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diamong [38]
3 years ago
7

A rocket is launched with an initial velocity of 360 ft/s. The height of the rocket in meters is modeled by the function shown b

elow, where t is time in seconds. h(t)=‒10t2 + 360t Which statement is true?
A. The rockets maximum height is 324 feet.
B. The rockets maximum height is 3240 feet.
C. In the interval from 9 seconds to 18 seconds, the rocket is descending.
D. The rocket hits the ground in 18 seconds.
Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0
The answer for this question is d 
hope it helps
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If U = {x: X € N, 1 < × < 15)
Inessa05 [86]

Answer:

Step-by-step explanation:

Given:

U = {x: X € N, 1 < × < 15) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}

A = {2,4,6,8,10,12,14}

B = {3,6,9,12,15}

C = {5,10,15}

(a) Verify A(BnB)=(AUB)(AUB)

A U (B n B)

=  {2,4,6,8,10,12,14} U (  {3,6,9,12,15} n  {3,6,9,12,15} )

=  {2,4,6,8,10,12,14} U {3,6,9,12,15}

=  {2,3,4,6,8,9,10,12,14,15}

( A U B) n (A U B)

= {2,3,4,6,8,9,10,12,14,15} n {2,3,4,6,8,9,10,12,14,15}

= {2,3,4,6,8,9,10,12,14,15}

Therefore

A U (B n B)  =  ( A U B) n (A U B)

verifies

(b) Verify An(BUC)=(AnB)u(AnC)

A n ( B U C)

=  {2,4,6,8,10,12,14} n ( {3,6,9,12,15} U {5,10,15} )

=  {2,4,6,8,10,12,14} n {3,5,6,9,10,12,15}

= {6,10,12}

( A n B ) U ( A n C )

= ( {2,4,6,8,10,12,14} n {3,6,9,12,15} ) U ( {2,4,6,8,10,12,14} n {5,10,15} )

= {6,12} U {10}

= {6,10,12}

Therefore

A n ( B U C) = ( A n B ) U ( A n C )

verifies

(c) Verify AU(BUC)=(AUB)U(AUC)​

AU(BUC)

=  {2,4,6,8,10,12,14}U{3,6,9,12,15}U{5,10,15}

= {2,3,4,5,6,8,9,10,12,14,15}

(AUB)U(AUC)​

=  ({2,4,6,8,10,12,14}{3,6,9,12,15})U({2,4,6,8,10,12,14}U{5,10,15})

= {2,3,4,6,8,9,10,12,14,15}U{2,4,5,6,8,10,12,14,15}

= {2,3,4,5,6,8,9,10,12,14,15}

Therefore

AU(BUC)=(AUB)U(AUC)​

verifies

5 0
3 years ago
Which of the following are solutions to the equation below? Check all that apply. 9x^2-64=0
nikdorinn [45]

Answer:

E. -8/3

F. 8/3

Step-by-step explanation:

9x^2-64=0

Add 64 to each side

9x^2-64+64 = 0+64

9x^2 =64

Divide each side by 9

9x^2/9 = 64/9

x^2 = 64/9

Take the square root of each side

sqrt(x^2) = ±sqrt(64/9)

We know that sqrt(a/b) = sqrt(a)/sqrt(b)

x = ±sqrt(64)/sqrt(9)

x = ± 8/3

4 0
3 years ago
A study indicates that 62% of students have have a laptop. You randomly sample 8 students. Find the probability that between 4 a
Scrat [10]

Answer:

72.69% probability that between 4 and 6 (including endpoints) have a laptop.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they have a laptop, or they do not. The probability of a student having a laptop is independent from other students. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A study indicates that 62% of students have have a laptop.

This means that n = 0.62

You randomly sample 8 students.

This means that n = 8

Find the probability that between 4 and 6 (including endpoints) have a laptop.

P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{8,4}.(0.62)^{4}.(0.38)^{4} = 0.2157

P(X = 5) = C_{8,5}.(0.62)^{5}.(0.38)^{3} = 0.2815

P(X = 6) = C_{8,6}.(0.62)^{6}.(0.38)^{2} = 0.2297

P(4 \leq X \leq 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2157 + 0.2815 + 0.2297 = 0.7269

72.69% probability that between 4 and 6 (including endpoints) have a laptop.

3 0
3 years ago
One square megameter is equal to 1.0×106 square kilometers. How many square megameters are in 9,000,000 square kilometers?
Firlakuza [10]
9, because one square megameter is equal to one million square kilometers.
7 0
3 years ago
Read 2 more answers
Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x)=2(3x+4)(x^2+2)
Salsk061 [2.6K]

Answer:

Step-by-step explanation:

The best way to find out the answer to your question is to graph the cubic. As you can see, the y intercept is (0,16).

How was this obtained. notice that if x = 0 then

f(0) = 2(3*0+4)(0^2 + 2)

f(0) = 2(4)(2)

f(0) = 16 just as the graph tells us.

3 0
3 years ago
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