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2 years ago

The diameter of a circle is ___________the length of its radius?

Mathematics

1 answer:

serg [7]2 years ago

8 0

Answer:

Twice the length of the radius

Step-by-step explanation:

A radius by definition is half of the diameter which means the diameter is twice the radius.

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Reserve Problems Chapter 4 Section 5 Problem 2 A laptop company claims up to 10.1 hours of wireless web usage for its newest lap

Viktor [21]

Answer:

0.1151

Step-by-step explanation:

Given that a laptop company claims up to 10.1 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 9.5 hours and standard deviation 30 minutes.

If X is the battery life then X is N(9.5, 0.5)

(we convert into one unit for calculations purpose here hours)

a) the probability that the battery life is at least 10.1 hours

= $P(X\geq 10.1)\\=P(Z\geq \frac{10.1-9.5}{0.5} )\\= P(Z\geq 1.2)\\=0.1151$

we get the probability that the battery life is at least 10.1 hours is 0.1151

4 0

2 years ago

In a recent survey, 60% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find

andreev551 [17]

Answer:

Probability that exactly 5 of them favor the building of the health center is 0.0408.

Step-by-step explanation:

We are given that in a recent survey, 60% of the community favored building a health center in their neighborhood.

Also, 14 citizens are chosen.

The above situation can be represented through Binomial distribution;

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

where, n = number of trials (samples) taken = 14 citizens

r = number of success = exactly 5

p = probability of success which in our question is % of the community

favored building a health center in their neighborhood, i.e; 60%

<em>LET X = Number of citizens who favored building of the health center.</em>

So, it means X ~ $Binom(n=14, p=0.60)$

Now, Probability that exactly 5 of them favor the building of the health center is given by = P(X = 5)

P(X = 5) = $\binom{14}{5} \times 0.60^{5} \times (1-0.60)^{14-5}$

= $2002 \times 0.60^{5} \times 0.40^{9}$

= 0.0408

Therefore, Probability that exactly 5 of them favor the building of the health center is 0.0408.

4 0

3 years ago

Use the mid-point rule with n = 4 to approximate the area of the region bounded by y = x3 and y = x. (10 points)

USPshnik [31]

See the graph attached.

The midpoint rule states that you can calculate the area under a curve by using the formula:
$M_{n} = \frac{b - a}{2} [ f(\frac{x_{0} + x_{1} }{2}) + f(\frac{x_{1} + x_{2} }{2}) + ... + f(\frac{x_{n-1} + x_{n} }{2})]$

In your case:
a = 0
b = 1
n = 4
x₀ = 0
x₁ = 1/4
x₂ = 1/2
x₃ = 3/4
x₄ = 1

Therefore, you'll have:
$M_{4} = \frac{1 - 0}{4} [ f(\frac{0 + \frac{1}{4} }{2}) + f(\frac{ \frac{1}{4} + \frac{1}{2} }{2}) + f(\frac{\frac{1}{2} + \frac{3}{4} }{2}) + f(\frac{\frac{3}{4} + 1} {2})]$
$M_{4} = \frac{1}{4} [ f(\frac{1}{8}) + f(\frac{3}{8}) + f(\frac{5}{8}) + f(\frac{7}{8})]$

Now, to evaluate your f(x), you need to look at the graph and notice that:
f(x) = x - x³

Therefore:
$M_{4} = \frac{1}{4} [(\frac{1}{8} - (\frac{1}{8})^{3}) + (\frac{3}{8} - (\frac{3}{8})^{3}) + (\frac{5}{8} - (\frac{5}{8})^{3}) + (\frac{7}{8} - (\frac{7}{8})^{3})]$

$M_{4} = \frac{1}{4} [(\frac{1}{8} - \frac{1}{512}) + (\frac{3}{8} - \frac{27}{512}) + (\frac{5}{8} - \frac{125}{512}) + (\frac{7}{8} - \frac{343}{512})]$

M₄ = 1/4 · (2 - 478/512)
= 0.2666

Hence, the <span>area of the region bounded by y = x³ and y = x</span> is approximately 0.267 square units.

6 0

3 years ago

on monday mrs jones spent 32 dollars on 4 books. on tuesday she spent $16 on more books.each book cost the same amount. how many

Gala2k [10]

She bought 6 books in all because if you divide the whole number of all the books in all which is $32 divide that by 4 so..

32 ÷4=8

so thats just the 4 books then she buys 16 more dollars worth that which you then multiply 4 times 8 which give you 16 so you then add the 4 books to the other 2 books spent on the next day

ANSWER: 6 BOOKS IN ALL

6 0

2 years ago

Pyotr Tchaikovsky Sporting Goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 o

lapo4ka [179]

Answer:

Selling price of hockey game set is $145.32 , markup price is $210.54 and profit is $96 .

Step-by-step explanation:

Let us assume that the selling price of hockey game set be x .

As given

Pyotr Tchaikovsky Sporting Goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 on the newest version of an air hockey game set.

45% is written in the decimal form .

$= \frac{45}{100}$

= 0.45

Thus the equation becomes

0.45 × x = 65.34

0.45x = 65.34

$x = \frac{65.34}{0.45}$

x = 145.2

Therefore the selling price of the hockey game set is $145.2 .

Thus

Markup price = Selling price + Overhead Price

= $145.2 + $65.34

= $ 210.54

As given

If the air hockey game set costs Pyotr Tchaikovsky Sports $49.32 .

i.e Cost price of the hockey game set = $ 49.32

Profit = Selling price - Cost price

= 145.32 - 49.32

= $ 96

Therefore selling price of hockey game set is $145.32 , markup price is $210.54 and profit is $96 .

7 0

2 years ago