Simplify. Write the expression using only positive exponents.

The answer to 68 + (-43) is?

Zinaida [17]

Answer:

The answer is 25

4 0

2 years ago

Read 2 more answers

A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per

pishuonlain [190]

Answer:

y = -16 (x - 1)^2 + 112

The object lands on the ground in approximately 3.6s

Explanation:

The equation given is that of a parabola.

Now the maximum (local) point of a parabola is the vertex. Therefore, if we want to rewrite our function in the form that would be used to find the maximum height, then that form must be the vertex form of a parabola.

The vertex form of a parabola is

$y=a(t-h)^2+k$

where (h, k) is the vertex.

The only question is, what is the vertex for our function h(t)?

Remember that if we have an equation of the form

$y=ax^2+bx+c$

then the x-coordinate of the vertex is

$h=-\frac{b}{2a}$

Now in our case b = 32 and a = -16; therefore,

$h=\frac{-32}{2(16)}=1$

We've found the value of the x-coordinate of the vertex. What about the y-coordinate? To get the y-coordinate, we put x = 1 into h(t) and get

$k=-16(1)+32(1)+96=112$

Hence, the y-coordindate is k = 112.

Therefore, the vertex of the parabola is (1, 112).

With the coordinates of the vertex in hand, we now write the equation of the parabola in vertex form.

$h(t)=a(t-1)^2+112$

The only problem is that we don't know what the value of a is. How do we find a?

Note that the point (0, 96) lies on the parabola. In other words,

$h(0)=-16(0)^2+32(0)+96=96$

Therefore, the vertex form of the parabola must also contain the point (0, 96).

Putting in t = 0, h = 96 into the vertex form gives

$96=a(0-1)^2+112$ $96=a+112$

subtracting 112 from both sides gives

$a=-16$

With the value of a in hand, we can finally write the equation of the parabola on vertex form.

$\boxed{h\mleft(t\mright)=-16\left(t-1\right)^2+112.}$

Now when does the object hit the ground? In other words, for what value of t is h(t) = 0? To find out we just have to solve the following for t.

$h(t)=0.$

We could either use h(t) = -16t^2 + 32t + 96 or the h(t) = -16(t - 1)^2 + 112 for the above equation. But it turns out, the vertex form is more convenient.

Thus we solve,

$-16\left(t-1\right)^2+112=0$

Now subtracting 112 from both sides gives

$-16(t-1)^2=-112$

Dividing both sides by -16 gives

$(t-1)^2=\frac{-112}{-16}$ $(t-1)^2=7$

taking the square root of both sides gives

$t-1=\pm\sqrt{7}$

adding 1 to both sides gives

$t=\pm\sqrt{7}+1$

Hence, the two solutions we get are

$t=\sqrt{7}+1=3.6$ $t=-\sqrt{7}+1=-1.6$

Now since time cannot take a negative value, we discard the second solution and say that t = 3.6 is our valid solution.

Therefore, it takes about 3.6 seconds for the object to hit the ground.

3 0

11 months ago

If the function f(x)=-1/2x-7 were graphed, which of the following is true? hurry I have 10 minutes

jeka94

WE NEED ANSWER CHOICES

4 0

2 years ago

According to a survey, 60 % of the residents of a city oppose a downtown casino. Of these 60 % about 8 out of 10 strongly opp

katrin [286]

Answer:

(a) 0.48

(b) 0.20

(c) it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.

Step-by-step explanation:

(a) Find the probability that a randomly selected resident opposes the casino and strongly opposes the casino.

The probability that a radomly selected resident opposes the casino and strongly opposes the cassino is the product of the two probabilities, that a resident opposes the casino and that it strongly opposes the casino (once it is in the first group) as it is shown below.

Use this notation:

Probability that a radomly selected resident opposes the casino: P(A)

Probability that a resident who opposes the casino strongly opposes it: P(B/A), because it is the probability of event B given the event A

i) Determine the probability that a radomly selected resident opposes the casino, P(A)

Probability = number of favorable outcomes / number of possible outcomes

P(A) is given as 60%, which in decimal form is 0.60

ii) Next, determine,the probability that a resident who opposes the casino strongly opposes it, P(B/A):

It is given as 8 out of 10 ⇒ P(B/A) = 8/10

iii) You want the probability of both events, which is the joint probability or intersection: P(A∩B).

So, you can use the definition of conditional probability:

P(B/A) = P(A∩B) / P(A)

iv) From which you can solve for P(A∩B)

P(A∩B) = P(B/A)×P(A) = (8/10)×(0.60) = 0.48

(b) Find the probability that a randomly selected resident who opposes the casino does not strongly oppose the casino.

In this case, you just want the complement of the probability that a radomly selected resident who opposes the casino does strongly oppose the casino, which is 1 - P(B/A) = 1 - 8/10 = 1 - 0.8 = 0.2.

(c) Would it be unusual for a randomly selected resident to oppose the casino and strongly oppose the casino?

You are being asked about the joint probability (PA∩B), which you found in the part (a) and it is 0.48.

That is almost 0.50 or half of the population, so you conclude it is not unusual for a radomly selected resident to oppose the casino and strongly oppose the casino.

8 0

3 years ago

During one month there were 7 days of precipitation.What if there had only been 3 days of precipitation that month?How would tha

faust18 [17]

We've hit on a case where a measure of center does not provide all the information spread or variability there is in month-to-month precipitation. based on how busy each month has been in the past, lets managers plan Unit 6: Standard Deviation | Student Guide | Page 3 If you sum the deviations from the mean, (. ).

7 0

2 years ago