Find the sum of the series:

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)

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

Answer:

x=-6

Step-by-step explanation:

Let x be the number

A) 12x-12=-84

B) 12x=-72

x=-6

Answer:

volume is 36.25inches

145/4

Step-by-step explanation:

L= 3 5/8inches

W= 2 1/2inches

H= 4inches

VOLUME = L×W×H

3 5/8 × 2 1/2 × 4 =

29/8 × 5/2 × 4 = 36.25inches

36.25→145/4

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

Read more about perimeter at:

https://brainly.com/question/24571594

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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:

brainly.com/question/24875240

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:

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

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]\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]

_____________________________

_____________________________

( 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:

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.

Answer:

Step-by-step explanation:

in 6 years we know that it will be half,  because that's what "half life" means

in 3 years it's only  loses  1/2 * 1/2 = 1/4 of it's mass

in 1 year it's only loses 1/6 * 1/2 = 1/12 of it's mass

from that we can make the formula that

current weight of radium  = Wr

Mass of radium orginal = Mo

year of time = t   ( must be in years, not days, months or weeks )

Wr = (1/12)*t* Mo

Answer:

Infinite solutions

Step-by-step explanation:

3x+6 = 3(x+2)

3x+6 = 3x+6

6 = 6

Answer:

A solar panel is the best way to transform electrical energy into other forms of energy

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:

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:

[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]

[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 :)

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

Answer:

18

Step-by-step explanation:

36 divided by two is 18 therefore 18+18  is 36

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.

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:

[tex]y\approx24.129[/tex]

Step-by-step explanation:

[tex]y=0.05-10\ln x;\: x=0.09\\y=0.05-10\ln(0.09)\\y\approx24.129[/tex]

Answer:

24.129

the answer is that and I need 20 characters

Answer:

Stable. They're solid in they're emotions

Step-by-step explanation:

[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]