18:a = 14:21 what does a equal?

A quarterback throws a football with a velocity of 41 mph and a direction of 168°. The wind on the field is 11 mph with a direct

Cerrena [4.2K]

The true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.

<h3>Relative velocity of the football</h3>

The true speed and direction of the football is determined by applying the concept of relative velocity.

Vr/w = Vb - Vw

where;

Vr/w is the velocity of the football with respect to the wind
Vb is the velocity of the football
Vw is the velocity of the wind

Vr/w = 41 mph - 11 mph = 30 mph

The direction speed can be determined by sketching a triangle

Direction of the speed, θ = (360 - 339) - (180 - 168)

θ = 21 - 12 = 9⁰

<h3>Resultant speed;</h3>

R² = 41² + 11² - 2(41 x 11 x cos9)

R² = 911.105

R = √911.105

R = 30.185 mph

Thus, the true speed and direction of the football thrown by the quarterback is 30.185 mph and 9⁰ respectively.

Learn more about relative velocity here: brainly.com/question/17228388

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8 0

2 years ago

One hamster weighs 300g less than half the weight of the second. If their combined weight is 1950g,how much does each hamster we

deff fn [24]

Answer: masses are 825 g and 1125 g

Step-by-step explanation: masses of hamsters are x and x+ 300 g.

Total mass is x+(x+300) = 1950

2x = 1650 g and x= 825

3 0

3 years ago

A sedan will drive ten miles north, 15 miles east, 13 miles south, 15 miles west, and 22 miles north. The sedan gets 20 miles pe

larisa [96]

You would have enough gas to go another 25 miles

3 0

3 years ago

GRE Test: The Graduate Record Examination (GRE) is a test required for admission to many US graduate schools. Student’s scores o

Zepler [3.9K]

Answer:

a) $\bar X=144.3$

b) The 95% confidence interval would be given by (138.846;149.754)

c) n=34

d) n=298

e) n=1190

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=8.8$ represent the population standard deviation

n=10 represent the sample size

a) Find a point estimate of the population mean

We can calculate the sample mean with this formula:

$\bar X = \frac{\sum_{i=1}^n x_i}{n}$

$\bar X=144.3$

b) Construct a 95% confidence interval for the true mean score for this population.

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$144.3-1.96\frac{8.8}{\sqrt{10}}=138.846$

$144.3+1.96\frac{8.8}{\sqrt{10}}=149.754$

So on this case the 95% confidence interval would be given by (138.846;149.754)

Part c

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (5) we got: