The budget for a project on voting trends includes $3200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews for $100. Each graduate student will conduct 32 interviews for $150. Each faculty member will conduct 33 interviews for $200. No more than 20 interviewers can be hired.
(a) How many of each type of interviewer should be hired in order to maximize the number of interviews?
(b) What is the maximum number of interviews?

Answer:

(5w - 3)(2w - 5)

Step-by-step explanation:

As this polynomial is of the form ax² + bx + c, where a = 10, b = -31, and c = 15 (and x = w), in this case, as a is a number other than 1, the first step is to multiply a and c, replacing c with that product and removing the coefficient from the w² term, giving us:

w² - 31w + 150 (as 10 × 50 is 150)

Now, we are looking for two numbers that when they're multiplied together you get c, which is 150, and those same two numbers when added together gives us b, -31.

After looking through all of the possible factors of 150, we see that -25 and -6 fulfill both of these requirements (as -25 × -6 = 150 and -25 + -6 = -31)

Now, as we have our two numbers we can set up our factors:

(w - 6)(w - 25)

However, as we had to get rid of the 10 in front of the w², we now have to bring it back in front of both w's, giving us:

(10w - 6)(10w - 25)

Now we look and see if we can simplify.

We can see that 10 and -6 can both be simplified by 2, giving us:

(5w - 3)(10w - 25)

We can also see that 10 and -25 can be simplified by 5, giving us:

(5w - 3)(2w - 5)

The simplified expression by using box method to distribute is [tex]5x^2 - 6x - 8.[/tex]

In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, -, x, ÷, etc.) that represents a quantity or a relationship between quantities. Expressions can be simple, such as a single number or variable, or complex, such as an algebraic expression with multiple terms and variables. Expressions can be evaluated, simplified, and manipulated using various algebraic techniques.

To use the box method, we draw a box and divide it into four parts, with each part representing a multiplication of one term from the first expression with one term from the second expression:

We then add up the terms in each box to simplify:

(5x + 4)(x - 2) = [tex]5x^2 - 10x + 4x - 8[/tex]

                      = [tex]5x^2 - 6x - 8[/tex]

Hence, the simplified expression is [tex]5x^2 - 6x - 8.[/tex]

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Answer:

Step-by-step explanation:ok first you add 3 to 2 and the x is for times

According to Yaseen's demand function, if she can produce 60 kits, the function cost per kit should be set at:

[tex]p = 30 - 0.5q\s60 = q = > p = 30 - 0.5(60) (60) > p = $15[/tex]

Probability theory is an area of mathematics that deals with calculating the likelihood that an event will occur or a proposition will be true. A risk is a number between 0 and 1, where 0 represents the possibility of an event occurring and 1 represents certainty.

Probability is a mathematical expression of the possibility that an event will occur. The proportion of equally plausible options that actually occur relative to all potential outcomes when an event happens is known as the probability, and it may also be written as an integer between 0 and 1.

According to Yaseen's supply function, if she can produce 15 kits, the cost per kit she should charge is:

[tex]p = 10 + 0.5q[/tex]

[tex]p = 10 + 0.5(15) (15)[/tex]

[tex]p = $17.50[/tex]

According to Yaseen's demand function, if she can produce 15 kits, the cost per kit she should charge is:

[tex]p = 30 - 0.5q\sp = 30 - 0.5(15) (15)[/tex]

[tex]p = $22.50[/tex]

According to Yaseen's supply function, if she can provide 60 kits, the cost per kit should be as follows:  [tex]p = 10 + 0.5q 60 = q p = 10 + 0.5 (60)[/tex]

[tex]p = $40[/tex]

According to Yaseen's demand function, if she can produce 60 kits, the cost per kit should be set at:

[tex]p = 30 - 0.5q\s 60 = q[/tex]

[tex]p = 30 - 0.5(60) (60)[/tex]

[tex]p = $15[/tex]

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Answer:

Step-by-step explanation:

1. Demand- 0<=x<=85 /  Supply- 0<=x<=100

The company is estimating that no more then 85 kits will be demanded each month. The company can supply no more then 100 kits per month.

2. x=15

S(15)=0.01(15)^2+0.5(15)=9.75

D(15)=0.02(15-100)^2=144.5

3. x=60

S(60)=0.01(60)^2+0.5(60)=66

D(60)=0.02(60-100)^2=32

4. The supply in question 3 is larger then the demand. Supply>Demand- No, because the demanding price is much lower.

5. X^2- Quadratics because in math the quadratic equation of degree 2 is the highest exponent of the equation with the standard as y=ax^2+bx+c

6. See attachment

7. f(x)=0.02(x-100)^2      g(x)=0.01x^2+0.5x

They intersect on the graph at (50, 50) so the products is 50.

8. See Attachment

f(x)=0.02(x-100)^2

g(x)=0.01x^2+0.5x

The reduced price of the piano is $301 if Lou went shopping for a piano at our ST store a piano originally priced at $860 had a price reduction of 65%

What is percentage ?

Percentage can be defined as the product of ratio of given value, total value and hundred.

To find the reduced price of the piano, we need to multiply the original price by the discount percentage (65%) and then subtract the result from the original price.

The amount of the discount is:

65% of $860 = 0.65 x $860 = $559

So, the reduced price of the piano after the discount is:

Reduced price = Original price - Discount

Reduced price = $860 - $559

Reduced price = $301

Therefore, the reduced price of the piano is $301.

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Mu X is a statistical concept used to measure the difference between two means.

It is calculated by subtracting the mean of one group from the mean of another group. Mu X is often used to compare the means of two or more groups, or to compare the means of two subgroups within a group. It can also be used to measure the relative size of a group's mean compared to the grand mean or the size of a group's mean compared to the mean of another group. Mu X is a useful tool for distinguishing between true and false differences between two means. It is also useful for understanding the relative importance of different factors in a study. Mu X is sometimes referred to as the difference in means or the mean difference, and it is an important concept in inferential statistics.

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The number 85, written as the sum of two square numbers in two different ways is 2² + 9² and 6² + 7²

From the question, we are to write the given number as the sum of two square numbers in two different ways.

From the given information, the given number is 85

First, we will evaluate the squares of numbers from 1 to 9

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

From above,

4 + 81 = 85

Thus,

2² + 9² = 85

and

36 + 49 = 85

Thus,

6² + 7² = 85

Hence, the sum of the squares are 2² + 9² and 6² + 7²

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Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5-2(4+3(-1))}{2} \\ \\ =\frac{5-2(4-3)}{2} \\ \\ =\frac{5-2(1)}{2} \\ \\ =\frac{3}{2}[/tex]

The percent change in the price of cellphone from 2010 to today is 58.3%

The price of a cellphone today is $380

In 2010, the price of a similar cellphone was $240

The percent change can be calculated as follows

380-240/240 × 100

= 140/240 × 100

= 0.583 × 100

= 58.3

Hence the percent of change in the price of a cellphone from today is 58.3%

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The least polynomial that contains the roots - 6, 0, 3 - √5 is equal to y = x⁴ - 5 · x³  - 2 · x² + 4 · x.

In this problem we must determine a polynomial function that contains the following roots: - 6, 0, 3 - √5. By quadratic formula we understand the quadratic polynomial may contain two roots of this kind: x₁ = α + β and x₂ = α - β. Therefore, the complete set of roots of the least polynomial is:

x₁ = - 6, x₂ = 0, x₃ = 3 - √5, x₄ = 3 + √5

And the factor form of the least polynomial is:

y = (x + 6) · x · (x - 3 + √5) · (x - 3 - √5)

y = (x² + x) · [(x - 3)² - 5]

y = (x² + x) · (x² - 6 · x + 4)

y = x⁴ + x³ - 6 · x³ - 6 · x² + 4 · x² + 4 · x

y = x⁴ - 5 · x³  - 2 · x² + 4 · x

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The QS would be QS = PQ(1 + PQ/13)

What are the sides and angles of a parallelogram?

S = (n 2) 180°, where 'n' specifies the number of sides in the polygon, can also be used to determine this.

Since PQRS is a parallelogram, opposite sides are parallel and equal in length. Therefore, we can say that PQ = SR and QS = PR.

If QX = 13, then we can use the fact that PQRS is a parallelogram to find the length of QS. We can draw a line segment from Q that is parallel to SR, and call the point where this line segment intersects PS as Y. This forms two triangles, QXY and QSR, which are similar because they share an angle and have parallel sides.

By the properties of similar triangles, we can set up a proportion:

QY/QX = QS/SR

Since QY is the same as PS, we can substitute PQ + QY for PS:

(QX + PQ)/QX = QS/SR

Substituting the value of QX and recognizing that PQ = SR, we get:

(13 + PQ)/13 = QS/PQ

Simplifying this equation, we get:

1 + PQ/13 = QS/PQ

Multiplying both sides by PQ, we get:

PQ + (PQ^2/13) = QS

Since PQ = SR and PQRS is a parallelogram, we know that SR = PQ, so we can substitute PQ for SR:

QS = PQ + (PQ^2/13)

Simplifying further, we get:

QS = PQ(1 + PQ/13)

Therefore, The QS would be QS = PQ(1 + PQ/13)

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Answer: 40 fluid ounces is approximately equal to 1182.94 milliliters.

Step-by-step explanation:

A fluid ounce (oz) is a unit of volume used in the United States and some other countries, while milliliters (ml) are used in the metric system. To convert ounces to milliliters, we can use the conversion factor of 29.5735 ml per fluid ounce.

So, 40 fluid ounces is equal to:

40 oz * 29.5735 ml/oz = 1182.94 ml

Therefore, 40 fluid ounces is approximately equal to 1182.94 milliliters.

The function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.

A function can be transformed by flipping its graph around an axis, which is known as a reflection function. Reflecting or reflection in mathematics, and more precisely in geometry, refers to flipping. Hence, a function's reflection is essentially the mirror image of the supplied function or graph. As a result, reflecting functions are a common name for them.

The given function is: f(c) = 6 (1/3)ˣ.

When a function is reflected along the y-axis the coordinates of the graph change as follows:

(x, y) → (-x, y)

The function f(c) = 6 (1/3)ˣ when reflected will have the function g(c) as:

g(c) = -6(1/3)⁻ˣ

Hence, the function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.

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you can get 25 full cases of oil from a full 150-gallon oil tank.

Quarts (abbreviated as "qt") is a unit of measurement commonly used for volume in both the US customary and British imperial measurement systems. One quart is equal to 32 fluid ounces, 2 pints, or 0.25 gallons.

given by the question: -

There are 4 quarts in a gallon, so a 150-gallon oil tank contains:

150 gallons * 4 quarts/gallon = 600 quarts of oil

To pack a full case of oil, we need 24 quarts of oil. So, the number of full cases of oil that can be obtained from a 150-gallon oil tank is:

600 quarts of oil / 24 quarts per case = 25 cases of oil

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Answer:

24%

Step-by-step explanation:

It’s easy all u have to do is add the 95% and 15%

And when u get the answer u add it with 1.10$ and boom u subtract the number and u get 24%.

Answer: $1.80 and $11.40

Step-by-step explanation:

We know that Chris was short on cash by $1.20, but we need to create an equivalent percentage.

95% + 15% = 110% (how much does it cost)

110% - 110% (how much he had) = 10% (amount short) = $1.20

10% = $1.20

100% (how much he had) = $12.00

Mouse = 95% of $12.00 (how much he had) = $11.40

Mouse pad = 15% of $12.00 (how much he had) = $1.80

Check your work:

$1.80 (Mouse pad) + $11.40 (Mouse) = $13.20

$13.20 - $12.00 = $1.20 (amount short)

We were correct!

Final Answer: $1.80 and $11.40

Answer:

b = -0.5

Step-by-step explanation:

−3b + 2.5 = 4

-3b = 1.5

b = -0.5

Let's check

-3(-0.5) + 2.5 = 4

1.5 + 2.5 = 4

4 = 4

So, b = -0.5 is the correct answer.

$3,600

Simple interest is the amount of money earned based on the initial amount invested.

Simple Interest Formula

The formula for simple interest is A = P(1 + rt). Let's define each of these variables.

To solve for simple interest, we need to plug in the information we are given.

Solving Simple Interest

In the question, we're told that $3000 is the initial amount deposited, so P = 3000. The rate is 2%, which means that r = 0.02. Also, this interest is earned over 10 years, thus t = 10. Now, plug this into the formula above.

Then, just simplify the right side of the equation.

This means that after 10 years, there will be a total of $3600 in the account.

The probability of people in the survey who likes dogs is given by the equation P ( D ) = 26 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of people who likes dogs be represented as P ( D )

Now , the equation will be

The probability of people who likes cats P ( C ) = 4 %

The probability of people who likes cats and dogs = P ( C ∩ D ) = 63 %

The probability of people who likes dogs P ( D ) = 26 %

The probability of people who doesn't like cats or dogs 1 - P ( C∪D ) = 7 %

Therefore , the value of P ( D ) = 26%

Hence , probability of people in the survey who likes dogs is 26 %

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Answer:

C. 3

Step-by-step explanation:

One of the (many) properties of definite integrals is
[tex]\mbox{\large \int\limits _{a}^{b}f(x)\,dx + \int\limits _{b}^{c}f(x)\,dx = \int\limits }_{a}^{c}f(x)\,dx[/tex]

Therefore
[tex]\mbox{\large \int\limits _{-2}^{5}f(x)\,dx + \int\limits _{5}^{2}f(x)\,dx = \int\limits }_{-2}^{2}f(x)\,dx[/tex]

Given

[tex]\mbox{\large \int\limits _{-2}^{5}f(x)\,dx = 11}}}\para[/tex]

and

[tex]\mbox{\large \int\limits _{-2}^{2}f(x)\,dx = 14}}[/tex]

We get

[tex]\mbox{\large 11+ \int\limits _{5}^{2}f(x)\,dx} = 14[/tex]

Subtracting 11 from both sides we get

[tex]\mbox{\large \int\limits _{5}^{2}f(x)\,dx} = 14 - 11 = 3\\[/tex]

Answer: Choice C which is 3

By writing this program, you will gain a better understanding of how this process works and how databases are used in real-world applications.

Here you will write a program that takes two inputs: the current price of a house and the price of the same house from last month. These inputs should be integers. The program will then use these inputs to produce a summary of the house price information.

The first part of the summary will simply list the current price of the house. This information is stored in the database and is retrieved by the program when it starts.

The next part of the summary will be the change in the house price since last month. This information is also stored in the database and is calculated by subtracting the price from last month from the current price.

Finally, the program will output the estimated monthly mortgage payment for the house. This is calculated by multiplying the current price of the house by 0.051 and then dividing the result by 12. This information is also stored in the database and is retrieved by the program when it starts.

In conclusion, websites like Zillow use databases to gather and store information about house prices, and they use that information to create summaries for their readers.

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Answer:

Step-by-step explanation:

-150

Answer: -15x + 30

Step-by-step explanation:

-3(5x) = -15x (positive x negative = negative)

-3(-10) = 30 (negative x (negative = positive)

(same symbols = positive)

(Different symbols = negative)

Answer:

WJENW

Step-by-step explanation:

Answer:

[tex]\textsf{C)} \quad \dfrac{23}{60}[/tex]

Step-by-step explanation:

The odd number outcomes are 1, 3 and 5.

The probability for rolling each of the odd numbers is the frequency of the outcome divided by the total number of rolls.

[tex]\implies \sf P(x=1)=\dfrac{8}{60}[/tex]

[tex]\implies \sf P(x=3)=\dfrac{6}{60}[/tex]

[tex]\implies \sf P(x=5)=\dfrac{9}{60}[/tex]

Therefore, the experimental probability that the number rolled was odd is:

[tex]\begin{aligned}\sf P(x\;is\;odd)&=\sf P(x=1)\;or\;P(x=3)\;or\;P(x=5)\\\\&=\sf \dfrac{8}{60}+\dfrac{6}{60}+\dfrac{9}{60}\\\\&=\sf \dfrac{8+6+9}{60}\\\\&=\sf \dfrac{23}{60}\end{aligned}[/tex]

The solution to the system of equations is x = 35/9 and y = -20/27.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

I assume the second equation is supposed to be equal to zero, so the system of equations is:

-2x + 3y = -10

-7x + 3y = -25

To solve this system of equations using elimination, we can add the two equations together. This will eliminate the y variable and give us an equation in terms of x:

-2x + 3y + (-7x + 3y) = -10 - 25

-9x = -35

x = 35/9

Now that we know x, we can substitute it into either equation to solve for y. Let's use the first equation:

-2x + 3y = -10

-2(35/9) + 3y = -10

-70/9 + 3y = -90/9

3y = -20/9

y = -20/27

Therefore, the solution to the system of equations is x = 35/9 and y = -20/27.

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linear  function would best fit the data because as x increases, the y values ​​change values by 4518. The slope of this function is approximately 4518

What is a linear equation?

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

linear  function would best fit the data because as x increases, the y values ​​change values by 4518.

The slope of this  function is approximately 4518

Slope = change in y values /  change in x values

         =( 27520.99-23002.99)/(2-1)

         = 4518/1

        = 4518

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Answer:

12

Step-by-step explanation:

The large triangle is 4 times the size of the smallest one.

17*4=68, 8*4=32, and 15*4=60.

We know what the side length is now, so we set up an equation.
60=4x+12
Subtract 12 from both sides.
60-12=4x+(12-12)
48=4x
Divide
48/4=4x/4
12=x

Answer:

[tex]12xy-20xz[/tex]

Step-by-step explanation:

From trigonometric ratios, the value of x and y are 11 [tex]\sqrt{3}[/tex] and 11, respectively.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) ,  cos  (x) and tan  (x) , where:

sin (x) =[tex]\frac{opposite\ leg}{hypotenuse}[/tex]

cos(x)=[tex]\frac{adjacent\ leg}{hypotenuse}[/tex]

tan (x) = [tex]\frac{sin (x)}{cos(s)}= \frac{opposite\ leg}{adjacent\ leg}[/tex]

Therefore, for finding x you can apply the trigonometric ratio sin (x). See below:

sin (60) =[tex]\frac{opposite\ leg}{hypotenuse}=\frac{x}{22}[/tex], knowing that  sin (60)=[tex]\frac{\sqrt{3} }{2}[/tex] you have

[tex]\frac{\sqrt{3} }{2}=\frac{x}{22} \\ \\ 2x=22\sqrt{3} \\ \\ x=11\sqrt{3}[/tex]

For finding y you can apply the trigonometric ratio tan (x). See below:

tan (60) =[tex]\frac{opposite\ leg}{adjacent\ leg}=\frac{x}{y}[/tex], knowing that  tan (60)=[tex]\sqrt{3}[/tex] and x=[tex]11\sqrt{3}[/tex], you have

[tex]\sqrt{3} =\frac{x}{y} \\ \\ \sqrt{3} =\frac{11\sqrt{3} }{y}\\ \\ y\sqrt{3} =11\sqrt{3} \\ \\ y=11[/tex]

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Answer:

Type of sequence: Geometric

Common ratio:  [tex]\mbox{\large \dfrac{1}{2}}[/tex]

Explicit equation:
[tex]a_n = a_1 \cdot \left(\dfrac{1}{2}\right)^{n-1 }[/tex]

Recursive Equation:
[tex]\mbox{\large a_n = \dfrac{1}{2} \cdot a_{n-1}}[/tex]

Step-by-step explanation:

Looking at the first and fifth terms it appears to be a geometric sequence where each successive term is r x previous term

r is referred to as the common ratio = aₙ/aₙ₋₁ where aₙ is the nth term and aₙ₋₁ the previous term

The nth term can be found by using the formula
aₙ = a₁ x rⁿ⁻¹

where a₁ is the first term

We have a₁ = -2

a₅ = - 1/8

Plugging these into the general equation for a geometric sequence we get

[tex]-\dfrac{1}{8} = -2 \cdot r^{5-1}\\\\\\-\dfrac{1}{8} = -2 \cdot r^{4}\\\\r^4 = -\dfrac{1}{8} \div -2\\\\\\r^4 = \dfrac{1}{16}\\\\\\r = \sqrt[4]{\dfrac{1}{16}} \\\\r = \dfrac{1}{2} \;\;\;\;\textrm(since \; 2^4 = 16)[/tex]

Recursive equation relates the nth term to the (n-1)th term and is

[tex]a_n = \dfrac{1}{2} \cdot a_{n-1}[/tex]

If we start at the first term

a₁ = -2

a₂ = 1/2 x (-2) = - 1

a₃ = 1/2 x (-1) = - 1/2

a₄ = 1/2 x (-1/2) = -1/4

a₅ = 1/2 x (-1/4) = - 1/8

So everything pans out fine