Computer salespeople at a local store earn a $100 commission per computer for the first 5 computers they sell each month. For every additional computer they sell during that month, the commission per computer is 1.5 times the rate for the first five. Which of the following is the total commission earned by a salesperson who sells 8 computers in a month?

A. $190
B. $800
C. $950
D. $1,050
E. $1,200

The factored expression of the expression given as (a + b)^2 = 4 is (a + b + 2)(a + b - 2) = 0

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(a + b)^2 = 4

Express 4 as 2^2

So, we have

(a + b)^2 = 2^2

Rewrite as

(a + b)^2 - 2^2 = 0

Apply the difference of two squares

So, we have

(a + b + 2)(a + b - 2) = 0

Hence, the equivalent expression of the expression given as (a + b)^2 = 4 when it is factored is (a + b + 2)(a + b - 2) = 0

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Answer:

1) 25deg. Angle EGF

2) 25deg. Angle BGC

3) Angle 2 and BGC or Angle 1 and EGF

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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Answer:

x ≈ 14.7

Step-by-step explanation:

use pythagorean therorem

a^2 + b^2 = c^2

c is hypotenuse and we know the hypotenuse is 21

a^2 + b^2 = c^2

x^2 + 15^2 = 21^2

x^2 + 225 = 441

x^2 = 216

x = √216

x ≈ 14.7

Answer: yes

Step-by-step explanation:

yes

Answer:

2x-1

Step-by-step explanation:

Answer:

b) 30^2 + b^2 = 40^2

Step-by-step explanation:

This is cuz the diagonal is the hypotenuse of the diagonal formed so it'll be c^ 2

c ^ 2 always is on the right hand side of the equation.

In this case since 40^2 is c^2 is should be on the right side of the equation.

we can conclude that the sum of (-2+3÷4) and 5÷g is rational, The sum is not necessarily an integer, since it could be a fraction.

Why it is?

To determine if the sum of (-2 + 3÷4) and 5÷g is rational, we need to first simplify the expression:

(-2 + 3÷4) + 5÷g = (-8÷4 + 3÷4) + 5÷g = -5/4 + 5÷g

Now, we can see that the sum is rational if -5÷4 and 5÷g are both rational.

-5÷4 is rational because it can be expressed as a fraction (-5÷4 = -1.25).

For 5÷g to be rational, g must be a non-zero rational number, because the product of a rational number and a non-zero rational number is always rational.

Therefore, we can conclude that the sum of (-2+3÷4) and 5÷g is rational.

The sum is not necessarily an integer, since it could be a fraction.

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The odds of the event happening are 3:1.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

To calculate the odds of an event happening, we can use the formula:

Odds of event happening = Probability of event happening / Probability of event not happening

In this case, the probability of the event happening is 0.75, and the probability of the event not happening is 0.25.

Using the formula, we can calculate the odds as follows:

Odds of event happening = 0.75 / 0.25 = 3

Therefore, the odds of the event happening are 3:1.

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The largest number which divides 70 and 125 , leaving remainders of 5 and 8 is 13.

To find the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, we can follow these steps:

Subtract the remainders from their respective numbers:

70 - 5 = 65 and

125 - 8 = 117.

Find the factors of each resulting number:

Factor of 65 = 5 and 13

factor of 117 = 3 and 13

Determine the highest common factor (HCF) of the resulting factors:

The HCF of 5 = 1

the HCF of 13 = 1

the HCF of 3 = 3

the HCF of 13 = 13

Therefore, the largest number that divides 70 and 125, leaving remainders of 5 and 8, respectively, is 13.

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The false statement is (a) P( A^c n B^c)=P(A^c) P(B^c). The probability of the intersection of complements is generally not equal to the product of individual complements.

The misleading assertion including p, and the erratic occasions An and B is (a) P( A^c n B^c)=P(A^c) P(B^c).

This assertion is bogus in light of the fact that by and large, the likelihood of the convergence of the supplements of two occasions, A^c and B^c, isn't equivalent to the result of their singular supplements.

For instance, assume we flip a fair coin. Let A be the occasion of getting heads and B be the occasion of getting tails. Then, P(A) = P(B) = 1/2, so P(A^c) = P(B^c) = 1/2. In any case, A^c and B^c are a similar occasion (getting heads or tails, separately), so P(A^c n B^c) = P(A^c) = 1/2. Then again, P(A^c) P(B^c) = (1/2)(1/2) = 1/4, which isn't equivalent to P(A^c n B^c).

Consequently, proclamation (a) is misleading.

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Answer:

Left graph - not a function

Middle graph - function

Right graph - function

Step-by-step explanation:

An easy way to see if a graph represents a function is to do what's called the vertical line test. If you can draw a vertical line and move it across any place on the graph without intersecting more than one point, then it is a function. I recommend looking at some videos online to explain it better visually.

The factorize expression of 25x²-4x²-9 is 3(7x²-3).

Factorization is a process to simplify the expression by finding the factors of that expression.

And to find the same expression from factors, you have to reverse the process.

We have the quadratic function,

25x²-4x²-9.

To factorize the function:

First, combine similar terms,

25x²-4x²-9,

= 21x²-9.

Now, factor out the common factor.

That means,

3(7x²-3).

Therefore, the required function is 3(7x²-3).

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Quality Homes Construction Company orders only lumber that is at least 80% clear-free of defects. including knots and edge defects. in an order containing 65,500 linear feet, 52,400 linear feet of lumber will be free of defects.

Percentage of Defect-Free Lumber-

Quality Homes Construction Company orders lumber that is at least a certain percentage clear-free of any sort of defects. then they go ahead and order a big supply of lumber. Using percentages from Algebra we calculate the amount of the lumber that will be totally free of any defects. Percentages play an important role in Algebra as well as in Probability and Statistics.

Gives that at least 80% = 0.8 of the lumber is clear free of all defects, the minimum amount of lumber free of all defects will then be

0.8 x 65,500 = 52,400 linear feet of lumber.

Hence, 52,400 linear feet of lumber will be free of defects.

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A line graph is best suited for showing changes in statistics over time or space.

Line graphs are commonly used to visualize trends, patterns, and fluctuations in data over a continuous or discrete period. The x-axis represents time or space, while the y-axis represents the corresponding statistic being measured. The line graph connects the data points, allowing for a clear representation of how the statistic changes over the given time or space interval.

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It is true that the A shift is a type of permutation where elements in a sequence or set are moved to the right or left by a certain number of positions.

For example, shifting the sequence (1,2,3,4,5) to the right by 2 positions would result in the sequence (4,5,1,2,3). This can be represented mathematically as (1,2,3,4,5) → (4,5,1,2,3), which is a permutation of the original sequence. Shifts can be useful in various applications, such as cryptography or data compression, where rearranging elements in a sequence can improve efficiency or security.

True. A shift is a specific type of permutation. In general, a permutation refers to the arrangement of objects in a particular order. A shift, also known as a cyclic permutation, involves moving elements of a set in a fixed direction, such that the order is maintained, but the elements change positions. In a shift, the first element moves to the last position, while all other elements move one position forward. This maintains the relative order of the elements and results in a new arrangement. Therefore, a shift is a type of permutation, as it represents an altered ordering of the elements in a set.

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Given:

The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.

Required:

What test score is 0.8 standard deviations below the mean?

Explanation:

Answer:

answered the question.

The scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we have that the original and the dilated figures are given as follows:

Hence the scale factor is found dividing one side length of the right triangle on the right by the equivalent side length on the right triangle on the left.

The problem is incomplete, hence the general procedure to obtain the scale factor was presented.

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The personnel team should not believe that the mean number is ten

From the question, we have the following parameters that can be used in our computation:

x = the number of sick days they took for the past year

Also, we have the following representation of the values of x

x = 12; 4; 15; 3; 11; 8; 6; 8

The mean of a set of observations can be calculated using the following equation

Mean = Sum of observations/Count of observations

Substitute the known values in the above equation, so, we have the following representation

Mean = (12 + 4 + 15 + 3 + 11 + 8 + 6 + 8)/8

Evaluate the sum in the above equation

So, we have the following representation

Mean = 67/8

Evaluate the quotient in the above equation

So, we have the following representation

Mean = 8.375

8.375 does not approximate to 10

So, the mean number is not ten

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The upper and lower control limits for an X-bar chart and R-chart is as follows:
UCL for X-bar chart = 171.54, LCL for X-bar chart = 120.12
UCL for R-chart = 79.87, LCL for R-chart = 0

Therefore, corrective action is needed.

The upper and lower control limits for an X-bar chart and R-chart can be determined using the following formulas:

Upper Control Limit (UCL) for X-bar chart = X-bar + A2 * R-bar
Lower Control Limit (LCL) for X-bar chart = X-bar - A2 * R-bar

Upper Control Limit (UCL) for R-chart = D4 * R-bar
Lower Control Limit (LCL) for R-chart = D3 * R-bar

Where X-bar is the average of the sample means, R-bar is the average of the sample ranges, A2 is a constant based on the sample size, and D3 and D4 are constants based on the sample size.

First, we need to calculate the average of the sample means (X-bar) and the average of the sample ranges (R-bar):

X-bar = (120 + 90 + 150 + 130 + 110 + 140 + 200 + 180 + 175 + 165 + 155 + 140) / 12 = 145.83

R-bar = ((150 - 90) + (140 - 110) + (200 - 175) + (165 - 140)) / 4 = 35

Next, we need to find the values of A2, D3, and D4 for a sample size of four:

A2 = 0.729
D3 = 0
D4 = 2.282

Now we can calculate the upper and lower control limits for the X-bar chart and R-chart:

UCL for X-bar chart = 145.83 + (0.729 * 35) = 171.54
LCL for X-bar chart = 145.83 - (0.729 * 35) = 120.12

UCL for R-chart = 2.282 * 35 = 79.87
LCL for R-chart = 0 * 35 = 0

The average of these observations is 197.25, which is above the upper control limit for the X-bar chart (171.54). Therefore, corrective action is needed.

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1 container = 5 gallon

The household uses 4 containers that is 20 gallons.

The family uses 20 gallons a week.

1 week = 20 gallons

2.5 weeks = 50 gallons.

1 gal = 3.7584L

50 gallons = 187.92L

The family uses 187.92L in 2.5 weeks.

Answer:

2x^2 - x + 1 + 9/(x - 2)

Step-by-step explanation:

Long division:

x - 2 )2x^3 - 5x^2 + 3x + 7 (2x^2 - x  + 1 <------------Quotient.

        2x^3 - 4x^2

                  -x^2 + 3x

                  -x^2 + 2x

                               x + 7

                                x - 2

                                    9  <-------Remainder.

Answer:

0.01428 hope this is correct and it helps!

Answer:

X=19

Y=20

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Not all students who perform well in Science are good at Maths but some are good at both.

Answer:

Step-by-step explanation:

3x + 4x + x = 16

7x + x = 16

8x = 16

x = 16 : 8

x = 2

----------------------

3 × 2 + 4 × 2 + 2 = 16  (remember PEMDAS)

6 + 8 + 2 = 16

16 = 16

same value the answer is good

Based on the information given, the college administrator has collected a sample of n=100 students and obtained the following statistics: Mean: 7.4 hours per week Standard deviation: 3 hours

Why it is?

These statistics can be used to estimate the average amount of time that all students spend on homework assignments during a typical week, as well as to assess the variability in the data.

To estimate the population mean, the sample mean can be used as an unbiased estimator. This means that the sample mean of 7.4 hours per week is likely a good estimate of the true population mean. However, there is always some uncertainty associated with this estimate due to the fact that it is based on a sample.

To quantify the variability in the data, the standard deviation can be used. A standard deviation of 3 hours indicates that there is a relatively large amount of variability in the amount of time that students spend on homework assignments. Some students may spend significantly more or less time on homework than the average of 7.4 hours per week.

Overall, the college administrator can use this information to gain insights into the amount of time that students spend on homework assignments and to make informed decisions based on this knowledge.

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Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise