In the base-ten number system, ten digits {0, 1, 2, 3, 4, 5, 7, 8, 9) are used for number
representations. The base-ten number 825 therefore means 8 x 102+2 x 10+5 x 1
Similarly, in the base-three number system, three digits {0, 1, 2) are used for number
representation. A base-three number 1212 means 1 x 3 +2 x 32 + 1 x 3+2 x 1. What
is the base-three representation of the base-ten number 35?

Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

Compound interest simply means that the interest associated with a bank account, loan, or investment increases exponentially over time.

Given monthly income of Ron is $3,142.23

Ron is 25 years old and is retiring at the age of 65. so he has 40 years to contribute.

Total amount he contribute in 40 years paying 5.5% compounded monthly is given by

interest rate(r) = 0.055/12

time period = 40 years = 480 months

Principal amount = $314.223

Future value = [tex]P(\frac{(1+r)^{n}-1 }{r} )[/tex]

Substitute, we get,

= 3142.23 [tex].10(\frac{(1+\frac{0.055)^{12.40}-1) }{12} }{\frac{0.055}{12} }[/tex]

Thus, future value is $547074.681009.

After retirement his monthly income when he has $547074.681009 amount.

P = (A.i/2)/(1-(1+i/12)⁻ⁿ)

Putting values, we get,

P = (547074.68×0.55/12)/1-(1+0.055/12)⁻²⁴⁰

P = $3763.25

He will receive a monthly income of $3763.25.

But  given he will need a monthly income of $4,123 for 20 years, which is not met by Ron.

So, the amount he needs to supplement his monthly income when he retires by (4123-3763.25)= $359.74

Hence, Ron will not make his monthly goal of $4,123 and will need $359.74 to supplement his monthly income when he retires.

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Answer:Answered 2 years ago. The total of the sum of the measures of any triangle has been proven to be 180 degrees. If the ratio of angle measure is 1:3:6.

Step-by-step explanation:

Answer:

1: 18 3: 54 6: 108

Step-by-step explanation:

A triangle has 180 degrees.

You need to add up all the ratios 1+3+6

Then divide that by 180----> 180/10=18

Then multiply all the ratios by but answer(18)

1*18=18

3*18=54

6*18=108

Answer:

x-12

Step-by-step explanation:

let us say that the other number is n. then we have n+12=x or n=12-x

Using the speed - distance relationship, the time left before the appointed time is 27 minutes.

Recall :

At 10mph :

At 12 mph :

Equate (1) and (2) :

10t + 30 = 12t - 24

Collect like terms

10t - 12t = - 24 - 30

-2t = - 54

Divide both sides by - 2

t = 54 / 2

t = 27

Hence, the time left before the appointed time is 27 minutes.

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Answer:

7

Step-by-step explanation:

Answer:

A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F

B) [tex]f(x)=-0.4x+88[/tex]

Step-by-step explanation:

A)

In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.

So we have:

x = minutes after the air conditioner started to cool the house

f(x) = temperature

Here we want to find what is the meaning of

[tex]f(30)=76[/tex]

Which implies that:

[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house

[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F

So, the interpretation of f(30) =76 is that:

"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"

B)

Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.

We know the following information:

- At time x = 0, the temperature inside the house is 88°F

- At time x = 30 min, the temperature inside the house is 76°F

We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:

[tex]f(x)=mx+q[/tex]

where

[tex]q[/tex] is the value of the temperature at x = 0, so q = 88

m is the rate of change of the temperature

The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:

[tex]m=\frac{76-88}{30-0} =-0.4[/tex]

which means that the temperature decreases by 0.4°F every minute. So, the function can be written as

[tex]f(x)=-0.4x+88[/tex]

Answer:

Line 1 : y = -2x - 5

Line 2 : y = -3x + 3

Step-by-step explanation:

note the slope, and then note the y intercept

Answer:

y = - 2x - 5 and y = - 3x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = - 2, - 1) and (x₂, y₂ ) = (0, - 5) ← 2 points on the line

m = [tex]\frac{-5-(-1)}{0-(-2)}[/tex] = [tex]\frac{x- 5+1}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

The line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - 2x - 5 ← equation of line 1

Repeat with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (1, 0) ← 2 points on line 2

m = [tex]\frac{0-3}{1-0}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

The line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 3x + 3 ← equation of Line 2

Answer:

11/20

Step-by-step explanation:

Answer:  33 gallons

Step-by-step explanation:

The water tank is a cube, with one dimension of x meters. Its volume will be x^3.

X^3 = 729m^3

x = 9 meters.  The cube has 4 side walls and a top and bottom, for a total of 6 interior walls.  Each wall has an area of x^2, or 81 m^2.

(6 walls)*(81 ft^2) = 486 m^2

One gallon of paint will cover 15 m^2.  The conversion factor is (1 gallon/15 m^2)

(486 m^2)*(1 gallon/15 m^2) = 32.4 gallons, rounded up to 33 gallons

Answer:

$243

Step-by-step explanation:

Answer:

x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}

Step-by-step explanation:

(x-50)^2 is x^2+2500-100x*.0048 is .0048x. 2500*0.0048 is 12, and -100*0.0048=-.48.

So, we have .0048x^2+12-.48x+6, which is

.0048x^2+18-.48x=10. USing the quadratic formula, we get

x=\frac{0.48+\sqrt{0.0768}}{0.0096},\:x=\frac{0.48-\sqrt{0.0768}}{0.0096}

(Enter into symbolab.com to see theanswer)

Answer:

[tex]y = + - \sqrt[4]{ \frac{3}{2} x} [/tex]

Answer: y = -66x + 201

Step-by-step explanation:

Answer:

  a) b^3

  b) x^3

Step-by-step explanation:

It can be helpful to think of the exponent as specifying the number of times the base is a factor in the product. Of course, common factors in the numerator and denominator cancel.

  [tex]\dfrac{b^7}{b^4}=\dfrac{b\cdot b\cdot b\cdot b\cdot b\cdot b\cdot b}{b\cdot b\cdot b\cdot b}=b\cdot b\cdot b=b^{7-4}=\boxed{b^3}[/tex]

__

  [tex]\dfrac{x\cdot x^5}{x^2\cdot x}=\dfrac{x\cdot x\cdot x\cdot x\cdot x\cdot x}{x\cdot x\cdot x}=x\cdot x\cdot x=x^{6-3}=\boxed{x^3}[/tex]

Answer:

look at the slope rise of 2 run of -1 or other way around so slope is

[tex] y = - \frac{2}{1}x + 5[/tex]

Answer:

Ben has 19 marbles

Step-by-step explanation:

First taking that josh and ricks ratio is 1:2, this would set up in an equation as [tex]2j = r[/tex] and with ben having 15 less than rick, his formula would be [tex]r = b + 15[/tex] as well as the total of all the boys marbles together being this [tex]j+r+b=70[/tex]

Now we put all of these equations into a set to answer them.

[tex]2j = r\\ r = b + 15\\j+r+b=70[/tex]

First we solve for j

[tex]2j = r\\ j=\frac{1}{2} r[/tex]

Then substitute j

[tex]j+r+b=70\\ \frac{1}{2}r+r+b=70\\ 2b+3r=140[/tex]

Then simplify and multiply by 2 to even out

[tex]r = b + 15\\ -b+r=15\\2b+3r=140[/tex]

Now eliminate the b variable and combine equations

[tex]2b+3r=140\\-2b+2r=30[/tex]

[tex]5r=170[/tex]

Now divide and solve for r

[tex]5r=170\\r=34[/tex]

Now we know Rick has 34 marbles of the 70 marbles, so we can substitute his number back into the original equation

[tex]-b+34=15\\b=19[/tex]

Now we know Ben has 19 marbles of the remaining 36, and can substitute his number as well

[tex]j=\frac{1}{2}(34)\\j=17[/tex]

And now we know how much everyone has, to check we rewrite all the equations with their respective numbers

[tex]11+34+19=70\\2(17)=34\\34=19+15[/tex]

[tex]70=70\\34=34\\34=34[/tex]

Which means the ordered pairing of (b, j, r) is (19, 17, 34)

Answer:

1 cm

Step-by-step explanation:

Answer:

2x  + 3 )(x   + 2 )

Step-by-step explanation:

2x² + 7x + 6          

Find two numbers multiplied together to get 6

and if you multiply one by 2, the answer is 7:

Tested:                                  

6 & 1  but 6 · 2 + 1 = 13 or 6 + 2 · 1  = 8 No

2 & 3  and 2 · 2 + 3 = 7    Yes

2x² = 2x  & x

 all signs are positive

   trinomial  factoring  (            )(            )

                                     (     +     )(      +    )

    2 and 3 are the numbers to use    (2x  + 3 )(x   + 2 )   or     (2x + 2) (x + 3)

The largest number goes with the 2x.

Therefore (2x  + 3 )(x   + 2 )

Check 2x(x + 2) + 3(x + 2)

              2x² + 4x + 3x + 6

              2x² + 7x + 6         checked                            

Answer:

11[tex]x[/tex]+6

Step-by-step explanation:

2[tex]x^{2}[/tex]= 4[tex]x[/tex] because 2 *2 = 4 + x = 4[tex]x[/tex]

since 7[tex]x[/tex] is a like term we add it to 4[tex]x[/tex] and it becomes : 11[tex]x[/tex]

Since 6 does not have a variable we do not add anything to it so, it stays the same and the simplified expression becomes : 11[tex]x[/tex] + 6

Answer:

alan received 24 votes

Step-by-step explanation:

bark

Answer: Ill show you some not everything so u can try

Step-by-step explanation: for example 8+y=92

you can make a new problem...

move the 92...

92

subtract

92-

subtract the other number which isnt the variable

92-8

subtract and you get your answer!

Step-by-step explanation:

an equation means that whatever is on one side of the "=" sign is truly equal to whatever is on the other side.

it is like a balance.

you can change the content on one side of the balance, but then you have to make the same change on the other side of the balance. otherwise the balanced relation between both sides is destroyed. and it is no longer an equation.

for the same reason, you can perform any mathematical operation on an equation, as long as you do it simultaneously on both sides.

all these equations are equations with one variable.

so, if we find a way to bring all terms with the variable to one side, and everything else (typically constant numbers) to the other side, while still maintaining the equation relation, then we can solve this by saying "this is only an equation, if the variable has this is that value".

and that is the whole trick.

so, for e.g. t + 3 = 5, how can we get only the variable on one side ? well, the "+ 3" is disturbing, so we subtract 3.

and to keep the balance, we need to subtract 3 on both sides.

that gives us then

t + 3 - 3 = 5 - 3

t = 2

and boom ! the equation has solved itself right in front of our eyes.

and the same thing for all the other equations.

find what is the disturbing additional term on the side of the variable, then get rid of it (and repeat that exact action on the other side) and see what is left on the other side. and you have solved the equation.

that works in every direction like

n + 22 = 5

n + 22 - 22 = 5 - 22

n = -17

12.5 = 7.4 + z

12.5 - 7.4 = 7.4 - 7.4 + z

5.1 = z or

z = 5.1

remember, it is an equation like a balance. you can switch the balance bowls from left to right and right to left, and still they are in balance.

A family-wise inflation of error rate is the increase in the probability that one or more results of a numerous, independently (separately) conducted statistical analyses to become statistically significant, but these results can actually be attributed to random variation or measurement error.

In Statistics, a family-wise inflation of error rate is also referred to as family-wise error rate (FWER) and it can be defined as the probability of making at least one false conclusion or type I errors in numerous, separate statistical analyses or hypothesis tests.

Hence, a family-wise inflation of error rate increases the probability that one or more of the results among groups within an independent data set to be statistically significant, especially due to random variation or measurement error.

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Answer:

15°

brainlest

Step-by-step explanation:

Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)

The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.

Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°.  Angle PQC has the same measure as angle RQC, so is 15°.

Angle PQC is 15°.

Answer:

600,000 cm²

Step-by-step explanation:

We know the conversion from meters to centimeters to be

1 m = 100 cm.

We need the conversion factor from square meters to square centimeters.

Start with

1 m = 100 cm

Square both sides.

(1 m)² = (100 cm)²

1 m² = 10,000 cm²

Now that we have the correct conversion factor from m² to cm², we can do the conversion of 60 m² into cm².

60 m² × (10,000 cm²)/(1 m²) = 600,000 cm²

Answer:

The surface area of the given triangular prism = 920 square cm.

In the given triangular prism

S1 = 25 cm

S2 = 25 cm

S3 = 14 cm = base

Height = 24 cm

length = 10 cm

Perimeter = S1 + S2+ S3

                 = 25+25+14

                 = 64 cm

Area of base =  length x base

                      = 10x14

                       = 140 square cm

Since we know that,

Surface area of triangular prism = (Perimeter × Length) + (2 × Base Area)

                                                     = (64x10) + 2x140

                                                     = 640 + 280

                                                     = 920 square cm

Hence,

The required surface area =  920 square cm.

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Answer:

Step-by-step explanation:

(a) 2x + 4 (x - 1) = 2 + 4x

 2x +4x - 4 = 2 + 4x

 6x -4 = 2 + 4x

 2x = 6

   x = 3  One solution

(b) 25 - x = 15 - (3x + 10)

 25 - x = 15 - 3x - 10

2x = 15 - 25 - 10

2x = -20

 x = -10  One solution

(c) 4x = 2x + 2x + 5 (x - x)

 4x = 4x + 5x - 5x

  0 = 0

No solutions

Answer:

yes the ratio are equivalent

Answer:

yes they are egivalent

Step-by-step explanation:

Answer: y=-1/4x+4

Step-by-step explanation:

slope goes down 1, and right 4 so it's -1/4. Y-intercept is positive 4 so it will be +4

Answer:

3.0233088 x 10 raise to power 7

Answer:

Where's the question?

Step-by-step explanation: