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3 years ago

E=mc^2 in terms of m

Mathematics

1 answer:

JulijaS [17]3 years ago

7 0

E/(c^2) = mc^2/(c^2)
m = E/(c^2)

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An investment services company experienced dramatic growth in the last two decades. The following models for the company's reven

zlopas [31]

Answer: a) 138.32 and b) 35 years approx.

Step-by-step explanation:

Since we have given that

$R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}$

So, Profit is given by

$Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}$

Difference in years of 1990 and 2020=30

So, Profit becomes :

$P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32$

(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.

So, profit doubles , we get :

$138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t$

Hence, a) 138.32 and b) 35 years approx.

6 0

3 years ago

An exit poll of 1000 randomly selected voters found that 515 favored measure A. a. Construct a 99% confidence interval for the s

never [62]

Answer:

Step-by-step explanation:

Given that an exit poll of 1000 randomly selected voters found that 515 favored measure A.

Sample proportion p = $\frac{515}{1000} =0.515$

$q=1-0.515 =0.485\\n =1000\\SE = \sqrt{\frac{pq}{n} } \\=0.158\\$

Margin of error 99% = 2.58*SE

= $2.58*0.0158\\=0.0408$

99% confidence interval = $(0.515-0.0408, 0.515+0.0408)\\= (0.474, 0.556)$

------------------------

$H_0: p =0.5\\H_a: p >0.5\\$

(Right tailed test)

STd error = $\sqrt{\frac{0.5*0.5}{1000} } \\=0.0158$

Test statistic Z = p diff/std error = $\frac{0.015}{0.0158} \\\\=0.9487$

p value = 0.1714

6 0

3 years ago

What is 1.1 in fraction form?

bonufazy [111]

11/10 is the fraction form of 1.1

6 0

3 years ago

Please I need some help!!!!!

Gnom [1K]

Answer:

1/6 i think it is

1 foot is 12 inch

5 0

2 years ago

The equation of a circle whose center is at (4, 0) and radius is length 2√(3) is

soldier1979 [14.2K]

ANSWER

${(x - 4)}^{2} + {y}^{2} = 12$

EXPLANATION

The equation of a circle given the center (h,k) and radius r is given by:

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

The circle has center (4,0) and radius

$r = 2 \sqrt{3}$

We substitute the center and radius to get,

${(x - 4)}^{2} + {(y - 0)}^{2} = {(2 \sqrt{3)} }^{2}$

${(x - 4)}^{2} + {(y - 0)}^{2} = 12$

${(x - 4)}^{2} + {y}^{2} = 12$

3 0

3 years ago