Five bulbs of which three are defective are to be tried in two bulb points in a dark room
Number of trials the room shall be lighted is
(a) 6
(b) 8
(c) 5
(d) 7.​

Answer:Priya ran 19 miles last week

Step-by-step explanation:

4 x 3 = 12

12 + 7 = 19

Answer:

28π cm²

Step-by-step explanation:

Circumference Formula: C = 2πr

Simply plug in r into the formula:

C = 2π(14)

C = 28π or 87.9646

Answer:

28π cm

Step-by-step explanation:

The circumference of a circle has the formula 2πr.

2 × π × r

Where r is the radius.

2 × π × 14

28 × π

= 28π

The circumference is 28π and the unit is centimeters.

Answer:

The probability that a piece of pottery will be finished within 95 minutes is 0.0823.

Step-by-step explanation:

We are given that the time of wheel throwing and the time of firing are normally distributed variables with means of 40 minutes and 60 minutes and standard deviations of 2 minutes and 3 minutes, respectively.

Let X = time of wheel throwing

So, X ~ Normal([tex]\mu_x=40 \text{ min}, \sigma^{2}_x = 2^{2} \text{ min}[/tex])

where, [tex]\mu_x[/tex] = mean time of wheel throwing

            [tex]\sigma_x[/tex] = standard deviation of wheel throwing

Similarly, let Y = time of firing

So, Y ~ Normal([tex]\mu_y=60 \text{ min}, \sigma^{2}_y = 3^{2} \text{ min}[/tex])

where, [tex]\mu_y[/tex] = mean time of firing

            [tex]\sigma_y[/tex] = standard deviation of firing

Now, let P = a random variable that involves both the steps of throwing and firing of wheel

SO, P = X + Y

Mean of P, E(P) = E(X) + E(Y)

                   [tex]\mu_p=\mu_x+\mu_y[/tex]

                        = 40 + 60 = 100 minutes

Variance of P, V(P) = V(X + Y)

                               = V(X) + V(Y) - Cov(X,Y)

                               = [tex]2^{2} +3^{2}-0[/tex]  

{Here Cov(X,Y) = 0 because the time of wheel throwing and time of firing are independent random variables}

SO, V(P) = 4 + 9 = 13

which means Standard deviation(P), [tex]\sigma_p[/tex] = [tex]\sqrt{13}[/tex]

Hence, P ~ Normal([tex]\mu_p=100, \sigma_p^{2} = (\sqrt{13})^{2}[/tex])

The z-score probability distribution of the normal distribution is given by;

                           Z  =  [tex]\frac{P- \mu_p}{\sigma_p}[/tex]  ~ N(0,1)

where, [tex]\mu_p[/tex] = mean time in making pottery = 100 minutes

           [tex]\sigma_p[/tex] = standard deviation = [tex]\sqrt{13}[/tex] minutes

Now, the probability that a piece of pottery will be finished within 95 minutes is given by = P(P [tex]\leq[/tex] 95 min)

     P(P [tex]\leq[/tex] 95 min) = P( [tex]\frac{P- \mu_p}{\sigma_p}[/tex] [tex]\leq[/tex] [tex]\frac{95-100}{\sqrt{13} }[/tex] ) = P(Z [tex]\leq[/tex] -1.39) = 1 - P(Z < 1.39)

                                                            = 1 - 0.9177 = 0.0823

The above probability is calculated by looking at the value of x = 1.39 in the z table which has an area of 0.9177.                                        

Answer:

85

Step-by-step explanation:

im new↑∵∴∵∴∞

Answer:

841

Step-by-step explanation:

If the number is divided by 4 and the remainder is 1, the last digit must be 1, 3, 5, 7 or 9.

If the number is divided by 5 and the remainder is 1, the last digit must be 6 or 1.

So we already know the last digit must be 1.

The numbers between 800 and 900, with last digit 1, that divided by 6 have a remainder of 1 are:

811, 841, 871

The numbers between 800 and 900, with last digit 1, that divided by 7 have a remainder of 1 is just 841

So Tommy's number is 841.

Tommy's number is 841.

In this question we must determine first the least common number of 4, 5, 6 and 7, which is the product of these four numbers, that is to say:

[tex]x = 4\times 5\times 6 \times 7[/tex]

[tex]x = 840[/tex]

This is the least number that is divisible both for 4, 5, 6 and 7. Now we add this number by 1 to determine what number Tommy thought:

[tex]y = x + 1[/tex]

[tex]y = 841[/tex]

Tommy's number is 841.

To learn more on divisibility, we kindly invite to check the following verified question: https://brainly.com/question/369266

Hey there! :)

Answer:

A = 10 units².

Step-by-step explanation:

To solve this, we need to find the distance between the two points to derive the side-lengths of the square. Use the distance formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

Plug in points into the formula to find the distance:

[tex]d = \sqrt{(3 - 2)^2 + (4-1)^2}[/tex]

Simplify:

[tex]d = \sqrt{(1)^2 + (3)^2}[/tex]

[tex]d = \sqrt{(1) + (9)}[/tex]

[tex]d = \sqrt{10}[/tex]

Find the area of the square using the formula A = s² where s = √10:

A = (√10)²

A = 10 units².

Answer:

10

Step-by-step explanation:

We use the distance formula to find the distance between the two points, which is the side length of the square.. Therefore, the area of the square is 10.

Answer:

8.5 inches

Step-by-step explanation:

First let's find the time t when the depth of the snow is 7 inches.

To do this, we just need to use the value of D = 7 then find the value of t:

[tex]7 = 1.5t + 4[/tex]

[tex]1.5t = 3[/tex]

[tex]t = 2\ hours[/tex]

We want to find the depth of snow one hour from now, so we just need to use the value of t = 3 to calculate D:

[tex]D = 1.5*3 + 4[/tex]

[tex]D = 4.5 + 4 = 8.5\ inches[/tex]

The depth of snow one hour from now will be 8.5 inches.

The depth of the snow one hour from now is 8.5 inches.

Let D represent the depth of snow in inches at time t. It is given by the relationship:

D=1.5t + 4

Since  the depth of the snow is 7 inches now, hence, the time now is:

7 = 1.5t + 4

1.5t = 3

t = 2 hours

One hour from now, the time would be t = 2 + 1 = 3 hours. Hence the depth at this time is:

D = 1.5(3) + 4 = 8.5 inches

Therefore the depth of the snow one hour from now is 8.5 inches.

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Answer:

the answer is integers if helpful please give 5 star

Answer:

Step-by-step explanation:

[tex] - \frac{1}{2} + c = \frac{31 }{4} \\ \\ c = \frac{31}{4} + \frac{1}{2} = \frac{31 - 2}{4} \\ \\ c = \frac{29}{4} [/tex]

Hope this helps you

Answer:

[ 5.456, 5.544]

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 5.5 ounces

Standard deviation r = 0.2 ounces

Number of samples n = 80

Confidence interval = 95%

z value (at 95% confidence) = 1.96

Substituting the values we have;

5.5+/-1.96(0.2/√80)

5.5+/-1.96(0.022360679774)

5.5+/-0.043826932358

5.5+/-0.044

= ( 5.456, 5.544) ounces

Therefore the 95% confidence interval (a,b) = ( 5.456, 5.544) ounces

Answer:

(a) Yes, Fredrick’s data set contains an outlier.

(b) No, the median value is not 12 home runs.

(c) Yes, the mean value is about 12.6 home runs.

(d) Yes, the median describes Fredrick’s data more accurately than the mean.

(e) No, the mean value doesn't stay the same when the outlier is not included in the data set.

Step-by-step explanation:

We are given that Fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play.

Firstly, arranging our data set in ascending order we get;

1, 12, 12, 12, 13, 13, 14, 15, 16, 18.

(a) The statement that Fredrick’s data set contains an outlier is true because in our data set there is one value that stands out from the rest of the data, which is 1.

Hence, the outlier value in the data set is 1.

(b) For calculating median, we have to first observe that the number of observations (n) in the data set is even or odd, i.e;

                    Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations in Fredrick's data set is even, i.e. n = 10.

SO,  Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{(\frac{10}{2})^{th} \text{ obs.}+(\frac{10}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{(5)^{th} \text{ obs.}+(6)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{13+13 }{2}[/tex]  = 13 home runs

So, the statement that the median value is 12 home runs is not correct.

(c) The mean of the data set is given by;

          Mean =  [tex]\frac{1+ 12+ 12+ 12+ 13+ 13+14+ 15+ 16+ 18}{10}[/tex]

                     =  [tex]\frac{126}{10}[/tex]  = 12.6 home runs

So, the statement that the mean value is about 12.6 home runs is correct.

(d) The statement that the median describes Fredrick’s data more accurately than the mean is correct because even if the outlier is removed from the data set, the median value will remain unchanged but the mean value gets changed.

(e) After removing the outlier, the data set is;

12, 12, 12, 13, 13, 14, 15, 16, 18.

Now, the mean of the data =  [tex]\frac{12+12+ 12+ 13+ 13+ 14+ 15+ 16+ 18}{9}[/tex]

                                             =  [tex]\frac{125}{9}[/tex]  =  13.89

So, the statement that the mean value stays the same when the outlier is not included in the data set is incorrect.

Answer:

Fredrick’s data set contains an outlier.

The mean value is about 12.6 home runs.

The median describes Fredrick’s data more accurately than the mean.

Step-by-step explanation:

Answer:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 58.33[/tex]

[tex]s= 10.78[/tex]

Then we can fin the limits for one deviation within the mean like this:

[tex]\mu -\sigma = 58.33-10.78= 47.55[/tex]

[tex]\mu -\sigma = 58.33+10.78= 69.11[/tex]

And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:

[tex]\% =\frac{4}{6}*100 =66.7\%[/tex]

Step-by-step explanation:

First we need ot calculate the mean and deviation with the following formulas:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 58.33[/tex]

[tex]s= 10.78[/tex]

Then we can fin the limits for one deviation within the mean like this:

[tex]\mu -\sigma = 58.33-10.78= 47.55[/tex]

[tex]\mu -\sigma = 58.33+10.78= 69.11[/tex]

And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:

[tex]\% =\frac{4}{6}*100 =66.7\%[/tex]

Answer:

y = 2x/3 - 15

Step-by-step explanation:

Step 1: Find slope of perpendicular line

Take the negative reciprocal of the other line

m = 2x/3

Step 2: Rewrite equation (You already found b because it gave you y-int)

y = 2x/3 - 15

Answer: 11/12

Step-by-step explanation:

First find the LCM of 4 and 3(12).  Then make the denominator of both fractions 12(3/12 and 8/12).  Then add the fractions to get that they ate 11/2 of the lasagna.

Hope it helps <3

Answer:

it indicates that it is infinitely many solutions

If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate. For each point (x, y) on the graph, ž is equal to k, where k is the unit rate. The point (1, k) is a point on the graph.

Hope this helps...

Answer:

(c) [tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b) The probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c) The probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Step-by-step explanation:

The random variable X follows a Uniform (25, 35).

(a)

The probability density function of an Uniform distribution is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{B-A};\ A<X<B} \atop {0;\ Otherwise}} \right.[/tex]

Then the probability density function of the random variable X is:

[tex]f_{X}(x)=\left \{ {{\frac{1}{35-25}=\frac{1}{10};\ 25<X<35} \atop {0;\ Otherwise}} \right.[/tex]

(b)

Compute the value of P (X > 33) as follows:

[tex]P(X>33)=\int\limits^{35}_{33} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{35}_{33} {1} \, dx \\\\=\frac{1}{10}\times [x]^{35}_{33}\\\\=\frac{35-33}{10}\\\\=\frac{2}{10}\\\\=0.20[/tex]

Thus, the probability that time taken by Ayesha to prepare breakfast exceeds 33 minutes is 0.20.

(c)

Compute the mean of X as follows:

[tex]\mu=\frac{A+B}{2}=\frac{25+35}{2}=30[/tex]

Compute the probability that cooking or preparation time is within 2 mins of the mean time as follows:

[tex]P(30-2<X<30+2)=P(28<X<32)[/tex]

                                      [tex]=\int\limits^{32}_{28} {\frac{1}{10}} \, dx \\\\=\frac{1}{10}\cdot\int\limits^{32}_{28}{1} \, dx \\\\=\frac{1}{10}\times [x]^{32}_{28}\\\\=\frac{32-28}{10}\\\\=\frac{4}{10}\\\\=0.40[/tex]

Thus, the probability that cooking or preparation time is within 2 mins of the mean time is 0.40.

Answer:

B. because A and B cannot occur at the same time.

Step-by-step explanation:

If two events are mutually​ exclusive, why is ​? Choose the correct answer below.

A. because A and B each have the same probability.

B. because A and B cannot occur at the same time.

C. because A and B are independent.

D. because A and B are complements of each other.

Answer:

[tex]296.693\leq x\leq 319.307[/tex]

Step-by-step explanation:

The confidence interval for the population mean x can be calculated as:

[tex]x'-z_{\alpha /2}\frac{s}{\sqrt{n} } \leq x\leq x'+z_{\alpha /2}\frac{s}{\sqrt{n} }[/tex]

Where x' is the sample mean, s is the population standard deviation, n is the sample size and [tex]z_{\alpha /2}[/tex] is the z-score that let a proportion of [tex]\alpha /2[/tex] on the right tail.

[tex]\alpha[/tex] is calculated as: 100%-99%=1%

So, [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex]

Finally, replacing the values of x' by 308, s by 17, n by 15 and [tex]z_{\alpha /2}[/tex] by 2.576, we get that the confidence interval is:

[tex]308-2.576\frac{17}{\sqrt{15} } \leq x\leq 308+2.576\frac{17}{\sqrt{15} }\\308-11.307 \leq x\leq 308+11.307\\296.693\leq x\leq 319.307[/tex]

Answer:

Use the formula

a

n

=

a

1

r

n

−

1

to identify the geometric sequence.

Step-by-step explanation:

a

n

=

64

4

n

−

1 hope this helps you :)

Answer: The answer is in the steps.

Step-by-step explanation:

f(1)= 64  

f(n)=1/4(n-1)      n in this case is the nth term.

Answer:

Answer is A

Step-by-step explanation:

The equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.

The general equation of a circle is of the form (x - h)² + (y - k)² = r², where (h, k) is the point where the center of the given circle lies, and r is the radius of this given circle.

In the question, we are asked to find the graph from the given options which represents the equation (x - 3)² + (y - 1)² = 9.

Comparing the given equation, (x - 3)² + (y - 1)² = 9, to the general equation, (x - h)² + (y - k)² = r², we can say that h = 3, k = 1, and r = 3.

Thus the center of the given circle lies at the point (3, 1) and its radius is 3 units.

Now we check the options to find the matching circle:

Therefore, the equation (x - 3)² + (y - 1)² = 9, is represented by the second graph as its center is at point (3, 1) and its radius is 3 units, both similar to the equation. Thus, option B is the right choice.

Learn more about circles at

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Answer:

The 20th digit is 6.

Step-by-step explanation:

1. Add 2/9 and 1/7.

2/9 + 1/7 = 23/63

2. Convert to a decimal.

23 ÷ 63 = 0.365079...

If you continue to divide, you will notice that the number repeat. So, the decimal would be 0.365079365079...

3. Find the 20th digit.

0.365079365079365079365079

Answer:

6

Step-by-step explanation:

Aops question

We have $\frac29 + \frac17 = \frac{14}{63} + \frac{9}{63} = \frac{23}{63}$. Expressing $\frac{23}{63}$ as a decimal using long division, we find $\frac{23}{63}=0.\overline{365079}$. Therefore, every 6th digit after the decimal point is a 9. So, the 18th digit is a 9; the 20th digit is 2 decimal places later, so it is a $\boxed{6}$.

It's in Latex

Answer: We have two solutions:

1000 - 998 = 2

1001 - 999 = 2

Step-by-step explanation:

So we have the problem:

****-*** = 2

where each star is a different digit, so in this case, we have a 4 digit number minus a 3 digit number, and the difference is 2.

we know that if we have a number like 99*, we can add a number between 1 and 9 and we will have a 4-digit as a result:

So we could write this as:

1000 - 998 = 2

now, if we add one to each number, the difference will be the same, and the number of digits in each number will remain equal:

1000 - 998 + 1 - 1 = 2

(1000 + 1) - (998 + 1) = 2

1001 - 999 = 2

now, there is a trivial case where we can find other solutions where the digits can be zero, like:

0004 - 0002 = 2

But this is trivial, so we can ignore this case.

Then we have two different solutions.

Answer:

Step-by-step explanation:

Ya que mezclan café colombiano, brasileño, guineano y venezolano en un paquete de un kilo. Igualmente deben agregar los cafés juntos.

Para encontrar la cantidad igual para cada café en 1 kilo, divida 1 kilo y los 4 cafés. Entonces la cantidad sería 1/4 (o 0.25) de café por kilo. La respuesta significa que cada uno de los cuatro cafés pesa 1/4 kilo.

Como cada café representa 1/4 kilo, el café colombiano representa 1/4 kilo.

Si necesita ayuda adicional, comente a continuación.

Answer:

y(x) = (7/25)x^2 + 4

Step-by-step explanation:

Given:

x = 5*sqrt(t) .............(1)

y = 7*t+4 ..................(2)

solution:

square (1) on both sides

x^2 = 25t

solve for t

t = x^2 / 25  .........(3)

substitute (3) in (2)

y = 7*(x^2/25) +4

y= (7/25)x^2 + 4

Answer:

The variance is "9475" and standard deviation is "97.3396112".

Step-by-step explanation:

Let's all make the assumption that X seems to be the discrete uniformly distributed random indicating demand for units, and that f(x) has been the corresponding probability.

The expected value of the monthly demand will be:

⇒  [tex]E(X)=\sum_{x} x\times f(x)[/tex]  

⇒            [tex]=00\times 0.20+400\times 0.30+500\times 0.35+600\times 0.15[/tex]

⇒            [tex]=445 \ units[/tex]

The variance will be:

⇒  [tex]Var(X)=E(X^2)-{E(X)}^2[/tex]

⇒  [tex]E(X^2)=\sum_{x} x^2\times f(x)[/tex]

                [tex]=(300)^2\times 0.20+(400)^2\times 0.30+(500)^2\times 0.35+(600)^2\times 0.15[/tex]

                [tex]=207500[/tex]

⇒  [tex]Var(X)=207500 - (445)^2[/tex]

                  [tex]=9475[/tex]

The standard deviation will be:

⇒  [tex]X=\sqrt{var(X)}[/tex]

         [tex]=97.3396112[/tex]

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

the ways of choosing 2 cards out of 4, is calculator by

[tex] \binom{4}{2} = 6[/tex]

so, 6 ways to select 2 cards.

but in only one way we can have 2 even cards. thus, the answer is

[tex] \frac{1}{6} [/tex]

Answer:

m<2 = 73

Step-by-step explanation:

Since <1 and <2 are complementary (which means that they equal 90), all you have to do is subtract 17 from 90 to find your answer:

90 - 17 = 73

thus, m<2 = 73

Answer:

73

Step-by-step explanation:

Answer:

b. 14

Step by step explanation: