The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?

Answer:

For this case we have this function:

[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]

We can factor the denominator and we got:

[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]

And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:

Continuous at every real number except x=1 and x=-9

Step-by-step explanation:

For this case we have this function:

[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]

We can factor the denominator and we got:

[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]

And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:

Continuous at every real number except x=1 and x=-9

Answer:

A or continuous at every real number except x=1 and x=-9

Step-by-step explanation:

Just took the test :)

Answer: 60.9 u^2

Step-by-step explanation:

The area of a trapezoid can be calculated as seen in the attachment.

Thus:

[tex]A = \frac{3.7+14.2}{2} * 6.8\\A = \frac{17.9}{2} *6.8\\A = 8.95*6.8\\A = 60.86\\Round\\\left[\begin{array}{c}A=60.9\end{array}\right][/tex]

Hope it helps <3

Answer:

60.9 units^2

Step-by-step explanation:

Well the formula for the area of a trapezoid is,

[tex]\frac{b1+b2}{2} h[/tex]

So b1 and b2 are 142 and 3.7,

14.2 + 3.7 = 17.9

17.9 ÷ 2 = 8.95

8.95 × 6.8 = 60.86

60.9 units^2 rounded to the nearest tenth.

Thus,

the area of the trapezoid is 60.9 units^2.

Hope this helps :)

Answer:

30 same day 15 advance

Step-by-step explanation:

Answer:

[tex]\boxed{x\geq -99}[/tex]

Step-by-step explanation:

[tex]\frac{x}{3} \geq -33[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 3.[/tex]

[tex]\frac{x}{3} (3) \geq -33(3)[/tex]

[tex]x\geq -99[/tex]

Answer:

[tex]\boxed{\red{x \geqslant - 99}}[/tex]

Step-by-step explanation:

[tex] \frac{x}{3} \geqslant - 33 \\ x \geqslant - 33 \times 3 \\ x \geqslant - 99[/tex]

hope this helps you!

Answer:

The given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0

Step-by-step explanation:

This is a very trivial exercise, follow the steps below for the solution:

Step 1: Since n = 0, 1, 2, 3, 4, ........, Substitute the values of n into equation (1) below.

[tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex].....................(1)

[tex]y = 1 - x^2 + x^4 - x^6 + x^8.........[/tex]

Step 2: Find the derivative of y, i.e. y'

[tex]y' = -2x + 4x^3 - 6x^5 + 8x^7 .............[/tex]

Step 3: Substitute y and y' into equation (2) below:

[tex](1+x^2)y' + 2xy = 0\\\\(1+x^2)(-2x + 4x^3 - 6x^5 + 8x^7......) + 2x(1 - x^2 + x^4 - x^6 + x^8.......) = 0\\\\-2x+ 4x^3 - 6x^5 + 8x^7........ - 2x^3 +4x^5 - 6x^7 + 8x^9 ......+ 2x - 2x^3 + 2x^5 - 2x^7 + 2x^9...... = 0\\\\0 = 0[/tex]

(Verified)

Since the LHS = RHS = 0, the given power series [tex]y =\sum^{\infty}_{n=0} {(-1)^n x^{2n}}[/tex] is a solution of the differential equation (1+x^2)y' + 2xy = 0

Similar triangles have side lengths that are proportional to each other. To find each of the missing lengths, we need to set up proportions.

The proportions will look as follows:

(length or unknown of triangle 1) / (length or unknown of triangle 2) = (length of triangle 1) / (length of triangle 2)

-On both sides, remember to be consistent with which length/unknown you put on top! If a triangle 1 length is the numerator on the left, then it also needs to be the numerator on the right! And this also works vice versa with triangle 2.

In each proportion equation, we can only have one unknown. On the left side of the equation, we choose one length or unknown of triangle 1, and the corresponding side length of unknown of triangle 2 (whichever you did not choose from triangle 1). On the right side of the equation, we use a completed proportion. This is because all of the sides of one triangle are proportional to the other triangle, but we need to know that proportion/ratio in order to find other side lengths.

Let's start with problem a, to show how this works:

Triangle 1 side lengths - 16, a, 11

Triangle 2 side lengths - 8, 3, b

As you can tell, the side lengths match up (corresponding!) on each triangle, as in they are in the same position on each triangle. Now, we will set up a proportion to find the length of side a on triangle 1.

a / 3 = 16 / 8

48 = 8a

a = 6

Next, let's find the length of side b on triangle 2.

11 / b = 16 / 8

16b = 88

b = 5.5

Moving on to problem b, we'll apply the same concept and steps from problem a in order to find the missing side lengths.

Triangle 1 side lengths: 5, 5.5, d

Triangle 2 side lengths: 15, c, 18

5 / 15 = 5.5 / c

5c = 82.5

c = 16.5

5 / 15 = d / 18

15d = 90

d = 6

Hope this helps!! :)

Answer:

On a) you can see the shapes are simular. The blue line signatures that they are equal just reduced. You can see that 8 goes into 16 two times so for the orange line 3 must times 2. Which would mean a is 6. Now on the red line all you see is 11. So divide 11 by 2 and your answer should be 5.5 for b.

On b) it is the same thing but you have to find how the blue line is divisible. 5 divided by 15 is 3. So 3 is the number you will be using to divide or multiply. For the orange line you divide 18 by 3. The answer is 6 for d. For the red line 5.5 times 3 and you should get 11 for c.

Step-by-step explanation:

Hope this helped

Answer:

f(x)= 8(0.5)^x

Step-by-step explanation:

As you can see on the graph there are two specific points labeled:

(0,8) and (1,4)

The 8 would be the initial value and starting point of the "design"

A is always the initial value so replace that.

Then proceed to divide 4 by 8 to figure out the percentage change its 0.5

leave x as it is

Answer:

Income after 20 years = 162550.01

Step-by-step explanation:

In cell B2, enter 90000

In cell B3, enter +B2*1.03

Copy cell B3 to cells B4:B22

Set number format for column B to 2 decimal places.

Read cell B22 = 162550.01

Income after 20 years = 162550.01

Their income after 20 years would be; 72,550 dollars.

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

The income after 20 years can easily be determine by using compounding

Thus the formula;

Future Value = Present Value (1 + I)^ 20

                     = 90,000 (1 + 0.03)^ 20

                     = 162,550 dollars

Income can be determing by subtracting Pv from Fv i.e

Income = 162,550 - 90,000 = 72,550

Calculation on excel sheet;

      A                        B                  C                         D                

1     90,000             1.03            = A1 x1.03        = C1-A1        

2      = D1                  1.03           = A2 x 1.03       = C2-A2

20    = D19               1.03           = A20 x 1.03      = A20 - C20

Thus, In work sheet colunm D will show the income on investment.

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Answer: 3 kids take 3 pieces of candy each

Step-by-step explanation:

Let the number of children that took 3 pieces is x ( total take 3*x pieces of candy)

Number of children that took 5 pieces is y ( total take 5*y pieces of candy)

1 child took 1 piece that actually means that x+y=18 and 3*x+5*y=84.

( Because total number of all kids is 19. We just deduct one kid (Let his name is John) who took only 1 candy.  So we have 19-1 =18 kids without John. The similar is with the candies. Total number is 85. We deduct 1 piece which John has taken. )

So we have 2 equations or the system of 2 equations:

1).  x+y=18

2). 3*x +5*y=84

Multuply both sides of equation 1) by 3

We have   3*x+3*y=18*3

Deduct 3*y from both sides of this equation

3*x+3*y-3*y=54-3*y

3*x=54-3*y

Substitute 3*x in equation  2).  by 54-3*y

2) 54-3*y+5*y=84

2*y=30

y=15  ( kids take 5 pieces of candy each)

Using equation 1) find x

x+15=18

x=3 (kids take 3 pieces of candy each)

Answer:

[tex]\boxed{x^3+6x^2+9x}[/tex]

Step-by-step explanation:

[tex]x(x+3)(x+3)[/tex]

Resolving the first parenthesis

[tex](x^2+3x) (x+3)[/tex]

Using FOIL

[tex]x^3+3x^2+3x^2+9x[/tex]

Adding like terms

[tex]x^3+6x^2+9x[/tex]

[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]

[tex]x(x+3)(x+3) =0[/tex]

[tex]\boxed{x_1 =0}[/tex]

[tex]x_2+3 =0[/tex]

[tex]\boxed{x_2 = -3}[/tex]

[tex]x_3+3 =0[/tex]

[tex]\boxed{x_3 = -3}[/tex]

Answer:  [tex]\bigg(-3,\dfrac{1}{2}\bigg)[/tex]

Step-by-step explanation:

G = (-7, 3)    H = (1, -2)

[tex]M_{GH}=\bigg(\dfrac{X_G+X_H}{2},\dfrac{Y_G+Y_H}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-7+1}{2},\dfrac{3+(-2)}{2}\bigg)\\\\\\.\qquad = \bigg(\dfrac{-6}{2},\dfrac{1}{2}\bigg)\\\\\\.\qquad = \large\boxed{\bigg(-3,\dfrac{1}{2}\bigg)}[/tex]

The mid point of the line GH whose end points are (-7,3) and (1,-2) is (-3,1/2).

The mid point is a line which divides the line into two equal parts. The formula to calculate the mid point of line whose end points are (x1,y1) and (x2,y2) is {(x1+x2)/2,(y1+y2)/2}.

To calculate the mid point of the line GH we have to put x1=-7, x2=1,y1=3 and y2=-2 so,

the mid point is {(-7+1)/2,(3-2)/2}

=(-3,1/2)

Hence the mid points of a line GH whose end points are g(-7,3) and h(1,-2) is (-3/1/2).

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Answer:

d. 38

Step-by-step explanation:

AB = AD - BD = 54 - 36 = 18

AC = AB + BC = 18 + 20 = 38

Answer:

D)$732.84

Step-by-step explanation:

A=p(1+r/n)^nt

P=principal=$600

r=5%=0.05

t=4 years

n=12 months

A=p(1+r/n)^nt

=600(1+0.05/12)^12*4

=600(1+0.0041666666666 )^48

=600(1.0041666666666 )^48

=600( 1.2208953550215 )

=732.53

A=$732.53

Option D)$732.84 is the answer

Answer:

200km

Step-by-step explanation:

Car A purchase worth = $14000

Car B purchase worth = $15000

Car A drive worth= 25€ per km

Car B drive worth= 20€ per km

For the worth of the two cars to be equal let's first assume all of the currency to be in dollars$

For A

Worth= 14000+25(x)

For B

Worth= 15000+20(x)

Where x is the distance covered

For the both worth to be equal we equate.

14000+25(x)= 15000+20(x)

25x-20x= 15000-14000

5x= 1000

X= 200

The distance covered by the two cars for the worth to be equal is 200km

Complete Question

Assume that when adults with smartphones are randomly selected 42% use them in meetings or classes if 15 adult smartphones are randomly selected, find the probability that "fewer" than 4 of them use their smartphones

Answer:

The  probability is  [tex]P[X < 4]= 0.00314[/tex]

Step-by-step explanation:

From the question we are told that

      The proportion of those that use smartphone in meeting and classes is  p = 0.42

     The sample size is  [tex]n = 15[/tex]

   The proportion of those that don't use  smartphone in meeting and classes is  

          [tex]q = 1- p[/tex]

=>        [tex]q = 1- 0.42[/tex]

=>         [tex]q = 0.58[/tex]

Now  from the question we can deduce that the usage of the smartphone is having a  binomial  distribution since there is only two outcome  

So  the probability that "fewer" than 4 of them use their smartphones is mathematically evaluated as

       [tex]P[X < 4 ] = P[X = 0] + P[X = 1] +P[X = 2] +P[X = 3][/tex]=

=>     [tex]P[X < 4] = [ \left 15} \atop {0}} \right. ] p^{15-0} * q^0 + [ \left 15} \atop {1}} \right. ] p^{15-1 }* q^1 + [ \left 15} \atop {2}} \right. ] p^{15-2 }* q^2 + [ \left 15} \atop {3}} \right. ] p^{15-3 }* q^3[/tex]

Where  [tex][\left 15} \atop {0}} \right. ][/tex] implies 15  combination 0 which has a value of  1 this is obtained using a scientific calculator

  So for the rest of the equation we will be making use of a scientific calculator to obtain the combinations

      [tex]P[X < 4] = 1 * ^{15} * q^0 + 15 * p^{14 }* q^1 + 105 * p^{13 }* q^2 + 455 * p^{12 }* q^3[/tex]

substituting values

       [tex]= 1 * (0.42)^{15} * (0.58)^0 + 15 * (0.42)^{14 }* (0.58)^1[/tex]

                     [tex]+ 105 * (0.42)^{13 }* (0.58)^2 + 455 * (0.42)^{12 }* (0.58)^3[/tex]

=>       [tex]P[X < 4]= 0.00314[/tex]

Answer: C. 3, 11, 23, 31

Step-by-step explanation:

None of these can be divided by anything except themselves and 1.

Answer:

21.75m

Step-by-step explanation:

14.5×150 =2175cm

1m =100cm

to convert into m divide 2175 by 100

=21.75m

Answer: B

Step-by-step explanation:

Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.

Hope it helps <3

Answer:

It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.

Step-by-step explanation:

for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).

Answer:

700✖️0.08=56 people is late

700✖️0.12=84 people bought the shirt.

Step-by-step explanation:

8%=0.08

12%=0.12

700✖️0.08=56 people is late

700✖️0.12=84 people bought the shirt.

HOPE THIS HELPS!

Answer:

The selling price in other to maximize his profit is $13

Step-by-step explanation:

In the above question we are given the following information:

Cost of material per necklace = $6

Firstly, terry sold 20 necklaces per day

= $10 each

Later he increased he increased the prices by 1 dollar and the number of necklaces he sold reduced by 2

Mathematically

18 necklaces = $11 each

Step 1

We find the Cost function C(x)

Let's assume that x = number of necklaces sold

If each material cost $6 , then

C(x) = 6 × x = 6x

Step 2

P(Profit) = R(x) - C(x)

R(x) = Revenue

Where Revenue = x × p(x)

Since p(20) = 10 and p(18) = 11

p(x) = -1/2x + 20

P(Profit) = x ( -1/2x + 20) - C(x)

C(x) = 6x

P = x(-1/2x + 20) - 6x

P = -1/2x² + 20x - 6x

P = -1/2x² + 14x

Step 3

We maximise the profit by differentiating P

P = Profit

P = -1/2x² + 14x

We differentiate P to find x

∆P/∆x = dp/dx = -x + 14

-x + 14 = 0

-x = -14

x = 14

Hence, we substitute 14 for x in the price function

p(x) = - 1/2x + 20

since , x = 14

p(14) = - 1/2 × 14 + 20

= -7 + 20

= $13

Therefore, the selling price function to maximize his profit is $13

Above question the given data:  

1.Cost function C(x)

Let's assume that x = number of necklaces sold

If each material cost $6 , then

C(x) = 6 × x

C(x) = 6x  

2.P(Profit) = R(x) - C(x)

R(x) = Revenue ,Where Revenue = x × p(x)

Given data:

p(20) = 10

p(18) = 11

p(x) = -1/2x + 20

P(Profit) = R(x) - C(x)

P(Profit) = x ( -1/2x + 20) - C(x)

P = x(-1/2x + 20) - 6x

P = -1/2x² + 20x - 6x

P = -1/2x² + 14x

3.Maximise Profit

P = Profit  

P = -1/2x² + 14x

We differentiate P to find x

∆P/∆x = dp/dx = -x + 14

-x + 14 = 0

-x = -14

x = 14

Now, we will substitute 14 for x in the price function

Now ,p(x) = - 1/2x + 20

since , x = 14

p(14) = - 1/2 × 14 + 20  

p(14)= -7 + 20  

p(14)= $13

Thus, the selling price function to maximize his profit is $13.

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Answer:

332.88 million

Step-by-step explanation:

you do the thing

Answer:

domain is:(-∞,-3]∪ [3,∞)

Step-by-step explanation:

f(x)=√(x²-9)

f(x)=√(x-3)(x+3)

domain is:(-∞,-3]∪ [3,∞)

Answer:

-3.5 meters per second

Step-by-step explanation:

Take the distance and divide by the time

-17.5 meters/ 5 seconds

-3.5 meters per second

Answer:

-3.5 m/s

Step-by-step explanation:

Rate of the anchor =  [tex]\frac{distance}{time}[/tex]

[tex]\frac{-17.5}{5}[/tex]

-3.5 meters per second.

Answer:

a. [tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]

Step-by-step Explanation:

Given:

Distance Ottawa to Québec = 425 km

Initial flight rate = v + 60

Return flight rate = v - 40

[tex] t = \frac{d}{r} [/tex]

Required:

Flight times difference of the initial and return flights

Solution:

=>Flight time of the initial flight:

[tex] t = \frac{d}{r} [/tex]

[tex] t = \frac{425}{v + 60} [/tex]

=>Flight time of the return flight:

[tex] t = \frac{425}{v - 40} [/tex]

=>Difference in flight times:

[tex] \frac{425}{v + 60} - \frac{425}{v - 40} [/tex]

[tex] \frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)} [/tex]

[tex] \frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)} [/tex]

[tex] \frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)} [/tex]

[tex] \frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)} [/tex]

[tex] \frac{- 42,500}{(v + 60)(v - 40)} [/tex]

Answer:

C . Sea level

Step-by-step explanation:

If points below the sea level are represented using negative numbers; and

Points above the sea level are represented using positive numbers.

The point labeled 0 meters represents the sea level since it is the indicator of whether a point is positive or negative.

The correct option is C.

Answer:

A)  Sea level

Step-by-step explanation:

Answer:

2250

Step-by-step explanation:

Balance : 2100

2 Years

2100 ÷ 100 x 103.5 ÷ 100 x 103.5 = 2249.5725

Answer:

56

Step-by-step explanation:

Answer:

C. -30

Step-by-step explanation:

We would have to do order of operations or P.E.M.D.A.S. So fist we would do 7 times -4 which is -28 than we would do the absolute value of -6 which is 6 so we would do -28-6 which is -34 and we would do the absolute value of 4 which is 4 and we would add it to -34 which is -30 so our final answer would be C. -30

Answer:

7 and 3 respectively

Step-by-step explanation:

Peanuts (p/lb) = $1.80

Cashews (p/lb) = $4.50

Total pound = 10 pounds

Aggregate amount (at $2.61 per lb) = $26.1

Pound of peanut to buy = x

Pound of cashew to buy = y

x + y = 10..........(i)

1.8x + 4.5y = 26.1.....(ii)

Multiply equ (i) by 1.8 and equ (ii) by 1

1.8x + 1.8y = 18

1.8x + 4.5y = 26.1

Subtract (i) from (ii)

4.5y - 1.8y = 26.1 - 18

2.7y = 8.1

y = 3

Sub y = 3 into (i)

x + y = 10

x + 3 = 10

x = 10 - 3

= 7

Pounds of peanut to buy = 7 pounds

Pounds of cashew to buy = 3 pounds