The records at a particular two-year college classify a student as a freshman, a sopho- more, a student that has transferred out, or a student that has graduated. Each year 25% of students transfer, 15% have to repeat the year, and 60% complete the year. Once a student has transferred or graduated they have a 100% chance of staying clas- sified that way. Currently there are 2,000 freshmen, 1,500 sophomores, 500 students that have transferred, and 3,000 graduates. Determine the number of students in each category one year from now. You may use a calculator for any computations in this problem only.

Answer:

40

Step-by-step explanation:

accumulated vacation Minus used vacation = remaining vacation

55  -15 = 40

Using the Factor Theorem, the quadratic functions are given as follows:

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

For this problem, the roots are given as follows:

[tex]x_1 = -3, x_2 = 8[/tex]

Hence:

f(x) = a(x + 3)(x - 8)

f(x) = a(x² - 5x - 24).

It opens upward with a positive leading coefficient, that is, a > 0, hence one example is a = 1 as follows:

f(x) = x² - 5x - 24.

It opens downward with a negative leading coefficient, that is, a < 0, hence one example is a = -1 as follows:

f(x) = -x² + 5x + 24.

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Answer:

NAH THIS ANSWER IS EASY: ANSWER 2500

Step-by-step explanation:

Answer:

198.5

Step-by-step explanation:

Answer: [tex]2x^{2} +17x+36[/tex]

Step-by-step explanation:

FOIL:
[tex]2x^{2} +8x+8x+36[/tex]

Combine like terms:

[tex]2x^{2} +17x+36[/tex]

Answer: 88

Explanation: You always round up if the number before is greater than 4!

The property that justifies the following statement, 5(3 x+1)=15 x+5 is the distributive property.

Distributive property can be described as one of the properties of multiplication which states that if we multiply two or more values that are added together with a number then the result will be the same even if we multiply each value separately with that number and then add them together. This can be given as:

x(y + z) = xy + xz

Therefore, as 5 x 3 = 15 and 5 x 1 =5, we can write the equation 5(3x+1) as 15x + 5 as the result will be the same in both circumstances.

The distributive property not only justifies the equations when two or more values are added but also justifies the equations in which they are subtracted which can be given as:

x(y-z) = xy - xz

So, according to the distributive property, the statement, 5(3 x+1)=15 x+5 is valid.

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The unit rate represented by the information is  6/5 mile per hour

The given parameters are

Distance = 2/5 mile

Time = 1/3 hour

The ratio of distance in time is calculated as

Ratio = Distance : Time

This gives

Ratio = 2/5 mile : 1/3 hour

Divide both ratio by 1/3

So, we have

Ratio = 6/5 mile : 1 hour

Express as fraction

Ratio = 6/5 mile/1 hour

This gives

Ratio = 6/5 mile per hour

Hence, the unit rate represented by the information is  6/5 mile per hour

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The team's expected value for a hand is 0.75.

Probability:

Probability refers the possible occurrence of any required event.

Given,

You are playing a team card game where a team can get 0 points, 1 point, or 3 points for a hand.

The probability of your team getting 1 point for a hand is 60% and of getting 3 points for a hand is 5% .

Here we need to find the team's expected value for a hand.

The expected value is calculated by the sum of the product of each point value and its corresponding probability.

So, the sum of the each probability value is,

E = sum ( point value x probability)

E = 0 + (1 x 60%) + (3 x 5%)

Convert the percentage values onto decimal,

Then

E = 0 + ( 1 x 0.60) + (3 x 0.05)

E = 0 + 0.60 + 0.15

E = 0.75

Therefore, the team's expected value for a hand is 0.75.

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A chord is a segment with endpoints on the circle. EF, DF are chords of the circle.

The chord of a circle is defined as the line segment connecting any two points on its circumference. It should be noted that the diameter of a circle is the longest chord passing through its center.

A circle chord is a straight line with both ends on a circular arc. A secant line, or simply secant, is the infinite line extension of a chord. A chord is a segment of a line that connects two points on a curve, such as an ellipse.

A chord is a segment with endpoints on the circle.

Therefore, EF, DF are chords of the circle.

The complete question is:

Identify each.

a chord

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The value of HI is 28.

Given that HJ=7x-27, HI=3x-5 and IJ=x-1 as shown in the attached image.

We have to find the value of HI.

As a line given in image it shows that the line HJ is the sum of Hi and IJ and we can write it as

HI+IJ=HJ

Now, we will substitute all the given values which is shown in the attached image, we get

3x-5+x-1=7x-27

Now, we will simplify the left-hand side by combining all the like terms, we get

4x-6=7x-27

Further, we will subract 4x from both sides, we get

4x-6-4x=7x-27-4x

6=3x-27

Furthermore, we will add 27 on both sides, we get

6+27=3x-27+27

33=3x

Now, we will divide by 3 from both sides, we get

33/3=3x/3

11=x

Further, we will simplify the value of HI by substituting the value of x, we get

HI=3x-5

HI=3(11)-5

HI=33-5

HI=28

Hence, the value of HI when HJ=7x-27 and the attached image is 28.

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Answer:

335

Step-by-step explanation:

you put -18 in for x

you multiply -18 by -18 because it's the exponent of 2

then add 11

The following is the absolute value equation for figuring out the maximum and minimum period of time: t = |d/v| + |25/v|.

The parameters provided;

The number of hours required for the plane to travel just at given values is determined as follows:

Time= distance / speed

The equation for calculating the maximum number of hours is as follows:

t = (d + 25)/v = (160 + 25)/150

t = 1.23 hours.

The equation and for shortest number of hours is as follows:

t = (d - 25)/v = (160 - 25)/150

t = 0.9 hours.

Thus, the absolute value equation for determining the maximum and minimum amount of time is as follows:

t = |d/v| + |25/v|.

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The midpoint is at (3/10 , 3/2 , 4/10)

In the given statement is

To find the midpoint of the line segment joining the pair of points

F (3/5, 0, 4/5) and G(0,3,0)

Midpoint:

The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.

m = (A +B)/2

If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =([tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2} , \frac{z_{1}+z_{2} }{2}[/tex])

where:

(x1 , y1 ,z1) are the coordinates of the first point:

(x2 , y2 , z2) are the coordinates of the second point:

Now, We are given the three points F (3/5, 0, 4/5) and G(0,3,0)

Solving for the midpoint , we have,

m = ([tex]\frac{3/5+0}{2} , \frac{0+3}{2} ,\frac{4/5+0}{2}[/tex])

m = (3/10 , 3/2 , 4/10)

Therefore, the midpoint is at (3/10 , 3/2 , 4/10)

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{3}x\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex][tex]~\dotfill\\\\ \stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is -1/3 and it passes through (2 , -6)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-6})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-6)}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{2}) \implies y +6= -\cfrac{1}{3} (x -2) \\\\\\ y+6=-\cfrac{1}{3}x+\cfrac{2}{3}\implies y=-\cfrac{1}{3}x+\cfrac{2}{3}-6\implies y=-\cfrac{1}{3}x-\cfrac{16}{3}[/tex]

Answer:

b = 99

Step-by-step explanation:

b and 81° are same- side interior angles and sum to 180° , that is

b + 81 = 180 ( subtract 81 from both sides )

b = 99

With the help of linear equtions it can be concluded that we downloaded 54 songs in which 28 songs were free and 26 songs were paid.

A linear equation is an algebraic equation in which each term has an exponent of one and when graphed produces a straight line. That's why it is considered a 'linear equation.'

Let a represent paid downloaded songs.

Total cost of songs downloaded = a x cost of each additional download.

a x $0.59 = $0.59a

The overall cost of downloaded songs is $15.34.

$15.34 =   $0.59a

Divide both sides of the equation by  $0.59.

a = 26 songs

We downloaded 26 paid songs.

Total songs downloaded = total free songs + total paid songs

Total songs downloaded = 26 + 28 = 54 songs

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2)Main Answer: a)1,8,27,64,125,216,343,512

                        b)I,II,III,IV,V,VI,VII,VIII,IX,X,XI                                    

Concept and definitions should be there:

A conjecture is an educated guess that is based on known information. Example. If we are given information about the quantity and formation of section 1, 2 and 3 of stars our conjecture would be as follows.

Given data

a)Next five terms 1,8,27,64

b)Next five terms I,II,III,IV,V

Solving part

using conjecture

a)Next five terms 1,8,27,64,125,216,343,512

Notice that the difference between consecutive terms is 7.

Conjecture: n3, n=1,2,3...

Final Answer:1,8,27,64,125,216,343,512

b))Next five terms I,II,III,IV,V,VI,VII,VIII,IX,X,XI

Conjecture: n, n=i,ii,iii,...

Final Answe:I,II,III,IV,V,VI,VII,VIII,IX,X,XI

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3)Quastion incompleted

4)Main answer :The number 14 is even and therefore is divisible by 2. This is the correct statement.

Given data

The statement which uses deductive reasoning to draw the conclusion is C. The number 14 is even and therefore is divisible by 2.

Solving part

The number 14 is even and therefore is divisible by 2. This is the correct statement.

Final Answer:The number 14 is even and therefore is divisible by 2. This is the correct statement.

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5)Main Answer:X = -2

Concept and definitions should be there:This solution deals with linear equations with one unknown.

Given data

18x-2(3x+1)=5x-16

Solving part

We simplify the equation first:

18x−2(3x+1)=5x−16

18x+(−2)(3x)+(−2)(1)=5x+−16 (Distribute)

18x+−6x+−2=5x+−16

(18x+−6x)+(−2)=5x−16 (Combine Like Terms)

12x+−2=5x−16

12x−2=5x−16

Then we cancel out:

12x−2−5x=5x−16−5x

7x−2=−16

7x−2+2=−16+2

7x=−14

7x/7 = −14/7

x = -2

Final Answer:x = -2

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Answer:

X=6,2

Step-by-step explanation:

In order to know the appropriate number divisible by 2, 5 and 10. We need to have a look at what type of numbers are divisible by either of these number. So, let's discuss one by one

Divisible by 2

Divisible by 5

Divisible by 10

Let's have a look at the given numbers and see which ones are divisible by 2, 5 and 10

We'll write "yes" for the number which are divisible and "No" for the number which are not divisible by either of them.

105 - only by 5

183 - No

34 - only by 2

238 - only by 2

54 - only by 2

553 - No

260 - yes

85 - only by 5

450 - yes

365 - only by 5

745 - only by 5

360 - yes

270 - yes

390 -  yes

400 - yes

110 - yes

210 - yes

775 - only by 5

438 - only by 2

565 - only by 5

766 - only by 2

906 - only by 2

321 - No

347 - No

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This question is incomplete. You can have a look at the attached picture to know the complete question.

None of the equations are correct.

What is an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. In other languages, the word equation and its cognates may have slightly different meanings. In French, an équation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

For perpendicular equations, the product of slope is -1, but none of the options here is have slope whose product with the given equation is -1.

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If the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

Given that the top 2% of athletes will go pro.

We are required to find the Z-Score that is required to be the top 2%.

A Z-score is basically a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured basically in terms of standard deviations from the mean.

Because only 2% of the top is pro then it will be a two tailed test. The required percentage will be 2/2=1%

The value which we will require to catch up from table=0.01

Z value will be 0.0438 (Z table is attached)

Hence if the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

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When dividing 28 by 263.2, the approximate quotient is 0.1062 (rounded to four decimal places).

To divide 28 by 263.2, we can perform the division operation as follows:

Dividend ÷ Divisor = Quotient

Here, the dividend is 28, and the divisor is 263.2.

To simplify the division, we can remove the decimal point by multiplying both the dividend and divisor by a power of 10. In this case, we can multiply by 10 to eliminate the decimal point.

28 * 10 = 280

263.2 * 10 = 2632

Now, we can perform the division:

280 ÷ 2632 ≈ 0.10621761658

Hence, when dividing 28 by 263.2, the approximate quotient is 0.1062 (rounded to four decimal places).

In summary, to divide a number by another number, we divide the whole numbers and the decimal numbers separately, considering the appropriate place values, and then combine the results to obtain the final quotient.

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A. For every 4 apples, there are 3 oranges.

B. The ratio of bananas to oranges is 6:3

C. The ratio of apples to bananas is 4 to 6.

D. For every 1 orange, there are 2 bananas.

The distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

Two points J(-2 , 6) and K(1 , 4) are given .

We have to find out the distance between two points.

What is the distance formula ?

The distance formula is [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] where two points are ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) and ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]).

As per the question ;

J ([tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) = J (-2 , 6) and K ([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = K (1 , 4)

and

The distance formula is ;

[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex]

So ,

The distance between points J(-2 , 6) and K(1 , 4) will be ;

= [tex]\sqrt{(-2-1)^{2} + (6-4)^{2} }[/tex]

= [tex]\sqrt{(-3)^{2} + (2)^{2} }[/tex]

= [tex]\sqrt{(9)+ (4)}[/tex]

= √13

= 3.6 ( round to nearest tenth)

Thus , the distance between points J(-2 , 6) and K(1 , 4) will be equal to 3.6.

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Answer:

x=ay/4 +3

Step-by-step explanation:

The common difference of arithmetic sequence is 10.

according to a = 2 and d = 3, the sequence. Solution: We apply the method for finding the nth term to locate a specific term in an arithmetic series. Step 1: An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. Therefore, enter the numbers a = 2 and d = 3 into the formula to determine the nth term.

This is an arithmetic sequence.

a = 11

d = a2 - a1

d = 22 - 11

d = 10

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Answer:

20

Step-by-step explanation:

so if you do 3 -1 = 2

so 2 portions = 10

divide by 2

so 1 portion = 5

so do 5 x 1 = 5

5 x 3 = 15

5 + 15 = 20

so 20 students in total

if you do inverse you can check if it's right

hope this works :)

The total number of students who went on the field trip will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The proportion of young men to young ladies on the school field trip was 3:1. assuming there were 10 a larger number of young men than there were young ladies.

Let 'B' be the number of boys and 'G' be the number of girls. Then the equations are given as,

B/G = 3/1

B = 3G                 ....1

B = G + 10          ....2

From equations 1 and 2, then we have

3G = G + 10

2G = 10

G = 5

Then the number of boys is given as,

B = 5 + 10

B = 15

Then the total number of students who went on the field trip will be given as,

⇒ 5 + 15

⇒ 20

The total number of students who went on the field trip will be 20.

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