25.
26.
Domain / Range and Functions
Which of the following relations is a
function?
A. {(-2,-2),(-2,-1),(-2,0),(-2,1),(-2,2)}
B. {(1,0),(-1,0), (2,1),(-2,1),(3,2), (-3,2)}
C. {(-2,1),(-1,2), (0,0),(-1,1),(2,-2)}
D. {(-3,3), (1,3),(-3,2), (1,2), (-3,1),(1,1)}
What is answer

Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.

Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.

Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.

In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.

Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.

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Answer:

$2,981.67

Step-by-step explanation:

In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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Construct the histogram for the percentage increase in the starting salary by using 10 as the class width.

Answer Output using MINITAB software is given below at the end of answer (bar graph)

Frequency:

The frequencies are calculated by using the tally mark and the range of the starting salary is grouped and the range is from 40 to 120. Here the number of times each percentage increase repeats is the frequency of that particular class.

The width of class is 10.

Make a tally mark for each value in the corresponding revenue class and continue for all values in the data.

The number of tally marks in each class represents the frequency, f of that class.

Similarly, the frequency of remaining classes for the percentage increase is given below at the end of the answer.

The data represents the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary.

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Answer:

Step-by-step explanation:

If y=0

6=3(0) -2y

6= -2y

6÷ -2   -2y÷ -2

-3=y

If x=0

*Same steps*

6=3x - 2(0)

6/3=3x/3

x=2

Answer:

y=4

Step-by-step explanation:

If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.

A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.

The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.

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Answer:

37.5

Step-by-step explanation

your answer is 37.5

The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer: b

Step-by-step explanation:

Answer:

How many nickels make a 2 dollars?

40 nickels

50 per penny roll or 40 nickels to complete a $2 roll, the denominations can become less self-explanatory the higher the face value and physical thickness of a coin

Answer:

the two prime factors is (113) (97)

Step-by-step explanation:

The computation of the two prime factors is  is shown below:

The given expression is

105^2 - 8^2

Here we used the formula i.e.

a^2 - b^2 = (a + b) (a - b)

where,

a = 105

b = 8

Now

= (105 + 8) (105 - 8)

= (113) (97)

Hence, the two prime factors in descending order is (113) (97)

The factory will put 441 cans of soda in 7 cases.

If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.

Given:

Number of flavors = 9

Cans per flavor = 7

Number of cases = 7

To calculate the total number of cans, we can multiply these values:

Total cans = Number of flavors × Cans per flavor × Number of cases

Total cans = 9 × 7 × 7

Total cans = 441

To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).

Hence, the factory will put 441 cans of soda in 7 cases.

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Answer:

Step-by-step explanation:

1 ft= 12 inches

we know l=15 ft and 6 inches

2L=31 inch

P=2L+2W=40ft

2W=40-2*(15ft6inches)

2W=40-31=9 inch

w=9inch/2=4 ft 6 inches

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

Equilateral

Step-by-step explanation:

If the sides' lengths are equal then it's an equilateral triangle. Scalenes have no equal sides and isosceles have 2 equal sides

A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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Answer:

1)

A) \(\frac{}{X}\) ~ N(8.5;0.108)

B) P(\(\frac{}{X}\) > 9)= 0.0552

C) P(X> 9)= 0.36317

D) IQR= 0.4422

2)

A) \(\frac{}{X}\) ~ N(30;2.5)

B) P( \(\frac{}{X}\)<30)= 0.50

C) P₉₅= 32.60

D) P( \(\frac{}{X}\)>36)= 0

E) Q₃: 31.0586

Step-by-step explanation:

Hello!

1)

The variable of interest is

X: pollutants found in waterways near a large city. (ppm)

This variable has a normal distribution:

X~N(μ;σ²)

μ= 8.5 ppm

σ= 1.4 ppm

A sample of 18 large cities were studied.

A) The sample mean is also a random variable and it has the same distribution as the population of origin with exception that it's variance is affected by the sample size:

\(\frac{}{X}\) ~ N(μ;σ²/n)

The population mean is the same as the mean of the variable

μ= 8.5 ppm

The standard deviation is

σ/√n= 1.4/√18= 0.329= 0.33 ⇒σ²/n= 0.33²= 0.108

So: \(\frac{}{X}\) ~ N(8.5;0.108)

B)

P(\(\frac{}{X}\) > 9)= 1 - P(\(\frac{}{X}\) ≤ 9)

To calculate this probability you have to standardize the value of the sample mean and then use the Z-tables to reach the corresponding value of probability.

Z= \(\frac{\frac{}{X} - Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{9-8.5}{0.33}= 1.51\)

Then using the Z table you'll find the probability of

P(Z≤1.51)= 0.93448

Then

1 - P(\(\frac{}{X}\) ≤ 9)= 1 - P(Z≤1.51)= 1 - 0.93448= 0.0552

C)

In this item, since only one city is chosen at random, instead of working with the distribution of the sample mean, you have to work with the distribution of the variable X:

P(X> 9)= 1 - P(X ≤ 9)

Z= (X-μ)/δ= (9-8.5)/1.44

Z= 0.347= 0.35

P(Z≤0.35)= 0.63683

Then

P(X> 9)= 1 - P(X ≤ 9)= 1 - P(Z≤0.35)= 1 - 0.63683= 0.36317

D)

The first quartile is the value of the distribution that separates the bottom 2% of the distribution from the top 75%, in this case it will be the value of the sample average that marks the bottom 25% symbolically:

Q₁: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₁)= 0.25

Which is equivalent to the first quartile of the standard normal distribution. So first you have to identify the first quartile for the Z dist:

P(Z≤z₁)= 0.25

Using the table you have to identify the value of Z that accumulates 0.25 of probability:

z₁= -0.67

Now you have to translate the value of Z to a value of \(\frac{}{X}\):

z₁= (\(\frac{}{X}\)₁-μ)/(σ/√n)

z₁*(σ/√n)= (\(\frac{}{X}\)₁-μ)

\(\frac{}{X}\)₁= z₁*(σ/√n)+μ

\(\frac{}{X}\)₁= (-0.67*0.33)+8.5=  8.2789 ppm

The third quartile is the value that separates the bottom 75% of the distribution from the top 25%. For this distribution, it will be that value of the sample mean that accumulates 75%:

Q₃: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₃)= 0.75

⇒ P(Z≤z₃)= 0.75

Using the table you have to identify the value of Z that accumulates 0.75 of probability:

z₃= 0.67

Now you have to translate the value of Z to a value of \(\frac{}{X}\):

z₃= (\(\frac{}{X}\)₃-μ)/(σ/√n)

z₃*(σ/√n)= (\(\frac{}{X}\)₃-μ)

\(\frac{}{X}\)₃= z₃*(σ/√n)+μ

\(\frac{}{X}\)₃= (0.67*0.33)+8.5=  8.7211 ppm

IQR= Q₃-Q₁= 8.7211-8.2789= 0.4422

2)

A)

X ~ N(30,10)

For n=4

\(\frac{}{X}\) ~ N(μ;σ²/n)

Population mean μ= 30

Population variance σ²/n= 10/4= 2.5

Population standard deviation σ/√n= √2.5= 1.58

\(\frac{}{X}\) ~ N(30;2.5)

B)

P( \(\frac{}{X}\)<30)

First you have to standardize the value and then look for the probability:

Z=  (\(\frac{}{X}\)-μ)/(σ/√n)= (30-30)/1.58= 0

P(Z<0)= 0.50

Then

P( \(\frac{}{X}\)<30)= 0.50

Which is no surprise since 30 y the value of the mean of the distribution.

C)

P( \(\frac{}{X}\)≤ \(\frac{}{X}\)₀)= 0.95

P( Z≤ z₀)= 0.95

z₀= 1.645

Now you have to reverse the standardization:

z₀= (\(\frac{}{X}\)₀-μ)/(σ/√n)

z₀*(σ/√n)= (\(\frac{}{X}\)₀-μ)

\(\frac{}{X}\)₀= z₀*(σ/√n)+μ

\(\frac{}{X}\)₀= (1.645*1.58)+30= 32.60

P₉₅= 32.60

D)

P( \(\frac{}{X}\)>36)= 1 - P( \(\frac{}{X}\)≤36)= 1 - P(Z≤(36-30)/1.58)= 1 - P(Z≤3.79)= 1 - 1 = 0

E)

Q₃: P(\(\frac{}{X}\)≤\(\frac{}{X}\)₃)= 0.75

⇒ P(Z≤z₃)= 0.75

z₃= 0.67

z₃= (\(\frac{}{X}\)₃-μ)/(σ/√n)

z₃*(σ/√n)= (\(\frac{}{X}\)₃-μ)

\(\frac{}{X}\)₃= z₃*(σ/√n)+μ

\(\frac{}{X}\)₃= (0.67*1.58)+30= 31.0586

Q₃: 31.0586

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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In the given problem, the ramp weighs 10,125 pounds.

To calculate the weight of the ramp, first, determine its volume and then multiply it by the weight of concrete per cubic foot.

The ramp is shaped like a right triangle prism, with a triangular base and three rectangular faces. The ramp's measurements are as follows:1.5 feet in height15 feet is the length of the base (b).6 feet in length (l).

The area of the triangular base can be determined using the triangle area formula: A = 0.5 * b * h A = 0.5 * 15 * 1.5A = 11.25 ft^2

The volume of the ramp can be estimated by multiplying the base area by the ramp length: V = A * l V = 11.25 feet 2 feet 6 feet

V = 67.5 ft^3

Finally, the weight of the ramp can be calculated by multiplying the volume by the weight of concrete per cubic foot:W = V * 150 lbs/ft3 W = 67.5 feet * 150 lbs/ft3 W = 10,125 pounds

As a result, the ramp weighs 10,125 pounds.

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The other numbers are 2 and 50. These relationships are like this because the product of both numbers gives a 100

From the information given, we are to determine the other numbers like 5 and 20 that form the given relationship.

The other numbers that form this relationship are 2 and 50

1/2 * 100 = 50%

1/50 * 100 = 2%

Thesee relationships are like this because the product of both numbers gives a 100

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Answer:

Its 78,300

Step-by-step explanation:

Answer:

March through August

Step-by-step explanation:

Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:

\(S=56.9-40.7cos (\frac{\pi}{6}t)\)

and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:

\(77=56.9-40.7cos (\frac{\pi}{6}t)\)

if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:

\(56.9-40.7cos (\frac{\pi}{6}t)=77\)

and now we solve for t

\(-40.7cos (\frac{\pi}{6}t)=77-56.9\)

\(-40.7cos (\frac{\pi}{6}t)=20.1\)

\(cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}\)

\(cos (\frac{\pi}{6}t)=-0.4938\)

\(\frac{\pi}{6}t=cos^{-1}(-0.4938)\)

\(\frac{\pi}{6}t=2.087\)

\(t=\frac{2.087(6)}{\pi}\)

\(t=3.98 months\)

but there is a second answer to this problem. Notice that the function cos can be 2.87 at \(2\pi-2.087=4.1962 rad\) as well, so we repeat the process:

\(\frac{\pi}{6}t=4.1962\)

\(t=\frac{4.1962(6)}{\pi}\)

\(t=8.014 months\)

So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:

(1,3.98)  (3.98,8.014) and (8,014, 13)

and find a test value for each of the intervals and test it.

(1,3.98) t=2

\(S=56.9-40.7cos (\frac{\pi}{6}(2))\)

S=36.55

this is less than 77 so this is not our answer.

(3.98,8.014) t=5

\(S=56.9-40.7cos (\frac{\pi}{6}(5))\)

S=92.15

this is more than 77 so this is our answer.

(8.014,13) t=10

\(S=56.9-40.7cos (\frac{\pi}{6}(10))\)

S=36.55

this is less than 77 so this is not our answer.

so, since our answer is the interval (3.98,8.014)

this means that between the months of march and august we will be sellin more than 7700 units.

Recall the definition of the cross product:

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

The cross product is antisymmetric, or anticommutative, meaning that for any  vectors u and v, we have u x v = - (v x u).

It's also distributive, so for any vectors u, v, and w, we have (u + v) x w = (u x w) + (v x w).

Taking all of these properties together, we get

b x a = (6i - j + 2k) x (2i + 2j - 5k)

b x a = 12 (i x i) - 2 (j x i) + 4 (k x i)

............. + 12 (i x j) - 2 (j x j) + 4 (k x j)

............. - 30 (i x k) + 5 (j x k) - 10 (k x k)

b x a = 1 (j x k) + 34 (k x i) + 14 (i x j)

b x a = i + 34j + 14k

Answer:

Short answer, it is D)  i+34j + 14k

Step-by-step explanation:

Edge 2021.

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

\(\displaystyle{f(x)=3^x-5}\)

Step-by-step explanation:

Being translated up-down means that the value exists outside of x. Therefore, we can cancel B and C choice since those are horizontal (left-right) translation.

Our only choice is A and D. However, D is being translated up since it's +5. Thus, the only correct answer that a function is being translated down is:

\(\displaystyle{f(x)=3^x-5}\)

or A choice.

Answer:

Step-by-step explanation:

4(30+5)

4(30)+4(5)

120+20

140

this is the answer of the equation as a graph