A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stamps at $16/sheet plus $50 to create the image. They plan to sell each sheet for $20. a) Write an equation that represents the cost of obtaining the stamps. b) Write an equation that represents the income from sales. c) For each equation, set up a table of values. d) Graph each equation on the same set of coordinate axis. e) What is the minimum number of sheets the group must sell so they don't lose any money? f) How much profit will they make if they sell 500 sheets?

Answer:

The correct option is (D).

Step-by-step explanation:

The two expressions are:

[tex]\text{Exp}_{1}=5x^{2}-2x-4+6x+3\\\\\text{Exp}_{2}=6x^{2}-6x+6-x^{2}+10x-7[/tex]

On simplifying both the expressions we get:

[tex]\text{Exp}_{1}=5x^{2}+4x-1\\\\\text{Exp}_{2}=5x^{2}+4x-1[/tex]

Compute the value of both expressions for x = 2 as follows:

[tex]\text{Exp}_{1}=5(2)^{2}+4(2)-1=27\\\\\text{Exp}_{2}=5(2)^{2}+4(2)-1=27[/tex]

The value of both expressions are same for x = 2.

Thus, the correct option is:

"They are equivalent because when x = 2, the two expressions have the same value."

Answer:

d

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\cot\theta=\dfrac{1}{xy}}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\sin\theta=x\\\\\sec\theta=y\\\\\cot\theta=?\\\\\text{We know:}\\\\\sec x=\dfrac{1}{\cos x};\ \cot x=\dfrac{\cos x}{\sin x}\\\\\sec\theta=y\to\dfrac{1}{\cos \theta}=y\to\dfrac{\cos\theta}{1}=\dfrac{1}{y}\to\cos\theta=\dfrac{1}{y}\\\\\cot \theta=\dfrac{\frac{1}{y}}{x}=\dfrac{1}{xy}[/tex]

[tex]\bold{METHOD\ 2}[/tex]

[tex]\text{We know}\\\\\tan x=\dfrac{\sin x}{\cos x}\\\\\cot x=\dfrac{\cos x}{\sin x}=\dfrac{1}{\tan x}\\\\\sec x=\dfrac{1}{\cos x}\\\\\text{therefore}\\\\(sin x)(\sec x)=(\sin x)\left(\dfrac{1}{\cos x}\right)=\dfrac{\sin x}{\cos x}=\tan x\\\\\dfrac{1}{(\sin x)(\sec x)}=\dfrac{1}{\tan x}=\cot x[/tex]

[tex]\\\sin \theta=x;\ \sec\theta=y\\\\\text{substitute}\\\\\cot\theta=\dfrac{1}{xy}[/tex]

Answer:

[tex] x = 6.6 [/tex]

Step-by-step explanation:

Given ∆WXY,

<X = 15°

<Y = 23°

y = 10

x = ?

To find side x, use the Law of sines as shown below:

[tex] \frac{x}{sin X} = \frac{y}{sin Y} [/tex]

Plug in the values of y, Y, and X

[tex] \frac{x}{sin 15} = \frac{10}{sin 23} [/tex]

[tex] \frac{x}{0.2588} = \frac{10}{0.3907} [/tex]

Cross multiply

[tex] x*0.3907 = 10*0.2588 [/tex]

Divide both sides by 0.3907 to solve for x

[tex] \frac{x*0.3907}{0.3907} = \frac{10*0.2588}{0.3907} [/tex]

[tex] x = \frac{2.588}{0.3907} [/tex]

[tex] x = 6.624 [/tex]

[tex] x = 6.6 [/tex] (to nearest tenth)

Answer:

C = 314 m

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

Using 3.14 for pi

C = 3.14 * 100

C = 314 m

Answer:

The answer is option D.

Step-by-step explanation:

Circumference of a circle = πd

Where d is the diameter

From the question

d = 100m

Circumference of the circle is

100π

= 314.2

Which is 314m to the nearest whole number

Hope this helps you

Answer:

$3.60

Step-by-step explanation:

Convert the percentage to a decimal.

2% = 0.02

Multiply the cost of the dress by the decimal to find the sales tax.

$180 × 0.02 = $3.60

The sales tax $3.60.

Answer:

3.60

Step-by-step explanation:

sales tax = cost * tax rate

                = 180 * 2%

                 = 180 * .02

                 =3.60

Answer:

see explanation

Step-by-step explanation:

The restriction a ≠ 0 and b ≠ 0 is applied since division by zero would make

[tex]\frac{a}{b}[/tex] and its reciprocal [tex]\frac{b}{a}[/tex] undefined, thus meaningless

Answer:

(C)[tex]-6x+8(-x+6) = 6[/tex]

Step-by-step explanation:

Given the system of equations

[tex]x+y=6 \\-6x+8y = 6[/tex]

From the first equation:

x+y=6

Making y the subject, we have:

y=-x+6

Substituting y=-x+6 into the second equation, we obtain:

[tex]-6x+8(-x+6) = 6[/tex]

The correct option is C.

NOTE: The goal of substitution is to reduce the number of unknown variables to 1. Therefore, after the substitution, if you still have the two unknown, you might have done something incorrect.

Answer:

0.0003W/cm°C

Step-by-step explanation:

The question is not properly written. Here is the correct question.

The batting wang xiu ying uses to fill quilts has a thermal conductivity rate of 0.03 watts (W) per meter(m) per degree celsius. what is the batting thermal conductivity when w/cm•c

Given the thermal conductivity in W/m°C to be 0.03W/m°C

We are to rewrite the value in W/cm°C

The difference is the unit. The only thing we need to do is to simply convert the unit (metres) in W/m°C to centimeters (cm)

Since 100cm = 1m, 0.03W/m°C can be expressed as shown below;

= 0.03W/m°C

= 0.03 × W/1m×°C

Note that 1m = 100cm, substituting this conversion into the expression, it will become;

= 0.03 × W/100cm × °C

= 0.03/100 × W/cm°C

= 0.0003W/cm°C

Hence the battling thermal conductivity in W/cm°C is 0.0003W/cm°C

Answer:

0.0003W/cm°C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Since a coin only has two sides, the test must be referring to the fact that she has a 50, 50 shot at passing.

Answer: 0.1457

Step-by-step explanation:

Let p be the population proportion.

Given: The proportion of Americans who are afraid to fly is 0.10.

i.e. p= 0.10

Sample size : n= 1100

Sample proportion of Americans who are afraid to fly =[tex]\hat{p}=\dfrac{121}{1100}=0.11[/tex]

We assume that the population is normally distributed

Now, the probability that the sample proportion is more than 0.11:

[tex]P(\hat{p}>0.11)=P(\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}>\dfrac{0.11-0.10}{\sqrt{\dfrac{0.10(0.90)}{1100}}})\\\\=P(z>\dfrac{0.01}{0.0090453})\ \ \ [\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}} ]\\\\=P(z>1.1055)\\\\=1-P(z\leq1.055)\\\\=1-0.8543=0.1457\ \ \ [\text{using z-table}][/tex]

Hence, the probability that the sample proportion is more than 0.11 = 0.1457

Answer:

(x + 3)(x - 5)

Step-by-step explanation:

Well to factor  x^2-2x-15,

we need to find 2 numbers that multiply to get -15 and add to get -2.

3*-5 = -15

3x + -5x = -2x

x*x = x^2

Factored (x + 3)(x - 5)

Hope this helps :)

Answer:

(x - 5)(x + 3)

Step-by-step explanation:

Step 1- Find 2 number that multiplies to be -15, but also add to be -2

This would be -5 and 3

-5 * 3 = -15

-5 + 3 = -2

Step 2- write the equation

The equation can be written 2 different ways

1st way- (x - 5)(x + 3)

2nd way- (x + 3)(x - 5)  

Answer:

[tex]YZ = 48[/tex]

Step-by-step explanation:

Given

[tex]AB = 24[/tex]

[tex]XZ = 60[/tex]

Required

Find YZ

From the attachment, AB is parallel and equal to YC;

This implies that

[tex]AB = YC = 24[/tex]

Given that C is the midpoint of YZ;

This implies that

[tex]YC = CZ = 24[/tex] and [tex]YZ = YC + CZ[/tex]

Substitute values for YC and CZ

[tex]YZ = 24 + 24[/tex]

[tex]YZ = 48[/tex]

Answer:

48

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

-31p+79 > -59p+81

Group like terms

Send the constants to the right side of the expression and those with variables to the left side

That's

- 31p + 59p > 81 - 79

Simplify

We have

28p > 2

Divide both sides by 28

We have the final answer as

Hope this helps you

Answer:

18

Step-by-step explanation:

cm  15   -> 14

hours  6   ->?

cm 15  x3->45

hours 6 x3->18

the 45 cm long candle is 3 times as long ,so it would burn for 3 times as long A 45cm long candle would burn for 18 hours

Answer:

Real interest rate= 3%

Step-by-step explanation:

Giving the following information:

Suppose you place $10,000 in a retirement fund that earns a nominal interest rate of 8 percent. The inflation rate is 5 percent.

The effect of the inflation rate on the interest rate is counterproductive. The inflation rate diminishes purchasing power.

Real interest rate= nominal interest rate - inflation rate

Real interest rate= 0.08 - 0.05= 0.03

Answer:

3(1 - 20) + 10 = 4

3 * (-19) + 10 = 4

-57 + 10 = 4

-47 = 4

Since the two are not equal, this statement is false/invalid.

Hope this helps!

Answer:

3.92$

Step-by-step explanation:

The first step is to deduct 20% of 4.50 from 4.50.

20% of 4.50 is 0.2 x 4.50 = .90

4.50 - 0.90 = 3.60

That's the new price without the sales tax.

Now we need to add 9% of 3.60 to 3.60 to get the final cost.

9% of 3.60 is .09 x 3.60 = 0.32

3.60 + .32 = $3.92

Hope it helps.. If yes mark me BRAINLIEST

Tysm!

Answer:

$3.92

Step-by-step explanation:

Hello! For this question we need to gather up all the facts before we could answer it!

The original nail polish cost was $4.50

But the bottle was marked down by 20%

Then has a sales tax of 9%

So let's multiply 4.50 x 0.2 = 0.9

With that we need to subtract off of the original price because it is decreasing.

4.50 - 0.9 = 3.60

But that is not the final price because the bottle has a sales tax! We need to multiply the price after the 20% mark down, so, 3.60 x 0.09 = 0.324

And Then because we are dealing with money, we are going to make sure that we are only adding a decimal that goes up to the hundredths place.

Add: 3.60 + 0.32 = 3.92

The Final price of the nail polish that Dora bought would be $3.92. Which is actually a 0.58 cents drop!

I hope this helped!

Answer:

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.

$8 .   YES

$9 .    HELL NO

$11 .   DEFINITLY NOT

$13 .  GET OUTTA HERE

$14 .   MMM YES

Step-by-step explanation:

Answer:

A and E or 8, 14

Step-by-step explanation:

The coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

The table of values is given as:

Gallons       Cost

1                      1.25

2                     2.50

5                     6.25

15                     18.75

20                    25.00

The inverse of the above table would have the following header

Cost     Gallons

When the inverse table is populated, we have:

Cost    Gallons

1.25          1

2.50        2

6.25         5

18.75        15

25.00      20

The coordinates are: (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

Hence, the coordinates of the inverse are (1.25, 1) (2.50, 2), (6.25, 5), (18,75, 15) and (25.00, 20)

Read more about coordinates at:

https://brainly.com/question/10690059

#SPJ1

Answer:

First investment = $98000

Second = $413,000

Step-by-step explanation:

Given the following :

Investment 1:

Let first investment = f

Rate = 8% = 0.08

Investment 2:

$21,000 more than 4 times of investment 1:

4f + 21000

Rate = 10% = 0.1

Total annual interest earned from both :

$49,140

Interest on investment 1 + interest on investment 2 = $49,140

To solve:

Simple Interest = principal * rate * time

Time = 1 year

Total interest = (f * 0.08 * 1) + ((4f + 21000) * 0.1 * 1)

49140 = 0.08f + 0.4f + 2100

0.48f = 47040

f = 47040 / 0.48

f = 98000 = first investment

Second investment :

4f + 21000

= 4(98000) + 21000

= $413,000

Hey There!!

Your correct choice will be C.

Step-by-step explanation:

Because, The cosine function is just the sine function translated 90° to the left, so it's a sinusoid. So, They named after the function sine. By ♡Itsbrazts♡

Answer:

Step-by-step explanation:

y=cos(x)-2

Answer:

The second and fourth statements are correct.

Step-by-step explanation:

We are given the function for the graph of:

[tex]y=-(x-0.5)^2+9[/tex]

Note that this is a quadratic function in its vertex form, given by:

[tex]y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Rewriting our given equation yields:
[tex]\displaystyle y = (-1)(x-(0.5))^2 + (9)[/tex]

Therefore, a = -1, h = 0.5, and k = 9.

Therefore, the vertex of the graph is at (0.5 ,9).

Because the leading coefficient is negative, the parabola opens downwards.

Therefore, the parabola has a maximum value.

In conclusion, the second and fourth statements are correct.

1. the vertex is (0.5, 9)

2. it has a maximum.

Answer:

[tex]x=-1,5[/tex]

Step-by-step explanation:

[tex]x^2-4x-5=0[/tex]

In order to solve this quadratic, we have many methods. We can factor, complete the square, or use the quadratic formula. I'm going to factor since it's the easiest method.

To factor, find two numbers that when multiplied equal a(c) and when added equal b.

a=1, b=-4, and c=-5.

So we want two numbers that when multiplied equals 1(-5)=-5 and when added equals -4.

-5 and 1 are the possible numbers. Therefore:

[tex]x^2-4x-5=0\\x^2+x-5x-5=0\\x(x+1)-5(x+1)=0\\(x-5)(x+1)=0\\x=5, -1[/tex]

Answer:ITS A

Step-by-step explanation:

SAS: side angle side

SSA: is not a congruence theorem

AAS:angle angle side

SSS:side side side

Answer:

The answer is A.

Step-by-step explanation:

Just took the test

Answer:

Step-by-step explanation:

[tex]x \times 2 + 1 = 10[/tex]

[tex]2x + 1 = 10[/tex]

Move constant to R.H.S and change its sign

[tex]2x = 10 - 1[/tex]

Subtract the numbers

[tex]2x = 9[/tex]

Divide both sides of the equation by 2

[tex] \frac{2x}{2} = \frac{9}{2} [/tex]

Calculate

[tex]x = 4.5[/tex]

Hope this helps..

Best regards!!

Answer:

A. 770,000,000

Step-by-step explanation:

7.7x10^8 First step is to simplify

7.7x100,000,000 Then, multiply

770,000,000

Hope this helps, if it does, please consider giving me brainliest, it will help me a lot. If you still have any questions, feel free to ask.

Have a good day! :)

Answer:

6/100x

Step-by-step explanation:

Answer:6/100x

Step-by-step explanation:

Answer:

2383.14286

Step-by-step explanation:

The volume of a prism is length times width times height. Since we already know the height and length of the prism, we can divide the volume of the prism by the height and length. This becomes: 50046/3 = 16682. Next we divide by 7: 16682/7 = 2383.14286. Hope this helps!

Answer:

two I have no idea of the question

Answer:  49 ways

Step-by-step explanation:  7 possible ways up, 7 ways  down

Up and back on Rt 1, Up on Rt 1 down on Rt2 Up on  Rt 1 down on Rt3. .  . . .  Up on Rt 7, down on Rt7

You can imagine what was left out of the explanation.

Just Multiply 7×7 = 49