From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?
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Answer:

Using z table

                         = 0.0013

The probability = 0.0013

Step-by-step explanation:

Given that,

mean = μ = 45

standard deviation = σ   = 9

n=81

μT = μ =45

[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]

[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]

Using z table

= 0.0013

probability= 0.0013

Answer:

Decreased by 20%

Step-by-step explanation:

0.5 x ? = 0.4

? = 0.4/0.5

? = 0.8

1 - 0.8 = 0.2

0.2 = 20%

To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.

Answer:

a.5

b.3a+3

Step-by-step explanation:

in a,u need to replace 2 with x,so it will be 4-2+3

in b,replace 3a with x and so it will be6a-3a+3

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

Answer:

E(X)=3.125

Step-by-step explanation:

We are given that two four sided dice.

Then , the sample space

{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}

Total number of outcomes=16

Let the random variable X represent the maximum value of the two dice

Outcomes                            X                                 P(X)

(1,1)                                          1                                 1/16

(1,2),(2,1),(2,2)                                   2                        3/16

(1,3),(2,3),(3,1),(3,2),(3,3)                    3                           5/16  

(1,4),(3,4) ,(2,4),(4,1),(4,2),(4,3),(4,4)    4                            7/16

Using the probability formula

[tex]P(E)=\frac{Favorable\;outcomes}{Total\;number\;of\;outcomes}[/tex]

Now,

[tex]E(X)=\sum_{i=1}^{n}x_iP(x_i)[/tex]

[tex]E(x)=1(1/16)+2(3/16)+3(5/16)+4(7/16)[/tex]

[tex]E(x)=\frac{1+6+15+28}{16}[/tex]

[tex]E(x)=\frac{50}{16}=3.125[/tex]

Answer: -3/8

Step-by-step explanation:

Expanding z we get  

z = 4x^2 - 4xy + y^2 - 2y^2 - 3y

  = -y^2 - (4x + 3) y + 4x^2.

After Archimedes chooses x, Brahmagupta will choose

y=-(4x+3/2) in order to maximize z

Then  

z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2

z=8x^2+6x+9/4

To minimize this expression, Archimedes should choose x=-3/8

Answer:

D: y = 2x - 2

Step-by-step explanation:

1. [tex]\frac{16-8}{9-5}[/tex] = 2

2. y = 2x + b

3. Insert the points into the equation: 8 = 10 + b

4. b = -2

5. y = 2x - 2

=======================================================

Explanation:

Apply the slope formula

m = (y2-y1)/(x2-x1)

m = (16-8)/(9-5)

m = 8/4

m = 2

Then use this slope, along with another point such as (x,y) = (5,8) to find b

y = mx+b

8 = 2*5+b

8 = 10+b

8-10 = b

-2 = b

b = -2

Or you could use the other point (x,y) = (9,16)

y = mx+b

16 = 2*9+b

16 = 18+b

16-18 = b

-2 = b

b = -2

Either way, we get the same y intercept.

So because m = 2 is the slope and b = -2 is the y intercept, we go from y = mx+b to y = 2x-2

-------------------

To help verify the answer, note how plugging x = 5 leads us to...

y = 2x-2

y = 2*5 - 2

y = 10-2

y = 8

So x = 5 and y = 8 pair up together. This verifies (5,8) is on the line.

Through similar steps, you should find that the input x = 9 leads to the output y = 16. So that would confirm (9,16) is also on the line, and fully confirm the answer.

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{45}{35}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{x}{56}[/tex]

[tex]\\ \sf\longmapsto 7x=9(56)[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{9(56)}{7}[/tex]

[tex]\\ \sf\longmapsto x=72[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...

  0.15x +0.10(5-x) = 0.13(5)

  0.05x +0.5 = 0.65 . . . . . . . simplify

  0.05x = 0.15 . . . . . . . . . subtract 0.5

  x = 3 . . . . . . . . . . . . . divide by 0.05

3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.

Answer:

Step-by-step explanation:

x=120°

Answer:

The answer would be D

Step-by-step explanation:

This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.

Answer:

5

Step-by-step explanation:

The scale factor is 5. Answered by Gauthmath

The length and the width of rectangle a are expanded 5 times respectively.

The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.

According to the question

Rectangle a is dilated to form rectangle b.

By division operation, the ratio

[tex]\frac{20}{4} =\frac{30}{6} =5[/tex]

The length and the width of rectangle a are expanded 5 times respectively.

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Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.

Answer:

a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used 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.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

24​% say that they were too young when they got their tattoos.

This means that [tex]p = 0.24[/tex]

Six adults

This means that [tex]n = 6[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]

0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]

0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

This is:

[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]

0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

the answer would be -1,224 because the parentheses is your multiplication and the it is a negative

Answer:

b 34 the higest is 40 an the lowest 6 the diferens is 34

Step-by-step explanation:

Mark me brainlest pliz

Answer:

i would but this not my question this is theres he right A.

Step-by-step explanation:

Answer:

For some reason I cannot open the photo you have provided.

Step-by-step explanation:

Please try to re-upload?

Answer:

upper left...

there are zeros at (x)(x+3) (x-2)

Step-by-step explanation:

Answer:

1=2p+3

2=

Step-by-step explanation:

Answer:

30 miles

Step-by-step explanation:

Given that :

Scale = 2 inches represents 5 miles

This means that 2 inches in the map equals to 5 miles on ground ;

Hence, if the trail measures 12 inches on the map, the length on ground will be ; x

2 inches = 5 miles

12 inches = x miles

Cross multiply :

2x = (12 * 5)

2x = 60

x = 60 / 2

x = 30 miles

Answer:

x^(d+18)

Step-by-step explanation:

using the law of indices

you must add the powers

Answer:

[tex] {x}^{d + 18} [/tex]

Step-by-step explanation:

Answer:

scientists

Step-by-step explanation:

Answer:

S/100r

Step-by-step explanation:

S% of 1/r = (1/r x S) : 100

(1/r x S) : 100

S/r : 100

S/100r

Answer:

The equation of the point (4, 12) is y=4x+12

The base of the solid - call it B - is the set of points

B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}

Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².

Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².

Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,

[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]

Answer:

The constant is StartFraction 5 over 6 EndFraction

Step-by-step explanation:

StartFraction 5 over 6 EndFraction + one-fourth x minus y

5/6 + 1/4x - y

A. The constant is StartFraction 5 over 6 EndFraction.

True

B. The only coefficient is One-fourth.

False

There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1

C. The only variable is y

False

There are 2 variables: variable x and variable y

D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.

False

5/6 and 1/4x are not like terms

The only true statement is: The constant is StartFraction 5 over 6 EndFraction

Answer:

It's A if you don't want to read. A). The constant is 5/6

Step-by-step explanation:

Answer:

The point estimate that should be used in constructing the confidence interval is 3.5.

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

American students:

Sample of 12, mean height of 68.4 inches with a standard deviation of 1.64 inches. This means that:

[tex]\mu_A = 68.4[/tex]

[tex]s_A = \frac{1.64}{\sqrt{12}} = 0.4743[/tex]

Non-American students:

Sample of 17, mean height of 64.9 inches with a standard deviation of 1.75 inches. This means that:

[tex]\mu_N = 64.9[/tex]

[tex]s_N = \frac{1.75}{\sqrt{17}} = 0.4244[/tex]

Distribution of the difference:

[tex]\mu = \mu_A - \mu_N = 68.4 - 64.9 = 3.5[/tex]

[tex]s = \sqrt{s_A^2+s_N^2} = \sqrt{0.4743^2 + 0.4244^2} = 0.6365[/tex]

The point estimate that should be used in constructing the confidence interval is 3.5.

Confidence interval:

[tex]\mu \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower bound of the interval is:

[tex]\mu - zs = 3.5 - 1.96*0.6365 = 2.25[/tex]

The upper bound of the interval is:

[tex]\mu + zs = 3.5 + 1.96*0.6365 = 4.75[/tex]

The 95% confidence interval for the true mean difference between the mean height of the American students and the mean height of the non-American students, in inches, is (2.25, 4.75).

The missing side length is 10 unit.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have,

Perpendicular = 6

Base = 8

Using Pythagoras theorem

c² = P² + B²

c² = 6² + 8²

c²= 36 + 64

c² = 100

c= 10 unit.

Thus, the missing length is 10 unit.

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Answer:

10!

Step-by-step explanation:

Septillion-10 letters

1-s-10 places to be in

2-e-9

3-p-8

4-t-7

5-i-6

6-l-5

7-l-4

8-i-3

9-o-2

10-n-1

So, then

10×9×8×7×6×5×4×3×2×1=10!

or 3628800

The arrangement of the number will be equal to 3628800.

A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,

Arrangement = 10!

Arrangement = 10×9×8×7×6×5×4×3×2×1

Arrangement = 3628800

Therefore, the arrangement of the number will be equal to 3628800.

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9514 1404 393

Answer:

  $794.30

Step-by-step explanation:

The account balance for principal P invested at rate r compounded daily for t years is ...

  A = P(1 +r/365)^(365t)

We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.

  P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30

The interest earned in one year is $794.30.