To measure the length of the pond, Jacob marked off congruent triangles as shown in the diagram.

Susan throws a softball upward into the air at a speed of 32 feet per second from a 88 dash foot88-foot platform. the distance u

Rudiy27

D(t)=-16t²+32t+88
a] Maximum height
At maximum height d'(t)=0
from d(t);
d'(t)=-32t+32=0
thus
t=1
hence the maximum height will be:
d(t)=-16t²+32t+88
d(1)=-16(1)^2+32(1)+88
d(1)=104 ft

2] how many seconds does it take to reach the ground after first being thrown upward?
Here we solve for t intercept
when d(t)=0
thus
0=-16t²+32t+88
solving for t, we get:
t=1-√13/2
or
t=1+√13/2

t=-1.55 or t=3.55 sec
Thus the answer is t=3.55 sec

3 0

3 years ago

Determine if the equations are parallel, perpendicular, or neither

Gala2k [10]

Answer: Perpendicular.

Step-by-step explanation:

If you multiply the slopes together you will get -1:

$3 * -\frac{1}{3} = -1$

Parallel means they have the same slope, so that is easily ruled out here.

5 0

3 years ago

(1 point) The cost of unleaded gasoline once followed an unknown distribution with a mean of $4.59 and a standard deviation of $

marin [14]

Answer:

a) unknown

b) 1.43% probability that the average price for 30 gas stations is less than $4.55.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .