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Sonja [21]
3 years ago
5

Helen plays basketball. For free throws, she makes the shot 78% of the time. Helen must now attempt two free throws. C = the eve

nt that Helen makes the first shot. P(C) = 0.78. D = the event Helen makes the second shot. P(D) = 0.78. The probability that Helen makes the second free throw given that she made the first is 0.86. What is the probability that Helen makes both free throws?
Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
5 0

Answer:

0.6708 or 67.08%

Step-by-step explanation:

Helen can only make both free throws if she makes the first. The probability that she makes the first free throw is P(C) = 0.78, now given that she has already made the first one, the probability that she makes the second is P(D|C) = 0.86. Therefore, the probability of Helen making both free throws is:

P(C+D) =  P(C) *P(D|C) = 0.78*0.86\\P(C+D) = 0.6708

There is a 0.6708 probability that Helen makes both free throws.

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Solve the inequality for u<br>-5u+27 [less than or equal to] 2​
baherus [9]

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

6 0
3 years ago
A Simple random sample of 100 8th graders at a large suburban middle school indicated that 84% of them are involved with some ty
Setler [38]

Answer: a) (0.755, 0.925)

Step-by-step explanation:

Let p be the population proportion of 8th graders are involved with some type of after school activity.

As per given , we have

n= 100

sample proportion: \hat{p}=0.84

Significance level : \alpha= 1-0.98=0.02

Critical z-value : z_{\alpha/2}=2.33  (using z-value table)

Then, the 98% confidence interval that estimates the proportion of them that are involved in an after school activity will be :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

i.e. 0.84\pm (2.33)\sqrt{\dfrac{0.84(1-0.84)}{100}}

i.e. \approx0.84\pm 0.085

i.e. (0.84- 0.085,\ 0.84+ 0.085)=(0.755,\ 0.925)

Hence, the 98% confidence interval that estimates the proportion of them that are involved in an after school activity : a) (0.755, 0.925)

3 0
3 years ago
3x-10-4
snow_lady [41]

Answer/Step-by-step Explanation:

1. 3x - 10 +4 if x = 3

To evaluate, plug in the value of x in the expression given

3(3) - 10 + 4 = 9 - 10 + 4

= 3

2. \frac{x}{2} + 6x

if x = -12

\frac{(-12)}{2} + 6(-12)

- 6 - 72 = - 78

3. 8(x - y), if x = 2, y = 6

8(2 - 6) = 8(-4) = -32

4. x + xy, if x = 3, y = -2.5

3 + (3)(-2.5) = 3 + (-7.5)

= 3 - 7.5 = - 4.5

5. (2x)² + 6, if x = -2

(2*-2)² + 6 = (-4)² + 6

= 16 + 6 = 22

6. 3x + 4y - 3x, if x = 2, y = 4

3(2) + 4(4) - 3(2) = 6 + 16 - 6

= 16

7. -10x + \frac{4}{x}

If x = -2

-10(-2) + \frac{4}{-2}

20 + (-2) = 20 - 2 = 18

8. 3(8x - 10) + 5x, if x = ½

3(8*½ - 10) + 5(½)

3(4 - 10) + 2.5

3(-6) + 2.5 = -18+2.5 = - 20.5 or 20½

9. x + 8y - (x)², if x = -5, y = ¼

-5 + 8(¼) - (-5)² = -5 + 2 - (25)

= -3 - 25 = -28

10. (8x)² + 6x + 2, if x = -3

(8*-3)² + 6(-3) + 2 = (-24)² - 18 + 2

= 576 - 18 + 2 = 560

11. 2x² + 4y² + xy, if x = ½, y = 2

2(½)² + 4(2)² + (½)(2)

= 2(¼) + 4(4) + 1

= ½ + 16 + 1 = ½ + 17 = 17½

12. 8x + 2y, if x = 1.5, y = -2.2

8(1.5) + 2(-2.2)

12 - 4.4 = 7.6

13. \frac{5}{2}(x - 6) + 4

if x = 8.

\frac{5}{2}(8 - 6) + 4

\frac{5}{2}(2) + 4

= 5 + 4 = 9

14. 3x - 8x² + 7, if x = 4.5

3(4.5) - 8(4.5)² + 7

13.5 - 8(20.25) + 7

13.5 - 162 + 7 = -141.5

15. -2x² + 8y, if x = 3, y = -9

-2(3)² + 8(-9)

-2(9) - 72 = - 18 - 72 = 90

16. (-5x)² - 3x + x, if x = -3.5

(-5*-3.5)² - 3(-3.5) +(-3.5)

(17.5)² + 10.5 - 3.5

306.25 + 10.5 - 3.5 = 313.25

8 0
3 years ago
It takes james 2.5 minutes to type 150 words at that rate how mant words can james type in 6 minutes
sergey [27]

The number of words james can type in 6 minutes at the same rate is 360 words

Given:

Number of minutes to type 150 words = 2.5 minutes

let

number of words James can type in 6 minutes = x

Equate the ratio of the number of words to number of minutes

150 : 2.5 = x : 6

150/2.5 = x/6

cross product

150 × 6 = 2.5 × x

900 = 2.5x

x = 900/2.5

x = 360 words

Therefore, the number of words james can type in 6 minutes is 360 words

Learn more about ratio:

brainly.com/question/16981404

5 0
3 years ago
Read 2 more answers
Any suggestions or answers
OLEGan [10]
2nd answer.

any pts in the shaded region satisfies your simultaneous equation.
5 0
3 years ago
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