Ask question

Ask question

All categories

Karo-lina-s [1.5K]

3 years ago

15

A tennis player keeps track of the number of successful first serves he makes. During the first 8 service points of a game, only

2 of his first serves are playable, so his first serve percentage is 25%. How many more consecutive successful first serves must he have to raise his first serve percentage to 60%?

1 answer:

Andru [333]3 years ago

5 0

Answer:

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.

Step-by-step explanation:

After n consecutive serves, his total number of serves is going to be n+8, since he has already served 8 times. In the best case, his number of successful first serves is n+2.

His percentage of succesful first serves is the division of the number of succesful first serves divided by the total number of serves. So

$P = \frac{n+2}{n+8}$

We want $P = 0.60$ . So

$0.6 = \frac{n+2}{n+8}$

$n+2 = 0.6*(n+8)$

$n + 2 = 0.6n + 4.8$

$n - 0.6n = 4.8 - 2$

$0.4n = 2.8$

$n = \frac{2.8}{0.4}$

$n = 7$

He needs 7 more consecutive successful first serves to raise his first serve percentage to 60%.

You might be interested in

What number "c" completes the square: x^2 - 14x + c

Vladimir79 [104]

Answer:

49

Step-by-step explanation:

To complete the square we use the formula:

$c=(\frac{b}{2} )^{2}$

So we can plug in 14 for b to find c.

$c=(\frac{14}{2} )^{2}\\\\c=(7 )^{2}\\c=49$

Now this equation can be factored into:

$(x-7)^{2}$

6 0

3 years ago

What is the length, in meters, of the ramp, line segment AC, below? Round to the nearest whole number if necessary.

Brrunno [24]

<em>10 meters.</em>

Step-by-step explanation:

To find the missing side of a right triangle, we can use the <u>Pythagorean theorem</u>.

The Pythagorean theorem is...

$a^2+b^2=c^2$

Please be sure to note that a and b will <em>always </em>be the length of the sides and c will <em>always </em>be the hypotenuse, or in this case the ramp.

Since we know the values of both of the sides we can plug this into the theorem.

$6^2+8^2=c^2$

Now we can solve.

$36+64+c^2$

Add.

$100=c^2$

Many people will make the mistake of thinking 100 is the final answer, but since c is squared we need to find the square root of 100.

$\sqrt{100} =10$

c = 10

<em><u>The ramp is 10 meters.</u></em>

6 0

3 years ago

Do political science classes require less writing than history classes? The 55 randomly selected political science classes assig

tia_tia [17]

Answer:

No, political science classes does not require less writing than history classes.

Step-by-step explanation:

We are given that the 55 randomly selected political science classes assigned an average of 19.6 pages of essay writing for the course. The standard deviation for these 55 classes was 4.8 pages.

The 50 randomly selected history classes assigned an average of 20.2 pages of essay writing for the course. The standard deviation for these 50 classes was 3.3 pages.

<em>Let </em> $\mu_1$ <em> = mean writing required by political science classes</em>

<em /> $\mu_2$ <em> = mean writing required by history classes</em>

SO, Null Hypothesis, $H_0$ : $\mu_1-\mu_2\geq0$ or $\mu_1\geq \mu_2$ {means that political science classes require more or equal writing than history classes}

Alternate Hypothesis, $H_A$ : $\mu_1-\mu_2$ or $\mu_1$ {means that political science classes require less writing than history classes}

The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t__n__1+_n__2-2$

where, $\bar X_1$ = sample average writing for political science course= 19.6 pages

$\bar X_2$ = sample average writing for history course= 20.2 pages

$s_1$ = sample standard deviation for political science classes = 4.8 pages

$s_2$ = sample standard deviation for history classes = 3.3 pages

$n_1$ = sample of selected political science classes = 55

$n_2$ = sample of selected history classes = 50

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(55-1)\times 4.8^{2}+(50-1)\times 3.3^{2} }{55+50-2} }$ = 4.154

So, <u><em>the test statistics</em></u> = $\frac{(19.6-20.2)-(0)}{4.154 \times \sqrt{\frac{1}{55}+\frac{1}{50} } }$ ~ $t_1_0_3$

= -0.739

<em>Now at 0.01 significance level, the t table gives critical value of -2.367 at 103 degree of freedom for left-tailed test. Since our test statistics is more than the critical value of t as -0.739 > -2.367, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that political science classes require more or equal writing than history classes.

8 0

3 years ago

A line passes through the point (-4,9) and has a slope of

Brilliant_brown [7]

Answer:

y = 4x - 7

Step-by-step explanation:

Given the following data;

Points (x, y) = (4, 9)

Slope, m = 4

To write the equation in point-slope form;

The equation of straight line is y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

First of all, we would find the intercept c;

9 = 4*4 + c

9 = 16 + c

c = 9 - 16

c = -7

Next, we write the equation in point-slope form;

m = 4 and c = -7

y = 4x - 7

8 0

2 years ago

I need help on this problem

musickatia [10]

Answer:

42

Step-by-step explanation:

8 0

2 years ago