Ask question

Ask question

All categories

2 years ago

3

Harrison plays a game in which he uses a net to catch balls that are randomly launched from holes in the ground. The height of o

ne ball after t seconds is represented by the function f(t) = –16t2 + 20t. After how many seconds does the ball return to the ground? Round to the hundredths place as needed. seconds

2 answers:

ohaa [14]2 years ago

6 0

Answer:

The ball will return to the ground after 1.25 seconds

Step-by-step explanation:

Given

f(t) = -16t² + 20t

Required

After what time (in seconds) does the ball return to the ground?

Function f(t) is a function of time and it represents the displacement of the ball.

For the ball to return to the ground, it means the displacement is 0.

So, we have f(t) = 0.

Substitute 0 for f(t) in the above, we have

0 = -16t² + 20t ---- Factorize

0 = -4t(4t - 5) ---- Reorder

-4t(4t - 5) = 0

This above expression can be splitted to;

-4t = 0 or 4t - 5 = 0

For -4t = 0,

divide through by -4

This will give t = 0

For 4t - 5 = 0,

Collect like terms

4t = 5 + 0

4t = 5

Divide through by 4

t = 5/4

t = 1.25

So, we have that

t = 0 or t = 1.25

But t can't be 0 because the ball has already traveled some distance.

So, t = 1.25

Hence, the ball will return to the ground after 1.25 seconds

Deffense [45]2 years ago

3 0

Answer:

its 1.25....

Step-by-step explanation:

on edge, thank me later

You might be interested in

One way to measure whether the trees in the Wade Tract are uniformly distributed is to examine the average location in the north

tatyana61 [14]

Answer:

Null hypothesis be H₀ : μ = 100

Alternative hypothesis Hₐ : μ < 100

There is sufficient statistical evidence to suggest that the average location of Wade Tract is 100

Step-by-step explanation:

Here we have;

Let our null hypothesis be H₀ : μ = 100 Average location of trees in the Wade Tract is 100

Our alternative hypothesis becomes Hₐ : μ < 100 at 95% confidence level

Proposed average location in Wade Tract, μ = 100

Sample mean, $\bar x$ = 99.74

Standard deviation, s = 58

Sample size, n = 584

The t test formula is therefore;

$t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}}$

Therefore, with df = 584 -1 = 583, and α = (1 - 0.95)/2 = 0.025

We have $t_{\alpha /2}$ = -1.65

Plugging in the values into the t test formula, we have t = -0.108338, from which the p-value is given as p = 0.4569 which is much more than the value of α, therefore, we accept the null hypothesis as follows;

There is sufficient statistical evidence to suggest that the average location of Wade Tract = 100.

7 0

2 years ago

Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below: 3x + 12 + 2 = 2 + 5x – 20 3x + 14 = 5x – 18 14 = 2x

konstantin123 [22]

First, she distributed $3*x=3x , 3*4=12, 5*x= 5x, 5* -4= -20$
Which gave her $3x+12+2=2+5x-20$
Then, she combined like terms $12+2=14 and 2+ -20 = -18$
Which gave her $3x+14=5x-18$
Then, she subtracted $3x$ from both sided
Which gave her $14=2x-18$
Then, she added $18$ to both sides
Which gave her $32=2x$
And finally sh edivided 32 by 2 and got $16=x$
hope this helps if you have any questions please pm me :)

5 0

2 years ago

Read 2 more answers

NEED HELP ON NUMBER 13 AND 14

Kazeer [188]

Answer:

Question 13: For age groups y=1 and y=1.3 response is 8 microseconds.

Question 14: The club was making a loss between 11.28 and 4.88 years.

Step-by-step explanation:

Question 13:

The age group y for which the response rate R is 8 microseconds is given by the solution of the equation

$8=y^4 +2y^3 - 4y^2 -5y +14.$

We graph this equation and find the solutions to be

$y=1;$ $y=1.302;$ $y=-2;$ $y=-2.302.$

Since only positive solutions for y are valid in the real world we take only those.

Thus only for age groups y=1 and y=1.3 the response is 8 microseconds.

Question 14:

The footbal club is making a loss when $p(t)$

Or

$t^3 -14t^2 +20t +120$

We graph this inequality and find the solutions to be

$t$ and $4.88$

Since in the real world only positive values for t are valid, we take the the second solution to be true.

Thus the club was making a loss in years $4.88$

5 0

2 years ago

Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll

JulijaS [17]

Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

So, the possibility of getting a total of 7 = $\frac{6}{36}=\frac{1}{6}$

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = $\frac{2}{36}$ = $\frac{1}{18}$

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = $\frac{28}{36}$ = $\frac{7}{9}$

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

$\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11$

$\frac{11}{3}+\frac{11}{3}-\frac{77}{9}$

$\frac{22}{3}-\frac{77}{9}$

$\frac{66-77}{9}$

$-\frac{11}{9}$

$-1.22$

Therefore the expected payoff for this game is -$1.22.

4 0

2 years ago

a video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

7nadin3 [17]

slope is $0.10 <em>($1.00 per 10 tokens = $0.10)</em>

y-intercept is $60 <em>($60 is the annual fee)</em>

y = .10x + 60 <em>(y = mx + b)</em>

domain is x ≥ 0 <em>(you can't buy a negative number of token)</em>

range is y ≥ 60 <em>(input the domain (x ≥ 0) to find the range)</em>

Answer: the y-intercept of the function is $60

6 0

2 years ago

Read 2 more answers