Find the sum of the first n terms using the formula a(1-r^n)/1-r $50 + $50(1.1) + 50(1.1)^2 + … (6 terms)

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

( 3 )

the given figure resembles a rectangle !

now ,

[tex]Area \: of \: rectangle = length \times breadth \\ \\ given \: - \: length = 12 \: ft \\ \therefore \:breadth = x \: ft \\ \\ Area = 108 \: ft {}^{2} \\ \\ \implies \: length \times breadth = 108 \: ft {}^{2} \\ \\ \implies \: x \times 12 = 108 \\ \\ \implies \: x = \cancel\frac{108}{12} \\ \\ \bold\red{\implies \: x = 9 \: ft}[/tex]

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( 4 )

the given figure resembles a parallelogram!

[tex]Area \: of \: parallelogram = height \times base \\ \\ \implies \: height = x \: cm\\ \\ \implies \: base = 16 \: cm \\ \\ \: Area \: = 96 \: cm {}^{2} \\ \\ \implies \: x \times 16 = 96 \\ \\ \implies \: x = \cancel\frac{96}{16} \\ \\ \bold\red{\implies \: x = 6 \: cm}[/tex]

hope helpful :D

[tex]\huge \underbrace \mathfrak \red{Answer}[/tex]

To find :-

To get the value of 'di in figure 3 and 4.

Figure 3

Solution :-

Area of rectangle = length × width

area = 108 ft², length = 12 ft, width = x

[tex]108 = 12 \times x \\ \frac{108}{12} = x \\ 9 = x[/tex]

[tex] \\ [/tex]

Figure 4

Solution :-

Area of parallelogram = base × height

Area = 96 cm², base = 16 cm, height = x

[tex]96 = 16 \times x \\ \frac{96}{16} = x \\ 6 = x[/tex]

Answer:

$55

Step-by-step explanation:

Given:

A pair of shoes is $50, plus 10% tax.

To Find:

What is the total amount you will pay?

Solve:

Tax = Increase - Add on

Thus,

$50 × 10% = 5

$50 + 5 = $55

Hence, the total amount you will pay is $55.

Kavinsky

Answer:

Step-by-step explanation:

1/5 = 0.2

This is what I came up with, hopefully this helps!

The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

A nursing student works at a doctor's office for $15 per hour and tutors other students for $25 per hour.

Let x be the number of hours for the doctor's office and y be the number of hours for the tutor.

The student cannot work more than 20 hours each week.

      x + y < 20 ...1

15x + 25y > 375 ...2

The system of inequalities represents the given constraints will be x + y < 20 and 15x + 25y > 375.

More about the inequality link is given below.

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Answer:

The answer is c

scince I am not student so I don't use book n pen sorry

Answer:

a. y is quartered.

Step-by-step explanation:

y=1/x^2

when x is doubled, the equation becomes:

y=1/(2x)^2=1/(4x^2)

Answer:

If we double x, then the new value of x becomes 2x. So we can find the effect on y by substituting 2x for x in the given function.

y = 1/x^2

When x is replaced by 2x, we get:

y' = 1/(2x)^2

= 1/4x^2

Therefore, y' = (1/4)y

So, if x is doubled, then y is quartered (option a is the correct answer)

Answer:

15

Step-by-step explanation:

8² + 15² = c²

To find : Value of c

8² = 8 x 8 = 64

15² = 15 x 15 = 225

c² = 225

225 = 15 x 15 = 15²

So,

c² = 15²

c = 15

Answer:

Infinite solutions

Step-by-step explanation:

3x+6 = 3(x+2)

3x+6 = 3x+6

6 = 6

Answer:

see below

Step-by-step explanation:

will be of the form xxxx3.x    '3' will be just to the left of the decimal point

Answer:

3%

Step-by-step explanation:

Easy!

88 - 85 which is equivalent to 3.

Make the 3 a percentage

A = 3%

Answer:

x=-6

Step-by-step explanation:

Let x be the number

A) 12x-12=-84

B) 12x=-72

x=-6

Answer:

Step-by-step explanation:

A driver spent 45minutes to cover a distance of 120km

Convert minutes to hour

Use the distance equation

Find the speed

Substitute the distance and time value and find the value of speed

Answer:

  6. 14.9 years

  7. 4.8 years

  8. 28.91 years

Step-by-step explanation:

Exponential growth or decay is described by the function ...

  y = a·b^t

where 'a' is the initial value, and 'b' is the growth (or decay) factor. The growth (or decay) factor is one added to the growth rate.

__

This equation can be solved for t to get ...

  y/a = b^t . . . . . . . divide by a

  log(y/a) = t·log(b) . . . . take logarithms

  t = log(y/a)/log(b) . . . . divide by the coefficient of t

Note that the time period is in the same units as the growth rate. (If the growth rate is per quarter, then the value of t will be in quarters.)

__

The initial value is a=8000; the final value is y=35000; and the growth rate is 10%/4 = 0.025 per quarter. The above equation will give the time period in quarters.

  t = log(35000/8000)/log(1+0.025) ≈ 59.77 . . . quarters

Anisha will have $35,000 after 59.77/4 = 14.9 years.

__

No loan payment period is given, so we assume that the $43000 represents the repayment of the entire loan. The growth rate is 6% per year. The time required for the loaned amount to accumulate to a value of $43,000 is ...

  t = log(43,000/32,500)/log(1 +0.06) ≈ 4.80 . . . years

If the loan period is 4.80 years, Kevin will have paid 43,000 to pay it off.

__

The growth rate is 0.024/12 = 0.002 per month. The number of months to achieve the desired balance is ...

  t = log(3200/1600)/log(1 +0.024/12) ≈ 346.92 . . . . months

The balance in the account will be $3200 after 346.92/12 = 28.91 years.

_____

Additional comment

As a crude check on the answers, the "rule of 72" can be used. It says the doubling time is approximately 72 divided by the growth rate in percent. That is, a 10% growth rate will cause the value to double in approximately 72/10 = 7.2 years.

In the first problem, the value grows from 8000 to 35000, which represents a little more than 2 doublings (8000 to 16000 and 16000 to 32000). So, it is reasonable to expect the time period to be near 2 times 7.2 years, or 14.4 years. The value of 14.9 years is not unreasonable.

Answer:

Compound interest formula

[tex]\Large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]

where:

Given:

[tex]\begin{aligned}8000\left(1+\frac{0.1}{4}\right)^{4t} & = 35000\\(1.025)^{4t} & = \frac{35000}{8000}\\(1.025)^{4t} & = 4.375}\\\ln (1.025)^{4t} & = \ln 4.375\\4t \ln 1.025 & = \ln 4.375\\4t & = \frac{\ln 4.375}{\ln 1.025}\\t & = 0.25\left(\frac{\ln 4.375}{\ln 1.025}\right)\\t & = 14.9427947\end{aligned}[/tex]

Therefore, she will have $35,000 in 15 years.

Given:

[tex]\begin{aligned}32500\left(1+\frac{0.06}{1}\right)^{1t} & = 43000\\32500(1.06)^{t} & = 43000\\(1.06)^{t} & = \frac{43000}{32500}\\(1.06)^{t} & = \frac{86}{65}\\\ln (1.06)^{t} & = \ln \left(\frac{86}{65}\right)\\t \ln 1.06 & = \ln \left(\frac{86}{65}\right)\\t & = \dfrac{\ln \left(\frac{86}{65}\right)}{\ln 1.06}\\t & = 4.804621116\end{aligned}[/tex]

Therefore, Kevin will have paid $43,000 on the loan in 4 years and 10 months.

Given:

[tex]\begin{aligned}1600\left(1+\frac{0.024}{12}\right)^{12t} & = 3200\\1600(1.002)^{12t} & = 3200\\(1.002)^{12t} & = \frac{3200}{1600}\\(1.002)^{12t} & = 2\\\ln (1.002)^{12t} & = \ln 2\\12t \ln (1.002) & = \ln 2\\12t & = \dfrac{\ln 2}{\ln 1.002}\\t & = \frac{1}{12}\left(\dfrac{\ln 2}{\ln 1.002}\right)\\t & = 28.91000404\end{aligned}[/tex]

The balance of the account will be $3,200 in 28 years and 11 months.

Step-by-step explanation:

law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

extended Pythagoras :

c² = a² + b² - 2×a×b×cos(C)

and : the sum of all angles in a triangle is always 180°.

1.

b² = 42.1² + 37² - 2×42.1×37×cos(13) =

= 105.8575002...

b = 10.28870741...

b/sin(13) = 37/sin(C)

sin(C) = 37 × sin(13)/b = 0.808963525...

C = 53.99478824...° ≈ 54°

A = 180 - 13 - 54 ≈ 113°

2.

c² = 18² + 13² - 2×18×13×cos(115) = 690.7853465...

c = 26.28279564...

c/sin(115) = 18/sin(A)

sin(A) = 18 × sin(115)/c = 0.62069273...

A = 38.36673893...°

B = 180 - 115 - A = 26.63326107...°

3.

the length of b is missing.

this cannot be solved without the missing information

let x be the amount of times she visited the movie theater

[tex]70+12.5x=245\\\\12.5x=175\\\\x=14[/tex]

Alyssa needs to make 14 visits to earn a free movie ticket.

This is our y intercept

This is our slope.

So our equation is

Here v is visits

[tex]\Large\texttt{Answer\::}[/tex]

Please consult the "Calculations" section of this ans .

[tex]\Large\texttt{Calculations\::}[/tex]

The information we're given is below :

As per given information , we can do the following :

Point - slope form looks like so :

y-y₁=m(x-x₁)

y-6=-1/3(x-3)

y-6=-1/3x+1

y=-1/3x+1+7

y=-1/3x+6

↑ [tex]\small\textsc{EQUATION OF THE LINE}[/tex]

[tex]\small\textit{hope\:helpful~}[/tex]

Answer:

Probability of getting a green ball is more than that of getting a white ball.

Step-by-step explanation:

There are in all (5+3= 8) outcomes of the experiment. There are 5 outcomes in favour of the event of getting a green ball as there are 5 identical green balls in the bag.

Therefore, P(a green ball) = 5/8

In the same way,P(a white ball) = 3/8

Thus, clearly the probability of getting a green ball is more than that of getting a white ball.

Answer:

B. 49x^10

Step-by-step explanation:

(7x^3)^2 * (x^8)^1/2

multiply the exponents

49x^6 * x^4

add the exponents

49x^10

The perimeter of a triangle that has the side lengths is 6 + 10√3 cm

The side lengths are given as:

6 cm, 7√3 cm and √27 cm

The perimeter is the sum of the side lengths.

So, we have:

P = 6 + 7√3 + √27

Express 27 as 9 * 3

P = 6 + 7√3 + √(9 * 3)

Take the square root of 9

P = 6 + 7√3 + 3√3

Evaluate the sum

P = 6 + 10√3

Hence, the perimeter of a triangle that has the side lengths is 6 + 10√3 cm

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Answer:

x ≥ 6.

Step-by-step explanation:

Given : Kathy swims at least 6 laps every day.

To find: Write an inequality to show how long Kathy swims each day.

Solution : We have given that Kathy swims at least 6 laps every day.

We can see from given statement Kathy can swim 6 laps or greater then 6 laps in a day.

Then we use greater than or equal to sign  ( for at least)

Since x ≥ 6.

Therefore, x ≥ 6.

[tex]\boxed{\sf 186,000}\boxed[/tex]

Answer:

186,000

Step-by-step explanation:

1. Multiply 10 to the 5th power:

[tex]10^{5}[/tex] = 100,000

2. Multiply:

1.86 × 100,000 = 186,000

hope this helps :)

The probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Total number of marbles = 3+4+2+1 = 10

P(Yellow) = 1/10

P(Blue) = 4/9

Probability of extracting a Yellow marble followed by a Blue marble:

= (1/10)(4/9)

= 4/90

=  2/45

Thus, the probability of extracting a Yellow marble followed by a Blue marble is 2/45 if the bag of 10 Marbles has the following composition: Red – 3 Green – 4 Blue – 2 Yellow – 1

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Answer:

9.1

Step-by-step explanation:

To calculate the total interest payable, we use the formula

I=P0rt,

and substituting our values yields

I=$2,400×0.08×1812=$288.

Therefore the total amount he receives at loan drawdown is $2,400−$288=$2,112. To calculate the effective interest rate, we use to formula

A=P0(1+ret).

In this instance we have A=$2,400,P0=$2,112 (redefined from the value above) and t=1.5. We substitute into the formula to get

$2,400=$2,112(1+1.5re).

Solve for re.

24002112=1+1.5re

24002112−1=1.5re

24002112−11.5=re

This gives re=0.0909⋯=9.0909…%,  which is 9.1%

Answer: 12? im pretty sure

Step-by-step explanation: 1/4 of a unit so 4 for 1 unit, 4 x 3 is 12 units for 3

Answer:

[tex]8\sqrt[3]{-8x^3y^6z^{13}}[/tex]

Step-by-step explanation:

[tex]8\sqrt[3]{-8x^3y^6z^{13}}\\\\=8\sqrt[3]{(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z}\\\\=8\left[(-1)^3\cdot2^3\cdot x^3 \cdot y^6 \cdot z^{12} \cdot z \right]^{\tfrac 13}\\\\=-8\cdot 2 \cdot x \cdot y^2 \cdot z^4 \cdot z^{\tfrac 13}\\\\=-16xy^2 z^4 \sqrt[3]z[/tex]

Answer:

340 people did the survey in total.

What is Algebra?

Algebra is a branch of mathematics that deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they do not have predefined values.

These symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations in order to determine their values.

Given:

People who like the color purple = 187

Moreover, 45% of people prefer the color red.

Purple color enthusiasts = 100 - 45 = 55%

Let the total number of people polled be x.

So, 55% of x = 187

55/100x = 187

x= 18700/ 55

x= 340

Therefore, the answer is 340.

Learn more about Algebra here:

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