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3 years ago

Please help.

Mathematics

1 answer:

serious [3.7K]3 years ago

8 0

The number of throws that the player make X follows binomial distribution.

The probability that the player makes x throws out of eleven throws is

$P(X=x)=C(x,11)0.5^x(0.5)^{11-x}=C(x,11)0.5^{11}$

The probability that the player makes at most nine out of eleven free throws

$\sum_{x=0}^9C(x,11)0.5^{11}=1-\sum_{x=10}^{11}C(x,11)0.5^{11}\\ =1-C(10,11)0.5^{11}-C(11,11)0.5^{11}=1-\frac{12}{2^{11}} \\ =1-\frac{3}{512} =\frac{509}{512}$

Correct choice is (B).

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8th term of 1/4,1/8,1/16,1/32

sukhopar [10]

$a_1=\dfrac{1}{4};\ a_2=\dfrac{1}{8};\ a_3=\dfrac{1}{16};\ a_4=\dfrac{1}{32};...\\\\it's\ a\ geometric\ sequence\ where\ a_1=\dfrac{1}{4}\ and\ r=\dfrac{1}{8}:\dfrac{1}{4}=\dfrac{1}{2}\\\\a_n=a_1r^{n-1}\\\\n=8\\\\a_8=\dfrac{1}{4}\cdot\left(\dfrac{1}{2}\right)^{7-1}=\dfrac{1}{4}\cdot\left(\dfrac{1}{2}\right)^6=\dfrac{1}{4}\cdot\dfrac{1}{64}=\dfrac{1}{256}$

4 0

3 years ago

In year, 2004, I put $20.00 into an account to save. This account annual interest fee is 0.002%. However, every 10th year the in

olchik [2.2K]

9514 1404 393

Answer:

$20.01

Step-by-step explanation:

In 2004–2012, the interest rate is 0.002%. In 2013, it is 0.004%. In 2014–2021, the interest rate is 0.002%. That is, in the 18 years between 2004 and 2021 (inclusive), the interest rate is 0.002% for 17 of them. The effective account multiplier is ...

(1.00002^17)(1.00004^1) = 1.00038006801

Then the account balance is ...

$20 × 1.00038006801 ≈ $20.01

_____

<em>Additional comment</em>

The annual interest earned on $20.00 is $0.0004. If the account balance is rounded to the nearest cent annually, at the end of the 18 years, the balance will still be $20.00. Not enough interest is earned in one year to increase the balance above $20. At the end of the 18 years, the amount of interest earned is 0.76¢ (a fraction of a penny) <em>only if there is no rounding in intervening years</em>.

7 0

2 years ago

For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to les

kaheart [24]

Answer:

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error for this case is given by:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And replacing we got:

$ME = 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.0259$

And replacing into the confidence interval formula we got:

$0.52 - 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.4941$

$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

Step-by-step explanation:

Data given and notation

n=1000 represent the random sample taken

$\hat p=0.52$ estimated proportion of of U.S. employers were likely to require higher employee contributions for health care coverage

$\alpha=0.05$ represent the significance level (no given, but is assumed)

Solution to the problem

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error for this case is given by:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And replacing we got:

$ME = 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.0259$

And replacing into the confidence interval formula we got:

$0.52 - 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.4941$

$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

5 0

3 years ago

A new health drink has 130% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg.

Anika [276]

Answer:
58.5 mg

Step-by-step explanation:

Drink: 130% of RDA of vitamin X
RDA vitamin X = 45mg
130% of 45 = mg in the drink
130% = 130/100 = 1.3
130% of 45 = 1.3*45 = 58.5

So, this new drink has 58.5 mg of vitamin

4 0

3 years ago

The rectangular prism shown has a volume of 10 cubic centimeters, = 1 cm3 Choose all the rectangular prisms that also have a vol

SOVA2 [1]

Answer:

B and C

Step-by-step explanation:

We are given a rectangular prism that consists of 10 cubes. Each cube = 1 cm³. The volume of rectangular prism given = 10cm³.

Let's find out which of the options has same volume (10cm³) as that of the given rectangular prism.

Option A has 15 cubes = 15 cm³ in volume

Option B has 10 cubes = 10 cm³ in volume

Option C has 10 cubes also = 10 cm³ in volume

Option D has 12 cubes = 12 cm³

The rectangular prisms that have the same volume (10 cm³) with the given rectangular prism are option B and C.

4 0

3 years ago