MATHEMATICS MIDDLE SCHOOL

A person invests 7500 dollars in a bank. The bank pays 6% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 16200 dollars?

Answers

Answer 1

Answer:

Answer:

$13.0\ years$

Step-by-step explanation:

we know that

The compound interest formula is equal to

$A=P(1+(r)/(n))^(nt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=?\ years\n P=\$7,500\n r=0.06\nn=2\n A=\$16,200$

substitute in the formula above

$16,200=7,500(1+(0.06)/(2))^(2t)$

$(2.16)=(1.03)^(2t)$

Apply log both sides

$log(2.16)=(2t)log(1.03)$

$t=log(2.16)/[(2)log(1.03)]$

$t=13.0\ years$

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Jennifer had $30 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket at the museum, and 1/2 of it on a book. How much money does Jennifer have left over? Show all your work.

Answers

Answer:

Step-by-step explanation:

because 1/5 of 30 is 5

1/6 of 30 is 6

1/2 of 30 is 15

so you add 5+6+15

which equals 26

then you would subtract 30-26 to get how much is left over, which would be $4

Answer:

Step-by-step explanation:

1/2 is 30x.5=15 or 30/2 =15 or 50% of 30= $15

1/6 =30/6 = $5

1/5= 30/5 = $6

$15+$5+$6=$4

you could also convert into percentages to check your answer

A 30-minute TV program consists of three commercials, each 2 1/2 minutes long, and four equal-length entertainment segments. How long is each entertainment segment? What is the strategy plans and answer.

Answers

The length of each segment can be determine by subtract the length of three commercial.

The length of each segment is 5 minute 37.5 seconds.

Given:

Duration of TV program is 30 minute.

Duration of TV commercials is $2(1)/(2) \:\rm minutes$ .

Calculate the total length of three commercials.

$\begin{aligned}\rm {Total\: length}=(2(1)/(2))*3\n=2.5* 3\n=7.5\n\end$

Subtract 7.5 from total 30 min TV program.

$=30-7.5\n=22.5$

Now calculate the equal length of entertainment segments.

$\begin{aligned} \rm {Equal\: Length}=(22.5)/(4)\n= 5.625 \:\rm min\n\n=5 \:\rm min\:\rm and\: 37.5\: second\end$

Thus, the length of each segment is 5 minute 37.5 seconds.

Learn more about time calculation here:

brainly.com/question/5962504

for one show it will be 23.1 minutes if you multiply 2.30 minutes by 3 and get 6.9 you subtract 6.9 from the 30 minutes and you should 23.1 minutes

$10 + ($6-n) if n =$3
What is the final product
Of this mathematical question?

Answers

If n = $3 then plug it in
$10 + ($6-$3)
$6-$3 = $3
$10 + $3 = $13

$10+($6-$3)=
$10+$3=$13

HURRY PLEASE! i need this asap

Answers

Answer:

$4( \sqrt[3]{6 {x}^(2) } )$

Step-by-step explanation:

The given radical is

$\sqrt[3]{6 {x}^(2) }$

We want to choose from the given options, a like radical to the given expresion.

In general, the given expresion is of the form

$a( \sqrt[3]{6{x}^(2) } )$

where 'a' is a constant.

When a=1, we get the above expression.

When we substitute a=4, we get

$4( \sqrt[3]{6 {x}^(2) } )$

The volume of a sphere is 500
3
πcm3. What is the radius?

Answers

Answer:

Step-by-step explanation:

The volume of a sphere is 500 3 πcm3. what is the radius? sphere v = 4 3 πr3 1. substitute value into formula: 500 3 π = 4 3 πr3 2. undo multiplication of 4 3 : 125π = πr3 3. undo multiplication of π: 125 = r3 4. undo cube: 3√125 = r the radius of the sphere is 6 ⇒ 5 cm

Answer:

about 4.9 cm

Step-by-step explanation:

The equation for the volume of a sphere is V= $(4)/(3)\pi r^3$ . So, to solve this problem we will plug in 500 for V and solve for the radius, $r$ .

500= $(4)/(3) \pi r^3$
Multiply both sides by 3: $1500=4\pi r^3$
Divide both sides by 4: $375=\pi r^3$
Divide both sides by $\pi$ : $(375)/(\pi ) =r^3$
Find the cubed root of both sides: $4.9237=r$
The radius is about 4.9 cm

Need to find the value of y

Answers

Answer:

√55

Step-by-step explanation:

Notice that the small triangle in the bottom corner shares an angle with the overall triangle. Also, they are both right triangles. Therefore, they are similar triangles.

Notice that the large triangle at the top shares an angle with the overall triangle and is also a right triangle. Therefore it is also similar to the overall triangle and the smaller triangle.

Writing a proportion between the small and large triangles:

y / 11 = 5 / y

y² = 55

y = √55

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