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Likurg_2 [28]
3 years ago
13

A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If

she
serves 6 times, what's the probability that she gets...
All 6 serves in?
Exactly 4 serves in?
At least 4 serves in?
No more than 4 serves in?
​
Mathematics
1 answer:
EleoNora [17]3 years ago
6 0

this is a binomial problem: p = 0.7 and q = 0.3

a) (0.7)^6

b) (6C4)(0.7)^4(0.3)^2

c) Pr ( at least 4) = Pr(4) + Pr(5) + Pr(6) = (6C5)(0.7)^5(0.3) + (0.7)^6

d) Pr (no more than 4) = 1 - Pr(at least 4) = 1 - (answer from c)

You might be interested in
It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.
vova2212 [387]

Answer:

300%

Step-by-step explanation:

Given

y\ \alpha\ \frac{1}{x^2}

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

y\ = \ \frac{k}{x^2}

Where k is the constant of proportionality

When x decreased by 50%

Y = \frac{k}{(x - 0.5x)^2}

Y = \frac{k}{(0.5x)^2}

Y = \frac{k}{0.25x^2}

Expand

Y = \frac{1}{0.25} * \frac{k}{x^2}

Substitute \frac{k}{x^2} for y

Y = \frac{1}{0.25} * y

Y = 4 * y

Y = 4 y

The percentage change is then calculated as:

\%Change = \frac{Y - y}{y} * 100\%

\%Change = \frac{4y - y}{y} * 100\%

\%Change = \frac{3y}{y} * 100\%

\%Change = 3 * 100\%

\%Change = 300\%

<em>The percentage in y is 300%</em>

7 0
3 years ago
PLS HELP ME AND SHOW WORK.
Alex17521 [72]

Answer:

4 = (x  + 7 {)}^{2}  + (y  -  3 {)}^{2}

Step-by-step explanation:

equation of a circle

{r}^{2}  = (x -  {h} )^{2}  + (y -  {k)}^{2}

we know the center is (-7, 3)

the radius is 2

we replace (h,k) with the center coordinates

and input the radius

{2}^{2}  = (x -( - 7)) ^{2}  + (y  -  3)^{2}

simplify to this:

4 = (x  + 7 {)}^{2}  + (y  -  3 {)}^{2}

3 0
3 years ago
The line L is a tangent to the curve with equation y= 4x^2 +1 . The line L cuts the y axis at (0,8) and has a positive gradient.
sergeinik [125]

A generic point on the graph of the curve has coordinates

(x, 4x^2+1)

The derivative gives us the slope of the tangent line at a given point:

f(x) = 4x^2+1 \implies f'(x) = 8x

Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through (k, 4k^2+1) and have slope 8k

So, we can write its equation using the point-slope formula: a line with slope m passing through (x_0, y_0) has equation

y-y_0 = m(x-x_0)

In this case, (x_0, y_0)=(k, 4k^2+1) and m=8k, so the equation becomes

y-4k^2-1 = 8k(x-k)

We can rewrite the equation as follows:

y-4k^2-1 = 8k(x-k) \iff y = 8kx - 8k^2+4k^2+1 \iff y = 8kx-4k^2+1

We know that this function must give 0 when evaluated at x=0:

f(x) = 8kx-4k^2+1 \implies f(0) = -4k^2+1 = 8 \iff -4k^2 = 7 \iff k^2 = -\dfrac{7}{4}

This equation has no real solution, so the problem looks impossible.

5 0
3 years ago
Helpppppp meeeeeeeee​
seropon [69]

Answer:

its B im pretty sure.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
I really need the answer rnn so plss helpp
3241004551 [841]

Answer: Each shape has 12 edges

Step-by-step explanation:

7 0
3 years ago
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