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MrRa [10]
2 years ago
9

A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base with a speed of 24 ft/sec. A

t what rate is his distance from second base decreasing when he is halfway to first base?
Mathematics
1 answer:
sweet [91]2 years ago
6 0

9514 1404 393

Answer:

  10.73 ft/s

Step-by-step explanation:

When the runner is halfway to first base, the triangle formed by his position and the first and second bases is a right triangle with legs of 45 ft and 90 ft. The angle between the runner's direction and the line from his position to 2nd base is ...

  angle = arctan(90/45) ≈ 63.43°

The "speed made good" in the direction of 2nd base is the product of the cosine of this angle and the runner's speed toward first.

  speed toward 2nd = cos(63.43°)×(24 ft/s) ≈ 10.73 ft/s

The rate the runner's distance to 2nd base is decreasing is 10.73 ft/sec.

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The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean
Elden [556K]

Answer:

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

Step-by-step explanation:

Data given and notation  

\bar X=3.8 represent the sample mean

s=0.5 represent the sample standard deviation for the sample  

n=15 sample size  

\mu_o =4 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:  

Null hypothesis:\mu \geq 68  

Alternative hypothesis:\mu < 4  

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549    

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