Auto Loans ~ George works for a credit union that serves a large, urban area. For his annual report, he wants to estimate the mean interest rate for 60-month fixed-rate auto loans at lending institutions (banks, credit unions, auto dealers, etc. ) in his area. George selects a random sample of 12 lending institutions and obtains the following rates:

The given statement "A probability distribution is a mutually exclusive and collectively exhaustive listing of experimental outcomes that can occur by chance, and their corresponding probabilities." is False. Because probability distribution doesn't necessarily have to be a listing of experimental outcomes.

Probability distribution is a function that describes the likelihood of obtaining different outcomes in a random experiment. The outcomes need not be mutually exclusive or collectively exhaustive, as there can be overlap between different outcomes or some outcomes may not be accounted for in the distribution.

However, the probabilities assigned to each outcome must sum up to 1, indicating that one of the possible outcomes must occur. Probability distributions are an essential tool in probability theory and are used to model a wide range of real-world phenomena, from weather patterns to financial markets. So, the given statement is False.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Answer:

D.A fixed value that does not appear whith a Vatiable

Answer:

Two events that are mutually exclusive when rolling two number cubes are:

Getting an odd number on the first cube and getting an even number on the second cube.

Getting a 1 on the first cube and getting a 2 on the second cube.

Two events that are not mutually exclusive when rolling two number cubes are:

Getting a 4 on the first cube and getting a 3 on the second cube.

Getting a 5 on the first cube and getting an odd number on the second cube.

Step-by-step explanation:

Answer:

(i) a = 2

   b = -1

   c = -1

(ii) x= 1

Step-by-step explanation:

Step 1: Factorise

\(f(x) = 2(x^{2} -2x+\frac{1}{2})\)  

Step 2: Use the complete square method.

\(f(x)=2(x^{2} -2x+(\frac{-2}{2})^{2} + \frac{1}{2} - (\frac{-2}{2})^{2} )\)  

Step 3: Have it to \(a(x+b)^{2} +c\)

\(f(x)=2((x-1)^{2} -\frac{1}{2} )\\ = 2(x-1)^{2} -1\)

Line of symmetry:  

To find line of symmetry, we use -b/2a formula.

Based from \(2x^{2} -4x+1\):

a=2, b=-4

-b/2a = -(-4)/2(2) = 1

Thus, the set  A∩C, contains only one element, which is 4. We write  A∩C, = {4} in set notation.

To evaluate A∩C, we will need to find the intersection of the sets A and C.

The intersection of two sets consists of the elements that are present in both sets. In this case, A = {1, 2, 4, 8, 9} and C = {3, 4, 5, 6, 7}. By comparing the two sets, we can identify the common elements.

From the given sets, we see that the only common element between them is 4. Therefore, ac = {4}.

In set notation, we write ac = {x | x ∈ a and x ∈ c}.

This means that ac is the set of all elements x such that x belongs to a and x also belongs to c. In this case, the only element that satisfies this condition is 4, so we write ac = {4}.

By using set notation, we can avoid any confusion or misunderstandings that might arise from using vague or imprecise language.

In summary, the set  A∩C, contains only one element, which is 4. We write ac = {4} in set notation.

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In order to find the average increase in the price, we need to divide the difference in the price by the difference of time.

The price changed from $7.37 to 7.80, and the time changed from 2008 to 2009, so we have:

So the average increase in the price was $0.43.

Answer:

Step-by-step explanation:

180 yards :)

Answer:

length: 85

width: 40

Step-by-step explanation:

length: 2w + 5

width: w

perimeter = 2L + 2W

250 = 2(2w + 5) + 2w

250 = 4w + 10 + 2w

250 = 6w + 10

240 = 6w

w = 40

length: 2(40) + 5 = 85

width: 40

The points that lies on the same line are (-3, 12), and, (-1, 4).

Here, we have,

The given coordinate points are (-2, 8) and (5,-20).

Here, slope (m)= 8+20/-2-5

= 28/-7

=-4

Substitute m= -4 and (x, y)=(-2,8) in y=mx+c, we get

8 = 8+c

or, c = 0

So, the equation of a line is y= -4 x

Now,

(-6, -2) in the given equation is -2=-4 (-6)

-2≠ 24

(-3, 12)  in the given equation is y= -4 x

12 = 12

(4, 16) in the given equation is y= -4 x

16 ≠ -16

(0, 6) in the given equation is y= -4 x

6 ≠ 0

(-1, 4) in the given equation is y= -4 x

4 = 4

(7,5) in the given equation is y= -4 x

5 ≠ -28

Therefore, the points that lies on the same line are (-3, 12), and, (-1, 4).

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The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

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Answer: Yes, they can.

Step-by-step explanation: Since quarters weigh 0.2 oz. 1 dollar weighs 0.8 oz. 0.8x150=120oz. 120ozs is about 7.5 pounds, so yes.

Answer:

Step-by-step explanation:

first you would want to flip the equation then multiply 9 on both sides to get

5(F-32)=9C

Then you would want to divide both sides by 5 which crosses out the 5 from the equation and is moved to the other side which then were you simplify getting

F-32=9C/5

Lastly you want to add 32 to both sides causing - 32 to cross out getting

F=9C/5 +32

making F=9C/5 + 32 our answer

5,6 and6,5

Step-by-step explanation:

there is only two ordered pairs of 5,6that is itself and 6,5

Answer:

the two possible orders are 5,6 and 6, 5

The equations that, together with y = -1.5x + 3, make a system with one solution are: 1. Y = -1.5x + 6, 4. 2Y + 3x = 6, 5. Y = -2x + 3

To find the equation that makes a system with one solution when paired with y = -1.5x + 3, we need to find an equation with a different slope and/or a different y-intercept.

Let's analyze each given equation:

1. Y = -1.5x + 6: This equation has the same slope as y = -1.5x + 3 but a different y-intercept, so it has one solution.

2. Y = -1.5x: This equation has the same slope as y = -1.5x + 3, and therefore has an infinite number of solutions (or is dependent), so it's not the answer.

3. 2Y = -3x + 6: To compare with the given equation, let's put it in the same format. Divide both sides by 2 to get Y = -1.5x + 3, which is the same as the given equation, so it's not the answer.

4. 2Y + 3x = 6: To compare with the given equation, let's put it in the same format. Divide both sides by 2 to get Y + 1.5x = 3. This equation has a different slope, so it has one solution.

5. Y = -2x + 3: This equation has a different slope and y-intercept, so it has one solution.

Thus, the equations that, together with y = -1.5x + 3, make a system with one solution are:

1. Y = -1.5x + 6
4. 2Y + 3x = 6
5. Y = -2x + 3

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Answer:

I need the question or the graph to answer..

Step-by-step explanation:

Answer:

85

Step-by-step explanation:

425 divided by 8= 85

Answer:

He as 85 race cars.

Step-by-step explanation:

Just divide 425 by 5 and you have your answer.

Answer:

$14.10

Step-by-step explanation:

hope this helps

The statement is True. To construct a confidence interval about the mean, the population from which the sample size is drawn must be approximately normal.

This assumption is necessary to ensure that the sampling distribution of the sample mean is also approximately normal, which is a key assumption underlying many statistical tests and confidence interval constructions.

However, suppose the sample size is large enough (usually at least 30). In that case, the central limit theorem may allow for constructing a confidence interval about the mean even if the population is not normal.

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Please attached a diagram drawn with MS Word based on the question parameters, and from a diagram from a similar question.

The length of the rectangle that contains 10 identical squares and has a width of 15 centimeters is 21 centimeters

A square is a quadrilateral that has four sides of the same length and the the four interior angles are each equal to 90°.

Some parts of the question appear missing, please find attached the design of a rectangle based on a similar GCSE question online. The width of the rectangle = 15 cm

The number of squares = 10

The number of squares that make up the width from the drawing = 5

The side length of the square is therefore; 15 cm ÷ 5 = 3 cm

The number of squares that make up the length of the rectangle = 7

The length of the rectangle is therefore, L = 7 × 3 cm = 21 cm

The length of the rectangle = 21 centimeters

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Answer:

$6.75

Step-by-step explanation:

2.70 / 1/2 = 1.35

2.70 + 1.35 + 1.35 + 1.35 = 6.75

So the answer is $6.75

Answer:

61% is a reasonable choice

Step-by-step explanation:

The probability of a strike is 79% or 0.79

=> Independently, the probability of 2 consecutive strikes:

P = 0.79 x 0.79 = 0.6241 ~ 61%

Answer:

Adding the exponents

Step-by-step explanation:

Multiplying exponential terms with the same base

To multiply exponents with same base , we use exponential property

\(a^m \cdot a^m=a^{m+n}\)

When we multiply exponents with same base then we add the exponents

So, adding the exponents best explains to simplify the expression that has same base with exponents .

Answer:

Hello!

Step-by-step explanation:

Theoretical probability is what's expected to happen

Experimental probability is what's happen based on the experiment

Daisy gets 20 cats delivered to her shelter in the last month She expects to get 20 this month based on the theoretical probability but she actually gets 15 cats this month so her theoretical probability was 5 more then her experimental probability Hope that helps!

The correct answer is D: A and B ( Accounts receivable and cost goods )

Accounts receivable represents the amount of money owed to a company by its customers for goods or services that have been delivered but not yet paid for. As sales increase, the amount of accounts receivable also tends to increase since more customers will have outstanding balances.

Cost of goods sold (COGS) represents the direct costs associated with producing or purchasing the goods that are sold by a company. It includes the cost of raw materials, labor, and other direct expenses. As sales increase, the COGS also tends to increase since more goods are being produced or purchased for sale.

COGS is directly influenced by the level of sales because it is tied to the inventory turnover. When goods are sold, their associated costs are transferred from the inventory account to the COGS account. As sales increase, more goods are sold, and therefore, more costs are transferred to COGS.

COGS is calculated by subtracting the ending inventory value from the sum of the beginning inventory and the purchases made during a specific period. It is a key component in determining a company's gross profit and gross profit margin, which are important indicators of profitability.

On the other hand, administrative salaries (option c) typically do not vary directly with sales. Administrative salaries are usually fixed expenses that are paid to employees for their administrative roles regardless of the level of sales.

Therefore, the correct answer is option d. A and B, as both accounts receivable and cost of goods sold vary with sales.

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The expected returns on 10 stocks is 2.10.

The solution to the given problem is explained below:

a) Expected value of returns:

Expected value of A = -1*0.25+0*0.25+1*0.50 = 0.25

Expected value of B = -1*0.20+0*0.20+1*0.15+2*0.45+0.05*0.20 = 0.80

Expected value of C = (-1)*(-1)*0.05+(-1)*0*0.45+(-1)*1*0.15+0*(-1)*0.20+0*0*0.05+0*1*0.20+1*(-1)*0.10+1*0*0.20+1*1*0.05= 0.15

b) Variance of A, B:

Variance of A:σ(A)² = (0.25-0.25²) + (0-0.25²) + (0.50-0.25²) = 0.3125

Variance of B:σ(B)² = (-1-0.80)²*0.20 + (0-0.80)²*0.20 + (1-0.80)²*0.15 + (2-0.80)²*0.45 + (0.05-0.80)²*0.20 = 0.5825

c) Correlation A and B, Covariance B and C:

Covariance(A,B) = (-1-0.25)*(-1-0.80)*0.20 + (0-0.25)*(0-0.80)*0.20 + (1-0.25)*(1-0.80)*0.15 = -0.095

Correlation(A,B) = Covariance(A,B)/σ(A)σ(B) = -0.095/sqrt(0.3125*0.5825) = -0.347

Covariance(B,C) = Σ(x-B)(y-C)/n-1 = (-1-0.8)(-1-0.15)*1/3 + (-1-0.8)*0*(-1-0.15)/3 + (-1-0.8)*1*0.1/3 + (0-0.8)*(-1-0.15)*0.05/3 + (0-0.8)*0*0.05/3 + (0-0.8)*1*0.2/3 + (1-0.8)*(-1-0.15)*0.05/3 + (1-0.8)*0*0.2/3 + (1-0.8)*1*0.05/3 = -0.104

Expected returns on 10 stocks are:

Expected returns = (3*0.25 + 2*0.80 + 5*0.15) = 2.10

Therefore, the expected returns on 10 stocks is 2.10.

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The stopping distance for a car traveling at 50 mph is 208.3 feet.

We can set up a proportion using the given information and the formula for stopping distance:

D = k s²

where D is the stopping distance, s is the speed of the car, and k is a constant of proportionality.

Using the given information, we can solve for k:

75 = k * 30²

k = 75 / (30²) = 0.0833

Now we can use this value of k to find the stopping distance for a speed of 50 mph:

D = 0.0833 * 50² = 208.3 feet

Therefore, the stopping distance for a car traveling at 50 mph is 208.3 feet.

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Answer:

x < 20

Step-by-step explanation:

Answer:

X<20

Interval notation

(-oo,20)

Step-by-step explanation:

Answer: does this help you?

Step-by-step explanation: