A production facility employs 10 workers on the day shift, 8 workers on the swing shift, and 6 workers on the graveyard shift. A quality control consultant is to select 4 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 4 workers has the same chance of being selected as does any other group (drawing 4 slips without replacement from among 24).
(a) How many selections result in all 4 workers coming from the day shift? What is the probability that all 4 selected workers will be from the day shift? (Round your answer to four decimal places.)
(b) What is the probability that all 4 selected workers will be from the same shift? (Round your answer to four decimal places.)
(c) What is the probability that at least two different shifts will be represented among the selected workers? (Round your answer to four decimal places.)
(d) What is the probability that at least one of the shifts will be unrepresented in the sample of workers? (Round your answer to four decimal places.)

Answer:

The original price of the fan is $35.71

Step-by-step explanation:

Since Griffin’s General Store is having a 30% off sale on fans, it simply means that fans are paying for (100%-30%)= 70%.

Let the original price be x;

Therefore, 70% of x equal to $25;

[tex]\frac{70}{100}x=25[/tex]

70/100x = 25

0.7x = 25

[tex]x = \frac{25}{0.7}[/tex]

x = 35. 71

Hence, The original price of the fan is $35.71

Answer:

$35.71

Step-by-step explanation:

The statement indicates that Robert paid $25 for a fan and that it had a 30% discount. To be able to determine the original price, you have to divide the the price with the discount by the result of 1 minus the discount.

Original price= 25/(1-0.3)

Original price= 25/0.7

Original price= 35.71

According to this, the answer is that the original price of the fan is $35.71.

Answer:

Step-by-step explanation:

Answer:

B) (0,2)

Step-by-step explanation:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

Answer:

solution is [tex]\boxed{x=-1,x=-11}[/tex]

Step-by-step explanation:

f(x)=2|x+6|-4

either x+6 is positive and then |x+6|=x+6

or it is negative and |x+6| = -(x+6)=-x-6

case 1: x>=-6

f(x)= 2x+12-4=2x+8

f(x)=6 <=> 2x+8=6 <=> 2x = 6-8=-2 <=> x = -1

case 2: x<=-6

f(x)=-2x-12-4=-2x-16

f(x)=6 <=> -2x-16=6 <=> 2x=-16-6 = -22 <=> x = -11

so to recap, the solutions are x=-1 and x=-11

The value of x from the modulus value function is x = -1 and x = -11

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = 2 | x + 6 | - 4   be equation (1)

On simplifying , we get

when the value of f ( x ) = 6

Substituting the value of f ( x ) = 6 , we get

6 = 2 | x + 6 | - 4  

Adding 4 on both sides , we get

2 | x + 6 | = 10

Divide by 2 on both sides , we get

| x + 6 | = 5

And , If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

So , the two values of x are given by

when x + 6 = -5 and x + 6 = 5

x = -1 and x = -11

Hence , the values of x of modulus function is x = -1 and x = -11

To learn more about modulus function click :

https://brainly.com/question/13682596

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Answer:

The probability of selecting two red balls is 0.132.

Step-by-step explanation:

In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.

The conditions of selecting a ball are:

It is also provided that only one ball can be picked at a time.

Now, it is given that two balls are picked.

The number of ways to select a red ball in the first draw is: [tex]{4\choose 1}=4\ \text{ways}[/tex]

Compute the probability of selecting a red ball in the first draw as follows:

[tex]P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=\frac{4}{10}=0.40[/tex]

Now as a red ball is selected it will not be replaced.

So, there are 9 balls in the bag now.

The number of ways to select a red ball in the second draw is: [tex]{3\choose 1}=3\ \text{ways}[/tex]

Compute the probability of selecting a red ball in the second draw as follows:

[tex]P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=\frac{3}{9}=0.33[/tex]

Compute the probability of selecting two red balls as follows:

[tex]P(\text{Two Red balls})=P(\text{First ball is Red})\times P(\text{Second ball is Red})[/tex]

                            [tex]=0.40\times 0.33\\\\=0.132[/tex]

Thus, the probability of selecting two red balls is 0.132.

Answer:24600 , 16400

Step-by-step explanation:

Let the first part be x

So, second part will be 41000 - x

For amount x

SI = prt / 100

SI = x * 0.50 * 2

SI = 1x

For amount 41000 - x

SI = (41000-x) * 0.50 * 3

SI = 61500 - 1.5x

1x = 61500 - 1.5x

1.5x + x = 61500

2.5x = 61500

x = 61500 / 2.50 = 24600 for 2 years

2nd part = 41000 - 24600 = 16400 for three years

Answer:

subtract  -3

Step-by-step explanation:

–3 + 4x = 9

Add 3 to each side

This is the same as subtracting -3

-3 + 4x - (-3) = 9 - (-3)

4x = 9 +3

4x = 12

Answer:

The proportion of the variability seen in math achievement that can be predicted by math attitude is 0.78, the same value as the correlation coefficient.

Step-by-step explanation:

The correlation coefficient r between this two variables is found to be 0.78.

This coefficient can be calculated as:

[tex]r=\dfrac{SSY'}{SSY}[/tex]

where SSY' is the sum of the squares deviation from the mean for the predicted value and SSY is the sum of the squares deviation from the mean for the criterion variable.

Then, the value of the coefficient r is giving the proportion of the variability seen in the criterion value Y that can be explained by the predictor variable X.

Answer:

r=SSY'/SSY

Step-by-step explanation:

Answer:

C. can have more than one factor, each with several treatment groups.

Step-by-step explanation:

A completely randomized design can be used in experimental research of a primary factor or multiple factors. The factors could have several treatment groups which are assigned in a random manner. For example, a researcher, could want to determine the effect of a drug against a disease on a class of people. To do this, he designs a treatment group with different concentrations of the drug and a placebo group. He then gets an equal number of subjects, randomly assigning them to each of the groups. The effect of both treatments are compared to know if the drug is indeed effective against the disease the researcher is experimenting on.

Completely randomized design has found application in agricultural and environmental researches.

Answer:

She drove 8 miles each day.

Step-by-step explanation:

Given that she drove equal number of miles in 5 days. So in order to find the number of miles in each days, you have to divide it by 5,

[tex]5days = 40miles[/tex]

[tex]1day = 40 \div 5[/tex]

[tex]1day = 8miles[/tex]

Answer:

C: Multiply the first equation by -2

Step-by-step explanation:

-2 * (x + 3y = 16) = -2x-6y=-32

The resulting equation would be -2x-6y=-32

In the next if you add the two equations, you will successfuly eliminate x and can now solve for y.

-2x-6y=-32

2x + y = -18

Answer:

c

Step-by-step explanation:

x+3y=16________________eqn 1

2x+y=-18_______________eqn 2

multiply first equation by - 2

-2(x+3y=16)

-2x-6y= -32______________eqn 3

using elimination method

-2x-6y= -32

+

2x+y= -18

0-5y= -50

-5y= -50

divide both sides by -5

-5y/5= -50/5

y=10

substitute y in eqn 2 to find the value of x

2x+y= -18

2x+(10)= -18

2x+10= -18

2x= -18-10

2x= -28

divide both sides by 2

2x/2= -28/2

x= -14

Answer:

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Step-by-step explanation:

The observed values are given by:

A: 36

B: 42

C: 60

D: 14

E: 8

Total =160

We need to conduct a chi square test in order to check the following hypothesis:  

H0: There is no difference in the proportions for the final grades

H1: There is a difference in the proportions for the final grades

The level of significance assumed for this case is [tex]\alpha=0.01[/tex]  

The statistic to check the hypothesis is given by:  

[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]  

Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]  

And the calculations are given by:  

[tex]E_{A} =0.25*160=40[/tex]  

[tex]E_{B} =0.25*160=40[/tex]

[tex]E_{C} =0.4*160=64[/tex]

[tex]E_{D} =0.05*160=8[/tex]  

[tex]E_{F} =0.05*160=8[/tex]  

And now we can calculate the statistic:  

[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]  

The answer would be:

c. 5.25

Now we can calculate the degrees of freedom for the statistic given by:  

[tex]df=(categories-1)=(5-1)=4[/tex]

And we can calculate the p value given by:  

[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]  

The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis

Answer:

increase 40

% increase is 40 %

Step-by-step explanation:

Take the new amount and subtract the original amount

140-100 = 40

Divide by the original amount

40/100

.40

Multiply by 100 %

40%

The percent increase is 40%

Answer:

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Step-by-step explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :  

Null hypothesis:[tex]\mu \leq 5[/tex]  

Alternative hypothesis:[tex]\mu > 5[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

The degrees of freedom first given by:  

[tex]df=n-1=12-1=11[/tex]  

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

[tex] t_{\alpha}= 1.796[/tex]

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Answer:

a) Binomial.

b) n=20, p=0.01, k≥2

The probability hat a package sold will be refunded is P=0.0169.

Step-by-step explanation:

a) We know that

The most appropiate distribution to represent this random variable is the binomial.

b) The parameters are:

The probability of the package being refunded can be calculated as:

[tex]P(x\geq2)=1-(P(x=0)+P(x=1))\\\\\\P(x=k) = \dbinom{n}{k} p^{k}q^{n-k}\\\\\\P(x=0) = \dbinom{20}{0} p^{0}q^{20}=1*1*0.8179=0.8179\\\\\\P(x=1) = \dbinom{20}{1} p^{1}q^{19}=20*0.01*0.8262=0.1652\\\\\\P(x\geq2)=1-(0.8179+0.1652)=1-0.9831=0.0169[/tex]

Answer:

[tex]7x^2-2x-2[/tex]

Step-by-step explanation:

[tex]-3x^2+9+10x^2-11-2x[/tex]

Combine like terms:

[tex]10x^2-3x^2-2x+9-11[/tex]

Simplify:

[tex]7x^2-2x-2[/tex]

Hope this helps!

Answer: 7x^2 - 2x - 2

Step-by-step explanation:

in this expression, all you have to do is combine like terms. those are -3x^2 and 10x^2, 9 and -11.

-3x^2 + 9 + 10x^2 - 11 - 2x     rearrange to make easier

-3x^2 + 10x^2 - 2x + 9 - 11     combine like-terms

7x^2 - 2x - 2

Answer:

  2 + h = 14 and k - 25 = 2

Step-by-step explanation:

An equation has an equal sign.

Apparently, your answer choices are of the form ...

  (math expression) and (math expression)

In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...

  ( ... = ... ) and ( ... = ... )

Something like ...

  c -14  and  d +134

contains no equal signs, so has no equations.

It looks like your appropriate choice is ...

  2 + h = 14 and k - 25 = 2

Answer:

the answer is a

Step-by-step explanation:

i took the test

:)

note: have a wonderful day!

Answer:its 15.7

Step-by-step explanation:

Answer:

15.7

Step-by-step explanation:

Answer:

For ease of writing, θ [tex]=x[/tex]

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

Step-by-step explanation:

Our angle is [tex]x=\frac{3\pi }{4}[/tex]

To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).

Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.

And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.

For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]

This means that

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

4books=6.28inches

30books=?

(30x6.28)/4

47.1 inches

47.1 inches

Answer:

Test statistic t = 5.25

P-value = 0.000002 (one-tailed test)

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu> 7[/tex]

The significance level is 0.05.

The sample has a size n=49.

The sample mean is M=8.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√s^2=√4=2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{49}}=0.29[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{8.5-7}{0.29}=\dfrac{1.5}{0.29}=5.25[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

This test is a right-tailed test, with 48 degrees of freedom and t=5.25, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>5.25)=0.000002[/tex]

As the P-value (0.000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the average amount of time that a freshman at TAMU studies is significantly higher than 7 hours.

Answer:

4.76% probability that a randomly selected person from the population has a positive test result

Step-by-step explanation:

We have these following probabilities:

4% probability of having the disease.

If a person has a disease, 95% probability of a positive test.

100-4 = 96% probability a person does not have the disease.

If a person does not have the disease, 1% probability of a positive test.

What is the probability that a randomly selected person from the population has a positive test result

95% of 4% and 1% of 96%. So

p = 0.95*0.04 + 0.01*0.96 = 0.0476

4.76% probability that a randomly selected person from the population has a positive test result

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

Answer:

See Explanation

This question is answered using Microsoft Office Excel 2013

Step-by-step explanation:

Given

Browser A - 64%

Browser B - 24%

Browser C - 6%

Browser D - 3%

Browser E - 3%

Total Frequency = 50

a.

To tabulate the frequency of the choice of browser, the total frequency is multiplied by each individual percentage as follows;

Browser A - 64% * 50 = 32

Browser B - 24% * 50 = 12

Browser C - 6% * 50 = 3

Browser D - 3%* 50 = 1.5

Browser E - 3% * 50 = 1.5

See Attachment for frequency table (using software)

b. See Attachment for pie chart and bar chart.

Both charts are useful for data presentation but in this case, the pie chart is a better option to use because it shows how the distribution of each browser and how they make up as a whole.

The main circle of the pie chart shows how individual browser are distributed through segments; This is not so for the bars of the bar chart which.

c. Yes, there are changes in the choice of browser.

Aside from Browser D and E that has the same frequency, other browsers (A-C) have different frequency.

Also, the distribution shows that more users make use of browser A than other browsers and the least frequent used browser are browser D and E.

Answer:  The answer has one solution:

_______________________________

      →  x = 1 ;   y =  -4 ;  or, write as:  [1, -4].

_______________________________

Step-by-step explanation:

_______________________________

Given:

  y  =  - 1x – 3

  y  =   -7x + 3 ;

_______________________________

    -1x – 3  =   -7x + 3  ;  Solve for "x" ;

Add:  " +1x" ; and add " +3 " ;  to Each Side of the equation:

Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:

   -1x  + 1x  – 3  + 3  =  -7x  + 1x + 3 + 3 ;

         to get:  

             0  =  -6x + 6

          ↔  -6x + 6 = 0 ;

Now, subtract " 6 " from Each Side of the equation:

                -6x + 6 – 6  = 0 – 6  ;

       to get:

               -6x = -6 ;

Now, divide Each Side of the equation by " -6 ";  

      to isolate "x" on one side of the equation;

      & to solve for "x" ;

              -6x /-6  =  -6/-6 ;

      to get:

                x = 1 .

_______________________________

Now, let us solve for "y" ;  

We are given:  

 y =  -x – 3  ;

Substitute our solved value for "x" ; which is:  " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :

 y =  -x – 3  ;

    =  -1  – 3  

 y =   - 4 .

_______________________________

Let us check our answers by plugging the values for "x" and "y" ;

" 1 " ; and " -4 "; respectively);  into the second given equation; to see if these values for " x " and " y"  ; hold true:

Given:   y  =    - 7x  +  3 ;

           →  -4   =?  -7(1) + 3 ??  ;

           →  -4   =?   -7   + 3  ??  ;

           →  - 4 =?   -4 ?? ;

           →  Yes!

_______________________________

The answer has one solution:

      →  x = 1 ;   y =  - 4 ;  or, write as:  [1, -4 ].

_______________________________

Hope this is helpful!  Best wishes!

_______________________________

Answer:

The value of x^3 + 1/x^3 is 47/x + 1/x^3 - 1/x^5

Step-by-step explanation:

x^4 + 1/x^4 = 47

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(x^4 + 1/x^2)

x^4 = 47 - 1/x^4

x^3 + 1/x^3 = 1/x(47 - 1/x^4 + 1/x^2) = 47/x - 1/x^5 + 1/x^3 = 47/x + 1/x^3 - 1/x^5

Answer:

  AB = 2√106 ≈ 20.591

Step-by-step explanation:

The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.

For median AM, we have ...

  AM² = CM² +AC² = (BC/2)² +AC²

For median BN, we have ...

  BN² = CN² +BC² = (AC/2)² +BC²

The sum of these two equations is ...

  AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)

  AM² +BN² = (5/4)(AB²)

The hypotenuse of triangle ABC is then ...

  AB = √(4/5(AM² +BN²))

  AB = 2√((19² +13²)/5)

  AB = 2√106 ≈ 20.591

Answer: C

Step-by-step explanation:

To get all the constant terms on one side and variable terms on another, all we have to do is to add or subtract them on both sides.

3x+2x=10+5

Now that the like terms are on one side, we can combine them.

5x=15

To get x alone, we divide both sides by 5.

x=3

Now, we notice that x=3 is not an answer choice, but the next option that is equivalent to x=3 is C.

For C, if you divide both sides by -5, you still get x=3.

-15=-5x

x=3

Answer:

12

Step-by-step explanation:

f(-4) = -8-5(-4) = -8+20 = 12

Answer:

f(-4) = 12

Step-by-step explanation:

f(-4) = -8 - 5(-4)

= -8 + 20

= 12

the answer is 180°

Step-by-step explanation:

because it rotated 2x and 90+90 is 180

Answer:

C.

Step-by-step explanation:

Central angle = 360-52=308°

In radians

308° = 308π/180

Now

S = r∅

S = 3×308π/180

S = 924π /180

S = 77π/15 in.

Answer:

answer is 13π/15

Step-by-step explanation:

correct answer is 13π/15.