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frosja888 [35]
1 year ago
6

It is known that the distance in metres through which a body falls freely varies directly as the square of the time taken. If a

body falls through 80 metres in 4 seconds, find the distance it would fall in 5 seconds.
step-by-step easy explanation, please.
Mathematics
1 answer:
kobusy [5.1K]1 year ago
4 0

Answer:

K = 5 ; 125 m

Step-by-step explanation:

body falls through 80 metres in 4 seconds, find the distance it would fall in 5 seconds.

Given that:

Distance α (Timetaken)²

Distance = d ; Timetaken = t

d = Kt²

K = constant of proportionality

80 = k4²

80 = 16k

K = 80 / 16

K = 5

Distance it would fall in 5 seconds ; t = 5

D = Kt²

D = 5 * 5²

D = 5 * 25

D = 125

It will fall a distance of 125 m in 5 seconds.

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What is the present value of a $50,000 decreasing perpetuity beginning in one year if the discount rate is 7% and the payments d
Trava [24]

Answer:

Present Value = $1666666.67

Step-by-step explanation:

Present Value of a Growing Perpuity is calculated using the following formula

PV =D/(r - g)

Where D = Dividend

r = Discount Rate

g = Growth rate

D = $50,000

r = 7%

r = 7/100

r = 0.07

g = 4%

g = 4/100

g = 0.04

PV = D/(r-g)

Becomes

PV = $50,000/(0.07-0.04)

PV = $50,000/0.03

PV = $1,666,666.67

So the Present Value of the perpuity is $1,666,666.67

4 0
2 years ago
What is the approximate area of the shaded sector in the circle shown below
Akimi4 [234]
\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=4.5\\
\theta =150
\end{cases}\implies A=\cfrac{(150)(\pi )(4.5)^2}{360}\\\\\\ A=\cfrac{3037.5\pi }{360}
8 0
2 years ago
Read 2 more answers
Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services. Higher ratings on
Vlada [557]

Answer:

See the explanation

Step-by-step explanation:

(a)  

H0: Consultant with more experience has the higher population mean service rating.

H1: Consultant with more experience doesn't have the higher population mean service rating.

(b)  

t = 1.9923 (see the attached image)

(c)

The degrees of freedom for the test statistic,

df = 16

The P-value of the one tailed t- test with 16 degrees of freedom is,

P−value = tdist(X,df,tails)

P-value = tdist(1.9923,16,1)

P-value = 0.032

(d)​

Since, P-value 0.032 is less than the significance level 0.05, there is an enough evidence to reject the null hypothesis.

Hence, there is a sufficient evidence to conclude that Consultant with more experience doesn't have the higher population mean service rating.

Hope this helps!

8 0
2 years ago
The pillars in front of Mr. Jefferson's home are shaped like cylinders. The pillars have a height of 24 ft and a radius of 8 in.
GREYUIT [131]

Answer:

  • <u>Option A. about 100.5ft²</u>

<u />

Explanation:

Since the <em>bases</em> must not be painted, their areas are <em>not included</em> in the calculation.

The <em>surface</em> to paint, of each pillar, is equal to the lateral area of a<em> cylinder </em>with he dimensions given.

The formula for the laeral area of a cylinder is:

        Lateral\text{ }area=2\pi \times radius \times height

Substitute including the conversion factor to convert inches to feet:

        Lateral\text{ }area=2\pi \times 8in\times 1ft/12in \times 24ft=100.5ft^2

7 0
2 years ago
41 packages are randomly selected from packages received by a parcel service. the sample has a mean weight of 20.6 pounds and a
lina2011 [118]
Using normal distribution \alpha = 1-0.95=0.05
critical probability p^{*} = 1 -  \frac{ \alpha }{2}
critical value for the critical probability is CV = 1.96
standard error SE =  \frac{3.2}{ \sqrt{41} } = 0.5
margin of error = CV*SE = 1.96 * 0.5 = 0.98
95% confidence interval is between μ + 0.98 and <span>μ - 0.98, which is (19.62, 21.58)</span>
6 0
2 years ago
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