Are You Satisfied? According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82.

a. Suppose a random sample of 100 Americans is asked, "Are you satisfied with the way things are going in your life?" Is the response to this question qualitative or quantitative? Explain.

b. Explain why the sample proportion, p, is a random variable. What is the source of the variability?

c. Describe the sampling distribution of p, the proportion of Americans who are satisfied with the way things are going in their life. Be sure to verify the model requirements.

d. In the sample obtained in part (a), what is the probability the proportion who are satisfied with the way things are going in their life exceeds 0.85?

e. Would it 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? Why?

The central angles for the categories with the numbers 40, 100, 50, and 50 are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

To calculate the central angles for each category based on the given numbers 40, 100, 50, and 50, we need to find the proportion of each value to the total sum of all the values. Let's proceed with the following steps:

Step 1: Calculate the total sum of the given numbers: 40 + 100 + 50 + 50 = 240.

Step 2: Find the proportion of each value by dividing it by the total sum and multiplying it by 360 (since a full circle has 360 degrees).

Central angle for the first category: (40/240) * 360 = 60 degrees.

Central angle for the second category: (100/240) * 360 = 150 degrees.

Central angle for the third category: (50/240) * 360 = 75 degrees.

Central angle for the fourth category: (50/240) * 360 = 75 degrees.

The central angles for each category based on the given numbers are 60 degrees, 150 degrees, 75 degrees, and 75 degrees, respectively.

These central angles represent the relative proportions of each category's spending in relation to the total spending. They can be used to create a pie chart or visualize the distribution of expenses in a circular graph.

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Note the search engine cannot find the complete question

Answer:

The common ratio of this geometric sequence is -1/2, so we have

a(7) = 16 × -1/2 = -8, a(8) = -8 × -1/2 = 4.

Dividing by -1/2 is the same as multiplying by -2. Working backwards, we have:

a(5) = -2 × 16 = -32

a(4) = -2 × -32 = 64

a(3) = -2 × 64 = -128

a(2) = -2 × -128 = 256

a(1) = -2 × 256 = -512

Answer:

a)  The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

b)  P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

c) P ( z = 0 ) = 0.6

  P ( z = 1 ) = 0.4

Step-by-step explanation:

Number of head on first toss = Z

Total Number of heads on 2 tosses = W

% of head occurring = 40%

% of tail occurring = 60%

P ( head ) = 2/5 ,    P( tail ) = 3/5

a) Determine the joint probability distribution of W and Z

P( W =0 |Z = 0 ) = 0.6         P( W = 0 | Z = 1 ) = 0

P( W = 1 | Z = 0 ) = 0.4        P( W = 1 | Z = 1 ) = 0.6

P( W = 1 | Z = 0 ) = 0           P( W = 2 | Z = 1 ) = 0.4

The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

B) Marginal distribution of W

P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

C) Marginal distribution of Z ( pmf of Z )

P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

Part(a): The required joint probability of W and Z is ,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

Part(b): The pmf (marginal distribution) of W is,

\(P(w=0)=0.36,P(w=1)=0.48,P(w=2)=0.16\)

Part(c): The pmf (marginal distribution) of Z is,

\(P(z=0)=0.6,P(z=1)=0.4\)

Part(a):

The joint distribution is,

\(P(w=0\z=0)=0.6,P(w=1|z=0)=0.4,P(w=2|z=0)=0\)

Also,

\(P(w=0\z=1)=0,P(w=1|z=1)=0.6,P(w=2|z=1)=0.4\)

Therefore,

\(P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16\)

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The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.

This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.

For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.

This question is using the percentage decrease theory. According to this theory,

you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.

Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).

Original - Current = Change

120,000 - 3200 = 116,800

Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)

Change / Original = Percentage Change

116,800 / 120,000 = 97%

Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)

Percentage Change x Original = Estimated Original

97% x 120,000 = 116,400

Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.

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F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

42

Step-by-step explanation:

Since Gabrielle is 7 years older than Mikhail, we subtract 7 from 91. Then we divide it by 2. So 84/2=42. Since Gabrielle is 7 years older we add 7 to 42. She is 49 and Mikhail is 42 years old. To double check our answer we should add both of the ages we got to make sure they add up to 91, so 42+49 is 91.

Answer:

Geometric mean = 6.71

Arithmetic mean = 9

Step-by-step explanation:

\(geometric \: mean \\ = \sqrt{3 \times 15} \\ = \sqrt{45} \\ = 6.70820393 \\ = 6.71 \\ \\ arithmetic \: mean \\ \\ = \frac{3 + 15}{2} \\ \\ = \frac{18}{2} \\ \\ = 9\)

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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To solve for X

X + 90 + 75 = 180° (Sum of interior angle of a triangle)

X + 165 = 180°

Subtract 165 from both-side of the equation

X = 180° - 165°

X = 15°

To solve for x

opposite =50

Adjacent = x

θ=75

Using the trigonometric ratio;

SOH CAH TOA

To solve for w,

opposite = 50

hypotenuse= w

θ=75

Hence, we will use sine.

Cross-multiply

Divide both-side by sin75

Answer:

$539.52

Step-by-step explanation:

I added 160 and 379.52

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The lines for the given statements can be plotted as shown below.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The lines for the given statements can be plotted as shown below.

The coordinate grid can be filled as,

1)

x        0         3         1

y        3         0         2

2.)

x        0         1         -1

y         1         0          2

3.)

x         0         4         -1

y         -2         0          2

4.)

x         0         1           1

y         -2         0         -2

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Answer:

(B) {6,6,7}

Step-by-step explanation:

A criterion to determine if each triplet represents a triangle is the Law of Cosine, which states that:

\(a^{2} = b^{2}+c^{2}-2\cdot b \cdot c \cdot \cos \theta\)

Where \(a\), \(b\) and \(c\) are sides of the triangle and \(\theta\) is the angle opposite to side \(a\). Now, let is clear the cosine function:

\(2\cdot a \cdot b\cdot \cos \theta = b^{2}+c^{2}-a^{2}\)

\(\cos \theta = \frac{b^{2}+c^{2}-a^{2}}{2\cdot b \cdot c}\)

Cosine is a bounded function between -1 and 1, a triplet corresponds to a triangle if and only if result is located between upper and lower bounds. Now let is evaluate each triplet:

a) \(a = 2\), \(b = 5\), \(c = 9\)

\(\cos \theta =\frac{5^{2}+9^{2}-2^{2}}{2\cdot (5)\cdot (9)}\)

\(\cos \theta = 1.133\) (Absurd)

The triplet does not represent a triangle.

b) \(a = 6\), \(b = 6\), \(c = 7\)

\(\cos \theta =\frac{6^{2}+7^{2}-6^{2}}{2\cdot (6)\cdot (7)}\)

\(\cos \theta = 0.583\) (Reasonable)

The triplet represents a triangle.

c) \(a = 6\), \(b = 4\), \(c = 2\)

\(\cos \theta = \frac{4^{2}+2^{2}-6^{2}}{2\cdot (4)\cdot (2)}\)

\(\cos \theta = -1\) (Absurd)

The triplet does not represent a triangle, but a straight line.

d) \(a = 7\), \(b = 8\), \(c = 1\)

\(\cos \theta = \frac{8^{2}+1^{2}-7^{2}}{2\cdot (8)\cdot (1)}\)

\(\cos \theta = 1\) (Absurd)

The triplet does not represent a triangle, but a straight line.

Hence, the correct answer is B.

Answer:

(2,4)

Step-by-step explanation:

y=2x, x=-y+6

x=-y+6 ----> y = -x + 6

Now we have:

y = -x + 6

y = 2x

Now, we can set these equations to be equal to each other:

2x = -x + 6

3x = 6

x = 2

To find y, we can just substitue x into one of the originial equations:

y = 2x

y = 2(2)

y=4

Therefore, the answer to this system is (2,4).

Hope this helped!

Answer:

\(\Huge \boxed{\text{13.66$\%$}}\)

Step-by-step explanation:

To find the rate, we need to use the following formula:

\(\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}\)

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

\(\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}\)

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

Step-by-step explanation:

ans:7*(-(3-5))..........

The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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Answer:

C) 1

Step-by-step explanation:

f(x) = 3x - 4 when x = 3

= 3(3) - 4

= 9 - 4

= 5

g(x) = x^2 when x = 2

= 4

Subtract both values.

5 - 4 = 1

Best of Luck!

Answer:

hope this helps

Step-by-step explanation:

.55×78=42.9

78+42.9

=120.9 round off 121

Answer: 120.9 I believe.

Step-by-step explanation:

55% of 78 is 42.9.

(55 x 78 over 100 = 42.9)

Therefore take 78 + 42.9.

120.9

Answer:

\(\frac{6}{13} > \frac{4}{13}\), o que implica que esta afirmativa é incorreta.

Step-by-step explanation:

Uma probabilidade é dada pelo número de resultados desejados dividido pelo número total de resultados.

Probabilidade de sair um cartão contendo um quadrado:

4 com quadrados

6 + 4 + 3 = 13 total

4/13 de probabilidade de sair um cartão contendo um quadrado

Probabilidade de sair um cartão contendo um triângulo:

6 com triângulos

13 total

6/13 de probabilidade de sair um cartão contendo um triângulo

\(\frac{6}{13} > \frac{4}{13}\), o que implica que esta afirmativa é incorreta.

Answer:

x = 3.556 or \(\frac{32}{9}\)

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation:

(3*x-5)^2-((x+x+25))=0

Evaluate:  

\((3x-5)^{2}\) = \(9x^{2} -30x+25\)

Pull like factors:

9x^2 - 32x  =   x • (9x - 32)

 x • (9x - 32)  = 0

Remember roots of a product:

A product of several terms equals zero. When a product of two or more terms equals zero, then at least one of the terms must be zero. We shall now solve each term = 0 separately. In other words, we are going to solve as many equations as there are terms in the product. Any solution of term = 0 solves product = 0 as well.

Solve  :    9x - 32 = 0

Add  32  to both sides of the equation :

                     9x = 32

Divide both sides of the equation by 9:

                    x = 32/9 = 3.556

Answer:

Step-by-step explanation:

Both are essentially same questions, considering 30 = 25 + 5.

Solving c)

Solution:

Part-C)

Part-D)

Hoped this helped!

Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.

To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.

The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).

Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.

However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).

Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.

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Answer:

24/3 =8 with each friend

Step-by-step explanation:

Answer:

you give each one 12 and than eat them

Step-by-step explanation:

HISTOGRAM

Data are reported using visuals to make reporting easier and ease the understanding of the audience.

Some of the graphic used in statistics to report data and make inference include:

• Bar charts

• line charts

• Dot plot

• Box plot

• Histogram etc.

Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.

We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM

False it does have a solution or solutions

Answer:150?

Step-by-step explanation:

Answer:

\(r \geqslant - 16\)

Step-by-step explanation:

\( \frac{ - 10 + r}{2} \geqslant - 13\)

multiply both sides by 2:

\( - 10 + r \geqslant - 26\)

add 10 on both sides:

\(r \geqslant - 16\)

Answer:

\(r \ge -16\)

Step-by-step explanation:

To solve any equation/inequality:

1. get the variable to show up exactly once

2. isolate it

\(\frac{-10+r}{2} \ge -13\)

Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)

\(\frac{-10+r}{2} *2 \ge -13 *2\)

\(-10+r \ge -26\)

Add 10 to both sides, and simplify

\((-10+r)+10 \ge (-26)+10\)

\(r \ge -16\)