When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well.

Answer:

a = 8

Step-by-step explanation:

Explanation:-

Given P(x) = 2 x+4 a

          Q(x)=4 x - 2

          P( Q(4)) = 60

         P(4 (4) - 2) = 60

        P( 14 ) = 60

       2 (14) + 4 a = 60

        4 a + 28 = 60

Subtracting '28' on both sides , we get

       4 a +28 - 28 = 60 - 28

       4 a = 32

Dividing '4' on both sides , we get

        a = 8

Find the given attachments

1 × 18/100 = 12/100(g+11), is the equation. The answer is 12/100 gallons

Answer:

62.93%

Step-by-step explanation:

We have to solve it by a Poisson distribution, where:

p (x = n) = e ^ (- l) * l ^ (x) / x!

Where he would come being the number of birds that there would be in 40 minutes, we know that in 2 hours, that is 120 minutes there are 13, therefore in 40 there would be:

l = 13 * 40/120

l = 4,333

Now, we have p (x> 3) and that is equal to:

p (x> 3) = 1 - p (x <= 3)

So, we calculate the probability from 0 to 3:

 p (x = 0) = 2.72 ^ (- 4.33) * 4.33 ^ (0) / 0! = 0.01313

p (x = 1) = 2.72 ^ (- 4.33) * 4.33 ^ (1) / 1! = 0.0568

p (x = 2) = 2.72 ^ (- 4.33) * 4.33 ^ (2) / 2! = 0.12310

p (x = 3) = 2.72 ^ (- 4.33) * 4.33 ^ (3) / 3! = 0.17767

If we add each one:

0.01313 + 0.0568 + 0.12310 + 0.17767 = 0.3707

replacing:

p (x> 3) = 1 - 0.3707

p (x> 3) = 0.6293

Which means that the probability is 62.93%

Answer:

He should pay $2,790.7.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question:

Rate of 10%, so I = 0.1.

9 months, so [tex]t = \frac{9}{12} = 0.75[/tex]

How much should he pay for a note that will be worth $3,000 in 9 months?

We have to find P for which T = 3000. So

[tex]T = E + P[/tex]

[tex]3000 = E + P[/tex]

[tex]E = 3000 - P[/tex]

Then

[tex]E = P*I*t[/tex]

[tex]3000 - P = P*0.1*0.75[/tex]

[tex]1.075P = 3000[/tex]

[tex]P = \frac{3000}{1.075}[/tex]

[tex]P = 2790.7[/tex]

He should pay $2,790.7.

Answer:

[tex]-30[/tex]

Step-by-step explanation:

[tex]3\frac{3}{5} \times (-8 \frac{1}{3} )[/tex]

[tex]\frac{18}{5}\times \left(-\frac{25}{3}\right)[/tex]

[tex]\frac{18}{5}\times -\frac{25}{3}[/tex]

[tex]-\frac{18\times \:25}{5\times \:3}[/tex]

[tex]-\frac{450}{15}[/tex]

[tex]=-30[/tex]

Answer:-30

Step-by-step explanation:

3 3/5 x -8 1/3

18/5 x -25/3

-30

Answer:

Step-by-step explanation:

1) The given inequality is

[tex]|\sqrt{n} \frac{(\bar R_n-p)}{\sqrt{p(1-p)} } |<q_{\alpha /2}| \\\\ \to(\frac{(\sqrt{n} \bar R_n-p)}{\sqrt{p(1-p)} })<q^2_{\alpha /2}[/tex]

[tex]\to n( \bar R _n - p)^2<p(1-p)q^2_{\alpha /2}[/tex]

[tex]\to n\bar R +np^2-2nR_np<q^2_{\alpha /2 p- q^2_{\alpha /2}p^2[/tex]

Arranging the terms  with p² and p, we get

[tex]p^2(n+q^2_{\alpha /2)-p(2n \bar R _n+q^2_{\alpha / 2})+n \bar R ^2 _n <0[/tex]

Hence, the inequality is of the form

Ap² + Bp + c < 0

2. A quadratic equation of the form

Ap² + Bp + c < 0 with A > 0 looks like

Check the attached image

The region where the values are negative lies between p₁ and p₂ ...

The p₁ < p < p₂

Answer:

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

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

For this problem, we have that:

[tex]n = 1000, \pi = \frac{710}{1000} = 0.71[/tex]

95% confidence level

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

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Answer:

X = 4 x

  over  5 ( x − 1 ) − 1 5 ( x − 1 )

Answer:

x = 4

Step-by-step explanation:

10(x-1) = 8x-2

Distribute

10x-10 = 8x-2

Subtract 8 from each side

10x-10-8x = 8x-2-8x

2x-10 = -2

Add 10  to each side

2x-10+10 = -2+10

2x = 8

Divide each side by 2

2x/2 = 8/2

x = 4

Answer:

(C) 10

Step-by-step explanation:

x+y−z=8

Subtract y from both sides

x-z= -y+8

Add z to both sides

x= -y+z+8

Subtract 8 from both sides

x-8= -y+z

x−y+z=12

Add y to both sides

x+z=12+y

Subtract z from both sides

x=y-z+12

Subtract 12 from both sides

x-12=y-z

Multiply both sides by -1

-x+12= -y+z

Combine equations:

x-8= -x+12

Add x to both sides

2x-8+12

Add 8 to both sides

2x=20

Divide both sides by 2

x=10

The answer is (C) 10.

Answer:

80

Step-by-step explanation:

For every additional 10 hrs, you get 200 more dollars.

Answer:

19.82 units

Step-by-step explanation:

The number of units of tile simply refers to the perimeter.

So, we need to find all the sides of the rectangle.

Now, we have AB = 4.24 units and BD = 7.07 units.

So, we can find AD using pythagoras theorem.

So,

(AD)² + 4.24² = 7.07²

(AD)² + 17.978 = 49.985

(AD)² = 49.985 - 17.978

AD = √32.007

AD = 5.66 units

AD = BC = 5.66 units

Likewise, AB = DC = 4.24 units

Thus,

perimeter = 2(5.66) + 2(4.24) = 19.8 units

Closest answer among the options is approximately 19.82

Answer:

19.82 units

Step-by-step explanation:

just took test and got it right

Answer:

Due to the higher z-score, he did better on the SAT.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Determine which test the student did better on.

He did better on whichever test he had the higher z-score.

SAT:

Scored 1070, so [tex]X = 1070[/tex]

SAT scores have a mean of 950 and a standard deviation of 155. This means that [tex]\mu = 950, \sigma = 155[/tex].

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

[tex]Z = \frac{1070 - 950}{155}[/tex]

[tex]Z = 0.77[/tex]

ACT:

Scored 25, so [tex]X = 25[/tex]

ACT scores have a mean of 22 and a standard deviation of 4. This means that [tex]\mu = 22, \sigma = 4[/tex]

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

[tex]Z = \frac{25 - 22}{4}[/tex]

[tex]Z = 0.75[/tex]

Due to the higher z-score, he did better on the SAT.

Answer:

meh

Step-by-step explanation:

Answer:

105.12 ft^2

Step-by-step explanation:

Area of a rectangle: bh

In this case 8*10.... so area of the rectangle is 80

Area of a circle: pir^2

Half it for a semicircle.

so 1/2 pi r^2

radius is 4 cuz its half of 8.

so 1/2(3.14)(4^2)=(0.5)(3.14)(16)=25.12

Now add up 80+25.12

Total is 105.12

Hope I helped :)

Answer:

a. 50 turns

b. 0.0114 A

c. 0.25 A, 10 V

Step-by-step explanation:

Given:-

- The required current ( Is ) = 0.5 A

- The required voltage ( Vs ) = 5 V

- Transformer is 100% efficient ( ideal )

- The number of turns in the primary coil, ( Np ) = 2200

- The Voltage generated by power station, ( Vp ) = 220 V

Find:-

a. The number of turns in the secondary coil of the transformer

b. The current supplied by the power station

c. The effect on output current and voltage when the number of turns of secondary coil are doubled.

Solution:-

- For ideal transformers that consists of a ferromagnetic core with two ends wounded by a conductive wire i.e primary and secondary.

- The power generated at the stations is sent to home via power lines and step-down before the enter our homes.

- A household receives a voltage of 220 V at one of it outlets. We are to charge a phone that requires 0.5 A and 5V for the process.

- The outlet and any electronic device is in junction with a smaller transformer.

- All transformers have two transformation ratios for current ( I ) and voltage ( V ) that is related to the ratio of number of turns in the primary and secondary.

                     Voltage Transformation = [tex]\frac{N_p}{N_s} = \frac{V_p}{V_s}[/tex]

Where,

                 Ns : The number of turns in secondary winding

- Plug in the values and evaluate ( Ns ):

                           [tex]N_s = N_p*\frac{V_s}{V_p} \\\\N_s = 2200*\frac{5}{220} \\\\N_s = 50[/tex]

Answer a: The number of turns in the secondary coil should be Ns = 50 turns.

- Similarly, the current transformation is related to the inverse relation to the number of turns in the respective coil.

                  Current Transformation = [tex]\frac{N_p}{N_s} = \frac{I_s}{I_p}[/tex]

Where,

                 Ip : The current in primary coil

- Plug in the values and evaluate ( Ip ):

                        [tex]I_p = \frac{N_s}{N_p}*I_s\\\\I_p = \frac{50}{2200}*0.5\\\\I_p = 0.0114[/tex]  

Answer b: The current in the primary coil should be Ip = 0.0114 Amp.

- The number of turns in the secondary coil are doubled . From the transformation ratios we know that that voltage is proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output voltage is also doubled ( assuming all other design parameters remains the same ). Hence, the output voltage is = 2*5V = 10 V

- Similary, current transformation ratio suggests that the current is inversely proportional to the number of turns in the respective coils. So if the turns in the secondary are doubled then the output current is half of the required ( assuming all other design parameters remains the same ). Hence, the output current is = 0.5*0.5 A = 0.25 A

Answer:

# of pages   # of magazines

     1-20                    7

   21-40                    4

Step-by-step explanation:

Numbers 1 through 20:

10, 11, 14, 16, 17, 17, 20 (7 numbers)

Numbers 21 through 40:

21, 28, 29, 32 (4 numbers)

Answer:

Let's call the amount of 90% solution x.

We can write:

45% * 525 + 90%x = 55%(x + 525)

0.45 * 525 + 0.9x = 0.55(x + 525)

Solving for x we get x = 150 so the first blank is 150 and the second blank is 525 + 150 = 675.

Answer:

D. Pilot error isPilot error is the most serious threat to aviation safety. Pilots could be better trained.

Step-by-step explanation:

We can construct the relative frequency distribution dividing the amount of incidents for each category by the total amount of incidents.

This amount is:

[tex]\sum x_i=627+64+113+382+481=1667[/tex]

Then, the relative frequency for each category is:

[tex]\text{Pilot error}=627/1667=0.38\\\\\text{Human error}=64/1667=0.04\\\\\text{Weather}=113/1667=0.07\\\\\text{Mechanical problems}=382/1667=0.23\\\\\text{Sabotage}=481/1667=0.29\\\\[/tex]

As the pilot error has the largest relative frequency, we can conclude that pilot error is the most serious threat to aviation safety.

Here is the full question .

We are interested in finding an estimator for [tex]Var (X_i )[/tex] and propose to use :

[tex]\hat {V} = \bar {X}_n (1- \bar {X} )_n[/tex]

Now; we are interested in the basis of [tex]\hat V[/tex]

Compute :

[tex]E \ \ [ \bar V] - Var (X_i) =[/tex]

Using this; find an unbiased estimator [tex][ \bar V][/tex] for [tex]p(1-p) \ if \ n \geq 2[/tex]

Write [tex]bar \ x{_n} \ for \ X_n[/tex]

Answer:

Step-by-step explanation:

[tex]\bar X_n = \dfrac{1}{n} {\sum ^n _ {i=1} } \\ \\ E(X_i) = - \dfrac{1}{n=1} \sum p \dfrac{1}{n}*np = \mathbf{p}[/tex]

[tex]V(\bar X_n) = V ( \dfrac{1}{n_{i=1} } \sum ^n \ X_i )} = \dfrac{1}{n^2} \sum ^n_{i=1} Var (X_i) \\ \\ = \dfrac{1}{n^2} \ \sum ^n _{i=1} p(1-p) \\ \\ = \dfrac{1}{n^2}*np(1-p) \\ \\ = \dfrac{p(1-p)}{n}[/tex]

[tex]E( \bar X^2 _ n) = Var (\bar X_n) + [E(\bar X_n)]^2 \\ \\ = \dfrac{p(1-p)}{n}+ p \\ \\ = p^2 + \dfrac{p(1-p)}{n} \\ \\ \\ \hat V = \bar X_n (1- \bar X_n ) = \bar X_n - \bar X_n ^2 \\ \\ E [ \hat V] = E [ \bar X_n - \bar X_n^2] \\ \\ = E[\bar X_n ] - E [\bar X^2_n] \\ \\ = p-(p^2 + \dfrac{p(1-p)}{n}) \\ \\ = p-p^2 -\dfrac{p(1-p)}{n}[/tex]

[tex]=p(1-p)[1-\dfrac{1}{n}] = p(1-p)\dfrac{n-1}{n}[/tex]

[tex]Bias \ (\bar V ) = E ( \hat V) - Var (X_i) \\ \\ = p(1-p) [1-\dfrac{1}{n}] - p(1-p) \\ \\ - \dfrac{p(1-p)}{n}[/tex]

Thus; we have:

[tex]E [\hat V] = p(1-p ) \dfrac{n-1}{n}[/tex]

[tex]E [\dfrac{n}{n-1} \ \ \bar V] = p(1 -p)[/tex]

[tex]E [\dfrac{n}{n-1} \ \ \bar X_n (1- \bar X_n )] = p (1-p)[/tex]

Therefore;

[tex]\hat V ' = \dfrac{n}{n-1} \bar X_n (1- \bar X_n)[/tex]

[tex]\mathbf{ \hat V ' = \dfrac{n \bar X_n (1- \bar X_n)} {n-1}}[/tex]

Answer:

B.

Step-by-step explanation:

A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.

Answer:

1/25

Step-by-step explanation:

5^-2

We know that a^ -b = 1/ a^b

5^-2 = 1/ 5^2

       = 1/25

Answer:

85.56% probability that less than 6 of them have a high school diploma

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they have a high school diploma, or they do not. The probability of an adult having a high school diploma is independent of other adults. So 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.

[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.

50% of adult workers have a high school diploma.

This means that [tex]p = 0.5[/tex]

If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma

This is P(X < 6) when n = 8.

[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which

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

[tex]P(X = 0) = C_{8,0}.(0.5)^{0}.(0.5)^{8} = 0.0039[/tex]

[tex]P(X = 1) = C_{8,1}.(0.5)^{1}.(0.5)^{7} = 0.0313[/tex]

[tex]P(X = 2) = C_{8,2}.(0.5)^{2}.(0.5)^{6} = 0.1094[/tex]

[tex]P(X = 3) = C_{8,3}.(0.5)^{3}.(0.5)^{5} = 0.2188[/tex]

[tex]P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734[/tex]

[tex]P(X = 5) = C_{8,5}.(0.5)^{5}.(0.5)^{3} = 0.2188[/tex]

[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0039 + 0.0313 + 0.1094 + 0.2188 + 0.2734 + 0.2188 = 0.8556[/tex]

85.56% probability that less than 6 of them have a high school diploma

Answer:

the distance written as a decimal is 3.7

37/10 = 3,7

Achievements :)

Pass = $21 , Souvenir = 2x/3 = $14 , Burger = x/6 =$3.5 .

Answer:

-15

Step-by-step explanation:

The solution of expression for x = - 4 is,

⇒ - 15

We have to given that,

An expression is,

⇒ 2x - 7

Now, We can simplify the expression for x = - 4 as,

An expression is,

⇒ 2x - 7

Plug x = - 4;

⇒ 2 × - 4 - 7

⇒ - 8 - 7

⇒ - 15

Thus, The solution of expression for x = - 4 is,

⇒ - 15

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ6

Answer: B. although none are exactly 0.3 B is closest

Step-by-step explanation:

a. 35/999 = .0350

b. 31/99 = .3153

c. 105/7333 = .0143

d. 35/111 = .3135

Answer:

D. G(x) = |x| + 7

Step-by-step explanation:

→For the function G(x) to shift upwards, there needs to be a number being added to the whole function.

→The answer isn't "A," because the 1 is being subtracted, making it shift downwards 1 unit, not upwards.

→The answer isn't "B," because adding the 2 there would cause the function to shift to the left for 2 units, not upwards.

→The answer isn't "C," because 10 is being multiplied, which would cause the function to narrow, and not shift upwards.

This means the correct answer is "D," because the 7 is being added, making the function shift upwards 7 units.

Answer:

A.

Step-by-step explanation:

So you would have f(3) = 3 + [tex]\frac{2}{2}[/tex]

f(3) = 3 + 1

f(3) = 4

Answer:

Step-by-step explanation: f(x)

3+ a square root of 3+1 / x-1

3+ a square root (4/2)

3+ square root of 2. That's the answer