find two complex numbers whose sum is 12 and whose product is 37.​

Answer:

The impact on the objective function is that it is increased by 50.

Step-by-step explanation:

In this case we have that the value of the objective function is 150, and they tell us that 10 more units of resource one are added, but they tell us that the shadow price ranges from 1 to 5, therefore:

10 * 5 = 50

Which means that the impact on the objective function is that it is increased by 50.

Answer:

1234567891234567890

Answer: 25 years

Step-by-step explanation:

t = I / Pr

t = 5700 / ( 3800 × 0.06 ) = 25

t = 25 years

Step-by-step explanation:

might be option c is a correct answer of your given question

Answer:

it indicates that it is infinitely many solutions

the answer is the bottom left option

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:

B ). IF = IT

Step-by-step explanation:

IG is perpendicular to FT, means that the line IG divides the line FT into two equal parts without remainder.

Line IG does not only divide line FT, it also bisect the arc FT into two equally parts also.

It also divide the segment of the circle FIT into two equal parts.

So to the correct answer to the question, IF = IT

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:

(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:

true

Step-by-step explanation:

it is so because they are brother and sister

And in the chapter there is that they had farm with a new barn

if in your book lesson there is that they had no farm with a new barn then there will be false

Now did you understood?

Answer:

True

Step-by-step explanation:

Answer:

9/49

Step-by-step explanation:

The probability of landing on an even number is 3/7.

Because there are only 3 numbers even out of 7 total numbers.

[tex]3/7 \times 3/7[/tex]

[tex]= 9/49[/tex]

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:

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:

the greatest common factor of this is 3

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:

a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.

b. [tex]M =0.60x[/tex]

c. $43.2

d. $1416.67

Step-by-step explanation:

Given that:

The World Issues club donates 60% of the total of their fundraising activities.

Answer a.

Let us choose the variable [tex]x[/tex] to represent the money earned during fundraising activities and [tex]M[/tex] for the revenue generated for foundation.

Answer b.

Foundation will receive 60% of the total of the fundraising activities.

Equation to determine the money that will be received by foundation:

[tex]M = 60\%\ of\ x\\OR\\M = 0.6x[/tex]

Answer c.

Given that x = $72, M = ?

Putting the value of x in the equation above:

[tex]M = 0.6 \times 72\\\Rightarrow \$43.2[/tex]

Answer d.

Given that M = $850, x = ?

Putting the value of M in the equation above to find x:

[tex]850= 0.6 \times x\\\Rightarrow x = \dfrac{850}{0.6}\\\Rightarrow x = \$ 1416.67[/tex]

So, the answers are:

a. Let the variable be [tex]x[/tex] for the fundraising activities and [tex]M[/tex] as the revenue for foundation.

b. [tex]M =0.60x[/tex]

c. $43.2

d. $1416.67

Answer:

85

Step-by-step explanation:

im new↑∵∴∵∴∞

Answer:

1/17

Step-by-step explanation:

There are 13 diamond cards in a standard 52-card deck.

First drawing:

13 diamonds

52 total cards

After the first drawing you already took a diamond, so there are 12 diamonds left out of 51 total cards.

p(diamond and diamond) = 13/52 * 12/51 = 1/4 * 4/17 = 1/17

Answer:

1 1/2 > - 4 1/2  and                                                                                                      Manuela scored more points against the Canada Moose than against the China Dragons.

Answer:

the answer is integers if helpful please give 5 star

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:

[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:

(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:

12.566370614359172953850573533118

Step-by-step explanation:

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:

0.181818

Step-by-step explanation:

There are total 11 candies. The possibility of combinations is 165 which is found by using computation technique 11C3. It is assumed that order does not matter. There are 3 pieces of candy are selected at random. There are 6C2 which is 15 different ways to select cherry and lemon. There are 30 ways to choose 2 cherry and a lemon combination. The probability is [tex]\frac{30}{165}[/tex] = 0.181818

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: 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:

[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:

4x^3 + 2x^2 +8x -9

Step-by-step explanation:

A third degree polynomial is a  is a polynomial whose highest power of x is to the power of three.  Standard form is

Ax^3 + Bx^2 + Cx + D where A is non zero

An example would be

4x^3 + 2x^2 +8x -9