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2 years ago

A 48-year-old person is 4.2048 × 105 hours old. Write this number in standard form.

1 answer:

6 0

4.2048 x 105 = 441.504

the standard form should be between 1 and 9 so the decimal point should be after the first digit (4)

it would look like this 4.41504 x 10 to the power of 2 because it moved back two places. hope it makes sense? (:

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Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

3 years ago

The width of a rectangle is 8 inches shorter than its length. The perimeter of the rectangle is 18 inches. What are the length a

VashaNatasha [74]

Answer:

Step-by-step explanation:

Let length be l

Width, w=l-8

Perimeter = 2(l+w) = 2l+2w

2l+2(l-8)=18

6 0

2 years ago

Pllssss help I put B, but I got it wrong the first time. NO LINKS

Mamont248 [21]

Answer:

D.1767.1 in³

Step-by-step explanation:

volume of a sphere=4/3πr³

where r=radius of the sphere

Given diemeter= 15in

so radius=15/2=7.5in

volume=4/3×π×(7.5)³

=4/3×22/7×(7.5)³

=1767.1in³

hope it helps...

have a great day!!

6 0

2 years ago

Question is attached

Arlecino [84]

Answer:

Let v = ml of 100% vinegar

Then 150-v = ml of dressing

v + .05(150-v) = .24(150)

v + 7.5 - .05v = 36

.95v = 28.5

v = 28.5/.95

v = 30 ml of vinegar

dressing = 150-30 = 120 ml

Step-by-step explanation:

7 0

2 years ago

If 1 inch is 500 miles, then 4 inches is how many miles?

tiny-mole [99]

Answer:

2,000 miles

Step-by-step explanation:

We are given:

$1 inch=500 miles$

This can be rewritten as:

$\frac{500 miles}{1inch}$

This is representative of a unit rate, as we have a $1$ in the denominator. To calculate the number of miles in $4$ inches, simply multiply the unit rate by $4$ :

$\frac{500 miles}{1inch}*4=$

$\frac{2000 miles}{4 inches}$

This can rewritten as:

$4inches=2000miles$

Therefore, there are 2,000 miles in 4 inches.

We can check our solution by simplifying the fraction $\frac{2000 miles}{4 inches}$ by dividing both $2000$ and $4$ by $4$ to see if we achieve the unit rate:

$\frac{500 miles}{1 inch}$

Since this is in fact the unit rate, our solution is correct!

6 0

2 years ago

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