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ra1l [238]
3 years ago
11

Natalie and Preston would like to accumulate $25,000 at the end of 3.5 years for a future down payment on a house in Prescott. H

ow much should they deposit at the end of each week in a savings account that pays 7.2%/a compounded monthly to meet their goals?
Mathematics
1 answer:
Brrunno [24]3 years ago
3 0

Answer:

$7.4 should be deposited at the end of each week

Step-by-step explanation:

In this question, we are asked to calculate the principal amount that should be deposited to get a house of $25,000 at the interest and time given in the question

To solve this problem, we use the compound interest formula.

Mathematically;

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

From the question, we identify the following;

A is the amount that is targeted which is the principal plus the targeted interest = $25,000 according to the question

P is the amount invested at the beginning which we are looking for

r is the rate which is 7.2% = 7.2/100 = 0.072

n is the number of times we compound per year which is 12 times( compounding is per month)

t is the number of years which is 3.5 years

To get the principal, we can rewrite the equation to be;

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

25,000/(1 + 0.072/12)^(12 * 3.5) = P

P = 25,000/18.54 = $1,348

But the question asks how much to be deposited at the end of each week

The number of weeks in 3.5 years is 3.5 * 52 =182 weeks

Thus, the amount deposited at the end of each week will be 1,348/182 = $7.4

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Find x so that l || m.
fredd [130]

Answer:

x = 17

Step-by-step explanation:

Line l and m are two parallel lines cut across by the transversal line, therefore, the angle measuring 53° and (8x - 9)° are interior angles on the same side. Interior angles on the same side are supplementary.

Therefore:

53° + (8x - 9)° = 180°

Solve for x

53 + 8x - 9 = 180

Collect like terms

53 - 9 + 8x = 180

44 + 8x = 180

Subtract 44 from both sides

44 + 8x - 44 = 180 - 44

8x = 136

Divide both sides by 8

8x/8 = 136/8

x = 17

3 0
2 years ago
Vanessa throws a tennis ball in the air. the function h(t) = -16t2 + 45t + 7 represents the distance, in feet, that the ball is
antiseptic1488 [7]
Given that height, h(t) of a tennis ball is modeled by the equation h(t)=<span>-16t^2 + 45t + 7, the time taken for the ball to reach maximum height will found as follows:
at maximum height:
h'(t)=0
but from the equation:
h'(t)=-32t+45=0
solving for t we get
t=45/32
t=1.40625~1.4 seconds
Thus the time taken to reach maximum height is 1.4 seconds


</span>
4 0
3 years ago
Sue buys 5 pieces of fabric.Each piece is 1 7/10 yards long.What is the total length of the fabric she buys?One yard of the fabr
irina [24]

Answer:

The total length of fabric sue buys is 8.5 yards and total cost of the fabric is $42.5 .

Step-by-step explanation:

As given

Sue buys 5 pieces of fabric.

Each\ piece\ is\ 1 \frac{7}{10}\ yards\ long.

i.e

Each\ piece\ is\ \frac{17}{10}\ yards\ long.

Total\ length\ of\ fabric\ sue\ buys = \frac{5\times 17}{10}\ yards

Total\ length\ of\ fabric\ sue\ buys = \frac{85}{10}\ yards

In the decimal form

Total length of fabric sue buys = 8.5 yards

As given

One yard of the fabric costs $5

Total\ cost\ of\ fabric\ sue\ buys = 8.5\times 5

                                                            = $ 42.5  

Therefore the total length of fabric sue buys is 8.5 yards and total cost of the fabric is $42.5 .


5 0
3 years ago
A ball is thrown from a height of
Alika [10]
Define
g = 9.8 32.2 ft/s², the acceleration due to gravity.

Refer to the diagram shown below.
The initial height at 123 feet above ground is the reference position. Therefore the ground is at a height of - 123 ft, measured upward.

Because the initial upward velocity is - 11 ft/s, the height at time t seconds is
h(t) = -11t - (1/2)gt²
or
h(t) = -11t - 16.1t²

When the ball hits the ground, h = -123.
Therefore
-11t - 16.1t² = -123
11t + 16.1t² = 123
16.1t² + 11t - 123 = 0
t² + 0.6832t - 7.64 = 0

Solve with the quadratic formula.
t = (1/2) [-0.6832 +/- √(0.4668 + 30.56) ] = 2.4435 or -3.1267 s
Reject the negative answer.

The ball strikes the ground after 2.44 seconds.

Answer: 2.44 s

5 0
2 years ago
A circle has a diameter of 10 centimeters. of a sector with a central angle of 50 degrees is cut out, what is the area of this s
kramer

Answer:

D. 10.91 square centimeters

Step-by-step explanation:

Area of a sector of a circle = \frac{\theta}{360}\\ \pir^{2}

where \theta = 50^{o} C

radius (r) = half of diameter = 10/2 = 5 cm

Area  = \frac{50}{360} * \frac{22}{7} * 5^{2}

= 10.91 cm^{2}

8 0
3 years ago
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