Which of the following functions describes the graph of h(x)?

While sitting on a rooftop 95 feet off the ground Mary flicks a twig up and off of the ledge with the initial vertical velocity

cestrela7 [59]

Answer:

The maximum height of the twig is 96.6 feet off the ground

Step-by-step explanation:

To determine the maximum height of the twig,

First, we will determine the height distance covered by the twig after Mary flicks the twig up.

From the question,

Mary flicks a twig up and off of the ledge with the initial vertical velocity of 10 feet per second, that is

the initial velocity of the twig is 10 feet/second

At maximum height, the final velocity is 0

From on the equations of motions for bodies moving upwards,

v² = u² - 2gh

Where v is the final velocity

u is the initial velocity

g is the acceleration due to gravity (Take g = 9.8m/s² = 32.17 ft/s²)

and h is the height

From the question

u = 10 feet/second

and v = 0 feet/second

Putting the values into the equation

v² = u² - 2gh

0² = 10² - 2(32.17)h

0 = 100 - 64.34h

64.34h = 100

h = 100/64.34

h = 1.6 feet

This is the height distance covered by the twig after Mary flicks it up.

Now, the maximum height of the twig will be the sum of the height of the rooftop from the ground and the height distance covered by the twig.

That is,

Maximum height = 95 feet + 1.6 feet

Maximum height = 96.6 feet

Hence, the maximum height of the twig is 96.6 feet off the ground.

7 0

3 years ago

2) Give two names for a triangle with all 3 sides having the same length.

melamori03 [73]

I believe one
is named congruent triangle
not sure for the other one

6 0

3 years ago

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$

Now we calculate the F statistic as:

$F=MSB/MSE=172/23.78=7.23$

The degrees of freedom of the numerator are:

$dfn=a-1=3-1=2$

The degrees of freedom of the denominator are:

$dfd=N-a=3*4-3=12-3=9$

The P-value of F=7.23, dfn=2 and dfd=9 is:

$P-value=P(F>7.23)=0.01342$

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

3 0

3 years ago

The numbers 1-4 are each written on an index card. The 4 cards are put into a bag and 2 of them are drawn at random. What is the

devlian [24]

Answer:

Step-by-step explanation:

Write a list of all possible outcomes

1-2

1-3

1-4

2-1

2-3

2-4

3-1

3-2

3-4

4-1

4-2

4-3

There are 12 possible outcomes. How many of them have totals of 6 or 7

I count 4

So the probability is 4/12 = 1/3, just as you said.

Is there an easier way?

You might be able to get the 12 easier.

You have 4 choices for the first number and 3 for the second.

P(12) = 4*3 = 12

Getting 6 or 7 might be somewhat trickier.

4 and 3 make seven. That gives two ways 4-3 and 3-4

4 and 2 make six. That gives 2 more ways 4-2 and 2-4

That's all that's possible.

answer: 4 ways make success. The total number of ways is 12.

7 0

3 years ago

Kenny bought a new car stereo that cost $220, but he had a coupon for a 14% discount. How much did Kenny pay for the car stereo?

mrs_skeptik [129]

Kenny bought the stereo for $30.80

3 0

3 years ago