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elena-14-01-66 [18.8K]

3 years ago

11

Simplify.

rt16+ \sqrt8" alt="\sqrt32 + \sqrt16+ \sqrt8" align="absmiddle" class="latex-formula">

1 answer:

svetoff [14.1K]3 years ago

5 0

Answer:

$4 + 6 \sqrt{2}$

Step-by-step explanation:

$\sqrt{32} + \sqrt{16} + \sqrt{8}$

$\sqrt{32} = \sqrt{4 \times 4 \times 2} = 4\sqrt{2}$

$\sqrt{16} = \sqrt{4 \times 4} = 4$

$\sqrt{8} = \sqrt{2 \times 2 \times 2} = 2 \sqrt{2}$

$4 + 4\sqrt{2} + 2 \sqrt{2} = 4 + 6 \sqrt{2}$

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The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medic

Ymorist [56]

Answer:

(a) 0.00605

(b) 0.0403

(c) 0.9536

(d) 0.98809

Step-by-step explanation:

We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012) and suppose ten first-round appeals have just been received by a Medicare appeals office.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 10

r = number of success

p = probability of success which in our question is % of first-round

appeals that were successful, i.e.; 40%

So, here X ~ $Binom(n=10,p=0.40)$

(a) Probability that none of the appeals will be successful = P(X = 0)

P(X = 0) = $\binom{10}{0}0.40^{0}(1-0.40)^{10-0}$

= $1*0.6^{10}$ = 0.00605

(b) Probability that exactly one of the appeals will be successful = P(X = 1)

P(X = 1) = $\binom{10}{1}0.40^{1}(1-0.40)^{10-1}$

= $10*0.4^{1} *0.6^{10-1}$ = 0.0403

(c) Probability that at least two of the appeals will be successful = P(X>=2)

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - $\binom{10}{0}0.40^{0}(1-0.40)^{10-0} - \binom{10}{1}0.40^{1}(1-0.40)^{10-1}$

= 1 - 0.00605 - 0.0403 = 0.9536

(d) Probability that more than half of the appeals will be successful = P(X > 0.5)

For this probability we will convert our distribution into normal such that;

X ~ N( $\mu = n*p=4,\sigma^{2}= n*p*q = 2.4$ )

and standard normal z has distribution as;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

P(X > 0.5) = P( $\frac{X-\mu}{\sigma}$ > $\frac{0.5-4}{\sqrt{2.4} }$ ) = P(Z > -2.26) = P(Z < 2.26) = 0.98809

3 0

3 years ago

ASAP!!!! 10 POINTS!!!!

S_A_V [24]

Completing the Square

2. Solve the equation by completing the square. Show your work.

x^2 – 30x = –125

Step 1: Add to both sides of the equation. (2 points)

Add 225 both sides of the equation

x^2 – 30x + 225 = –125 + 225

x^2 - 30x + 225 = 100

Step 2: Factor the left side of the equation. Show your work. (2 points)

Hint: It is a perfect square trinomial.

x^2 - 30x + 225 = 100

Factor the left side of the equation:

(x - 15)^2 = 100

Step 3: Take the square root of both sides of the equation from Step 2. (1 point)

√(x - 15)^2 = √100

Step 4: Simplify the radical and solve for x. Show your work. (1 point)

x - 15 = + - 10

x - 15 = 10

x = 25

x - 15 = -10

x = 5

Solutions x = 25, 5

3 0

4 years ago

Pls help me get this correct its not a lot please if you can just finish it with good credit.

Mice21 [21]

1) 63 degrees
2) 44 degrees
3) 160 degrees
4) 89 degrees
5) 76 degrees
6) 143 degrees
7) 105 degrees

4 0

3 years ago

Please help me with this. If you show your work I will give brainliest if there are 2 answers

AfilCa [17]

<h3>Answer: 22.5</h3>

Work Shown:

450 calories = 20 ounces

450/20 calories = 20/20 ounces ..... divide both sides by 20

22.5 calories = 1 ounce

This smoothie has 22.5 calories per ounce.

6 0

3 years ago

Use the equation below to answer the question.

JulijaS [17]

Answer:

The signa notation to represent the first five ten f(x) is given by $f(x)=\sum\limits^{5}_{n=1}a_n$

Step-by-step explanation:

Given sequence is -5, -9, 13...

Let f(x) be the given sequence and is denoted by

$f(x)=\{-5,-9,-13,...\}$

Let the first term be $a_1, 2^{\textrm{nd}}$ term be $a_3,...$

ie, $a_1=-5,a_2=-9, a_3=-13,...$

To find the common difference d:

$d=a_2-a_1$

$=-9-(-5)$

$=-9-(+5)$

$d=-4$

$d=a_3-a_2$

$=-13-(-9)$

$=-13+9$

$d=-4$

Therefore the common difference d is -4 for given sequence f(x) with $a_1=-5$ and d=-4, the seqence f(x) is an arithmetic sequence

By defintion of arithmetic sequence

$a_n=a+(n-1)d\hfill(1)$

Now to find $a_4, a_5$ :

put n=4 in equation (1)

$a_4=a+(4-1)d$

$a_4=-5+(3)(-4)$ [since a=-5, d=-4]

$=-5-12$

$a_4=-17$

in equation (1)

$a_5=a+(5-1)d$

$a_5=-5+(4)(-4)$ [since a=-5, d=-4]

$=-5-16$

$a_5=-21$

Therefore $a_4=-17$ and $a_5=-21$

Therefore $f(x)=\{-5,-9,-13,-17,-21,...\}$

Now to represent the sum of the first five terms of f(x) using sigma notation as below

$f(x)=\sum_{n=1}^5 a_n$

where $\sum_{n=1}^5 a_n=a_1+a_2+a_3+a_4+a_5$

$-5-9-13-17-21$

$\sum_{n=1}^5 a_n=-65$

4 0

4 years ago