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3 years ago

Solve the equation. If necessary, round your answer to the nearest tenth.

Mathematics

2 answers:

d1i1m1o1n [39]3 years ago

5 0

Answer:

16, -16

Step-by-step explanation:

x^2 = 256

x = $\sqrt{256}$

x = $\sqrt{4 * 64}$

x = $\sqrt{4}$ * $\sqrt{64}$

x = 2 * 8

x = 16

Hopes this helps >.<

horrorfan [7]3 years ago

3 0

There was to solutions
x=16
x=-16

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This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 90 customer orders to fi

svp [43]

Answer:

a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b) 0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.

c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

Step-by-step explanation:

For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

3% of the components are identified as defective

This means that $p = 0.03$

a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?

0 defective in a set of 90, which is $P(X = 0)$ when $n = 90$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645$

0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.

b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?

At most 102 - 100 = 2 defective in a set of 102, so $P(X \leq 2)$ when $n = 102$

Then

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447$

$P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411$

$P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062$

0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.

c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?

At most 105 - 100 = 5 defective in a set of 105, so $P(X \leq 5)$ when $n = 105$

Then

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408$

$P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326$

$P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133$

$P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265$

$P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786$

$P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116$

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034$

0.9034 = 90.34% probability that the 100 orders can be filled without reordering components

3 0

3 years ago

Mikayla is building a pyramid of paper cups. The bottom row has 61 cups while the top row has only one cup. If there are 16 tota

worty [1.4K]

The number of cups will be equal to 496.

<h3>What is arithmatic progression?</h3>

The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmatic progression

Here we have the data:-

The bottom row has 61 cups

If there are 16 total rows

The number of the cups will be calculated as:-

$S_n=\dfrac{n(a_1+a_n)}{2}$

Here a1 is first term 1

an is last term 2

n is the total number of the rows

By putting the values in the question we will get:-

$S_n=\dfrac{16(1+61)}{2}=\dfrac{16\times 62}{2}=496\ cups$

Hence the number of cups will be equal to 496.

To know more about arithmetic progression follow

brainly.com/question/6561461

#SPJ1

3 0

2 years ago

Christopher weighs 211 pounds and has a BMI of 28.5. How many whole ponds must be gain or lose to get into the healthy BMI range

eduard

BMI = (pounds * 703) / (height^2)

so in the information you are missing the height
let's find it :)
first plug in what you know:
28.5 = (211 * 703) / (height)^2 then solve for (height)
28.5 (height)^2 = (211 * 703) multiplied both sides by (height)^2
(height)^2 = (211 * 703) / 28.5 divided both sides by 28.5
(height) = square root [(211 * 703) / 28.5] square rooted both sides
(height) = 72.143 inches

The healthy BMI is about 25
so 25 = (pounds)(703) / (72.143^2)
25(72.143^2) / (703) = (pounds) divide by 703, multiply by (72.143^2)
pounds = 185

211 - 185 = 26
Therefore Christopher would have to lose 26 pounds.

*Note: If the BMI you wanted to use was not 25, then just replace it like this
(pounds) = (BMI)(72.143^2) / (703) = goal weight

5 0

3 years ago

A rectangular board is 18 feet by 24 feet. How far from the center of the board should the foci be located in order to cut the l

solniwko [45]

<span>x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b

Center (0, 0):

h = 0
k = 0

a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:

General : (x - h)² / a² + (y - k)² / b² = 1

(x - 0)² / (12)² + (y - 0)² / (9)² = 1

x² / 144 + y² / 81 = 1

Focus = c:
        _____
c = √a² - b²
        _______
c = √(12)² - (9)²
        ______
c = √144 - 81 = sqrt63 = 7.9372</span>

Focus : ( -7.9372, 0) and ( 7.9372, 0)

7 0

3 years ago

I am STRESSED. Please answer the following questions below that are HIGHLIGHTED.

Katyanochek1 [597]

Answer:

1.5 tons and 256 pounds OR 1 ton and 1256 pounds

Step-by-step explanation:

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2 years ago