15 people received an email and sent it to 3 different friends each, who in turn each sent it to 2 new people. What percent of the total number of people who received the e-mail are the original 15 people?

Answer:

x<103/40

Step-by-step explanation:

-13(6x-15)+6x>8x-11

-78x+195+6x>8x-11

-78x-8x+6x+195>-11

-78x-2x>-11-195

-80x>-206

80x>206

x>206/80

x>103/40

x<103/40

Answer:

3a²  

Step-by-step explanation:

least common denominator of a² and 3a

a²  = a *a

3a = 3 * a

least common denominator = 3 * a*a =3a²  

Answer:

The answer is 3a², where a ≠ 0

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Rational expressions are 4/a² and 5/3a

2. Find the least common denominator for these two rational expressions.

Denominators of the expressions are:

a² and 3a ⇒ a² = a * a, 3a = 3 * a

The least common denominator will be:

3a², where a ≠ 0

3a²/a² = 3 and 3a²/3a = a

Answer:

Step-by-step explanation:

X={0,12,23}

Y={3,12,15}  

X \ Y = { 0 , 23}

X/Y means the element should be only in X. We have remove the element in X if it is in Y

In this 0 and 23 is only in X

12 is X and Y. So it wont come in X/Y

The set X \ Y represents the difference of two sets, indicating all the elements that are in set X but not in set Y. For X={0, 12, 23} and Y={3, 12, 15}, the elements that are in X but not in Y are '0' and '23', so X \ Y = {0, 23}.

In set theory, the notation X \ Y represents the difference of two sets. This indicates all the elements that are in set X but not in set Y. In this case:

X={0, 12, 23}, Y={3, 12, 15}

So the elements that are in X but not in Y are '0' and '23'.

Therefore, X \ Y = {0, 23}.

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The probability of drawing two green marbles, with replacement is [tex]\frac{9}{25}[/tex]

Given that There are 4 red and 6 green marbles in a jar

To find: probability of drawing two green marbles, with replacement

The probability of an event is given as:

[tex]\text {probability }=\frac{\text { number of favourable outcomes }}{\text { total number of possible outcomes }}[/tex]

Here total number of possible outcomes = 4 red + 6 green marbles = 10

Favourable outcome is drawing two green marbles with replacement

So favourable outcome = 6

So probabilty of choosing green marble:

[tex]probability = \frac{6}{10} = \frac{3}{5}[/tex]

Now given that with replacement, so we get

[tex]\text { probability }=\frac{3}{5} \times \frac{3}{5}=\frac{9}{25}[/tex]

Thus probability is [tex]\frac{9}{25}[/tex]

Answer:

d = 5

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a₂ - a₁ = a₃ - a₂ = [tex]a_{n}[/tex] - [tex]a_{n-1}[/tex]

Given

[tex]a_{n}[/tex] = 5n - 3

Generate the first 2 terms of the sequence by substituting n = 1, n = 2

a₁ = 5(1) - 3 = 5 - 3 = 2

a₂ = 5(2) - 3 = 10 - 3 = 7

d = 7 - 2 = 5

Answer: -9r+3

Step-by-step explanation:

In order to simplify this expression, all you have to do is combine the like terms. However, because there is an addition and a subtraction sign next to each other, we have to multiply them together to find which sign will stay.

Positive x Positive = Positive

Positive x Negative = Negative   <---

Negative x Negative = Positive

Because we know that multiplying a negative sign by a positive sign will give us negative, we have to keep the subtraction sign and remove the addition sign. This leaves us with 4-9r-1. All that is left to do is simplify.

Combine the like terms: 4-1 = 3

Answer: -9r+3

Hope this helps!

Answer:

Step-by-step explanation:

Group Like Terms:

A: -9r + 4 - 1,

Add/Subtract numbers:

If you have any questions feel free to comment below.

Best of Luck to you.

Answer:

Step-by-step explanation:

You could complete the square to do this, or you could just evaluate the h coordinate using the simple formula

[tex]h=-\frac{b}{2a}[/tex]

then find k by subbing that h value into the equation for x to find y which is the same as k.  In our quadratic, a = 4, b = -8, and c = -4.

[tex]h=\frac{-(-8)}{2(4)}=1[/tex]

Now sub that value into the quadratic to find y (k):

[tex]4(1)^2-8(1)-4=4-8-4=-8[/tex]

The vertex of the quadratic is (1, -8)

Answer:

b.18

Step-by-step explanation:

18/4=4.5

Answer: The answer would be b, or 18. 4x4.5 is 18, but you are not multiplying it by a whole number. so it CAN'T be B.

Hope this helps!

===============================================

How I got that answer:

r = radius

h = height

LA = lateral surface area of cylinder

LA = 2*pi*r*h

Let's find the lateral surface area of each silo. The smallest lateral surface area will lead to the lowest total cost.

-------------

Silo A

LA = 2*pi*r*h

LA = 2*pi*6*60

LA = 720pi

-------------

Silo B

LA = 2*pi*r*h

LA = 2*pi*8*50

LA = 800pi

-------------

Silo C

LA = 2*pi*r*h

LA = 2*pi*10*34

LA = 680pi

-------------

Silo D

LA = 2*pi*r*h

LA = 2*pi*12*20

LA = 480pi

-------------

If we ignore the "pi" terms for each of the four answers above, we see that 480 is the smallest value. Silo D has the smallest lateral surface area at 480pi square feet.

-------------

Side note: to determine the total cost, you multiply the surface area by the cost per square foot ($1.20)

For example, the total cost to paint silo D is

cost = (surface area)*(price per square foot)

cost = (480*pi)*(1.20)

cost = 1809.557

cost = 1809.56

This section is optional as your teacher isnt requiring you to find the actual costs, but rather just the silo with the least amount of area. You could go the longer route to find each surface area, compute the total cost, and then compare the total costs. You should find that silo D's cost is the lowest.

Answer:

Part 1) [tex]-\sqrt{15}[/tex]

Part 2) [tex]x=\frac{b+ac}{2c-ab}[/tex]

Step-by-step explanation:

Part 1) we know that

To put factor back into the square root, we have to put squared value

we have

[tex]-5\sqrt{0.6}[/tex]

Remember that

[tex]5=\sqrt{5^2}[/tex]

substitute in the expression above

[tex]-5\sqrt{0.6}=-\sqrt{(5^2)(0.6)}=-\sqrt{25*0.6}=-\sqrt{15}[/tex]

Part 2) we have

[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]

Solve for x

That means----> Isolate the variable x

Multiply in cross

[tex](2x-a)c=(ax+1)b[/tex]

Apply distributive property

[tex]2cx-ac=abx+b[/tex]

Group terms

[tex]2cx-abx=b+ac[/tex]

Factor x left side

[tex]x(2c-ab)=b+ac[/tex]

Divide by (2c-ab) both sides

[tex]x=\frac{b+ac}{2c-ab}[/tex]

Answer:

-13x + 6y

Step-by-step explanation:

combine like terms

-7x + 6y - 6x

-7x - 6x = -13x

-13x + 6y

Answer:

Step-by-step explanation:

-7x+6y-6x

Solution:

Put like terms together from left to right; that is the equation will assume a new order from -7x+6y-6x to

-7x-6x+6y

Sum the figures with like terms

= -13x+6y (answer)

Answer:

Closed.

Step-by-step explanation:

Answer:

Equation: 178 - x = - 62

Explanation:

Start of the wee: 178

One withdrawal: x

End of the week: -62

178 - x = -62

Simplify both sides of equation

178−x=−62

178+−x=−62

−x+178=−62

Subtract 178 from both sides

−x+178−178=−62−178

−x=−240

Divide both sides by -1

-x / -1 = -240 / -1

x=240

Trevor withdrew $240 from his bank account. This was calculated by setting up an equation with his initial positive balance and final negative balance, and solving for the withdrawal amount.

To determine how much money Trevor withdrew from his bank account, we can set up an equation representing the transactions in his account. Let x represent the amount of money withdrawn. We start with Trevor's initial balance, subtract the withdrawal, and set that equal to his final negative balance:

Initial balance - Withdrawal = Final balance

178 - x = -62

To solve for x, we add x to both sides to get the withdrawal amount on its own and then add 62 to both sides to isolate x:

178 - x + x = -62 + x

178 = x - 62

178 + 62 = x

240 = x

So, Trevor withdrew $240 from his bank account.

It will take you 2 hours since ur going 70 mph divide the 140 mph by 70mph . Hope this helps :)

Answer:

The value of car after 5 years of exponentially depreciation is $16,213.36  

Step-by-step explanation:

The initial amount of the car = i = $24,600

The depreciates rate of interest applied = r = 8%

Let The value of car after n years = A  

The number of years = n = 5 years

Now,According to question

The value of car after n years = initial price of car  × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, The value of car after 5 years = i × [tex](1-\dfrac{\textrm r}{100})^{\textrm n}[/tex]

Or, $A = $24,600 × [tex](1-\dfrac{\textrm 8}{100})^{\textrm 5}[/tex]

Or, $A = $24,600 × [tex](0.92)^{5}[/tex]

Or, $A = $24,600 × 0.65908

Or, $A = $16,213.36

So, The value of car after 5 years = A = $16,213.36

Hence , The value of car after 5 years of exponentially depreciation is $16,213.36  . Answer

The distance from the point (-6,8) to the line y=-3x+10 is calculated using the distance formula which yields a value of approximately 6.32, when rounded to the nearest hundredths.

The subject of this question is mathematics, specifically it pertains to finding the distance between a point and a line. The distance between a point (x1, y1) and a line ax + by + c = 0 can be calculated using the formula: distance = |ax1 + by1 + c|/sqrt(a²+b²). In your case, the given point is (-6,8) and the line is y = -3x + 10, which can be rewritten as 3x + y - 10 = 0. Therefore, a = 3, b = 1, c = -10, x1 = -6, and y1 = 8.

Substituting these values into the distance formula: distance = |3*(-6) + 1*(8) - 10|/sqrt((3)² + (1)²) = |-18 + 8 - 10|/sqrt(10) = |-20|/sqrt(10) = 20/sqrt(10) = 6.32, rounded to the nearest hundredths.

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There were 100 student tickets sold

Step-by-step explanation:

The given is:

We need to find how many student tickets were sold

Assume that the number of student tickets is x and the number of adult tickets is y

∵ The number of student tickets is x

∵ The number of adult tickets is y

∵ They sold 300 tickets

∴ x + y = 300 ⇒ (1)

∵ The price of the student ticket = $4

∵ The price of the adult ticket = $6

∵ The total sales = $1600

- Add the prices of the students tickets and the adult tickets

  and equate the sum by the total sales

∴ 4x + 6y = 1600 ⇒ (2)

Now we have a system of equation to solve it

Multiply equation (1) by -6 to eliminate y

∵ -6x - 6y = -1800 ⇒ (3)

- Add equations (2) and (3)

∴ -2x = -200

- Divide both sides by -2

∴ x = 100

There were 100 student tickets sold

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Answer:

Step-by-step explanation:

(2/5 * 30) * 6^2 - 3^2           Reduce 2/5 * 30

180 * 6^2 - 3^2                    Raise the bases of the power

180 *36 - 9                           Multiply 36 and 180

6480 - 9                               Subtract 9

6471

Answer:

The midpoints are ( 6, 5 ).

Step-by-step explanation:

Given that the endpoints are  A ( 3, 7) and B (9, 3)-

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] then the mid points C are-  

C = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex], [tex]\frac{ y_{1} + y_{2}  }{2}[/tex]  )

Here,

A ( 3, 7 ) and B ( 9, 3 )-

Then the  midpoints C are-

C = ( [tex]\frac{ 3 + 9}{2}[/tex], [tex]\frac{ 7 + 3 }{2}[/tex] )

C= ( 12/2 , 10/2 )

C = ( 6, 5 )

Hence the midpoints are (6, 5).

In this question, you're plugging in g(x) into f(x) to simplify.

You would plug the g(x) equation into the x variable in the f(x) equation.

Plug g(x) into f(x):

(2x+3)² - 1

Solve:

(2x+3)² - 1

Use FOIL:

F = First

O = Outsides

I = Insides

L = Last

4x² + 12x + 9 - 1

Combine like terms:

4x² + 12x + 8

Answer:

4x² + 12x + 8

Answer:

OPTION A: [tex]$ \frac{1}{2^{15}} $[/tex]

Step-by-step explanation:

We should know that:

[tex]$ (a^b)^c = a^{b . c} $[/tex]

So, [tex]$ (2^3)^{-5} = 2^{3 . (-5)}} $[/tex]

[tex]$ = 2^{-15} $[/tex]

This is equivalent to [tex]$ \frac{1}{2^{15}} $[/tex]

Hence, OPTION A is the answer.

Answer:

Option A does not give the right expression.

Step-by-step explanation:

On the number line if there are two points P(a) and Q(b) given by coordinates a and b, then the distance between those two points will be given by  

d = |a - b| ......... (1)

which is independent of the position of the points.

Therefore, if point A is at - 3.5 and point B is at 7.5, then the distance between point A and point B will be given by  |7.5+3.5| or |- 3.5-7.5| or |7.5-(-3.5)|, but not by  |7.4-3.5|.

Hence, option A does not give the right expression. (Answer)

The volume of Duante's bedroom is 1080 cubic feet.

Given that, the area of the floor is 90 square feet, and the height of the bedroom is 12 feet.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

Volume of a rectangular prism = Area of a base × Height.

Here, volume of a rectangular prism = 90 × 12

= 1080 cubic feet

Therefore, the volume of Duante's bedroom is 1080 cubic feet.

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Answer: 96mm²

Step-by-step explanation:

c=31 mm

m=6mm

b=8mm

d=10mm

l=24 mm

-----------------------

c=31 mm

a=24+6=30 mm

b=8mm

A of ΔM=30*8/2=

120 mm²

A of ΔS=b*m/2=8*6/2=24mm²

Area od shaded triangle is=area of ΔM-area ofΔS=120-24=96mm²

Answer:

f(6)

Step-by-step explanation:

Answer:

f(2)

Step-by-step explanation:

a)The scale of the number line is 1 unit represents 8 units.

b) On both x and y axes 1 unit represents 4 units.

How to find scale of a graph.

a) The difference between 64 and 32 is

= 64 - 32 = 32

On the number line there are 4 divisions between 32 and 64

Each division = 32/4 = 8

Therefore,the scale of the number line is 1 unit represents 8 units.

b) vertical axis (y axis)

From 0 to 12 there are 3 divisions

Each unit of the division = 12/3 = 4

Therefore, 1 unit represents 4 units on the y axis.

Horizontal axis (x axis)

From 0 to 20, there are five divisions

Each division = 20/5 = 4

Therefore, each 1 unit of division represents 4 unit

Complete question

Answer:

Step-by-step explanation:

Answer:

[tex]\large\boxed{slope=\dfrac{7}{2}=3.5}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (3, 1) and (5, 8).

Substitute:

[tex]m=\dfrac{8-1}{5-3}=\dfrac{7}{2}[/tex]

Answer:

[tex]\boxed{\bold{Slope \ \frac{7}{2} \ = \ 3.5 }}[/tex]

Explanation:

Slope Intercept Form: y = mx + b

Slope Formula: [tex]\bold{\frac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\bold{\left(x_1,\:y_1\right)=\left(3,\:1\right),\:\left(x_2,\:y_2\right)=\left(5,\:8\right)}[/tex]

[tex]\bold{m=\frac{8-1}{5-3}}[/tex]

[tex]\bold{m=\frac{7}{2}}[/tex]

[tex]\bold{Slope \ in \ fraction \ form: \frac{7}{2} }[/tex]

[tex]\bold{Slope \ in \ decimal \ form: \ 3.5}[/tex]

Option 1: $71.00 is the correct answer

Step-by-step explanation:

Let x be the money Karen started with:

Then

22% of x is $15.62

Mathematically writing

[tex]15.62 = 22\%\ of\ x\\15.62 = 0.22 * x\\x = \frac{15.62}{0.22}\\x = 71[/tex]

Hence,

Karen had $71.00 to start.

Option 1: $71.00 is the correct answer

Keywords: Percentage, percent

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