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The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function

777dan777 [17]

The maximum height of an object is the greatest height the object can reach. The maximum height the rocket reaches is 40.2 feet

<h3>Vertex form of an equation</h3>

The maximum height of an object is the greatest height the object can reach. Given the equation that represent the height of the rocket.

f(t) = -15t² + 48t

The maximum height of the rocket occur at the point where:

t = -b/2a
t = -48/2(-15)
t =48/30
t = 1.6secs

Substitute t = 1.6 into the function as shown:

f(1.6) = -15(1.6)² + 48(1.6)

f(1.6) = -38.4 + 76.8

f(1.6) = 40.2

Hence the maximum height the rocket reaches is 40.2 feet

Learn more on maximum height here: brainly.com/question/12446886

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6 0

2 years ago

I. In a shipment of 300 connecting rods, the mean tensile strength is found to be 45 kpsi and has a standard deviation of 5 kpsi

CaHeK987 [17]

Answer:

a) Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

b) 260 rods are expected to have a strength between 39.4 and 60 kpsi

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 45, \sigma = 5$

(a) Assuming a normal distribution, how many rods can be expected to have a strength less than 39.4 kpsi?

The percentage of rods with a stength less than 39.4 is the pvalue of Z when X = 39.4. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

13.14% of rods have a strength less than 39.4 kpsi.

Out of 300

0.1314*300 = 39.42

Between 39 and 40 rods can be expected to have a strength less than 39.4 kpsi.

(b) How many are expected to have a strength between 39.4 and 60 kpsi?

The percentage of rods with a stength in this interval is the pvalue of Z when X = 60 subtracted by the pvalue of Z when X = 39.4. So

X = 60

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{60 - 45}{5}$

$Z = 3$

$Z = 3$ has a pvalue of 0.9987

X = 39.4

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{39.4 - 45}{5}$

$Z = -1.12$

$Z = -1.12$ has a pvalue of 0.1314

0.9987 - 0.1314 = 0.8673

86.73% of the rods are expected to have a strength between 39.4 and 60 kpsi

Out of 300

0.8673*300 = 260

260 rods are expected to have a strength between 39.4 and 60 kpsi

4 0

4 years ago

What is .825 as a fraction and how do I find it

JulsSmile [24]

$0.1 = \frac{1}{10}
$
$0.01 = \frac{1}{100}

$
$0.001 = \frac{1}{1000}$

hence
$0.825 = \frac{825}{1000}$

now you just simplify the fraction

6 0

3 years ago

Fran has a plank of wood 4.65 meters long. She wants to cut it into pieces 0.85 meters long. How many pieces of wood that length

DochEvi [55]

5 pieces. 4.65÷0.85=5. so u divide and ur answer is 5

3 0

3 years ago

50 POINTS!!!!

soldier1979 [14.2K]

Answer:

I would say ask him out, if not she'll continue to wonder if he was ever going to be a great relationship or just a short relationship. it's also a good way to experience dating!

Step-by-step explanation:

hope this HELPS her out!

✧◝(⁰▿⁰)◜✧

6 0

3 years ago