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

Step-by-step explanation:

We can find the other point using the axis of symmetry.

The axis of symmetry for a parabola passes through the x coordinate of the vertex.

So our axis of symmetry is x=4, which is a vertical line.

For any point on a parabola curve except the vertex, there will two points that share the same y value. The two x coordinates of those points midpoints should be the axis of symmetry.

So,

If we know (0,-6) and the vertex is 4, let's find the other point

[tex]( \frac{0 + b}{2} = 4[/tex]

[tex]b = 8[/tex]

So our other point is

(8,-6).

So the answer to #1 is we found point (8,-6) by using the axis of symmetry. By reflecting the point (0,-6) about the vertical line x=4, we end up getting the point (8,-6)

To find q, q(x) has the same vertex, so it is (4,10).

We know the axis of symmetry is x=4, we also know the y intercept is 18 so we have point (0,18)

Using the axis of symmetry we will get (8,18).

So the graphs above are the graphs of p and q

The graph facing upwards is q

The graph facing downwards is p.

For #2, you can say we know the vertex is (4,10) and using the y intercept and axis of symmetry we found the other point on the curve.

I don't fully see the table but if the other coordinates have a higher y value, the vertex is a minimum.

Else, of the other coordinates have a lower y value, the vertex is a maximum.

The radius of the circle is 21.92 feet

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

A square lawn has an area of 1922 square feet

This means that

Area = 1922

Take the square root of both sides to determine the side length

side length = 43.84

This represents the circle diameter

So, we divide by 2

radius = 21.92

Hence, the radius is 21.92

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The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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Answer:

Step-by-step explanation:

480 meters is the whole field.

One quarter of it is equal to 480 ÷ 4 = 120.

She is traveling 20 meters per minute.

120 ÷ 20 = 6

It takes her six minutes.

The value of side DE of the triangle is 14.91 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

In triangle CDF,

tan 61° = DF/24

DF = 24 * tan 61°

DF = 43.30 units

In triangle DEF,

tan 19° = DE/43.30

DE = 43.30 * tan 19°

DE = 14.91 units

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The probability that he teleports at least once per day is [tex]\frac{5}{9}[/tex].

the Marvin must select one of the three transportation alternatives at random.

The likelihood of selecting any one of the three alternatives is the same since the selection is random.

The likelihood of successful teleportation on the first try is:

[tex]P_t=\frac{1}{3}[/tex]

Consequently, the likelihood that you do not teleport is

q=1-p

q=1-[tex]\frac{1}{3}[/tex]

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

The likelihood that the Marvin won't teleport when leaving for work and returning from work is as follows:

P=[tex]\frac{2}{3}[/tex]×[tex]\frac{2}{3}[/tex]

P=[tex]\frac{4}{9}[/tex]

As a result, the probability that someone will teleport at least once is:

P=1-[tex]\frac{4}{9}[/tex]

P=[tex]\frac{5}{9}[/tex]

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Answer:  

4

Step-by-step explanation:

Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.

A restaurant is a business that prepares and serves food and drinks to customers. [1] Meals are generally served and eaten on the premises, but many restaurants also offer take-out and food delivery services.

18/100 = .18

58 x .18 = 10.44

⇒ 58 + 10.44 = 68.44

Hence, Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. The correct answer is $68.44.

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The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The integration equation is given below.

[tex]\begin{aligned} \rm I = \int _1^2 \sqrt{x^2 - 4} \ dx \end{aligned}[/tex]

We know that the formula is given as,

∫√(x² - a²) dx = (x/2)√(x² - a²) + (a² / 2) log [x + √(x² - a²)]

Then by the integration, we can write it as,

[tex]\begin{aligned} \rm I &= \int _1^2 \sqrt{x^2 - 4} \ dx \\\rm I &= \int _1^2 \sqrt{x^2 - 2^2} \dx\\\rm I &= \left [ \dfrac{x}{2}\sqrt{x^2-2^2} + \dfrac{2^2}{2} \log (x + \sqrt{x^2 - 2^2}) \right ]^2_1\\\end{aligned}[/tex]

Simplify the equation further, then we have

I = [(1/2) i√3 + 2 log (1 + 3i)]

The integration of the given equation will be [(1/2) i√3 + 2 log (1 + 3i)].

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Answer:

Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era

The measure of the side FG that is h using the sine law will be 786.63 centimeters.

The sine law in the triangle ΔFGH is given as,

FG / sin H = GH / sin F = FH / sin G

In ΔFGH, f = 600 cm, m∠F = 32°, and m∠G = 12°.

We know that the aggregate of the gradient of the triangle is 180°. Then the angle H is given as,

∠F + ∠G + ∠H = 180°

32° + 12° + ∠H = 180°

                  ∠H = 136°

The length of the triangle 'h' is given as,

FG / sin H = GH / sin F

h / sin 136° = f / sin 32°

h = 600 (sin 136° / sin 32°)

h = 600 x 1.31

h = 786.63 cm

The measure of the side FG that is h using the sine law will be 786.63 centimeters.

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Based on the ratios of sand, silt, and clay particles contained in a soil sample, soil scientists and farmers use the soil texture triangle to categorize and define the texture of soil. It is a graphic representation of the system for classifying soil textures.

Agricultural experts and soil scientists utilize the Soil Texture Triangle, a graphic representation, to categorize soil according to its texture. The triangle's three portions stand in for the three major categories of soil particles: sand, silt, and clay.

Based on the proportion of each type of particle present in a soil sample, the Soil Texture Triangle can be used to determine the texture of the soil. A soil scientist can rapidly categorize a soil as sandy, loamy, or clayey by plotting the percentage of sand, silt, and clay on the triangle.

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A. The equation is given as C = 0.1T + 0.05M

B. It will cost Laura $1.05 to send 4 texts and talk for 13 minutes.

C. Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.

D. The equation for T is T = (C - 0.05M) / 0.1.

A. The equation for the cost, C, of sending both texts and talking for M minutes is:

C = 0.1T + 0.05M

where T is the number of texts sent.

This equation assumes that each text costs 10 cents and each minute of talk time costs 5 cents.

B. To calculate the cost of sending 4 texts and talking for 13 minutes, we can use the equation from part A:

C = 0.1T + 0.05M

C = 0.1(4) + 0.05(13)

C = 0.4 + 0.65

C = 1.05

Therefore, it will cost Laura $1.05 to send 4 texts and talk for 13 minutes.

C. To determine how many minutes Laura can talk if she wants to send 18 texts and only has eight dollars, we need to use the equation from part A and solve for M:

C = 0.1T + 0.05M

8 = 0.1(18) + 0.05M

8 = 1.8 + 0.05M

6.2 = 0.05M

M = 124

Therefore, Laura can talk for 124 minutes if she wants to send 18 texts and has eight dollars.

This will cost her $6.20, which is less than the amount of money she has, so she will have some money left over.

subtract the cost of talking and texting from the amount of money she has:

Money left = 8 - 6.20

Money left = 1.80

Therefore, Laura will have $1.80 left after sending 18 texts and talking for 124 minutes.

D. To solve the equation from part A for T, we can rearrange the terms:

C = 0.1T + 0.05M

0.1T = C - 0.05M

T = (C - 0.05M) / 0.1

Therefore, the equation for T is T = (C - 0.05M) / 0.1.

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The error in the solution is that the answer is written as 3000 instead of 30.

Percentage is defined as the parts of a number per fraction of 100 and it is denoted by the symbol '%'.

Percentage of a number is calculated as dividing the number with it's whole and then multiplying with 100.

We have to find the percentage of 40% of 75.

That is, the number which corresponds to the 40 parts per 100 of the number 75.

40% of 75 = 40% × 75

                 = (40 / 100) × 75

                 = 0.4 × 75

                 = 30

The correct percentage is 30, not 3000.

Hence the error is in the answer for which 30 is the correct answer.

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The height of the cylindrical tub of ice cream is 6.75 inches.

A cylinder is a 3 dimensional shape which has a curved side and two circular surfaces. The total surface area can be determined by the expression;

total surface area of a cylinder = 2πr^2 + 2πrh

where r is the radius of it circular surface, and h is its height.

Considering the given question, we have;

total surface area of a cylinder = 2πr^2 + 2πrh

But total surface area = 183.69 square inches

r = D/2

  = 6/ 2

r = 3 inches

Thus,

183.69 = 2*3.14*3^2 + 2*3.14*3*h

           = 56.52 + 18.84h

183.69 - 56.52 = 18.84h

127.17 = 18.84h

h = 127.17/ 18.84

  = 6.75

The height of the cylindrical tub of ice cream is 6.75 inches.

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Answer: The answer is (C) 6.75

Step-by-step explanation:

The formula for Surface Area is: SA = 2πr^2 + 2πrh

Let's do the first part: 2πr^2

So you need to find the radius, which is half the diameter. 6 is the diameter so half that, and you get 3.

Now, times 3 by itself

3 * 3 = 9

And then times 9 by 2

9 * 2 = 18

And times 18 by pi, 3.14

18 * 3.14 = 56.52

Now that we have our first value, lets move on to the second part of the formula: 2πrh

So we need the diameter, and the question gives us the value of the diameter.

6 is the diameter

so times 6 by pi, 3.14

6 * 3.14 = 18.84h  (leave h there because we don't know the height)

Now do this:

183.69 =  56.52 + 18.84h

You cannot add 56.52 and 18.84h because they are not like terms

So take away 56.52 from both sides

56.52 - 56.52 = 0

183.69 - 56.52 = 127.17

Now divide 127.17 by 18.84h

127.17/18.84  = 6.75 inches

Here is proof that my answer is correct. I have a photo of my results and it shows that 6.75 inches is correct. Here is the photo:

Have a an amazing day

Therefore, after answering the given query, we can state that the as we can multiply it as 7 multiply by 7 = 7*7 = 49.

Multiplication is one of the four matrix multiplication, along with arithmetic, addition, and subtraction. Multiplication in mathematics is the process of repeatedly combining subgroups of the same size. Multiplication is calculated using the formula multiplicand multiplier gives product. multiplicand: Starting number, to be more exact (factor). as a separator, use number two (factor). The result is what remains after splitting both the multiplicand and the multiplier. There are numerous additions necessary when adding numbers. similar to 5 x 4 = 5 x 5 x 5 x 5 = 20. What I did was multiply 5 by 4. Because to this, multiplication is frequently referred to as "doubling."

The standard form for seven squared is 49.

as we can multiply it as 7 multiply by 7 = 7*7 = 49.

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Answer:

205

Step-by-step explanation:

3hrs is 180 min

5/12 hours is just 25 min

180+25=205

Answer:

205 minutes

Step-by-step explanation:

*60 minutes = 1 hour

3 x 60 = 180

5/12 x 60 = 5/12 x 60/1 = 300/12 = 25

180 + 25 = 205 minutes

The values of 65 euros is 76.70 US dollars.

To convert 65 euros to dollars, you need to know the current exchange rate between the two currencies. As of September 2021, the exchange rate is 1 euro = 1.18 US dollars.

To calculate the conversion, you can simply multiply the amount of euros by the exchange rate.

65 euros x 1.18 US dollars = 76.70 US dollars

Therefore, 65 euros is equivalent to 76.70 US dollars.

It's important to note that exchange rates can fluctuate, so the conversion may not be the same in the future. It's always best to check the current exchange rate before making a conversion.

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The numbers of flowers spaced every 4 feet, are needed

to surround a circular garden with a 70-foot radius, 105

Circumference is the distance around the perimeter of a circular object. It is defined as the length of the circle that is found by multiplying the diameter of the circle by π (pi), which is approximately equal to 3.14.

The formula for the circumference of a circle is given by:

C = 2πr,

To calculate the circumference of the circular garden, we can use the formula:

C = 2πr

where C is the circumference, π is the mathematical constant pi (approximated as 3 in this case), and r is the radius. Plugging in the given values, we have:

C = 2 x 3 x 70

  = 420 feet

Now, since the flowers are spaced every 4 feet, we can divide the circumference by 4 to find the number of flowers needed:

number of flowers = C / 4

                               = 420 / 4

                               = 105

Therefore, 105 flowers spaced every 4 feet are needed to surround a circular garden with a 70-foot radius.

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One mile is equal to 5,280 feet. Therefore, to convert the altitude of Denver from miles to feet, we can multiply by 5,280:

1 mile × 5,280 feet/mile = 5,280 feet

So, Denver's altitude of 1 mile is equal to 5,280 feet.

Answer:

Step-by-step explanation:

make a tree, first list out the sports then draw two branches for the clubs (speech and science) then circle each club to each sport, like how the picture shown . You will find there are 6 ways Janelle could pick out her extracurriculars

Answer:

x > - 1

How to find your answer:

-3x + 3 < 6 (Move the constant to the right)

-3x < 6 - 3 (now calculate)

-3x < 3 (divide both sides)

x > -1

I hope this helped.

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

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The graph the depicts the solution set of the inequality is graph D. Option 4 is the correct answer.

There is a significant exception to the general rule that inequality manipulation is quite similar to equation manipulation.

An inequity still exists if the same amount is added to both sides.

The inequality still holds true if the same amount is subtracted from each side.

An inequality still holds true if both sides are multiplied or divided by the same positive value.

However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid.

The given inequality is x² + 10x + 16 / x-3 > 0.

Expand the quadratic equation:

x² + 8x + 2x + 16/ x-3 > 0

x(x + 8) + 2(x + 8) / x-3 > 0

(x + 2)(x + 8)/ x-3 > 0

x + 2 > 0 and (x + 8) < 0 and x - 3 > 0

x > -2 and x < -8 and x > 3

The intervals of x are:

-8 < x < -2 and x > 3

Hence, the graph the depicts the given interval is graph D. Option 4 is the correct answer.

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Answer: [tex](x+10)(x-10)[/tex]

Step-by-step explanation: Difference of squares is an important element in understanding square functions. In order to identify difference of squares, the equation should be given in the form a^2-b^2. You can factor it completely when b^2 can be square rooted perfectly and write the factored expression as (a-b)(a+b) as I have done above.

The solution for x is x ≤ -3/4.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

To solve for x in the inequalities:

5x - 4 ≥ 12 and 12x + 5 ≤ -4

We'll solve each inequality separately:

5x - 4 ≥ 12

Adding 4 to both sides, we get:

5x ≥ 16

x ≥ 16/5

So the first inequality is solved for x as x ≥ 16/5.

Now, 12x + 5 ≤ -4

Subtracting 5 from both sides, we get:

12x ≤ -9

x≤ -9/12

x≤ -3/4

The only values of x that satisfy both inequalities are those that are less than or equal to -3/4.

Therefore, the solution for x is x ≤ -3/4.

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The whole fraction of a pizza that shows 6 pieces is 6/1 or simply 6.
The whole fraction of a pizza that shows 6 pieces is 6/6 or 1.

In a fraction, the numerator represents the number of parts being considered, and the denominator represents the total number of parts. In this case, there are 6 pieces of pizza being considered out of a total of 6 pieces, which means the fraction is 6/6. This fraction can be simplified to 1, meaning the whole pizza is represented.

So, the whole fraction of a pizza that shows 6 pieces is 1.

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The manager would expect 1000 defective players in the shipment.

A store receives a shipment of 5,000 mp3 players out of which 300 were found to be defective.

The clerk lets the numbers 1 through 300 represent defective mp3 players, and the numbers 301 through 5,000 represent working mp3 players.

The results are given AS:

2,806 623 232 3,955 3,799 657 2,140 262 844 561

This means that out of the 10 samples 2 were found to be defective and 8 were in the working condition.

( Since the number 232 and 262 represent the defective mp3 players as they are the numbers which are less than or equal to 300 )

Hence, the Probability that the mp3 players were defective is:

P( defective)=2/10=1/5

Hence, out of 5000 mp3 players the number of players that clerk predict to be defective are:

P( defective)×5000

= 1/5 × 5000

= 1000.

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Step-by-step explanation:

so, for x = 0, y = 30.5

that means the first answer is out.

for x = 1, y = 21.35

so, only

y = 30.5(0.7)^x

can be right.

all other functions have an y-value of way over 30.5 (because the factor of 30.5 is larger than 1).

and to verify :

30.5 × 0.7¹ = 30.5 × 0.7 = 21.35

correct.