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Serhud [2]
3 years ago
12

Three motorcyclists ride around a circular course starting at the same place and the same time. The first passes the starting po

int every 36 min, the second every 27 min, and the third every 24 min. After how many minutes will all three pass the starting point again at the same time? Explain your reasoning. (Simplify your answer.) minutes A. All three pass the starting point at the same time again after 36.27. 24 = minutes B. All three pass the starting point at the same time again after GCD(36,27,24)= minutes. C. All three pass the starting point at the same time again after LCM(36,27,24) = x​
Mathematics
1 answer:
Natali5045456 [20]3 years ago
5 0

Answer:

C I think

Step-by-step explanation:

Normally L.C.M is the method of finding it

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2. Harry just deposited $1500 into a savings account giving 6% interest compounded quarterly.a) How much will be in the account
Studentka2010 [4]

The formula for compound interest is:

\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ A=\text{ Final amount} \\ r=\text{ Interest rate} \\ n=\text{ Number of times interest applied per period} \\ t=\text{ Number of time period elapsed} \\ P=\text{ Intial principal balance} \end{gathered}

Given data:

\begin{gathered} P=\text{ \$1500} \\ r=6\text{ \%}=0.06 \\ n=4\text{ times (compounded quarterly)} \end{gathered}

a. After ten years, that is t = 10 years, the amount in the account will be

\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times10} \\ A=\text{ }1500(1+0.015)^{40} \\ A=\text{ }1500(1.015)^{40} \\ A=\text{ \$2721.03} \end{gathered}

b. After twenty years, that is t = 20 years, the amount in the account will be:

\begin{gathered} A=1500(1+\frac{0.06}{4})^{4\times20} \\ A=1500(1.015)^{4\times20} \\ A=1500(1.015)^{80} \\ A=\text{ \$}4935.99 \end{gathered}

c. The time it takes for Harry's initial account value to double will be:

\begin{gathered} A=2\text{ x initial value = 2 }\times\text{ \$1500 = \$3000} \\ 3000=1500(1.015)^{4t} \\ (1.015)^{4t}=\frac{3000}{1500} \\ (1.015)^{4t}=2 \\ \text{ Find the logarithm of both sides} \\ \ln (1.015)^{4t}=\ln 2 \\ 4t=\frac{\ln 2}{\ln 1.015} \\ 4t=46.56 \\ t=\frac{46.56}{4}=11.64 \end{gathered}

Therefore, the time it takes Harry's initial account to double is approximately 11 years

8 0
1 year ago
Which fraction is equivalent to -3/2?
mel-nik [20]
3/-2 so the first option
5 0
2 years ago
Read 2 more answers
PLS HELP ASAP WILL GIVE BRAINLIEST AND 100 POINTS
konstantin123 [22]
<h2><u>Part A</u>: He started with 4 miles. </h2>

<u>Explanation Part A</u>:    51.664 = (x((1.2⁷)-1)) / 0.2

<h2>
<u>Part B</u>: The equation is 51.664 = (x(1.2⁷)-1)/0.2</h2>

<u>Explanation</u>: n = 7 and on day 7 he traveled 51.664 so Sn = 51.664.

We get the second part of the equation because each day is increased by 20% so we have r = (1.2x) / x = 1.2

So our top half will be x multiplied by ((1.2)⁷-1) because it's the 7th day and we are increasing by 1.2x - 1.

Our bottom half is 1.2 - 1 which equals 0.2

<h2><u>Part C</u> : 103.83 miles</h2>

<u>Explanation: </u> We now have x which is 4 so we plug x into the equation above and remove the 51.664. We also change the 1.2⁷ to 1.2¹⁰ because it's the 10th day not the 7th.

Our equation now looks like (4(1.2¹⁰)-1) / 0.2 which is equal to 103.83 miles.

5 0
2 years ago
△ABC @ △DEF. Find the measures of the given angles or the lengths of the given sides
brilliants [131]

Answer:

BC = EF = 8

Step-by-step explanation:

Assuming you mean BC ≅ EF, then ...

... 3z +2 = z +6

... 2z = 4 . . . . . . . . add -2-z

... z = 2 . . . . . . . . . divide by 2

BC = EF = 2+6 = 8

7 0
3 years ago
(Score for Question 2: ___ of 10 points)
Vedmedyk [2.9K]

The area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.

<h3>What is the area of trapezoid?</h3>

The area of the trapezoid is the space occupied by it on the two dimensional plane. The area of this figure is half of the product of height and sum of sides.

A=\dfrac{(a+b)h}{2}

Here, (a and b) are the base sides of the trapezoid and (h) is the height.

A room is shaped like a trapezoid which has the height of 28 feet and the length of sides as 23 ft and 35 ft. Thus, the area of it is,

A=\dfrac{(a+b)h}{2}\\A=\dfrac{(23+35)28}{2}\\A=812\rm\; ft^2

Carpet costs $8.30 per square foot. Thus, the cost of carpet with area 812 ft² is,

C=812×$8.30

C=$6739.6

Furniture covers 25% of the floor. Thus, the remaining square feet of carpet are covered by furniture is,

A=\dfrac{25}{100}\times812\\A=203\rm\; ft^2

Thus, the area of room is 812 square feet, cost of carpet to cover the room is $6739.6 and the remaining square feet of carpet are covered by furniture is 203 square feet.

Learn more about the area of trapezoid here;

brainly.com/question/1410008

#SPJ1

4 0
1 year ago
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