Solution of inequality ((x - 1)(x - 5))/(x - 3) > 0

The retirement plans that do not come with a guaranteed benefit at retirement are C) I, III, and IV.

A guaranteed benefits refers to the fact that the retiree will be paid a certain amount at retirement.

The 401(k) is an employer-offered retirement plan with defined contributions from the employees.  The employee bears the investment risks and there is no guarantee of benefits.

With fixed annuity, there is a guarantee of an annual payment by the insurance company to the beneficiary or insured.

The Roth IRA does not offer guaranteed benefit just like the traditional IRA.

Thus, only the fixed annuity, an insurance contract, offers a guaranteed benefit at retirement.

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Answer:

75% correct

Step-by-step explanation:

The second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

The given sequence starts with C(1) = -20. Each subsequent term is obtained by adding 0 to the previous term, which means that the sequence is constant.

The recursive formula for this sequence is given as:

c(1) = -20 and c(n) = c(n-1) + 0

This means that the first term of the sequence is -20, and each subsequent term is obtained by adding 0 to the previous term

Therefore, the second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

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To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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Answer:

a = 3

Step-by-step explanation:

since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.

substitute x = 7 and y = 27 into the equation and solve for a

27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )

3 = a

Angela's score is in the 87th percentile, which means that 87% of the scores were at or below her score.

To calculate the percentage of scores above her score, we subtract 87% from 100%. Therefore, the percentage of scores above Angela's score is 13%.

In summary, Angela's score is at or below 87% of the scores, and 13% of the scores are above her score. The percentile score indicates the percentage of scores that fall below a particular score. Therefore, Angela performed better than 87% of the test takers who took the aptitude test in accounting.

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The probability of drawing either a queen or a diamond is 15/52

To determine the probability of drawing either a queen or a diamond, we have to find the sum of the probabilities of drawing a queen and drawing a diamond, then subtract the probability of drawing both a queen and a diamond. This is because the probability of drawing both a queen and a diamond has been added twice when we added the individual probabilities.

Thus, we have:P(queen or diamond) = P(queen) + P(diamond) - P(queen and diamond)

The probability of drawing a queen is 4/52, since there are four queens in a deck of 52 cards. The probability of drawing a diamond is 13/52, since there are 13 diamonds in a deck of 52 cards.

There are two ways to draw a card that is both a queen and a diamond, namely the queen of diamonds and the diamond queen. Thus, the probability of drawing both a queen and a diamond is 2/52. Therefore, P(queen or diamond) = 4/52 + 13/52 - 2/52 = 15/52 = 15/4 = 3.75 As a reduced fraction, this is 15/52.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Answer:

[tex]\frac{xa}{28}[/tex]

Step-by-step explanation:

   [tex]\frac{4x^2}{y7a^3} * \frac{a^4}{16+8x}[/tex]

= [tex]\frac{2x(2+x)}{7a^3} * \frac{a^4}{8(2+x)}[/tex]

= [tex]\frac{xa}{28}[/tex]

[tex]\frac{x^{2}a }{28}[/tex]

Explination:

Factor the numerator and the denominator and cancel the common factors

Answer:

$12

Step-by-step explanation:

Cans : Dollars

6 cans : 9 dollars

DIVIDE BY 3

2 cans : 3 dollars

MULTIPLY BY 4

8 cans : 12 dollars

Hope this helps :)

Have a great day!

The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.

Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.

Let,

[tex]B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right][/tex]

Then,

[tex]AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right][/tex]

Therefore, Ab is reflection about y = x .

As U = Bx and T∘U    

A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).          

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Answer: 500 cm

Step-by-step explanation:

multiply by 0.5 by 10000

The list after sorting in ascending order is C) {3 17 44 69}.

Sorting means arranging the numbers in ascending or descending order based on their value. In this case, the numbers are arranged in ascending order, meaning that the smallest number comes first, followed by the next smallest number and so on.

To sort the list, we can use any sorting algorithm such as selection sort, bubble sort, insertion sort, or quicksort. One simple way to sort the list is to use the built-in sort function provided by most programming languages. The sort function takes the list as input and returns a new list with the elements sorted in ascending order.

In summary, the sorted list in ascending order is {3 17 44 69}, and we can use sorting algorithms or built-in functions to sort a list in ascending or descending order based on our requirement.

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Answer:

y = 1/7x + 29/7

Step-by-step explanation:

Slope intercept form is y = mx + b

m = the slope

b = y-intercept

m = 1/7

Y-intercept is located at (0, 29/7)

So, the equation is y = 1/7x + 29/7

Answer:

fFind the sum of

4

4

​

 and

4

8

4

8

​

 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.

Step-by-step explanation:

The characteristic of a reliable scientific poll is small sampling error. The small sampling error is a characteristic of a reliable scientific poll.

What is a scientific poll?Scientific polls are surveys that gather and evaluate people's opinions or responses to questions. These surveys are done in a scientific way, implying that pollsters use scientifically proven techniques to gather responses and analyze data.A reliable scientific poll must have a small sampling error. A sampling error is the deviation of the sample mean from the population mean due to random error. The smaller the sample size, the more likely it is that the results will be imprecise. As a result, it's essential to conduct a reliable scientific poll with a sample size that is representative of the population as a whole.The option for the correct answer to this question is; (choice a) small sampling error.

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The experimental probability of the arrow stopping over section 1 is 7/13, or 0.538.

To calculate this, you need to take the number of times the arrow stopped on section 1 (45) and divide it by the total number of times the arrow was spun (80). This can be expressed as a fraction (45/80), which can be simplified to 7/13. To convert this fraction to a decimal, divide the numerator by the denominator (7/13 = 0.538).

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The shopper must spend at least $444.44 to get the 10% discount.

If a shopper gets a 10% discount, it means they pay only 90% of the original price. Let's say the original spending is represented by x. Then the spending after the 10% discount would be:

d = 0.9x

Now, we know that the shopper must spend at least $400 to get the discount, so we can set up an inequality:

d ≥ 400

Substituting the expression we found for d, we get:

0.9x ≥ 400

Dividing both sides by 0.9, we get:

x ≥ 444.44

So the shopper must spend at least $444.44 to get the 10% discount.

If a measure that is in 4/4 time has a half note, a quarter note, and an eighth note, a sixteenth note value is missing.

4/4 time signature is also known as a common time signature. In a 4/4 measure, we have four beats or counts, and each quarter note takes one beat or count. A half note gets two beats or counts, a quarter note gets one beat, and an eighth note gets half a beat.

Therefore, if a measure in 4/4 time has a half note, a quarter note, and an eighth note, then a sixteenth note value is missing because a sixteenth note gets one-quarter of a beat or count.

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the correct answer is option C: The company rejects H0, making a Type II error. In this hypothesis test, the null hypothesis H0 is that the machine produces no more than 98% high-quality candy, and the alternative hypothesis Ha is that the machine produces more than 98% high-quality candy. The significance level is α = 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed test statistic, assuming that the null hypothesis is true. A p-value of 0.15 is greater than the significance level of 0.05, which means that the result is not statistically significant.

However, the company is unaware that the machine is actually producing 99% high-quality candy. This means that the null hypothesis is actually false, and the alternative hypothesis is true. In other words, the machine is producing more than 98% high-quality candy.

Based on these observations, the company failing to reject the null hypothesis (option B) would be a Type II error, as it would mean that the company is not detecting a significant difference in the candy quality when, in fact, the machine is producing candy of higher quality than the null hypothesis assumes.

Therefore, the correct answer is option C: The company rejects H0, making a Type II error.

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The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.

We need to use the Poisson Distribution for solving the question, which is as follows:

P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]

where is the mean value of distribution and x is the number of events we want to calculate.

If a random variable follows a Poisson distribution, its variance is equal to its mean.

So, the mean will be λ.

Let the probability of filing four claims be p1.

Then, probability of filing two claims will be ⁵p₁

We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.

So,

p₁ + ⁵p₁ = 1

p₁ = 1/6

The mean number of claims is λ, which is given by:

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

The mean number of claims is λ, which is given by:

λ = ⁴p₁ + 2⁵p₁ = 2.5

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

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The probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

The possibility of an event occurring can be expressed in terms of probability and odds, but they are not the same thing. The ratio of positive events to all conceivable outcomes, represented as a fraction or decimal, is known as probability. On the other hand, odds represent the proportion of good outcomes to those that are unfavourable. Odds can be stated as a ratio, fraction, or by dividing the favourable outcomes by the total number of outcomes to get their equivalent in probability.

The binomial probability is given as:

[tex]P(x) = (nCx) * p^x * (1-p)^{(n-x)}[/tex]

Here, n = 3, p = 0.11, and q = 1 - p = 0.89.

Thus,

[tex]Pr(exactly 2) = P(2) = (3C2) * 0.11^2 * 0.89^{(3-2)} = 0.0283\\Pr(exactly 1) = P(1) = (3C1) * 0.11^1 * 0.89^{(3-1)} = 0.2901\\Pr(exactly 3) = P(3) = (3C3) * 0.11^3 * 0.89^{(3-3)} = 0.001331[/tex]

Hence, the probabilities for the given event is Pr(exactly 2) = 0.0283. Pr(exactly 1) = 0.2901, and Pr(exactly 3) = 0.001331.

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There will be a population of 2,097,152 rabbits after 5 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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New width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

The area of the tennis court is given by:

A = lw

where l is the length of the court and w is the width of the court.

Substituting the given values, we have:

[tex]$$260.7569 = l \cdot 10.97$$[/tex]

Solving for l, we get:

[tex]$l = \frac{260.7569}{10.97} \approx 23.76 \text{ m}$$[/tex]

To find the area of the court without the white bands, we need to subtract the areas of the two white bands from the total area. Since the white bands are on the top and bottom, we need to subtract twice the product of the width of the court and the width of the white band. The width of the white band is not given, but we know that the width of the court will be reduced by 25%, so the new width of the court will be:

w' = w - 0.25w = 0.75w

Substituting the given values, we have:

[tex]$$\begin{aligned}A' &= lw' - 2(0.75w)(l) \ &= l(0.75w) - 1.5wl \ &= 0.5625lw\end{aligned}$$[/tex]

where A' is the new area of the court without the white bands. Substituting the values of l and w that we found earlier, we have:

[tex]$$A' = 0.5625 \cdot 23.76 \cdot 10.97 \approx 146.17 \text{ m}^2$$[/tex]

Therefore, the new area of the court is reduced by 25%.

To find out if the width of the land is also reduced by 25%, we need to compare the original width w with the new width w'. We have:

[tex]$w' = 0.75w$$[/tex]

Dividing both sides by w, we get:

[tex]$\frac{w'}{w} = 0.75$$[/tex]

This means that the new width w'$ is 75% of the original width w. Therefore, the width of the land is reduced by 25%, just like the area.

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Solve the equation [tex]7/11=18/x+1[/tex] we find the solution is [tex]x = 27.2857[/tex]

Your example is an equation since an equation is any statement with an equals sign. Equations are frequently utilized for mathematical equations since mathematicians like equal signs. A set of instructions for achieving a certain result is called an equation.

A number, a constant, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by such an assignment operator form an equation.

we can cross-multiply,

[tex]7(x+1) = 11(18)[/tex]

Expanding the left side,

[tex]7x + 7 = 198[/tex]

Subtracting [tex]7[/tex] from both sides,

[tex]7x = 191[/tex]

Dividing both sides by [tex]7[/tex],

[tex]x = 191/7[/tex]

Therefore, the solution to the proportion is

[tex]x = 27.2857[/tex]

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Answer: Less than or equal to 45

Step-by-step explanation:

Let's use algebra to write the inequality.

Let h be the number of hamburgers purchased and t be the number of tacos purchased.

Each hamburger costs $5.50 and each taco costs $2, so the total cost of h hamburgers and t tacos is:

5.5h + 2t

Serenity has a total of $45 to spend, so we can write:

5.5h + 2t ≤ 45

This is the inequality that represents the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t.

Note that the inequality is less than or equal to 45, since Serenity cannot spend more than $45.

To represent the possible values for the number of hamburgers and tacos purchased, an Inequality can be written as 5.5x + 2y ≤ 45.

To write an inequality to represent the possible values for the number of hamburgers purchased (h) and the number of tacos purchased (t), we need to consider the cost of each item and the total amount Serenity has to spend.

Let's assume Serenity buys x hamburgers and y tacos. Each hamburger costs $5.50, so the total cost of hamburgers purchased would be 5.5x. Each taco costs $2, so the total cost of tacos purchased would be 2y.

The total amount Serenity has to spend is $45. Therefore, the inequality that represents the possible values for h and t is: 5.5x + 2y ≤ 45.

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The height that the T-short lands on the bleachers is x = 0.65.

The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.

Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.

The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3

To find the height of the T-shirt landing we find the intersection of the two equations as follows:

-18x² + 4x = (2x - 14)/3

-54x² + 12x = 2x - 14

54x² - 10x - 14 = 0

27x² - 5x - 7 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values;

x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)

x = (5 ± √(925)) / 54

x = (5 ± 5√37) / 54

x = (5 + 5√37) / 54 = 0.65 and

x = (5 - 5√37) / 54 = -0.47

Hence, the height that the T-short lands on the bleachers is x = 0.65.

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