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3 years ago

The volume of a sphere is 3,0001 m. What is the surface area of the sphere to the nearest square meter?

Mathematics

2 answers:

Wewaii [24]3 years ago

8 0

Answer:

503 m²

Step-by-step explanation:

Step 1: Determine the radius of the sphere from the volume-of-a-sphere formula V = (4/3)πr³: Here, V = 3,000 m³ = (4/3)πr³. We divide both sides by (4/3)π to obtain r³:

3,000 m³ 9,000 m³

r³ = ------------------ = ----------------- = 716.20 m³

(4/3)π 4π

The surface area is A = 4πr². We can obtain r² by raising both sides of r³ = 716.20 m³ to the power (2/3):

r² = [r³]^(2/3) = r² and 716.20^(2/3). Then:

r² = 80.05 m².

Then the surface area is A = 2πr² = 2π(80.05 m²) = 503 m² (to the nearest square meter)

viva [34]3 years ago

6 0

Answer:

approximately 21484

Step-by-step explanation:

Volume= 4/3 pi r^3

30001= 4/3 pi r^3

solve for r to get 41.34747142

Then, use surface area formula

SA= 4pi r^2

SA=4pi(41.34747142)^2

SA= 21483.6355

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Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

Setler [38]

Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

$n=5$ ---------- computer programmers

$p = 70\%$ --- proportion that are introverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

3 0

3 years ago

Find h(g(n)) when h(n) = 2n + 5 and g(n) = n +4

Evgen [1.6K]

Answer:

2n+13

Step-by-step explanation:

$h(g(n))\\h(n)=2n+5\\g(n)=n+4\\h(n+4)=2(n+4)+5\\=2n+8+5\\=2n+13$

5 0

3 years ago

Mr. Schwartz builds toy cars. He begins the week with a supply of 85 wheels, and uses 4 wheels for each car he builds. Mr. Schwa

Mazyrski [523]

136000 is the answer

5 0

3 years ago

Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant,

USPshnik [31]

By definition of tangent,

tan(2θ) = sin(2θ) / cos(2θ)

Recall the double angle identities:

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1

where the latter equality follows from the Pythagorean identity, cos²(θ) + sin²(θ) = 1. From this identity we can solve for the unknown value of sin(θ):

sin(θ) = ± √(1 - cos²(θ))

and the sign of sin(θ) is determined by the quadrant in which the angle terminates.

We're given that θ belongs to the third quadrant, for which both sin(θ) and cos(θ) are negative. So if cos(θ) = -4/5, we get

sin(θ) = - √(1 - (-4/5)²) = -3/5

Then

tan(2θ) = sin(2θ) / cos(2θ)

tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)

tan(2θ) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2θ) = 24/7

4 0

3 years ago

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otez555 [7]

In decimal form it is 1.8

3 0

3 years ago

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