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Tpy6a [65]
3 years ago
5

The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in me

ters) and t is the time (in seconds). What is the domain and range? Domain:
Mathematics
2 answers:
goblinko [34]3 years ago
5 0

Answer:

Step-by-step explanation:

when h(t)=0

-4.9 t²+19.6t=0

4.9t(-t+4)=0

either t=0 or t=4

so domain is 0≤t≤4

for range

h(t)=-4.9t²+19.6t

=-4.9(t²-4t+4-4)

=-4.9(t-2)²+19.6

so range is 0≤h≤19.6

snow_tiger [21]3 years ago
3 0

Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.

Range = 0<h<19.6, again, use less than or equal to signs.

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Simplify the expression.<br><br>x^5/x^9<br><br>a. 1/x^4<br><br>b.x^14<br><br>c. 1/x^14<br><br>d.x^4
bogdanovich [222]
Answer: B. 1/x^4
When you divide the coefficients of exponents you must subtract the exponents. In this cause it got to x^-4. You cannot leave it as a negative exponent so you must put it as the denominator in this cause to get rid of the exponent making the answer b. 1/x^4.
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Alexeev081 [22]
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3 years ago
A sample of 100 is drawn from a population with a proportion equal to 0.50. Determine the probability of observing between 43 an
diamong [38]

Answer:

The probability of observing between 43 and 64 successes=0.93132

Step-by-step explanation:

We are given that

n=100

p=0.50

We have to find the probability of observing between 43 and 64 successes.

Let X be the random variable  which represent the success of population.

It follows binomial distribution .

Therefore,

Mean,\mu=np=100\times 0.50=50

Standard deviation , \sigma=\sqrt{np(1-p)}

\sigma=\sqrt{100\times 0.50(1-0.50)]

\sigma=5

Now,

P(43\leq x\leq 64)=P(42.5\leq x\leq 64.5)

P(42.5\leq x\leq 64.5)=P(\frac{42.5-50}{5}\leq Z\leq \frac{64.5-50}{5})

=P(-1.5\leq Z\leq 2.9)

P(42.5\leq x\leq 64.5)=P(Z\leq 2.9)-P(Z\leq- 1.5)

P(42.5\leq x\leq 64.5)=0.99813-0.06681

P(43\leq x\leq 64)=0.93132

Hence, the probability of observing between 43 and 64 successes=0.93132

4 0
2 years ago
Solve the equation. <br> q − 11 = 16
SpyIntel [72]

Answer:

q = 27

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
To factor the quadratic expression x^2−8x−10 by completing the square, what value would be added? A. 64 B. 8 C. 16 D.-16
Elan Coil [88]

Answer:

C

Step-by-step explanation:

When completing the square, we essentially want to create a perfect square trinomial by adding a constant.

If we have the following expression:

x^2+bx

And we want to complete the square, we will need to divide the b-coefficient by half and then square it.

Thus, the added term should be:

(b/2)^2

In the given equation, we have:

(x^2-8x)-10

The b term here is 8. Therefore:

(8/2)^2\\=(4)^2\\=16

The value we would add would be 16.

The answer is C.

Further notes:

To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:

(x^2-8x)-10\\=(x^2-8x+16)-10-16\\

The expression inside the parentheses is now a perfect square trinomial. Factor it:

=((x)^2-2(4)(x)+(4)^2)-26\\=(x-4)^2-26

And we are done!

4 0
3 years ago
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