There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
1. What is the probability that the first machine produces an acceptable cork?
2. What is the probability that the second machine produces an acceptable cork?
3. Which machine is more likely to produce an acceptable cork?

Answer:

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

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.

The production manager claims they have a mean life of 83 months with a variance of 81.

This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]

Sample of 146:

This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]

What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?

This is 1 subtracted by the p-value of Z when X = 81.2. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

1 - 0.0078 = 0.9922.

0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.

Answer:

520 feets

Step-by-step explanation:

The height of the building, h can be obtuined using trigonometry ;

From the attached diagram, opposite side = 300 feets ; height, h = adjacent side

Hence,

Tan θ = opposite / Adjacent

Tan 30° = 300 / height

0.5773502 = 300 / height

Height = 300 / 0.5773502

Height = 519.615

Height = 520 feets

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Here given that,

Four students drive to school in the same car. The students claim they were late to school and missed a test because of a flat tire.

On the makeup test, the instructor asks the students to identify the tire that went flat; front driver's side, front passenger's side, rear driver's side, or rear passenger's side.

So, the probability of one person picking the tire is [tex]\frac{1}{4}[/tex].

Here four students so their probability is

[tex]\frac{1}{4(4)}=\frac{1}{16}[/tex]

Hence, the probability that all four students select the same tire is [tex]\frac{1}{16}[/tex].

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Answer:

N80

Step-by-step explanation:

One ruler is N60 and one pencil is N20.

We have two lines from the same point.

These two lines are also tangents to same circle which implies that they are of the same length.

That is 2x - 1 = 9

2x = 9 +1 = 10

x =10/2

x = 5

Answer:

3.) A,B,AB,O

Step-by-step explanation:

Non-numeric data refers to categorical data, or data that is not expressed quantitatively. Answers (1) and (2) contain quantitative data, so they would be eliminated as potential answer choices and therefore (4) would also be eliminated. This leaves answer (3), which does not have quantitative data and is therefore non-numeric.

Answer:

sin A = 4/5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin A = opp / hyp

sin A = 24/ 30

Dividing the top and bottom by 6

sin A = 4/5

sinØ=Perpendicular/Hypotenuse

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

Answer:

[tex]-32^\frac{3}{5} = -8[/tex]

Step-by-step explanation:

Given

[tex]-32^\frac{3}{5}[/tex]

Required

The equivalent expression

We have:

[tex]-32^\frac{3}{5}[/tex]

Rewrite as:

[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]

Expand

[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]

Remove bracket

[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]

[tex]-32^\frac{3}{5} = -2^3[/tex]

[tex]-32^\frac{3}{5} = -8[/tex]

Answer:

Step-by-step explanation:

The reasons for each statement are inside the parentheses

1. <1 and <2 are complementary (given)

2. m<1 + m<2 = 90° (definition of complementary angles)

3. m<2 = 74° (given)

4. m<1 + 74° = 90° (Substitution)

5. m<1 = 16° (Subtraction property of equality)

This is gotten by subtracting 74° from both sides as follows:

m<1 + 74° - 74° = 90° - 74°

m<1 = 16°

Given:

A credit card advertises an annual interest rate of 23%.

To find:

The equivalent monthly interest rate.

Solution:

We know that,

1 year = 12 months

It is given that, the credit card advertises an annual interest rate of 23%. So, the equivalent monthly interest rate is:

[tex]\dfrac{23\%}{12}=1\dfrac{11}{12}\%[/tex]

[tex]\dfrac{23\%}{12}\approx 1.9167\%[/tex]

Therefore, the equivalent monthly interest rate is [tex]1\dfrac{11}{12}\%[/tex] and the approximate equivalent monthly interest rate is 1.9167%.

Answer:

f(x) = 40(1 + 0.13)^x

Step-by-step explanation:

The general formula for an exponential growth function is;

f(x) = a(1 + r)^x

Where;

a= initial population of the city

r= population growth rate

x = number of years

Given that;

a= 40,000

r= 0.13

The population of the city in thousands of people in terms of x is;

f(x) = 40(1 + 0.13)^x

Answer:

The maximum number of minutes to keep the cost at $50 or less is 110 minutes

Step-by-step explanation:

Given

[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]

[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]

Required

[tex]C(x) = 50[/tex] ---- find x

We have:

[tex]C(x) = 30 + 0.40(x - 60)[/tex]

Substitute 50 for C(x)

[tex]50 = 30 + 0.40(x - 60)[/tex]

Subtract 30 from both sides

[tex]20 = 0.40(x - 60)[/tex]

Divide both sides by 0.40

[tex]50 = x - 60[/tex]

Add 60 to both sides

[tex]110 = x[/tex]

[tex]x =110[/tex]

Answer:

Cantor's intersection theorem refers to two closely related theorems in general topology and real analysis, named after Georg Cantor, about intersections of decreasing nested sequences of non-empty compact sets.

Answer:

Friday

Step-by-step explanation:

you need to count the number of circles, the half circle represents 5 skirts

Answer by Gauthmath

Answer:

q/N = g

Step-by-step explanation:

q = Ng

Divide each side by N

q/N = Ng/N

q/N = g

Answer:I just need points

Step-by-step explanation:

Hey

Answer:

yes

Step-by-step explanation:

o

The given table represents Exponential growth.

The process of Quantity rising over time is called exponential growth. An exponential function is used to create an exponential growth curve, which represents a pattern of data that shows a rise over time. Where the Exponential decay helps to understand the rapid decrease in a period of time

Here we have

The table

х     1       2       3       4          5  

у    14     56    224    896    3584  

From the given table, we can observe that

[tex]\frac{14}{56} = \frac{56}{224} = \frac{896}{3584} = \frac{1}{4}[/tex]    

Since the absolute value of the common ratio is less than 1 i.e 1/4

And the values are increasing

Therefore,

The given table represents Exponential growth.

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Answer:

a) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

b) 0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.

c) 0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Questions a/c:

Questions a and c are the same, so:

Event A: Brings lunch to work.

Event B: Is a woman.

Probability of a person bringing lunch to work:

9% of 15%(woman)

3% of 100 - 15 = 85%(man). So

[tex]P(A) = 0.09*0.15 + 0.03*0.85 = 0.039[/tex]

Probability of a person bringing lunch to work and being a woman:

9% of 15%, so:

[tex]P(A \cap B) = 0.09*0.15[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.039} = 0.3462[/tex]

0.3462 = 34.62% that a randomly selected employee is a woman given that the person brings their lunch to work.

Question b:

Event A: Woman

Event B: Brings lunch

15% of the employees are women.

This means that [tex]P(A) = 0.15[/tex]

Probability of a person bringing lunch to work and being a woman:

9% of 15%, so:

[tex]P(A \cap B) = 0.09*0.15[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09*0.15}{0.15} = 0.09[/tex]

0.09 = 9% probability that a randomly selected employee brings their lunch to work given that person is a woman.

Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

QUESTION:- SOLVE EQUATION BY FACTORISATION

EQUATION:-

[tex] {x}^{2} + x - 72 = 0[/tex]

ANSWER:-

[tex] {x}^{2} + x - 72 = 0\\{x}^{2} + 9x - 8x - 72 = 0 \\ x(x + 9) - 8(x +9) = 0 \\ (x - 8)(x + 9) = 0 \\ [/tex]

NOW FOR VALUE OF X ->

[tex]x - 8 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x + 9 = 0\\ x = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = - 9[/tex]

Answer:

D.) y = 2x + 2

Step-by-step explanation:

First, we need to find the slope.

Lets use the points (0, 2) and (-2, -2).

Using the formula for calculating slope, we get 2 as our slope.

Since the equation should be in slope-intercept form, we use this formula.

y = mx + b

We'll use our first point (0, 2) to substitute for x and y and use 2 to substitute for m (slope):

2 = 2(0) + b

2 x 0 = 0

2 = 0 + b

-0 = -0

= 2 = b

Now, substitute b for 2 for 2 for m.

= y = 2x + 2.

Hope this helps!

If there is something wrong, please let me know.

Answer:

25, 33

Step-by-step explanation:

let the length of the one with equal sides be x

third side = x+8

x+x+x+8 = 83

3x+8 = 83

3x = 75

x = 25

x+8 = 25+8 = 33

Answer:

Step-by-step explanation:

the mean is

{(12x1)+(13x1)+(14x2)+(15x2)+(17)+(18)+(19x2)+(20)+(21x2)+(22)+(24)}/11

mean=264/11

mean=24

Answer:

x = 2     y = 3

Step-by-step explanation:

-2x + 7 = 5x - 7

-7x + 7 = -7

-7x = -14

x = 2

y = -2(2) + 7

y = -4 + 7

y = 3

Answer:

48degrees

Step-by-step explanation:

From the circle geometry shown, traingle BDC is an isosceles triangle which shows means that their base angels are the same. Hence;

<B = <C

<CBD + <BCD + <D = 180

<BCD + <BCD + <D =180

2<BCD + <BDC = 180

Get <BCD;

<BCD+ <ECB = 90

<BCD + 48 = 90

<BCD = 90 - 48

<BCD = 42degrees

Get <BDC

2<BCD + <BDC = 180

2(42)+ <BDC = 180

84 + <BDC = 180

<BDC = 180 - 84

<BDC = 96

Since angle at the centre is twice that at the circumference, then;

<BAC = 1/2(<BDC )

<BAC = 96/2

<BAC = 48degrees

Answer:

7 7/80 or 7.0875

Step-by-step explanation:

product is the result of multiplication

7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875

Answer:

9.725%

Step-by-step explanation:

(1.0475)^2 =1.09725

one year 2 periods 4.75% per period