A quality control inspector has determined that 0.25% of all parts manufactured by a particular machine are defective. If 50 parts are randomly selected, find the probability that there will be at most one defective part.

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answer:

15 J

Step-by-step explanation:

There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.

1. Set up the equation

80 + x + 5 = 100

2. Simplify

x + 85 = 100

3. Solve for x by subtracting 85 from both sides

x = 15

Answer:

The correct answer is 15J which is B.

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

[tex]1x=\frac{1\sqrt{129} }{8}[/tex]

Step-by-step explanation:

In between the 1 and the [tex]\sqrt{129}[/tex] goes this symbol: ±

hope this helps!

Answer:

63%

225 buyers

Step-by-step explanation:

To find the percent take the number that liked it over the total

376/600

Change to decimal form

.62666666

Change to percent by multiplying by 100

62.66666666%

The nearest percent is 63%

37.5 % would but it then multiply by the number of shoppers

37.5 % ( 600)

Change to decimal form

.375 * 600

225

Answer:

-7/3x + 3

Step-by-step explanation:

Answer:

(9x-7)/3x or (3-7/3x)

Step-by-step explanation:

Divide each term of numerator by denominator.

-28x^5/12x^6 +36x^6/12x^6

-7/3x +3

Answer:

1)  m = negative StartFraction 10 over 4 EndFraction

2) m = negative five-halves

3) m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

Step-by-step explanation:

The given equation is:

=> [tex]\frac{3}{4} +m = -\frac{7}{4}[/tex]

Subtracting 3/4 to both sides

=> m = [tex]-\frac{7}{4} - \frac{3}{4}[/tex]

=> m = [tex]\frac{-10}{4}[/tex]

=> m = [tex]-\frac{5}{2}[/tex]

Answer:

-5/2 ye

cause ya do the math

Step-by-step explanation:

Answer:

[tex]\boxed{\sf A. \ 0.34}[/tex]

Step-by-step explanation:

The first triangle is a right triangle and it has one acute angle of 70 degrees.

We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.

The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.

The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.

[tex]\sf \frac{3.4}{10} =0.34[/tex]

Answer:

11[tex]\sqrt{x6/4[/tex]

Given:

The triangle on the left ( triangle 1) has a 60º, a 90º, and a side that equals 11.

So we know the triangle on the right (triangle 2) has a 45º and a 90º angle.

Triangle 2

Since triangle angles always have a sum of 180º, we can solve for the third angle of triangle 2. 180 - (45 + 90) = 45. So the third angle of triangle 2 is 45º.

This is a special type of right triangle called a 45-45-90. An image of the leg/hypotenuse is uploaded below. Meaning, if we solve for the leg that joins the two triangles, we can solve for the hypotenuse.

Triangle 1

To solve for the middle leg, we work with the information we have. So first, find the third angle. 190 - (60 + 90) = 30. This brings us to a second type of special right triangle. An image of the leg/hypotenuse is uploaded below.

Given that we have a side angle of 11, we know that is 2x due to orientation. So 2x=11 simplifies to x=5.5. We then plug that back in to find the leg that we want: 5.5[tex]\sqrt{3}[/tex] .

Triangle 2

Now that we have a side length for the second triangle we can solve. x for this triangle is 5.5[tex]\sqrt{3}[/tex] so to find the hypotenuse we plug into x[tex]\sqrt{2}[/tex]. This turns into (5.5[tex]\sqrt{3}[/tex][tex]\sqrt{2}[/tex]) which simplifies into 5.5[tex]\sqrt{6}[/tex] = 13.47

Answers

The answers are not in the correct form. By going through and finding the decimal form of each, you find out that 11[tex]\sqrt{6/4}[/tex] is equivalent to 13.47, therefore your answer.

Answer:

Step-by-step explanation:

From the given question, it can be concluded that Jessica and Kayla's planes took off an hour earlier than that of Lauren and at least two hours earlier than that of Maria. This implies that Maria's plane took off last among them.

Since each person's flight last 8 hours and Maria's plane lands at 4:45 pm, then Jessica and Kayla's planes land simultaneously at least at 2:45 pm. And that of Lauren lands exactly at 3:45 pm.

Answer:

There is no significant interaction between the number of sales calls and the miles driven.

Step-by-step explanation:

The variables are defined as follows:

Dependent (Y) = amount earned in commissions last month

Independent (X₁) = number of miles driven last month

Independent (X₂) = number of sales calls made last month

In this case we need to test whether there is a significant interaction between the number of sales calls and the miles driven.

The hypothesis can be defined as follows:

H₀: There is no significant interaction.

Hₐ: There is a significant interaction.

Assume that the significance level of the test is, α = 0.05.

Use the Data Analysis tool in Excel to form the regression equation.

For the regression equation, we need to compute the values of (X₁ × X₂).

Steps:

The output of the regression analysis is attached below.

The regression equation is:

[tex]Y=-455.07+3.128\cdot X_{1}+0.143\cdot X_{2}-0.001\cdot X_{1}X_{2}[/tex]

Consider the third table in the regression output.

The test statistic corresponding to the interaction term is:

t = -1.85

The p-value for the test of the interaction term is:

p-value = 0.078.

The p-value of the test is more than the significance value.

The null hypothesis will not be rejected.

Thus, concluding that there is no significant interaction between the number of sales calls and the miles driven.

Answer:

18.03 inches

Step-by-step explanation:

The cardboard is cut as shown below.

The line c cuts the rectangle into 2 right angled triangles.

To find the diagonal (hypotenuse), we have to apply Pythagoras Rule:

[tex]hyp^2 = opp^2 + adj^2\\\\=> c^2 = 10^2 + 15^2\\\\c^2 = 100 + 225 = 325\\\\[/tex]

=> c = 18.03" = 18.03 inches

The length of c, the diagonal, is 18.03 inches.

Answer:

viscosity is the state of being thick, sticky, and semifluid in consistency, due to internal friction.

"cooling the fluid raises its viscosity"

a quantity expressing the magnitude of internal friction, as measured by the force per unit area resisting a flow in which parallel layers unit distance apart have unit speed relative to one another.

plural noun: viscosities

"silicone oils can be obtained with different viscosities"

Step-by-step explanation:

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. hope this helps you :)

Answer:

O An oil's resistance to flow at different temperatures

Step-by-step explanation:

Internal friction of a moving fluid .

Answer:

the amount of money Ian invested is P =  £2,500

Step-by-step explanation:

The standard formula for compound interest is given as;

[tex]A = P(1+r/n)^{nt} \\P = \frac{A}{(1+r/n)^{nt}} ...........1\\[/tex]

Where;

A = final amount/value

P = initial amount/value (principal)

r = rate yearly

n = number of times compounded yearly.

t = time of investment in years

For this case, Given that;

A = £2652.25

t = 2 years

n = 1 (semiannually)

r = 3% = 0.03

substituting the given values into equation 1;

[tex]P = \frac{A}{(1+r/n)^{nt}} ...........1\\P = \frac{2652.25}{(1+0.03)^{2}} \\P = \frac{2652.25}{(1.03)^{2}} \\[/tex]

P =  £2,500

the amount of money Ian invested is P =  £2,500

Answer:

13

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

Answer:

[tex]\boxed{13}[/tex]

Step-by-step explanation:

=> [tex]\sqrt[3]{2197}[/tex]

Factorizing 2197 gives 13 * 13 * 13

=> [tex]\sqrt[3]{13*13*13}[/tex]

=> [tex]\sqrt[3]{13^3}[/tex]

We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]

=> [tex]13^{3 * 1/3}[/tex]

=> [tex]13^1[/tex]

=> 13

Answer:

[tex]y-4=2\,(x+1)[/tex]

which agrees with answer C in your list of possible answers.

Step-by-step explanation:

We can use the general point-slope form of a line of slope m and going through the point [tex](x_0, y_0)[/tex]:

[tex]y-y_0=m(x-x_0)[/tex]

which in our case, given the info on the slope (2) and the point (-1, 4) becomes:

[tex]y-y_0=m\,(x-x_0)\\y-4=2\,(x-(-1))\\y-4=2\,(x+1)[/tex]

Answer:

$153

Step-by-step explanation:

Since she claimed two exemptions, Grace Kelly income's tax will only be $153, and $1847 being the yearly take home.

Effective tax rate is set at 7.65%

Answer:

(2y + 22) years

Step-by-step explanation:

kamau is now 2 years older than Jane if Janes age is y now what will be the total age in 10 years​.

Answer: If Jane is y years old now and Kamau is 2 years older than Jane, therefore the age of Kamau now would be 2 + y years.

In ten years time Jane age would be y + 10 years while the age of Kamau would be y + 2 + 10 = y + 12 years.

To get their total age we just have to add their individual age. Therefore the total age in 10 years​  = Age of Kamau in ten years + age of Jane in ten years = (y + 12) + (y + 10) = y + 12 + y + 10 = y + y + 12 + 10 = 2y + 22 years

Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

x=5

Step-by-step explanation:

2 − x = −3

Subtract 2 from each side

2-2 − x = −3-2

-x = -5

Multiply by -1

x = 5

Answer:

x^2 +3

Step-by-step explanation:

f(x) = 2x^2 + 2

g(x) = x2 – 1,

find (f – g)(X).

f(x) - g(x) = 2x^2 + 2 -( x^2 – 1)

Distribute the minus sign

             = 2x^2 +2 -x^2 +1

             = x^2 +3

Answer:

[tex]y_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]  ,  [tex]y_2 = \left[\begin{array}{ccc}5\\1\\-6\\-1\end{array}\right][/tex]

Step-by-step explanation:

[tex]x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]    and [tex]x_2 = \left[\begin{array}{ccc}7\\-7\\-6\\1\end{array}\right][/tex]

Using Gram-Schmidt process to produce an orthogonal basis for W

[tex]y_1 = x_1 = \left[\begin{array}{ccc}1\\-4\\0\\1\end{array}\right][/tex]

Now we know X₁ , X₂ and Y₁

Lets solve for Y₂

[tex]y_2 = x_2- \frac{x_2*y_1}{y_1*y_1}y_1[/tex]

see attached for the solution of Y₂

Answer:

theres the screenshot of it

The solution to prove the sum of the interior angles of a triangle is 180° is

∠1 + ∠2 + ∠3 = 180°  ( angles in a straight line )

∠2 + ∠5 + ∠6 = 180°  ( interior angles of a triangle )

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the angles inside the triangle are ∠2 , ∠5 and ∠6

Now , the lines l₁ and l₂ are two parallel lines

From the figure ,

The measure of ∠1 = The measure of ∠5 ( alternate interior angles )

The measure of ∠3 = The measure of ∠6 ( alternate interior angles )

Now , for a straight line , the measure of angle = 180°

So , ∠1 + ∠2 + ∠3 = 180°  ( angles in a straight line ) ( angle addition )

And , the sum interior angles of a triangle is 180°

So , ∠2 + ∠5 + ∠6 = 180°  ( interior angles of a triangle ) ( substitution )

Hence , the sum of the angles inside a triangle is 180°

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ2

Answer:

( 2A - kn) /k = m

Step-by-step explanation:

A = k/2(m+n)

Multiply each side by 2/k

2/k *A =2/k * k/2(m+n)

2A /k = m+n

Subtract n from each side

2A /k - n = m+n -n

2A /k - n = m

Getting a common denominator

2A/k - kn/k = m

( 2A - kn) /k = m

Answer:

Step-by-step explanation:

[tex]A=\frac{k(m+n)}{2}\\2A=k(m+n)\\\frac{2A}{k} =m+n\\\frac{2A}{k}-n=m\\2A-kn=km\\\frac{(2A-kn)}{k}=m[/tex]

Answer:

52 dimes and 54 nickels

Step-by-step explanation: 52 dimes is $5.20 and 54 nickels is $2.70

Total coins 106 total $7.90

Answer: Speed = 5.6 mph

              Oxygen consumption = 71.6 mL/lb/min

Step-by-step explanation: For the oxygen consumption to be the same, functions must be equal:

f(x) = g(x)

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x+10=11x+10[/tex]

Resolving:

[tex]\frac{5}{3}.x^{2} + \frac{5}{3}.x - 11x =0[/tex]

[tex]\frac{5}{3}x^{2} + \frac{5}{3}x - \frac{33x}{3}=0[/tex]

[tex]\frac{5}{3}x^{2} - \frac{28x}{3}=0[/tex]

[tex]\frac{x}{3}(5x - 28)=0[/tex]

[tex]\frac{x}{3} = 0[/tex]

x=0

5x - 28 = 0

[tex]x = \frac{28}{5}[/tex]

x = 5.6

The speed when the oxygen consuption is the same is 5.6 mph.

For the level of oxygen consumption:

f(5.6) = g(5.6)

g(5.6) = 11*5.6 + 10

g(5.6) = 71.6

The level of oxygen consumption is 71.6 mL/lb/min

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption is 71.6 milliliter per pound per minute

The oxygen consumption for a person walking at x mph is given by,

             [tex]f(x)=\frac{5}{3} x^{2} +\frac{5}{3}x+10[/tex]

The oxygen consumption for a runner at x mph is approximated given by the function,

             [tex]g(x)=11x+10[/tex]

To be oxygen consumption same for both walker and runner, both function must be equal.

             [tex]f(x)=g(x)\\\\\frac{5}{3} x^{2} +\frac{5}{3}x+10=11x+10\\\\\frac{5}{3} x^{2} +\frac{5}{3}x-11x=0\\\\x(\frac{5}{3} x-\frac{28}{3} )=0\\\\x=0,x=28/5=5.6mph[/tex]

At speed of 5.6 mph the oxygen consumption is same for a walker as it is for a runner.

The level of oxygen consumption at that speed is,

             [tex]g(5.6)=11(5.6)+10=71.6[/tex]

Learn more:

https://brainly.com/question/6237128

Answer:

20%

Step-by-step explanation:

When you divide 40 by 8, you get 0.2. To convert a decimal into a percent, you multiply by 100 to get 20.

Hence,

8 is 20% of 40.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

The answer is option B.

Step-by-step explanation:

Let the percentage be x

We have

[tex] \frac{x}{100} \times 40 = 8 \\ \\ \frac{4}{10} x = 8 \\ \\ 4x = 80 \\ \\ x = \frac{80}{4} \\ \\ x = 20[/tex]

Hope this helps you

I suppose this is saying that 20%, 25% and 55% are each a whole number of science students.  The GCD is 5%, 1/20th, so minimum 20 people total.  55% are studying biology, that's 11.

Answer: C. 11