g Your underground used-book business is booming. Your policy is to sell all used versions of Calculus and You at the same price (regardless of condition). When you set the price at $10, sales amounted to 100 volumes during the first week of classes. The following semester, you set the price at $30 and sales dropped to zero. Assuming that the demand for books depends linearly on the price, what price gives you the maximum revenue?

Step-by-step explanation:

This expression will be;

m(m + 82).

Answer:

\( P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)\)

And using the probability mass function we got:

\(P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205\)

\(P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117\)

\(P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439\)

\(P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098\)

\(P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977\)

And adding the values we got:

\( P(X\geq 6) = 0.377\)

The best answer would be:

D. 0.377

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

\(X \sim Binom(n=10, p=0.5)\)

The probability mass function for the Binomial distribution is given as:

\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)

Where (nCx) means combinatory and it's given by this formula:

\(nCx=\frac{n!}{(n-x)! x!}\)

For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:

\( P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)\)

And using the probability mass function we got:

\(P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205\)

\(P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117\)

\(P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439\)

\(P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098\)

\(P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977\)

And adding the values we got:

\( P(X\geq 6) = 0.377\)

The best answer would be:

D. 0.377

Answer: 45

Step-by-step explanation:

\(f(-5)=2(-5)^{2} -5\)

\(f(-5)= 2(25) -5\)

\(f(-5) = 50-5\)

\(f(-5) = 45\)

The area that will be painted grey is approximately 38 ft².

The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.

Circumference of a circle = 2πr

30.77 = 2 x 3.14 x r

r = 30.77 / (2 x  3.14) = 4.9 feet

Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.

Area of a circle = π x r²

Area of half the circle = 0.5 x  π x r²

Area of half the circle = 0.5 x 3.14 x 4.9²

Area of half the circle = 37.73 ft²

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It equals a 9% decrease.

Answer:

9%

Step-by-step explanation:

We can do this problem by solving 91/100*100, which is 91, so 100-91=9

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

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

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

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The model for representing the ratio of the number of orange and green rolls are  \(\dfrac{3}{2}\).

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G

The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.

A model that represents the ratio of different colored streamers.

\(\dfrac{O}{G}=\dfrac{3}{2}\)

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.

D=3O   and  D=2G

3O=2G

Hence the models are  \(\dfrac{O}{G}=\dfrac{3}{2}\)  and  3O=2G.

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Answer:

(A) 7

Step-by-step explanation:

\( 4y > 10\)

\(y > \frac{10}{4} \)

\(y > 2.5\)

Since Y is more than 2.5,

the only possible solution is 7, which is (A)

Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

Step-by-step explanation:

look for the LCM of 3 and 10 and since it does not have a LCM you will multiply the two variables. After multiplying, you will then divide your answer by the denominator and multiply it with the denominator

CHECK THE ABOVE PHOTO FOR THE REST

Answer:

x = 36°, 2x° = 72°, 3x° = 108°, and 4x° = 144°

Step-by-step explanation:

Given the quadrilateral in which the sum of its four angles is 360°.

We can establish the following formula to find the value of x, and determine the measures of each angle:

x° + 2x° + 3x° + 4x° = 360°

Combine like terms:

10x° = 360°

Divide both sides by 10 to solve for x:

\(\mathsf{\frac{10x^{\circ}}{10}\:=\: \frac{360^{\circ}}{10}}\)

x = 36°

Substitute the value of x into each unknown angle measures:

x = 36°

2x° = 2(36)° = 72°

3x° = 3(36)° = 108°

4x° = 4(36)° = 144°

Verify whether the sum of the previously unknown angle measures equal 360°:

x° + 2x° + 3x° + 4x° = 360°

36° + 72° + 108° + 144° = 360°

360° = 360° (True statement).

Therefore, the following are the angle measures of the given quadrilateral: x = 36°, 2x° = 72°, 3x° = 108°, and 4x° = 144°

The arc DEB is major arc.

The arcs, arc EA, arc CB, arc DC and arc AB are minor arcs.

The arc CDA is semicircle.

An arc which has a measure of less than 180° is called minor arc.

An arc whose measure is more than 180° is major arc.

Measure of arc EA = 180° - (30° + 100°) = 50°

[Since AC is a diameter CD + DE + EA = 180°]

Measure of arc CB = 50°

Measure of arc DC = 100°

Measure of arc DEB = 360° - (100° + 50°) = 210°

[ Whole circle = 360°]

Measure of arc AB = DEB - (DE + EA) = 210° - (30° + 50°) = 130°

Measure of arc CDA = 180° [Since AC is a diameter.]

Hence the Major arcs are arc DEB, minor arcs are arc EA, arc CB, arc DC and arc AB. Semicircle is arc CDA.

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The figure is given below.

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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The word that describes the slope of the line representing the data in the table is "negative."

To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.

Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.

The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.

Therefore, the word that describes the slope of the line representing the data in the table is "negative."

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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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Answer: The square root of 283 lies between the square roots of 256 and 324, which are 16 and 18, respectively. Therefore, an estimate for the square root of 283 is between 16 and 18, and we can round to the nearest whole number, which is 16.

Step-by-step explanation:

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.

Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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Explanations:

The Price of the jeans = $1265

Percentage tax = 5.2%

Therefore, the total tax = $65.78

The speed limit during the first 125 miles of the trip is 55 mph.

So, it will take 2.3 hours to cover the first 125 miles.

Since the total time to arrive at the destination is 4.5 hours, then it means that they have to cover the rest of the distance in 4.5 - 2.3 = 2.2 hours

So, the speed for the remaining distance must be 81.8 mph which is 81.8 - 75 = 6.8 mph over the limit.

Therefore, 6.8 mph over the limit.

Answer:

E(X) = 9.

Step-by-step explanation:

That is 45 * (0.2) = 9.

The required expected value is given as 9 as per the given conditions.

Given that,

To Calculate the expected value E(X) of the given random variable X. Forty-five darts are thrown at a dartboard. The probability of hitting a bull's eye is .2. Let X be the number of bull's-eyes hit.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The expected value is the scenario predicting algorithm in maths that gives the prediction a value.
So,
According to the question,
E(x) = 0.2 × 45 = 9

Thus, the required expected value is given as 9 as per the given conditions.

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Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

see below

Step-by-step explanation:

Corresponding angles of similar triangles are equal and corresponding sides are proportional so:

m ∠P = m ∠D = 180° - (35° + 89°) = 56°

m ∠Q = m ∠F = 89°

m ∠ R = m ∠E = 35°

PR/DE =PQ/DF

40/DE = 20/24 cross multiply and solve for DE

DE = 40*24/20

DE = 48

scale factor is DF/PQ = 24/20 = 6/5 so  FE = 6/5 *RQ =6/5 *36 = 43.2

The measure of the angles and sides ∠P, ∠R, ∠D, ∠F, DE, and FE will be 56°, 35°, 56°, 89°, 48, and 43.2, respectively.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ∆PRQ is similar to the triangle ∆DEF. Then we have

∠P = ∠D

∠R = ∠E = 35°

∠Q = ∠F = 89°

Then the measure of the angle ∠P is given as,

∠P + ∠R + ∠Q = 180°

∠P + 35° + 89° = 180°

∠P = 56°

∠D = ∠P = 56°

Then the other equation is given as,

PR / DE = RQ / FE = PQ / FD

40 / DE = 36 / FE = 20 / 24

From the last two terms, then we have

36 / FE = 20 / 24

FE = 43.2

From the first and last terms, then we have

40 / DE = 20 / 24

DE = 48

The measure of the angles and sides ∠P, ∠R, ∠D, ∠F, DE, and FE will be 56°, 35°, 56°, 89°, 48, and 43.2, respectively.

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The three integers are 89,406, 89408 and 89410.

What are integers?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Let 'm' be a positive integer.

Then, 2m is an even integer ( as multiplying by 2 makes the number even)

So, 2m+2 is the next integer and 2m+4 is the next.

Now, we have three consecutive integers as 2m, 2m+2 and 2m+4.

We are given that twice the first integer added to the second is 2,68,220, this means

⇒2(2m) + (2m+2) = 2,68,220

⇒4m + 2m + 2 = 2,68,220

⇒6m + 2 = 2,68,220

⇒6m = 2,68,218

⇒m = 44,703

So, 2m = 89,406

2m+2 = 89408

2m+4 = 89410

Hence, the three integers are 89,406, 89408 and 89410.

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Answer:

$475

Step-by-step explanation:

First, we need to subtract 61 from 1011 which given us 950. Then, we divide 950 by 2 to give us the cost of the dryer :)

950 ÷ 2 = 475

This means the cost of the washer is $536 (not relevant to the answer, but at least now you know :) )