant of proportionality is the area of each paving stone, which is \(k^2\).

Therefore, the relationship between y and x can be expressed as \(y = k^2x.\)

From this relationship, we can see that the value of k will depend on the relationship between the units used for area (square feet) and the number of paving stones (unitless).

Since we want the side length k to be in feet, the value of k can be determined by considering the options provided: a) 1, b) 2, c) 3, d) 4.

We can eliminate options a) 1, b) 2, and d) 4 since these values would not result in a meaningful relationship between the area of the patio and the number of paving stones.

Therefore, the value of k must be c) 3, as it satisfies the requirement for the side length of the paving stone in feet, resulting in a meaningful relationship between the area of the patio and the number of paving stones.

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Explanation:

There are 5 choices for the first selection, 4 choices for the second, etc etc until we reach 1 for the last selection. We have the countdown {5,4,3,2,1}. We'll multiply those values together to get our answer.

5*4*3*2*1 = 120

This operation of starting with some integer, counting down and multiplying along the way, is done so very often that it's given a name which is "factorial". The shorthand notation is to use an exclamation mark. So we'd say 5! = 120

Answer:

0.10 of a day or 150/1440 of a day

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Answer:

A) 36

Step-by-step explanation:

So first we calculate the perimeter of the triangles. I can tell right away that it is a 3-4-5 triangle, so add 3+5+3+5=16 (not 4, since that is not on the outside). Then add the perimeter of the long side of the rectangle, so 10+10, then add to 16, so 36.

to divide big decimal b1 by b2 and assign the result to b1, you write the divide method.

To divide a BigDecimal b1 by b2 and update the value of b1 with the result, you can use the divide method provided by the BigDecimal class.

This method takes the divisor as its argument and returns a new BigDecimal object that represents the quotient of the division.

To update the value of b1, you can assign the result of the divide method back to b1. Here's an example:

b1 = b1.divide(b2);

This will divide b1 by b2 and assign the resulting quotient to b1.

Note that the divide method may throw an Arithmetic Exception if the divisor is zero or if the quotient cannot be represented with the current scale and rounding mode of the BigDecimal.

Therefore, you should handle this exception accordingly.

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The domain of the logarithmic function f(x)=log(x) is all real numbers x>0. The range of the logarithmic function is all real numbers y>-∞.

The domain of a logarithmic function f(x)=log(x) is all real numbers x>0. This is because the logarithm function is not defined for x ≤ 0, as log(x) is undefined for x ≤ 0.

The range of the logarithmic function is all real numbers y>-∞. This is because the logarithm of a real number is always negative and approaches negative infinity as x approaches 0. Therefore, the range of a logarithmic function is all real numbers y>-∞.

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There are 15 positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once.The prime numbers are:5, 7, 11, 13Product of two of the prime numbers are:35, 55, 65, 77, 85, 91, 115, 143, 165, 385

Product of three of the prime numbers is:385 Product of all the prime numbers is: 5005There are 15 positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once. Prime numbers are numbers that are only divisible by 1 and itself. 5, 7, 11, and 13 are prime numbers.

The question is asking to find the number of positive integers that can be expressed as a product of two or more of these prime numbers without including the same prime factor more than once. The products of two prime numbers are: 5 x 7 = 35, 5 x 11 = 55, 5 x 13 = 65, 7 x 11 = 77, 7 x 13 = 91, 11 x 13 = 143. There are six of these products. The products of three prime numbers is 5 x 7 x 11 = 385. There is only one of this product. There are fifteen possible positive integers that can be expressed as a product of two or more of the prime numbers 5, 7, 11, and 13 if no one product is to include the same prime factor more than once.

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Answer: The first one

Step-by-step explanation: first you have to subtract 5 from both sides and then you have -6n < 6 . Then you have to divide both sides by -6 then you get n < -1.

Answer:

20°

Step-by-step explanation:

A right triangle equals 90°.

So, you can subtract the angle that you already know.

90°

-50°

-----------

40°

Since the other two angles are congruent you can divide 40° into two parts.

40°

÷2

-----------

20°

So, each unknown measurement of the triangle is 20°.

Answer:

n = 18

Step-by-step explanation:

Corresponding parts of similar triangles are in same ratio

\(\frac{FG}{XY}=\frac{HG}{YZ}\\\\\frac{n}{6}=\frac{15}{5}\\\\n=\frac{15}{5}*6\\\\n=3*6\\\\n=18\)

Answer:

A

Step-by-step explanation:

Concept :-

On converting :-

\(\bf\implies y + 5 =\dfrac{1}{3}(x-9)\\\\\bf\implies y + 5 =\dfrac{1}{3}x - 3 \\\\\bf\implies y = \dfrac{1}{3}x - 3 - 5 \\\\\bf\implies\boxed{\red{y = \dfrac{1}{3}x -8 }}\)

Initial size of the culture = 400 , Doubling period = (35 minutes - 10 minutes) / (1900 - 400) = 0.1437 minutes , Population after 60 minutes = 400 * (2^(60/0.1437)) = 10201 and Population will reach 11000 after approx. 74.51 minutes.

The initial size of the culture can be found by substituting t = 0 into the exponential growth formula:

P(t) = P0 * (2^(t/T))

where P(t) is the population at time t, P0 is the initial population, and T is the doubling period. Substituting t = 0, we get:

400 = P0 * (2^(0/T))

Therefore, P0 = 400.

The doubling period can be found by rearranging the exponential growth formula:

T = (t2 - t1) / (ln(P2) - ln(P1))

where t1 and t2 are the time points, and P1 and P2 are the populations at those time points. Substituting t1 = 10, t2 = 35, P1 = 400, and P2 = 1900, we get:

T = (35 - 10) / (ln(1900) - ln(400)) = 0.1437 minutes

The population after 60 minutes can be found by substituting t = 60 into the exponential growth formula:

P(60) = P0 * (2^(60/T))

Substituting P0 = 400 and T = 0.1437, we get:

P(60) = 400 * (2^(60/0.1437)) = 10201

Finally, the population will reach 11000 after approx. 74.51 minutes can be found by setting P(t) = 11000 in the exponential growth formula and solving for t:

11000 = 400 * (2^(t/0.1437))

t/0.1437 = ln(11000/400)

Therefore, t = 0.1437 * ln(11000/400) ≈ 74.51 minutes

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Answer:

230-300= -70

All you have to do is subtract :)

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As we know, the sum of measures of interior angles of a triangle sum up to 180°

so, according to above question ~

Step-by-step explanation:

Here is your solution.!

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Rectangles' volumes are calculated using the formula length times width times height. The volume of one tennis ball is 372,057.

With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. The opposing sides of a rectangle are equal and parallel. Books, doors, table tops, blackboards, and other everyday objects are a few examples of rectangles. Having four right angles, a rectangle is a quadrilateral. a form having four equal-length sides. Four right angles and two sets of parallel sides make up the form. A rectangle is a four-sided polygon with internal angles that are all exactly 90 degrees. Each corner or vertex is a right angle intersection of the two sides. In contrast to squares, rectangles have equal-length opposite sides.

You may calculate how many tennis balls fit inside a rectangular limousine by dividing its volume by that of a tennis ball, assuming that the vehicle is empty of its wheels, engine, seats, and trunk. Thus, if you divide 1,555,2000 by 4.18, you get 372,057.45, or 372,057 tennis balls. If the limousine has seats or isn't a rectangle, you can calculate the volumes of those objects and deduct them from the rectangle's volume to determine the actual volume of the vehicle. Next, divide by the tennis ball's volume and round down.

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First, I'd find the volume of one tennis ball using the equation for sphere volume, 4/3πr³, where π = 3.14 and r = the radius of the tennis ball. If the tennis ball is 2 inches in diameter, its radius is 1 inch. The equation is (4/3)π(1)³ = 4.18 cubic inches. Next, I find the cubic inches of the limo. The equation for the volume of rectangles is length times width times height. Assuming a limo has a length of 360 inches, height of 60 inches, and width of 72 inches, the volume of the limo is 1,555,2000 inches.

Answer: 35%

Step-by-step explanation:

8 + 5 + 7 = 20

50% = 10

25% = 5

10% = 2

5% = 1

25% + 10% = 5+2

35% = 7