A large company must hire a new president. The Board of Directors prepares a list of five candidates, all of whom are equally qualified. Two of these candidates are members of a minority group. To avoid bias in the selection of the candidate, the company decides to select the president by lottery. a. What is the probability one of the minority candidates is hired?

Answer:

a. 13%

b. 20%

c. 2%

Step-by-step explanation:

The best way to solve this problem is by drawing a Venn diagram.  Draw a rectangle representing all the fourth-graders.  Draw two overlapping circles inside the rectangle.  Let one circle represent proficiency in reading.  This circle is 85% of the total area (including the overlap).  And let the other circle represent proficiency in math.  This circle is 78% of the total area (including the overlap).  The overlap is 65% of the total area.

a. Since the overlap is 65%, and 78% are proficient in math, then the percent of all students who are proficient in math but not reading is the difference:

78% − 65% = 13%

b. Since the overlap is 65%, and 85% are proficient in reading, then the percent of all students who are proficient in reading but not math is the difference:

85% − 65% = 20%

c. The percent of students not proficient in reading or math is 100% minus the percent proficient in only reading minus the percent proficient in only math minus the percent proficient in both.

100% − 20% − 13% − 65% = 2%

See attached illustration (not to scale).

The probability of a student being proficient in mathematics but not in reading is 13%, in reading but not in mathematics is 20%, and in neither reading nor mathematics is 2%.

To solve the student's query, we'll use the principle that the probability of an event is the number of favorable outcomes divided by the total number of outcomes. We can apply the addition rule for probabilities, which states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities, minus the probability of both events happening.

Let P(M) be the probability the student is proficient in mathematics, P(R) be the probability the student is proficient in reading, and P(M & R) be the probability the student is proficient in both. The question asks for P(M) - P(M & R), the probability of being proficient in mathematics but not in reading. That is 78% - 65% = 13%.

Similarly, the probability of a student being proficient in reading but not mathematics is P(R) - P(M & R), which equals 85% - 65% = 20%.

To find the probability of a student being proficient in neither subject, we can find the probability of a student being proficient in at least one subject and then subtracting this from 100%. The probability of being proficient in at least one subject is P(R) + P(M) - P(M & R), or 85% + 78% - 65% = 98%. Thus, the probability of being proficient in neither is 100% - 98% = 2%.

Answer:

Simplest function is f(x) = 2x - 1

Step-by-step explanation:

When a function has a zero, simply put, that point is where the graph goes through the x-axis.  At this point, the y value is 0.

If a function has a 0 of 1/2, that translates to x = 1/2 and also (1/2, 0).  That means that y = 0 when x = 1/2.

If x = 1/2 and is a zero, then x - 1/2 = 0 and 2x - 1 = 0 (notice that y = 0 here and solving for x would get you right back to x = 1/2).

The simplest function with a zero of 1/2 is

f(x) = 2x - 1

You know it is true that the zero is 1/2 for two reasons.  First one is to set the right side equal to 0 and solve for x.

The second one is to graph the line y = 2x - 1 and see that it goes through the x axis at 1/2 where y = 0.

Answer:

No solution. Inconsistent.

Step-by-step explanation:

The equations are

[tex]2x+4y\leq 16\\x\leq 5\\y\leq 2\\x=6[/tex]

As we can see here that x=6 and x<=5 the solution area will not be bounded i.e., there will be no common area.

The lines do not intersect

Therefore there will be no solution.

Plotting the equations we get the graph below.

A strategy to avoid the question would be by just looking at the linear equations. It can be clearly seen that there are two lines that will never intersect and hence will have no solution.

Answer:

(44)₁₆

Step-by-step explanation:

to convert it into hexa decimal we have select four pair of binary digit

(1000100)₂→(?)₁₆

  100  0100

to solve this we have to no the decimal conversion of

0100 which is '4'

so,

conversion of (1000100)₂→(44)₁₆

Answer:

a. A hypothesis test is better

b. confidence interval​ method; and critical value​ method will lead to the same conclusion

Step-by-step explanation:

a. A hypothesis test is better

b. confidence interval​ method; and critical value​ method will lead to the same conclusion

when samples are taken from a population, the mean values of these samples are approximately normally distributed,that is, the mean values forming the sampling distribution of means is approximately normally distributed. It is also true that if the standard deviations of each of the samples is found, then the standard deviations of all the samples are approximately normally distributed, that is, the standard deviations of the sampling distribution of standard deviations are approximately normally distributed.

Parameters such as the mean or the standard deviation of a sampling distribution are called sampling statistics, S.

Final answer:

When comparing two population proportions, a hypothesis test is favored at a 0.01 significance level. The confidence interval and P-value methods are equivalent when assuming equal population proportions.

Explanation:

Hypothesis Test vs. Confidence Interval:

When dealing with inferences for two population proportions, a hypothesis test is better to test the claim that one proportion is less than the other at a 0.01 significance level.

Equivalence of Methods in Statistic Testing:

The confidence interval method and the P-value method are equivalent in that they both rely on assumed equal population proportions to draw conclusions.

Answer:

$3316 should be invested.

Step-by-step explanation:

Since, the amount formula in compound interest is,

[tex]A=P(1+r)^t[/tex]

Where, P is the principal amount,

r is the rate per period,

t is the time in years,

Here,

A = $ 60,000,

r = 10.5% = 0.105

t = 29 years,

By substituting value,

[tex]60000=P(1+0.105)^{29}[/tex]

[tex]P=\frac{60000}{1.105^{29}}=\$3316.23415377\approx \$3316[/tex]

Hence, $ 3316 should be invested.

Before you do anything, you have to find [tex]c[/tex] such that [tex]f_{X,Y}(x,y)[/tex] is a proper joint density function. Doing the math, you'll find that [tex]c=2[/tex].

Now, determine the marginal densities:

[tex]f_X(x)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dy=\int_{-x}^x2(x^2-y^2)e^{-2x}\,\mathrm dy[/tex]

[tex]\implies f_X(x)=\dfrac83x^3e^{-2x}[/tex]

[tex]f_Y(y)=\displaystyle\int_{-\infty}^\infty f_{X,Y}(x,y)\,\mathrm dx=\int_0^\infty2(x^2-y^2)e^{-2x}\,\mathrm dx[/tex]

[tex]\implies f_Y(y)=\dfrac12-y^2[/tex]

a. Then the density of [tex]X[/tex] conditioned on [tex]Y=y[/tex] is

[tex]f_{X\mid Y}(x\mid Y=y)=\dfrac{f_{X,Y}(x,y)}{f_Y(y)}=\dfrac{4(x^2-y^2)e^{-2x}}{1-2y^2}[/tex]

b. The density of [tex]Y[/tex] conditioned on [tex]X=x[/tex] is

[tex]f_{Y\mid X}(y\mid X=x)=\dfrac{f_{X,Y}(x,y)}{f_X(x)}=\dfrac{3(x^2-y^2)}{4x^3}[/tex]

and so the distribution of [tex]Y[/tex] conditioned on [tex]X=x[/tex] is

[tex]F_{Y\mid X}(y\mid X=x)=\displaystyle\int_{-\infty}^uf_{Y\mid X}(y\mid X=x)\,\mathrm du[/tex]

[tex]F_{Y\mid X}(y\mid X=x)=\begin{cases}0&\text{for }y<-x\\\frac{2x^3+3x^2y-y^3}{4x^3}&\text{for }-x\le y\le x\\1&\text{for }y>x\end{cases}[/tex]

To find the conditional probability density of X, given Y=y>0, use Bayes' theorem. To find the conditional probability distribution of Y, given X=x, integrate the joint density over the range of y values.

To find the conditional probability density of X, given Y=y>0, we need to calculate the conditional density fX|Y(x,y). This can be done using Bayes' theorem. First, find the marginal density of Y by integrating the joint density over the range of y values:

fY(y) = ∫f(x,y) dx = c(e^(-2y) - e^(-2y)/3)

Then, use Bayes' theorem to find the conditional density:

fX|Y(x,y) = f(x,y)/fY(y) = 4(x^2-y^2)e^(-2x)/(1-2y^2)

To find the conditional probability distribution of Y, given X=x, we need to calculate the conditional distribution FY|X(y|x). This can be found by integrating the joint density over the range of y values:

FY|X(y|x) = ∫f(x,y) dy = 3/4(x^2-y^2)

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Answer:

Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

  = x(1080 - 138x + 4x²)

  = 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.

[tex]\frac{dV}{dx}=12x^{2}-276x+1080=0[/tex]

12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

The size of the square that should be cut away from each corner to obtain the maximum volume for a box made from a cardboard measuring 45 by 24 inches is 3 inches.

To find the size of the square that should be cut from each corner to obtain the maximum volume, we should first make an equation for the volume of the box. If x is the length of the side of the square, then the dimensions of the box are (45-2x) by (24-2x) by x, thus the volume of the box V is (45-2x)(24-2x)x.

By using calculus, we can find the derivative of this function, set it to zero and solve, this will give the critical points where the maximum and minimum volumes will be.

The derivative is found to be -4x^2 + 138x - 1080. Setting this to zero and solving, we find that x = 3 and x = 90 are the critical points for the maximum and minimum volumes. Since we cannot cut corners more than 24 inches (this would make the width negative), x = 3 inches is the only feasible solution.

So, 3 inches should be cut away from each corner to obtain the maximum volume.

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Step-by-step explanation:

Let's take "a" an element from A, a ⊆ A.

As A ⊆ B, a ⊆ A ⊆ B, so a ⊆ B.

Therefore, a ⊆ B ⊆ Cc, a ⊆ Cc.

Let's remember that Cc is exactly the opposite of C. That means that an element is in C or in Cc; it has to be in one of them but not in both.

As a ⊆ Cc, a ⊄ C.

As we can generalize this for every element of A, there is not element of A that is contained in C.  

Therefore, the intersection (the elements that are in both A and C) is empty.

Answer:

[tex](x-6)^2+(y-2)^2=16[/tex].

Step-by-step explanation:

[tex](x-h)^2+(y-k)^2=r^2[/tex] is the equation for a circle with center (h,k) and radius r.

You are given center (6,2) and radius 4.

So we will replace h with 6 and k with 2 and r with 4.

This gives us:

[tex](x-6)^2+(y-2)^2=4^2[/tex]

Simplify:

[tex](x-6)^2+(y-2)^2=16[/tex].

For this case we have that by definition, the equation of a circle is given by:

[tex](x-h) ^ 2 + (y-k) ^ 2 = r ^ 2[/tex]

Where:

[tex](h, k):[/tex]It is the center of the circle

r: It is the radius of the circle

According to the data we have to:

[tex](h, k) :( 6.2)\\r = 4[/tex]

Substituting:

[tex](x-6) ^ 2 + (y-2) ^ 2 = 4 ^ 2\\(x-6) ^ 2 + (y-2) ^ 2 = 16[/tex]

ANswer:

[tex](x-6) ^ 2 + (y-2) ^ 2 = 16[/tex]

Answer: second option.

Step-by-step explanation:

By definition, the measure of any interior angle of an equilateral triangle is 60 degrees.

Based in this, we know that the measusre of the angle ∠SRT is:

[tex]\angle SRT=\frac{60\°}{2}=30\°[/tex]

The, we can find the value of "y":

[tex]y+12=30\\y=30-12\\y=18[/tex]

To find the value of "x", we must use this identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

In this case:

[tex]\alpha=30\°\\adjacent=x\\hypotenuse=RU=RS=4[/tex]

Substituting values and solving for "x", we get:

[tex]cos(30\°)=\frac{x}{4}\\\\4*cos(30\°)=x\\\\x=\sqrt{12}[/tex]

Answer:

(x,y,z)=(5,0,3)

[tex]((x,y,z)-(2,3,0))*(-1,1,0)=0[/tex]

Step-by-step explanation:

a)

The problem requires to find the intersection point of the lines, at that point the position 'r' of the lines is the same:

[tex]r_{1} =r_{2} \\(2,3,0)+(3,-3,3)t=(5,0,3)+(-3,3,0)s\\[/tex]

First, built the parametric equation system; this is just a simplification coordinate to coordinate of the vector equation:

[tex]2+3t=5-3s\\3-3t=3s\\3t=3[/tex]

From the last equation,

[tex]t=1[/tex]

And for whatever of the other two,

[tex]s=0[/tex]

You can check that replacing t=1 and s=0 the point gotten is (5,0,3), which is the intersection point (the point that belongs to both lines).

b) The plane is defined by an orthogonal direction. The equation of the plane uses the fact that the dot product between two orthogonal vectors is always zero.

The general equation of a plane is:

[tex]((x,y,z)-(x_{0},y_{0},z_{0}))*(n)=0[/tex]

Where (x,y,z) are the variables that may be part of the plane or not, [tex](x_{0},y_{0},z_{0})[/tex] is a point that belongs to the plane and n is a vector which is orthogonal to the plane.

Due that both lines belong to the plane, the cross product between their direction vectors will give us the orthogonal vector.

[tex]n=(3,-3,3)X(-3,3,0)=(-9,-9,0)[/tex]

We can divide (-9,-9,0) by nine, because we only need the direction and the division does not affect it.

[tex]n=(-1,-1,0)[/tex]

Finally, we know that both lines are inside the plane, so any point that belong to a line, belong to the plane. For this reason, let's select any point, for example: (2,3,0) (It could be another). So, the equation of the plane is:

[tex]((x,y,z)-(2,3,0))*(-1,-1,0)=0[/tex]

The intersection point of the lines can be obtained by equating the parametric forms of the lines and finding the values of parameters. The equation of the plane containing these lines can be obtained using the directional vectors of these lines, which essentially define the plane.

First, we need to find the common point at which the given lines intersect. We can do this by setting r = 2, 3, 0 + t 3, −3, 3 and r = 5, 0, 3 + s −3, 3, 0 to be equal, and finding the values of t and s that make this true. This gives us the (x, y, z) coordinates of the intersection point.

To find the equation of the plane that contains these lines, we know that any point on this plane can be expressed as a linear combination of the directional vectors of these lines, which are (3, -3, 3) and (-3, 3, 0). Therefore, the equation of the plane can be written in the form of Ax + By + Cz = D, where (A, B, C) is a normal vector to the plane, and D is a constant that can be determined by substituting the coordinates of any point on the plane.

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Give me robux on robloz

Step-by-step explanation:

.........sd.....

Answer:

g(2y) = 8y^2 -3

Step-by-step explanation:

g(x)=2 x^2   -3

Let x=2y

g(2y) = 2 (2y)^2 -3

         = 2 (4y^2)  -3

         = 8y^2 -3

Answer:

27 degrees

Step-by-step explanation:

The standard deviation means it can be up or down by that many degrees. The temperatures can be between 20-28 degrees. 27 degrees is the only option in this set of numbers.

Answer:

your answer is C 27

Step-by-step explanation:

Answer:

44.72 Vanilla

24.08 Chocolate

Step-by-step explanation:

26% of 172 choose vanilla

14% of 172 choose chocolate

Answer:

see attachment

Step-by-step explanation:

The nurse will set the infusion of oxytocin at approximately 117 mL/hr.

To calculate the rate at which the nurse will set the infusion of oxytocin, we can use the formula:

Rate (mL/hr) = (Order dose × Volume ÷ Time)

Substituting the given values:

After calculating, we find that the nurse will set the infusion at approximately 117 mL/hr.

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Answer:

Total deposit in each month is $ 932.84

Step-by-step explanation:

Step 1:  Monthly interest rate.

Monthly Rate = (1+annual rate)112−1

we have  Annual rate = 3.5%

Monthly Rate = (1+0.035)112−1 = 0.0028709

Step 2:  monthly payment

Monthly payment can be determined by using below formula:

A=P×i×1−(1+i)−n

A = monthly payment amount

P = total pay amount

i = monthly interest rate

n = total number of payments

In this example we have

P=$150000 ,

i=0.0028709  and

n=12×18=216

Monthly payment = P×i×1−(1+i)−n

= 150000×0.00287091−(1+0.0028709)−216 = 430.6351−(1.0028709)−216

Monthly payment  =$ 932.84

To have $150,000 in 18 years with a 3.5% APR compounded monthly, you need to deposit approximately $499.58 each month. The formula for the future value of an annuity and the power of compound interest are key to understanding how regular savings can grow over time.

To determine how much you have to deposit each month to have $150,000 in 18 years with an account paying 3.5% APR, you'll need to use the formula for the future value of an annuity. The future value of an annuity formula is:

Future Value = [tex]Pmt * ((1 + r/n)^{(nt)} - 1) / (r/n)[/tex]

where:

Pmt = monthly payment

r = annual interest rate (decimal)

n = number of times the interest is compounded per year

t = number of years.

First, convert the APR to a monthly interest rate by dividing by 12, since there are 12 months in a year. The monthly interest rate is 0.035 / 12. The interest is compounded monthly, so n is 12. Let's solve for Pmt (monthly deposit) using the formula:

[tex]150,000 = Pmt * ((1 + 0.035/12)^{(12*18)} - 1) / (0.035/12)[/tex]

By using a financial calculator or algebra, you can find the monthly deposit required:

Pmt ≈ $499.58

Therefore, you would need to deposit approximately $499.58 each month into your savings account to have $150,000 in 18 years.

It's important to start saving money early and to let the power of compound interest work in your favor, as seen in the provided examples where initial investments grow significantly over time due to compound interest.

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Answer:

(2,0)

Step-by-step explanation:

The solution of the inequality [tex]y>-3x+2[/tex] is shown in attached diagram.

The boundary line is dotted line, because the sign of inequality is without notion "or equal to". The dotted line means that points lying on this line are not solutions of the inequality. The solutions are those points lying in the shaded region.

From the points (0,2), (2,0), (1,-2), (-2,1) only point (2,0) lies on the shaded region, so only point (2,0) is a solution to the inequality

Answer:

on ed it says its B

Step-by-step expla

Hence, we have:

[tex]proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}][/tex]

By the orthogonal decomposition theorem we have:

The orthogonal projection of a vector v onto the subspace W=span{w,w'} is given by:

[tex]proj_W(v)=(\dfrac{v\cdot w}{w\cdot w})w+(\dfrac{v\cdot w'}{w'\cdot w'})w'[/tex]

Here we have:

[tex]v=[19,12,14,-17]\\\\w=[-4,-1,-1,3]\\\\w'=[1,-4,4,3][/tex]

Now,

[tex]v\cdot w=[19,12,14,-17]\cdot [-4,-1,-1,3]\\\\i.e.\\\\v\cdot w=19\times -4+12\times -1+14\times -1+-17\times 3\\\\i.e.\\\\v\cdot w=-76-12-14-51=-153[/tex]

[tex]w\cdot w=[-4,-1,-1,3]\cdot [-4,-1,-1,3]\\\\i.e.\\\\w\cdot w=(-4)^2+(-1)^2+(-1)^2+3^2\\\\i.e.\\\\w\cdot w=16+1+1+9\\\\i.e.\\\\w\cdot w=27[/tex]

and

[tex]v\cdot w'=[19,12,14,-17]\cdot [1,-4,4,3]\\\\i.e.\\\\v\cdot w'=19\times 1+12\times (-4)+14\times 4+(-17)\times 3\\\\i.e.\\\\v\cdot w'=19-48+56-51\\\\i.e.\\\\v\cdot w'=-24[/tex]

[tex]w'\cdot w'=[1,-4,4,3]\cdot [1,-4,4,3]\\\\i.e.\\\\w'\cdot w'=(1)^2+(-4)^2+(4)^2+(3)^2\\\\i.e.\\\\w'\cdot w'=1+16+16+9\\\\i.e.\\\\w'\cdot w'=42[/tex]

Hence, we have:

[tex]proj_W(v)=(\dfrac{-153}{27})[-4,-1,-1,3]+(\dfrac{-24}{42})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=\dfrac{-17}{3}[-4,-1,-1,3]+(\dfrac{-4}{7})[1,-4,4,3]\\\\i.e.\\\\proj_W(v)=[\dfrac{68}{3},\dfrac{17}{3},\dfrac{17}{3},-17]+[\dfrac{-4}{7},\dfrac{16}{7},\dfrac{-16}{7},\dfrac{-12}{7}]\\\\i.e.\\\\proj_W(v)=[\dfrac{464}{21},\dfrac{167}{21},\dfrac{71}{21},\dfrac{-131}{7}][/tex]

Final answer:

The true probability of Cody winning at least one more soda is approximately 0.67.

Explanation:

Cody buys six sodas, each with a 1/6 probability of winning another soda. To find the probability of winning at least one more soda, we need to find the probability of not winning any sodas and subtract it from 1. The probability of not winning a soda with each individual purchase is 5/6. Since the purchases are independent events, we can multiply the probabilities together to find the probability of not winning any sodas in all six purchases: (5/6) * (5/6) * (5/6) * (5/6) * (5/6) * (5/6) = (5/6)⁶ = 0.3349. Finally, we subtract this probability from 1 to find the probability of winning at least one more soda: 1 - 0.3349 = 0.6651 (rounded to the nearest hundredth).

Answer:

expected value of x  is 1 and standard deviation of x is 0.7071

Step-by-step explanation:

Given data

coin flip = 40 time

heads noted

to find out

the expected value and the standard deviation

Solution

we know coin is flipped 40 times and the number of heads is noted only

so we find standard deviation for x i.e.

standard deviation of  x = [tex]\sqrt{variance x}[/tex]   .......1

first we calculate variance x .i.e.

variance x = expected value of x² - (expected value of x)²   .............2

so now we calculate expected value of x

we know when x = 0 , p(x) = 1/4

x = 1 , p(x) = 1/2

x = 2 , p(x) = 1/4

so  expected value of x  =  [tex]\sum_{0}^{2}[/tex] x p(x)

i.e.   expected value of x  =  0 P(x) + 1 p(x) + 2 p(x)

expected value of x  = 0 (1/4) + 1 (1/2) + 2 (1/4)

expected value of x  =  0  +  (1/2) + (1/2)

expected value of x  =    1             ....................3

now calculate expected value of x²

so so  expected value of x²  =  [tex]\sum_{0}^{2}[/tex] x²p(x)

i.e.  expected value of x²  =   x² P(x) + 1² p(x) + 2² p(x)

expected value of x²  =    0 (1/4) + 1 (1/2) + 4 (1/4)

expected value of x² =   0  +  (1/2) + (1)

expected value of x²  = 1.5         .........................4

now put equation 3 and 4 value in equation 2 we get

variance x =  expected value of x² - (expected value of x)²

variance x =  1.5 - (1)²

variance x =  0.5

now put variance value in equation 1 we get

standard deviation of  x = [tex]\sqrt{variance x}[/tex]  

standard deviation of  x = [tex]\sqrt{0.5}[/tex]  

standard deviation of  x = 0.7071

so standard deviation of x is 0.7071

The expected value is 20 and the standard deviation is 3.16

The expected value

The given parameters are:

n = 40 ---- the number of flips

p = 0.5 --- the probability of obtaining a head

The expected value is calculated as:

[tex]E(x) = np[/tex]

This gives

[tex]E(x) = 40 * 0.5[/tex]

[tex]E(x) = 20[/tex]

Hence, the expected value is 20

The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

So, we have:

[tex]\sigma = \sqrt{40 * 0.5 * (1 - 0.5)[/tex]

[tex]\sigma = 3.16[/tex]

Hence, the standard deviation is 3.16

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The answer is:

The only value of "x" that IS NOT in the domain of the function h,  is -3.

Since we are working with a quotient (or division), we must remember that the only restriction for this kind of functions are the values that make the denominator equal to 0, so, the domain of the function will include all the values of "x" that are different than the zeroes or roots of the denominator.

We have the function:

[tex]h(x)=\frac{x^2-5x-24}{x^2+6x+9}[/tex]

Where its denominator is :

[tex]x^2+6x+9[/tex]

Now, finding the roots or zeroes of the expression, by factoring, we have:

We need to find two numbers which product is equal to 9 and its addition is equal to 6, that number will be the same for both conditions (3):

[tex]3*3=9\\3+3=6[/tex]

So, the factorized form of the expression will be:

[tex](x+3)^2[/tex]

We have that the expression will be equal to 0 if "x" is equal to "-3", so, the only value of x that IS NOT in the domain of the function h,  is -3.

Hence, the domain will be:

Domain: (-∞,-3)U(-3,∞)

Have a nice day!

Final answer:

The only value that is not in the domain of the function h(x) is x = -3, since it makes the denominator of the function equal to zero, thus making the function undefined.

Explanation:

To determine the values that are not in the domain of the function h(x) = x² - 5x - 24}{x² + 6x +9}, we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined. To do this, we will factor the denominator and find its roots.

First, let's factor the denominator:

x² +6x + 9 = (x + 3)(x + 3)

Now, we set the factored denominator equal to zero to find the values of x that are not in the domain:

(x + 3)(x + 3) = 0

This equation has one distinct root, x = -3.

Therefore, the only value that is not in the domain of h is x = -3. If you substitute x = -3 into the original function, the denominator becomes zero, and the function is undefined.

Explained the mean, median, and standard deviation for a sample of CFOs' salaries in the electronics industry.

Mean: To find the mean, you add up all the salaries and divide by the number of salaries. For the CFOs, the mean salary is $544,773.

Median: To find the median, you arrange the salaries in order and find the middle value. For the CFOs, the median salary is $546,000.

Standard Deviation: The standard deviation measures the dispersion of data. For the CFOs, you can calculate it using the given formula to be approximately $29,534.

Answer:

The null hypothesis can't be rejected.

Step-by-step explanation:

Given information:

Null hypothesis:

H₀ : π ≤ 0.70

Alternative hypothesis:

H₁ : π > 0.70

We need to check whether the null hypothesis is rejected or accepted.

If P-value < α, then we reject the null hypothesis H₀.

If P-value ≥ α, then we accept the null hypothesis H₀.

A sample of 100 observations revealed that p = 0.75 at the 0.05 significance level.

Here 0.75>0.05, it means p > α, therefore we can not reject the null hypothesis.

Final answer:

Explaining the rejection of a null hypothesis at a 0.05 significance level based on a sample proportion of 0.75.

Explanation:

The question:
The hypotheses given are H0: π ≤ 0.70 and H1: π > 0.70. A sample of 100 observations resulted in p = 0.75. At the 0.05 significance level, can the null hypothesis be rejected?

Step 1: Calculate the z-score for the given sample proportion.

Step 2: Find the p-value associated with the z-score.

Step 3: Compare the p-value to the significance level α (0.05) to decide whether to reject the null hypothesis or not.

Conclusion:
At the 0.05 significance level, the null hypothesis can be rejected because the p-value is less than 0.05, indicating sufficient evidence to conclude that the proportion is indeed greater than 0.70.

Answer:

This example illustrates Homeostasis.

Step-by-step explanation:

Consider the provided information.

On a very hot summer day and a few months later on a very cold winter day, you go outside and take your temperature. Each time your body temperature is 37 degrees Celsius that means your body's tissues, and cells helps you to attain the stability and constancy required for proper functioning.

The medical definition of Homeostasis is:

Homeostasis is a property of tissues, and cells that helps the stability and constancy required for proper functioning to be maintained and regulated. it is a state maintained through the continuous adjustment of biochemical and physiological processes.

The provided example explain the process of Homeostasis.

Thus, this example illustrates Homeostasis.

Final answer:

The unchanging body temperature of 37 degrees Celsius in both hot and cold external conditions exemplifies thermoregulation, the body's ability to maintain a constant internal temperature through homeostasis.

Explanation:

The scenario of your body temperature remaining constant at 37 degrees Celsius, regardless of whether it is a hot summer day or a cold winter day, illustrates the concept of thermoregulation. Thermoregulation is the ability of an organism to keep its body temperature within certain boundaries, even when the surrounding temperature is very different.

Your body does this through negative feedback mechanisms similar to a thermostat in a house. For example, on a hot day, if your body temperature rises, your skin produces sweat and the blood vessels near your skin's surface dilate to release heat and cool you down. Conversely, in cold weather, the blood vessels constrict, and shivering generates heat to maintain your body temperature. This constant adjustment keeps your body's core temperature steady, enabling the efficient functioning of enzymes and bodily processes that are optimized for a temperature of around 37 degrees Celsius.

This biological thermostat works continuously to keep internal conditions stable, a state known as homeostasis. In physiological terms, about 60 percent of the energy generated from the production of ATP (adenosine triphosphate) by your cells is released in the form of heat, contributing to the maintenance of your body temperature.

Answer:

68 chickens and 12 cows.

Step-by-step explanation:

Let x represents the number of chicken and y represents the number of cows in the barnyard,

Given,

Total heads = 80

⇒ x + y = 80 ------(1),

Also, total legs = 184,

Since, a chicken has two legs and cow has 4 legs,

⇒ 2x + 4y = 184 -----(2),

Equation (2) - 2 × equation (1),

We get,

4y - 2y = 184 - 160

2y = 24

y = 12

From equation (1),

x + 12 = 80 ⇒ x = 80 - 12 = 68

Hence, the number of chicken = 68,

And, the number of cows = 12

Answer:

Is correct.

Step-by-step explanation:

If you don't write the n and t in the left part of the set (before the : ) we assume that are fixed.

(t, infinity) = {[tex]x \in \mathbb{R} : t<x<\infty, t\in \mathbb{R}[/tex]}

(0,1/n) =  {[tex]x \in \mathbb{R} : 0<x<\frac{1}{n}, n\in \mathbb{N}[/tex]}

Answer:  The required probability of event B is P(B) = 0.37.

Step-by-step explanation:  For two events A and B, we are given the following probabilities :

P(A) = 0.34,    P(A ∩ B) = 0.27   and   P(A ∪ B) = 0.44.

We are to find the probability of event B, P(B) = ?

From the laws of probability, we have

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow 0.44=0.34+P(B)-0.27\\\\\Rightarrow 0.44=0.07+P(B)\\\\\Rightarrow P(B)=0.44-0.07\\\\\Rightarrow P(B)=0.37.[/tex]

Thus, the required probability of event B is P(B) = 0.37.

Answer:

[tex] y=\frac{C}{x}[/tex].

Step-by-step explanation:

Given homogeneous equation

[tex] x^2ydy+xy^2dx=0[/tex]

[tex]\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{xy^2}{x^2y}[/tex]

Substitute y=ux , [tex]u=\frac{y}{x}[/tex]

[tex] \frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{y}{x}[/tex]

Now,

[tex]u+x\frac{\mathrm{d}u}{\mathrm{d}x}=\frac{\mathrm{d}y}{\mathrm{d}x}[/tex]

[tex]u+x\frac{\mathrm{d}u}{\mathrm{d}x}=-u[/tex]

[tex]\frac{\mathrm{d}u}{\mathrm{d}x}=-2u[/tex]

[tex]\frac{du}{u}=-\frac{dx}{x}[/tex]

Integrating both side we get

lnu=-2lnx+lnC

Where lnC= integration constant

[tex]lnu+ln{x}^2=lnC[/tex]

[tex]lnux^2=lnC[/tex]

Cancel ln on both side

[tex]ux^2=C[/tex]

Substitute [tex]u=\frac{y}{x}[/tex]

Then we get

xy=C

[tex]y=\frac{C}{x}[/tex].

Answer:[tex]y=\frac{C}{x}[/tex].