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Gnom [1K]
3 years ago
10

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops

a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds,
how far is the ball off the ground?
30 meters
40 meters
50 meters
60 meters
Mathematics
2 answers:
andrezito [222]3 years ago
6 0

Answer: 50 meters

Step-by-step explanation: I just finished the pretest

ivanzaharov [21]3 years ago
6 0

Answer:  The ball is <em><u>50 m</u></em> off the ground after 2 seconds

Step-by-step explanation:

Given the function relating the height of an object off the ground to the time spent falling is a quadratic relationship.

Therefore if h=height and t=time then

h=a+bt+ct^{2}       ----------(A)

where a,b and c are constants

Apply given conditions

At t=0s h=90 m

=> 90 m = a+0+0

=>a=90 m

Also the ball has been just dropped at t=0 s

=>\frac{\partial h}{\partial t}=0=>\frac{\partial (a+bt+ct^{2})}{\partial t}=0

=>b+2ct=0

For t=0s b = 0

Thus equation (A) is reduced to h=90+ct^{2}

At  t= 3 s , h=0 m

\therefore 0= 90 +9c=>c=-10 \frac{m}{s^{2}}

Finally we get h=90-10t^{2}

Therefore at t= 2.0 s , h=(90-10\times 2^{2})m=50 m

Thus the ball is <em><u>50 m</u></em> off the ground after 2 seconds

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slope -( 3)

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Step-by-step explanation:

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6 0
2 years ago
"An ordinance requiring that a smoke detector be installed in all previously constructed houses has been in effect in a particul
Galina-37 [17]

Answer:

a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15) = 0.0173

b) Probability of not rejecting the claim when p = 0.7, P(X > 15) = 0.8106

when p = 0.6, P(X > 15) = 0.4246

c) Check Explanation

The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.

Step-by-step explanation:

p is the true proportion of houses with smoke detectors and p = 0.80

The claim that 80% of houses have smoke detectors is rejected if in a sample of 25 houses, not more than 15 houses have smoke detectors.

If X is the number of homes with detectors among the 25 sampled

a) Probability that the claim is rejected when the actual value of p is 0.8 = P(X ≤ 15)

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials (probability that each house has a detector is 0.80)

It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure (we are sampling 25 houses with each of them either having or not having a detector)

The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 25 houses sampled

x = Number of successes required = less than or equal to 15

p = probability of success = probability that a house has smoke detectors = 0.80

q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.80 = 0.20

P(X ≤ 15) = Sum of probabilities from P(X = 0) to P(X = 15) = 0.01733186954 = 0.01733

b) Probability of not rejecting the claim when p= 0.7 when p= 0.6

For us not to reject the claim, we need more than 15 houses with detectors, hence, th is probability = P(X > 15), but p = 0.7 and 0.6 respectively for this question.

n = total number of sample spaces = 25 houses sampled

x = Number of successes required = more than 15

p = probability that a house has smoke detectors = 0.70, then 0.60

q = probability of failure = probability that a house does NOT have smoke detectors = 1 - p = 1 - 0.70 = 0.30

And 1 - 0.60 = 0.40

P(X > 15) = sum of probabilities from P(X = 15) to P(X = 25)

When p = 0.70, P(X > 15) = 0.8105639765 = 0.8106

When p = 0.60, P(X > 15) = 0.42461701767 = 0.4246

c) How do the "error probabilities" of parts (a) and (b) change if the value 15 in the decision rule is replaced by 14.

The error probabilities include the probability of the claim being false.

When X = 15

(Error probability when p = 0.80) = 0.0173

when p = 0.70, error probability = P(X ≤ 15) = 1 - P(X > 15) = 1 - 0.8106 = 0.1894

when p = 0.60, error probability = 1 - 0.4246 = 0.5754

When X = 14

(Error probability when p = 0.80) = P(X ≤ 14) = 0.00555

when p = 0.70, error probability = P(X ≤ 14) = 0.0978

when p = 0.60, error probability = P(X ≤ 14) = 0.4142

The error probabilities are evidently lower when 15 is replaced with 14 in the calculations.

Hope this Helps!!!

6 0
3 years ago
There are 40 markers in a bag. Of the 10 scented markers, 6 are permanent markers. Half of the unscented markers are erasable.
Vera_Pavlovna [14]

Answer:

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Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Heather has to solve this system of equations using elimination. What should be her first step?
charle [14.2K]
I don’t know what the equation is but when using elimination you should cancel out opposite numbers such as 4x and negative 4x
6 0
2 years ago
Read 2 more answers
Which equation does not represent a function? Why? A) y = x2; There are two outputs for each input. B) y2 = 4x; There are two ou
natita [175]

Answer:

B) y² = 4x; There are two outputs for each input

Step-by-step explanation:

For an equation to be called a function, the input values for x must only result in a single output for y.

Based on this definition if a function, the functions y = x², y = -x and y = x are all functions because for any value of x imputed in them, we can only get one equivalent value of y.

The only exception is the function y²= 4x

For this function, for any value of x, there will be more than one output for y. Take x = 1 for example

y² = 4(1)

y² = 4

y = ±√4

y = ±2

This shows that y = 2 and -2

Also if x = 4

y² = 4(4)

y² = 16

y = ±√16

y = ±4

y = 4 and -4

No matter the value of x imputed, the output value y will always be two (a positive and a negative value)

Hence, option B is correct.

3 0
3 years ago
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