An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $6500. On $60,000 in monthly sales, the account executive receives $6800.
(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x.


(b) Use this model to determine the account executive's compensation for $90,000 in monthly sales.
$

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =75 \end{cases}\implies s=\cfrac{(75)\pi (7)}{180}\implies s=\cfrac{35\pi }{12}\implies s\approx 9.2\)

Answer:

a .yes

b.no

c

d.yes

e.no

f

g

h

Therefore , the solution of the given problem of  probability comes out to be the right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

The primary objective of statistical inference, a branch of mathematics, is to determine the chance that a claim is true or that a specific event will occur. Chance can be represented by any number between 0 and 1, in which 1 typically represents certainty and 0 typically represents possibility. A probability diagram shows the chance that a specific event will occur.

Here,

Because the Queen of Hearts and Jack of Spades are not face cards or nines,

the occurrences "Drawing a Queen of Hearts or Jack of Spades from a standard deck of cards" and "Drawing a face card or a 9 from the a standard deck of cards" do not overlap.

A Queen of Hearts is both a red card and a queen, and a diamond is a type of red card and a club is a type of card, so the occurrences "Drawing a Diamond or a Club from a Standard Deck of Cards" and "Drawing a Red Card or a Queen from a Standard Deck of Cards" overlap.

The right response is thus: "Drawing a red card or a Queen from a regular deck of cards is an overlapping occurrence."

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Answer:

600/7% OR 85.71%

Step-by-step explanation:

increase in speed =v-u

I=115-85

I=30km/h

percentage increase =(I/u) ×100

30/85 ×100

6/17×100

600/7%

Answer: hello your question is poorly written hence I will provide the required matrix

answer :

A = \(\left[\begin{array}{ccc}1&0&1\\0&1&1\\1&-1&0\end{array}\right]\)

Step-by-step explanation:

Given that the basis of the orthogonal complement have been provided already by you in the question I will have to provide the Matrix

The required matrix

\(\left[\begin{array}{ccc}1&0&1\\0&1&1\\1&-1&0\end{array}\right]\)

column1 = column 3 - column2

where column 3 and column 2 are the basis of the orthogonal complement of the column space of the Matrix

Answer:

The 95% confidence interval   \( 81.852  <  \mu <  280.098 \)

Step-by-step explanation:

From the question we are told that

   The  sample mean is  \(\= x  =  180.975\)

   The standard deviation is  \(\sigma  =  143.042\)

   The sample size is n = 8

Given that the confidence level is  95%  then the level of significance is  

    \(\alpha =( 100- 95) \%\)

=>  \(\alpha =0.05\)    

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

      \(E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }\)

=>  \(E = 1.96 *  \frac{ 143.042 }{\sqrt{8} }\)

=>  \(E = 99.123 \)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=>    \(180.975 -99.123 <  p <  180.975 +99.123\)

=>    \( 81.852  <  \mu <  280.098 \)

Using the t-distribution, it is found that the 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

The information given is:

We have the standard deviation for the sample, hence, the t-distribution is used.

The interval is given by:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The critical value for a two-tailed 95% confidence interval with 8 - 1 = 7 df is t = 2.3646.

Then:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 180.975 - 2.3646\frac{143.042}{\sqrt{8}} = 61.39\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 180.975 + 2.3646\frac{143.042}{\sqrt{8}} = 300.56\)

The 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments, in millions of dollars, is (61.39, 300.56).

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We have to find derivative of t

\(\\ \sf\longmapsto \dfrac{d}{dx}3t^2-12t+4\)

\(\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}\)

\(\\ \sf\longmapsto \dfrac{d}{dx}3t^2-\dfrac{d}{dx}12t+\dfrac{d}{dx}40\)

\(\\ \sf\longmapsto 6t-12\)

Now

\(\\ \sf\longmapsto 6(8)-12\)

\(\\ \sf\longmapsto 48-12\)

\(\\ \sf\longmapsto 36\)

Answer: -15

Step-by-step explanation:

The average rate of change for the interval from x = 7 to x = 8 is -15. The correct option is B.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

Since the quadratic function has a vertex at (0,3), the equation for the function can be written in vertex form as:

y = a(x - 0)^2 + 3

Where "a" is a constant that determines the shape of the parabola. To find the value of "a", we can use one of the other points on the parabola. Let's use the point (1, 2):

2 = a(1 - 0)^2 + 3

Simplifying this equation, we get:

a = -1

So the equation for the quadratic function is:

y = -x^2 + 3

Now we can use this equation to find the average rate of change between x = 7 and x = 8. The value of the function at x = 7 is:

y = -7^2 + 3 = -46

The value of the function at x = 8 is:

y = -8^2 + 3 = -61

The average rate of change between x = 7 and x = 8 is:

(y2 - y1) / (x2 - x1) = (-61 - (-46)) / (8 - 7) = -15

Therefore, the average rate of change for the interval from x = 7 to x = 8 is -15.

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Using it's concept, the sample space for the experiment is:

The sample space is the set that contains all possible outcomes for an experiment.

In this problem:

Hence, considering the combinations, the sample space is, considering Shirt-Pants-Shoes:

{Blue-Blue-Black, Blue-Blue-Blue, Blue-Black-Black, Blue-Black-Blue, Red-Blue-Black, Red-Blue-Blue, Red-Black-Black, Red-Black-Blue, Black-Blue-Black, Black-Blue-Blue, Black-Black-Black, Black-Black-Blue}

The complement of P(John wears something red) is all outcomes in which he does not wear anything red, hence it is a Blue or Black shirt, along with any combination for the pants and the shoes.

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1) Using order of operations, the solution to the given expression is; 12

2) The estimated cost of groceries if the prices are estimated to the nearest dollar is; $42

In mathematics , the acronym for the right order of operations is PEMDAS which denotes;

P- Parentheses

E- Exponents

M- Multiplication

D- Division

A- Addition

S- Subtraction.

3) From the given statement, we are to add 6 to 12, then divide the sum by 4. Thereafter, we divide the quotient by negative nine and then multiply by twenty-four. This is expressed as;

[(6 + 12)/4] = 18/4 = 9/2

Then divide by -9 to get;

(9/2) ÷ 9 = 1/2

Then we multiply by 24 to get;

1/2 * 24 = 12

4) Let us first estimate each cost to the nearest dollar to get;

$6.47 ≈ $6

$14.72 ≈ $15

$7.99 ≈ $8

$9.40 ≈ $9

$2.79 ≈ $3

Total estimated cost = 6 + 15 + 8 + 9 + 3 = $42

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Answer:

A) The probability that a randomly selected medical student who took the test had a total score that was less than 484 = 0.06178

B) The probability that a randomly selected study participant's response was between 504 and 516 = 0.29019

C) The probability that a randomly selected study participant's response was more than 528 = 0.00357

D) Option D is correct.

Only the event in (c) is unusual as its probability is less than 0.05.

Step-by-step explanation:

The b and c parts of the question are not complete.

B) Find the probability that a randomly selected study participant's response was between 504 and 516

C) Find the probability that a randomly selected study participant's response was more than 528.

D) Identify any unusual event amongst the three events in A, B and C. Explain the reasoning.

a) None.

b) Events A and B.

C) Event A

D) Event C

Solution

This is a normal distribution problem with

Mean = μ = 500

Standard deviation = σ = 10.4

A) Probability that a randomly selected medical student who took the test had a total score that was less than 484 = P(x < 484)

We first normalize or standardize 484

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (484 - 500)/10.4 = - 1.54

To determine the required probability

P(x < 484) = P(z < -1.54)

We'll use data from the normal distribution table for these probabilities

P(x < 484) = P(z < -1.54) = 0.06178

B) Probability that a randomly selected study participant's response was between 504 and 516 = P(504 ≤ x ≤ 516)

We normalize or standardize 504 and 516

For 504

z = (x - μ)/σ = (504 - 500)/10.4 = 0.38

For 516

z = (x - μ)/σ = (516 - 500)/10.4 = 1.54

To determine the required probability

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

We'll use data from the normal distribution table for these probabilities

P(504 ≤ x ≤ 516) = P(0.38 ≤ z ≤ 1.54)

= P(z ≤ 1.54) - P(z ≤ 0.38)

= 0.93822 - 0.64803

= 0.29019

C) Probability that a randomly selected study participant's response was more than 528 = P(x > 528)

We first normalize or standardize 528

z = (x - μ)/σ = (528 - 500)/10.4 = 2.69

To determine the required probability

P(x > 528) = P(z > 2.69)

We'll use data from the normal distribution table for these probabilities

PP(x > 528) = P(z > 2.69) = 1 - P(z ≤ 2.69)

= 1 - 0.99643

= 0.00357

D) Only the event in (c) is unusual as its probability is less than 0.05.

Hope this Helps!!!

I suppose you meant z > 0, or meant to use x's in place of z's…

If z > 0, then

\(\dfrac{20\sqrt{z^6}}{\sqrt{16z^7}} = \dfrac{20\sqrt{\left(z^3\right)^2}}{\sqrt{4^2\left(z^3\right)^2z}} = \dfrac{20\left|z^3\right|}{4\left|z^3\right|\sqrt{z}} = \boxed{\dfrac{5}{\sqrt{z}}}\)

because

\(\sqrt{z^2} = |z|\)

and if z is positive, we have |z| = z, and we can eliminate common factors of z in the fraction,

\(\dfrac{\left|z^3\right|}{\left|z^3\right|} = \dfrac{z^3}{z^3} = 1\)

Answer:

A is the correct answer

Answer:

2 pounds

Step-by-step explanation:

so if we say we decrease 20% each year and we're only going one year. All you have to do is 2.5 - 20%

Answer:

90c^2 -30c - 420

Step-by-step explanation:

-3(-3c+7)5(4+2c)

(9c - 21) (20 + 10c)

180c + 90c^2 - 420 - 210c

90c^2 -30c - 420

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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Answer:

Hello again, my friend :3 here's your answer! sorry i was late, i was on my lunch break, haha.

2(cos 20º + i sin 20º)

2(cos 140º + i sin 140º)

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

Answer:

24

Step-by-step explanation:

Since we know what the variables are, we can substitute them. So, you’ll get 3 x 6 + 6. Next, do 3 x 6, which equals 18. Then add the 6, which finally equals 24.

Hope this helps! :)

Answer:

Nice to hear that, congrats with practice 7.3

Answer:

WHAT ARE WE SUPPOSE TO ANSWER...?

Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.

When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.

Scenario 1: With a down payment

In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.

The benefits of saving for a down payment include:

Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.

Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.

Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.

Scenario 2: Without a down payment

In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.

The drawbacks of not saving for a down payment include:

Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.

Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.

By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.

To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.

In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.

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Question

The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.

given that v1,v2 ,v3,v4 is linearly independent vector so in order for a set of vectors to be linearly independent it must satisfy the below conditon:

   \(x_1v1+x_2v2+x_3v3+x_4v4\) =0  --(i)

  where \(x_1, x_2,x_3 ,x_4\) is some real numbers.

a) so in order to show that v1,v2+v4,v3 is linearly independent we have to

check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have :

   \(x_1v1+x_2(v2+v4) +x_3v3\)   ---(ii)

    where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (ii) we have:

     \(x_1v1+x_2v2+x_3v3+x_2v4\)  

     so the above equation is now transformed in the form of equation (i) where \(x_2 = x_4\)  

and hence \(x_1v1+x_2v2+x_3v3+x_2v4\) =0  ----(iii)

equation (iii) shows that the set of given vectors are linearly independent.

b)  so in order to show that v1 +v2, v3, v4  is linearly independent we have to check if equations formed by these vectors can be transformed into some equation of equation (i) form.

 so we have this equation:

   \(x_1(v1+v2)+ x_2v3 + x_3v4\)      where \(x_1, x_2,x_3\) is some real numbers.

  after evaluating equation (iv) we have:

     \(x_1v1+x_1v2+x_2v3+x_3v4\)  

     so the above equation is now transformed in the form of equation (i) where the cofficient of v2 is also \(x_1\)  

and hence \(x_1v1+x_1v2+x_2v3+x_3v4\) =0  ----(v)

equation (v) shows that the set of given vectors are linearly independent.

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Complete question :

let v be a real vector space. suppose that v1, v2, v3, v4 are vectors in v which are linearly independent. show that the vectors a) v1, v2+v4, v3 and   b) v1 +v2, v3, v4 are also linearly independent.

The vectors v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent is hence proved.

let v be a real vector space.

The v1, v2, v3, v4 are vectors in v which are linearly independent.

V={v1, v2, v3, v4} then set V is called  linearly independent if \(\forall \alpha_i \in F \\\).

∝1v1+∝2v2+∝3v3+..........+∝nvn=0

then, \(\forall \alpha_i =0 \\\) i=1,2,3......n.

let ∝1,∝2,∝3,∝4 ε F

∝1v1+∝2(v1+v2)+∝3(v1+v2+v3)+∝4(v1+v2+v3+v4)=0

v1(∝1+∝2+∝3+∝4)+v2(∝2+∝3+∝4)+v3(∝3+∝4)+v4.∝4=0

Since  v1, v2, v3, v4 are linearly independent vectors.

So ∝1+∝2+∝3+∝4=0......(1)

∝2+∝3+∝4=0....(2)

∝3+∝4=0....(3)

∝4=0...(4)

Solving eq(1), (2), (3), (4)

we get ∝1=∝2=∝3=∝4=0

So according to definition of linearly independent vectors.

A set of vectors is called linearly independent if no vector in the set can be expressed as a linear combination of the other vectors in the set. If any of the vectors can be expressed as a linear combination of the others, then the set is said to be linearly dependent.

So v1, v1+v2, v1+v2+v3, v1+v2+v3+v4 are also linearly independent vectors hence proved.

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Answer:

the top right and bottom right

Step-by-step explanation:

the macadamia nuts cost the most, meaning there doesn't have to be as much as the peanuts to get a high price. And the peanuts are cheaper than the macadamia nuts and the blueberries, meaning that there has to be more of them causing more weight.

Answer: The 2nd one and the 4th one on the right side.

Answer: product distribution?

Answer:

80 deg

Step-by-step explanation:

add up to 180 deg, we can come up with the equation 4x +5x =180. Solving this out shows us that x = 20 and the measure of angle J is 100 deg while the measure of angle M is 80 deg.

Answer: 50! = 3.0414093e+64.       4!= 24.     46!=5.5026222e+57

hm this is weird, i thought i answered the question. or maybe they're two different questions? line graph because i said so. i know im so helpful