In a class of 10 boys and 12 girls, a committee of 4 members is to be formed. What is the probability to form a committee consisting of 2 boys and 2 girls?0.30400.40600.50600.2060

Answers

Answer 1

Consider all the different possible combinations of 4 members of the committee (b,b,b,b), (b,b,b,g),...(g,g,g,g). We need to use the binomial distribution given below

[tex]P(k)=(nbinomialk)p^k(1-p)^{n-k}[/tex]

In our case

[tex]k=2,n=4,p=\frac{10}{10+12}=\frac{10}{22}=\frac{5}{11}[/tex]

Then,

[tex]\begin{gathered} P(2)=(\frac{4!}{2!(4-2)!})(\frac{5}{11})^2(\frac{6}{11})^2 \\ \Rightarrow P(2)=6\cdot\frac{900}{14641} \\ \Rightarrow P(2)=0. \end{gathered}[/tex]


Related Questions

Find the time it would take for the general level of prices in the economy to double at an average annual inflation rate of 4%. The doubling time is aboutyears.

Answers

The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.

What is the doubling time?

Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.

The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.

The rule of 72 = 72 / inflation rate

72 / 4 = 18 years

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Clark and Lindsay Banks have agreed to purchase a home for $225,000. They made a down payment of 15%. They have obtained a mortgage loan at a 6.5% annual interest rate for 25 years. What is the mortgage total if they finance the closing costs?

Answers

SOLUTION

We will be using the annual compound interest formula to solve this question.

[tex]\begin{gathered} A=P(1+\frac{R}{100})^{mn} \\ \text{where m=1, n=25years, R=6.5,} \end{gathered}[/tex]

After a down payment of 0.15 x $225,000 = $33750

The principal value will be $225,000 - $33750 = $191250

Put all these values into the compound interest formula above,

we will have:

[tex]\begin{gathered} A=191250(1+\frac{6.5}{100})^{1\times25} \\ A=191250(1+0.065)^{25} \end{gathered}[/tex][tex]\begin{gathered} A=191250(1.065)^{25} \\ \text{ = 191250}\times4.8277 \\ \text{ =923,297.63} \end{gathered}[/tex]

The mortgage total if they finance the closing costs will be:

$923,297.63

Is y-x+wz=5 linear? And not, why and if so, can you put it in slope intercept form?

Answers

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of this kind of equation is given by:

[tex]Ax+By=C[/tex]

For the equation:

[tex]y-x+wz=5[/tex]

We can conclude is not a linear equation since there is a product between two variables.

please help me with this. four potential solutions.450, 780, 647, 354

Answers

So first of all let's take:

[tex]x_1=x\text{ and }x_2=y[/tex]

Then we get:

[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ x+y\ge300 \\ 2x+y\ge400 \\ 2x+5y\leq750 \\ x,y\ge0 \end{gathered}[/tex]

The next step would be operate with the inequalities and the equation so we end up having only the term y at the left side of each:

[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ 1.5x+2y=\text{Min}z \\ 2y=\text{Min}z-1.5x \\ y=\frac{\text{Min}z}{2}-0.75x \end{gathered}[/tex][tex]\begin{gathered} x+y\ge300 \\ y\ge300-x \end{gathered}[/tex][tex]\begin{gathered} 2x+y\ge400 \\ y\ge400-2x \end{gathered}[/tex][tex]\begin{gathered} 2x+5y\leq750 \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]

So now we have the following inequalities and equality:

[tex]\begin{gathered} y=\frac{\text{Min}z}{2}-0.75x \\ y\ge300-x \\ y\ge400-2x \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]

If we take the three inequalities and replace their symbols by "=' we'll have three equations of a line:

[tex]\begin{gathered} y=300-x \\ y=400-2x \\ y=150-\frac{2}{5}x \end{gathered}[/tex]

The following step is graphing these three lines and delimitating a zone in the grid that meets the inequalities:

Where the blue area is under the graph of y=150-(2/5)x which means that it meets:

[tex]y\leq150-\frac{2}{5}x[/tex]

And it is also above the x-axis, y=400-2x and y=300-x which means that it also meets:

[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ y\ge400-2x \\ y\ge300-x \end{gathered}[/tex]

All of this means that the values of x and y that give us the correct minimum of z are given by the coordinates of a point inside the blue area. The next thing to do is take the four possible values for Min(z) and use them to graph four lines using this equation:

[tex]y=\frac{\text{Min}z}{2}-0.75x[/tex]

Then we have four equations of a line:

[tex]\begin{gathered} y=\frac{450}{2}-0.75x \\ y=\frac{780}{2}-0.75x \\ y=\frac{647}{2}-0.75x \\ y=\frac{354}{2}-0.75x \end{gathered}[/tex]

The line that has more points inside the blue area is the one made with the closest value to Min(z). Then we have the following graph:

As you can see there are two lines that have points inside the blue area. These are:

[tex]\begin{gathered} y=-\frac{3}{4}x+\frac{450}{2} \\ y=-\frac{3}{4}x+\frac{354}{2} \end{gathered}[/tex]

That where made using:

[tex]\begin{gathered} \text{Min }z=450 \\ \text{Min }z=354 \end{gathered}[/tex]

Taking a closer look you can see that the part of the orange line inside the blue area is larger than that of the red line. Then the value used to make the orange line would be a better aproximation for the Min z. The orange line is -(3/4)x+450/2 which means that the answer to this problem is the first option, 450.

lily ordered a set of green and brown pin.she received 35 pins, and 80% of them were green.How many green pins did lily receive?

Answers

In total there are 35 pins so that correspound to the 100%, so we can use a rule of 3 to solve it so:

[tex]\begin{gathered} 35\to100 \\ x\to80 \end{gathered}[/tex]

So the equation is:

[tex]x=\frac{35\cdot80}{100}=28[/tex]

So there are 28 green pins

The sum of two numbers is ten. One number is
twenty less than four times the other. Find the
numbers.
Note: List numbers with a comma separating
them, e.g. 5, 12.

Answers

By solving the equations, we can conclude that the two numbers are 4 and 6.

What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.

So, the two numbers are:

Let the 2nd number be 'x'.Then, the 1st number will be '4x - 20'.

The equation will be:

4x - 20 + x = 10

Now, solve this equation for 'x' as follows:

4x - 20 + x = 105x = 10 + 205x = 30x = 6

Now, 4x - 20:

4(6) - 2024 - 204

Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.

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Quadrilateral PQRS is plotted in the coordinate plane. The quadrilateral is dilated by a scale factor of 3/4. What are the new ordered pairs for P'Q'R'S'?

Answers

Explanation:

The first thing is to state the coordinates of Quadrilateral PQRS

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

Then we find the distance between two points using the distance formula

[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex][tex]\begin{gathered} P(5,5),Q(3,5)\text{ = (x1, y1) and (x2, y2)} \\ \text{distance PQ = }\sqrt[]{(5-5)^2+(3-5)^2}\text{ = }\sqrt[]{0+(-2)^2}\text{ =}\sqrt[]{4} \\ \text{distance PQ = }2 \end{gathered}[/tex][tex]\begin{gathered} Q(3,5),R(3,1)\text{= (x1, y1) and (x2, y2)} \\ \text{distance QR = }\sqrt[]{(1-5)^2+(3-3)^2}\text{ = }\sqrt[]{(-4)^2+0}\text{ = }\sqrt[]{16} \\ \text{distance QR = 4} \end{gathered}[/tex]

It is a quadrilateral, meaning the two lengths are equal. Like wise the two widths are equal.

length PQ = length SR = 2

Length QR = length PS = 4

Scale factor = 3/4

Scale factor = corresponding side of new image/ corresponding side of original image

PQRS = original image, P'Q'R'S' = new image

3/4 = P'Q'/PQ

3/4 = P'Q'/2

P'Q' = 2(3/4) = 6/4 = 3/2

Since P'Q' = S'R'

S'R' = 3/2

3/4 = Q'R'/QR

3/4 = Q'R'/4

Q'R' = 3/4 (4) = 12/4 = 3

Since Q'R' = P'S

P (5, 5), Q (3, 5), R (3, 1), S (5, 1)

PQRS to P'Q'R'S' = 3/4(

P' = 3/4 (5, 5) = (15/4, 15/4)

Q' = 3/4 (3, 5) = (9/4, 15/4)

R' = 3/4 (3, 1) = (9/4, 3/4)

S' = 3/4 (5, 1)

1 point Esther thinks she understands how to find the midpoint of a segment on a graph. "I always look for the middle of the line segment. But what should I do if the coordinates are not easy to graph?" she asks. Find the midpoint of KL if (2.125) and L(98, 15). *

Answers

[tex]\begin{gathered} \text{ Given two points, on a graph} \\ (x_1,y_1)\text{ and }(x_{2,}y_2)\text{ then the} \end{gathered}[/tex][tex]\begin{gathered} \text{coordinate of the mid-point }(x_m,y_m)\text{ is given by} \\ x_m=\frac{x_1+x_2}{2},y_m=\frac{y_1+y_2}{2} \end{gathered}[/tex]

In this case, we can write out the parameters

[tex]\begin{gathered} x_1=2,_{}y_1=125, \\ x_2=98,y_2=15 \end{gathered}[/tex]

Thus, substitute the coordinates in the mid-point formula and simplify

[tex]\begin{gathered} x_m=\frac{98+2}{2}=\frac{100}{2}=50 \\ y_m=\frac{125+15}{2}=\frac{140}{2}=70 \end{gathered}[/tex]

Hence, the coordinate of the mid-point is (50, 70)

Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.

Answers

we have

then find c

[tex]\begin{gathered} c^2=3^2+9^2 \\ c^2=9+81 \\ c^2=90 \\ c=\sqrt[]{90} \\ c=3\sqrt[]{10} \end{gathered}[/tex]

therefore the distance is:

[tex]9+3\sqrt[]{10}+3=21.5[/tex]

answer: 21.5 ft

Multiply.(2x + 4)(2x - 4)A. 4x2 + 16x- 16B. 4x2 - 16C. 4x2 - 16x - 16D. 4x2 + 16

Answers

We have to multiply the expression (2x + 4)(2x - 4):

[tex]\begin{gathered} \left(2x+4\right)\left(2x-4\right) \\ 2x\cdot2x+2x\cdot(-4)+4\cdot2x+4\cdot(-4) \\ 4x^2-8x+8x-16 \\ 4x^2+(8-8)x-16 \\ 4x^2-16 \end{gathered}[/tex]

The answer is:

B. 4x^2 - 16

A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?

Answers

[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ Rise:1 ft, Run: 20ft} \end{gathered}[/tex]

a) Since the grade is given by the slope, and the grade has a 5%.

We can rewrite it as a fraction, like this:

[tex]\frac{5}{100}=\frac{1}{20}[/tex]

Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5

So, the slope is:

[tex]\frac{1}{20}[/tex]

b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1}{20}[/tex]

So the "rise" for this grade is 1 foot and the run is 20 feet.

3) Hence, the answers are:

[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}[/tex]

I got 4089 for the answer but it was incorrect

Answers

Let A be the event "person under 18" and B be the event "employed part-time". So, we need to find the following probability

[tex]P(A\text{ or B) =P(A}\cup B)[/tex]

which is given by

[tex]P(A\text{ or B) =P(A}\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Since the total number od people in the table is equal to n=4089, we have that

[tex]P(A)=\frac{28+174+395}{4089}=\frac{597}{4089}[/tex]

and

[tex]P(B)=\frac{174+194+71+179+173}{4089}=\frac{791}{{4089}}[/tex]

and

[tex]P(A\cap B)=\frac{174}{4089}[/tex]

we have that

[tex]P(A\text{ or B) =}\frac{597}{4089}+\frac{791}{{4089}}-\frac{174}{4089}[/tex]

which gives

[tex]P(A\text{ or B) =}\frac{597+791-174}{4089}=\frac{1214}{4089}=0.29689[/tex]

Therefore, the answer the searched probability is: 0.296

You play a game where you toss a die. If the die lands on a 6, you win $6. It costs $2 toplay. Construct a probability distribution for your earnings. Find your expected earnings.

Answers

SOLUTION

Now from the question, if the die lands on 6, I win $6. So probability of landing on 6 is

[tex]\frac{1}{6}\text{ since a die has 6 faces }[/tex]

Since I will pay $2 to play, we subtract this from $6 that we will win.

And probability of losing becomes

[tex]\frac{5}{6}\text{ }[/tex]

The table becomes

From the table the expected earnings is calculated as

[tex]\begin{gathered} E=\sum_^xP(x) \\ =4(\frac{1}{6})-2(\frac{5}{6}) \\ =\frac{4}{6}-\frac{10}{6} \\ =-\frac{6}{6} \\ =-1 \end{gathered}[/tex]

Hence expected earnings is -$1

Dr Taylor just started an experiment he will collect data for 5 days how many hours is this

Answers

In one day the total number of hours is 24 hours.

So, in 5 days the number of hours is,

[tex]24\times5=120\text{ hours}[/tex]

So, the required number of hours is 120 hours.

Read the following scenario and write two equations we could use to solve to find for the number of cars and trucks washed. Use the variables C for cars washed and T for trucks washed. (Hint: both equations should have T and C). SCENARIO: Western's eSports Team raised money for charity by organizing a car wash. They washed a total of 80 vehicles and raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.

Answers

Let:

C = Number of cars washed

T = Number of trucks washed

They washed a total of 80 vehicles, so:

[tex]C+T=80[/tex]

They raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.​ so:

[tex]5C+7T=486[/tex]

Let:

[tex]\begin{gathered} C+T=80_{\text{ }}(1) \\ 5C+7T=486_{\text{ }}(2) \end{gathered}[/tex]

From (1) solve for T:

[tex]T=80-C_{\text{ }}(3)[/tex]

Replace (3) into (2):

[tex]\begin{gathered} 5C+7(80-C)=486 \\ 5C+560-7C=486 \\ -2C=486-560 \\ -2C=-74 \\ C=\frac{-74}{-2} \\ C=37 \end{gathered}[/tex]

Replace the value of C into (3):

[tex]\begin{gathered} T=80-37 \\ T=43 \end{gathered}[/tex]

They washed 37 cars and 43 trucks

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x  and  "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .

In the question ;

it is given that

the inequality -3(2x-5)<5(2-x)

on solving this inequality further , we get

-3(2x-5)<5(2-x)

-6x+15<10-5x

which is option (c) .

Further solving

Subtracting 15 from both the sides of the inequality  , we get

-6x + 15 -15 < 10 -5x -15

-6x < -5 -5x

-6x +5x < -5

-x < -5

multiplying both sides by (-1) ,

we get

x > 5 .

x> 5 on number line means  an open circle is at 5 and a bold line starts at 5 and is pointing to the right .

Therefore , the correct representations of the inequality -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x  and  "an open circle is at 5 and a bold line that starts at 5 and is pointing to the right" , the correct option is (c) and (d) .

The given question is incomplete , the complete question is

Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.

(a) x < 5

(b) –6x – 5 < 10 – x

(c) –6x + 15 < 10 – 5x

(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.

(e) A number line from negative 7 to 3 in increments of 1,  An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.

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What’s the correct answer asap for brainlist

Answers

Answer:

Step-by-step explanation:its a  69420 dum as

The table represents a linear function.What is the slope of the function?y08-2.04х-4-2-112-10-14-22-26O 2O 5

Answers

Answer

Option B is correct.

The slope of this function = -4

Explanation

For a linear function, the slope of the line can be obtained when the coordinates of two points on the line or the values of the linear function (y) at different values of x are known. If the two points are described as (x₁, y₁) and (x₂, y₂), the slope is given as

[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the two extreme points, (x₁, y₁) and (x₂, y₂) are (-4, -2) and (2, -26).

x₁ = -4

y₁ = -2

x₂ = 2

y₂ = -26

[tex]\text{Slope = }\frac{-26-(-2)}{2-(-4)}=\frac{-26+2}{2+4}=\frac{-24}{6}=-4[/tex]

Hope this Helps!!!

5.) y = -5/4 x + 10 (Use Slope Int. Method Make apparent your Int. Point AND the point from your slope = RISE/RUN)

Answers

[tex]\begin{gathered} \text{slope}=m=\frac{rise}{\text{run}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=-\frac{5}{4} \\ m=-\frac{5}{4} \end{gathered}[/tex][tex]\begin{gathered} y=-\frac{5}{4}x+10 \\ m=slope=-\frac{5}{4} \\ y-\text{intercept}=10 \end{gathered}[/tex]

What number is 75% of 96?

Answers

The number 96 is equivalent to the 100%. So we can state the following rule of three:

[tex]\begin{gathered} 96\text{ ------ 100 \%} \\ x\text{ -------- 75 \%} \end{gathered}[/tex]

By cross-multiplying these numbers, we have

[tex]\text{ (100\%)}\times x=(96)\times\text{ (75 \%)}[/tex]

So, x is given by

[tex]\begin{gathered} x=\frac{(96)\times\text{ (75 \%)}}{\text{ 100\%}} \\ x=72 \end{gathered}[/tex]

Therefore, the answer is 72

Please show me how to solve this step by step im really confused

Answers

Given

[tex]-16t^2+v_0t+h_0[/tex]

initial velocity = 60 feet per second

initial height = 95 feet

Find

Maximum height attained by the ball

Explanation

we have given

[tex]\begin{gathered} h(t)=-16t^2+60t+95 \\ h^{\prime}(t)=-32t+60 \end{gathered}[/tex]

put h'(t) = 0

[tex]\begin{gathered} -32t+60=0 \\ -32t=-60 \\ t=\frac{60}{32}=1.875sec \end{gathered}[/tex]

to find the maximum height find the value of h(1.875)

[tex]\begin{gathered} h(1.875)=-16(1.875)^2+60(1.875)+95 \\ h(1.875)=-56.25+112.5+95 \\ h(1.875)=-56.25+207.5 \\ h(1.875)=151.25 \end{gathered}[/tex]

Final Answer

Therefore , the maximum height attained by the ball is 151.25 feet

Problem Solving: Fraction Division For exercises 1 and 2, write three problem situations for each division 56÷1/3 and 6/1/2÷1/2/3

Answers

56÷1/3

We have to model a problem where the solution is 56÷1/3.

So, we take something that is 56 and we have to divide it by 1/3rd.

So, we can say:

George had 56 large cakes.

Giving 1/3rd of each cake to each person is enough.

If George used all of the cake, how many person could he feed?

Bill Jensen deposits $8500 with Bank of America in an investment paying 5% compounded semiannually. Find the interest in 6 years

Answers

Amount deposited = $8500

Rate = 5%

time for interest = 6years

Compounded semiannually

The formula for semiannually is

[tex]A=P(1+\frac{r}{100n})^{nt}[/tex]

From the given information

P = $8500

r = 5

t = 6

Since the investment was compounded semiannually then

n = 2

Substitute the values into the formula

This gives

[tex]A=8500(1+\frac{5}{100\times2})^{6\times2}[/tex]

Solve for A

[tex]\begin{gathered} A=8500(1+0.025)^{12} \\ A=8500(1.025)^{12} \\ A=11431.56 \end{gathered}[/tex]

To find the interest

Recall

[tex]I=A-P[/tex]

Where I, is the interest

Hence

[tex]\begin{gathered} I=\text{\$}11431.56-\text{\$}8500 \\ I=\text{\$}2931.56 \end{gathered}[/tex]

Omar has $84 and maryam has $12. how much money must Omar give to maryam so that maryam will have three times as much as omar? let x be the amount of dollars Omar will give maryam. which equation best represents the situation described above? A.) 84 - x = 3(12) + xB.) 3(84 - x) = 12 - xC.) 3(84 - x ) = 12 + xD.) 3x = 84 - (12 + x)

Answers

Given data:

The given money Omar has $84.

The given money maryam has $12.

The expression for the money Omar give to maryam so that maryam will have three times as much as omar.

[tex]3(84-x)=12+x[/tex]

Thus, the final expression is 3(84-x)=12+x.

Kuta Software - Infinite Precalculus Angles and Angle Measure Find the measure of each angle.

Answers

Explanation:

We are to draw the angle that is equivalent to 5pi/4

First we need to convert the radian value to degree

Since pi rad = 180degrees

5pi/4 = x

Cross multiply

pi * x = 5pi/4 * 180

x = 5/4 * 180

x = 5 * 45

x = 225 degrees

This can also be written as 225 = 180 + 45

225degrees = 180 + pi/4

Note that 180degrees is an angle on a straight line. Find the digaram attached

The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension

5pi/4 = x

Cross multiply

pi * x = 5pi/4 * 180

x =

-14.4 + x = -8.2what does x equal?I NEED ANSWERS ASAPi will give brainliest

Answers

the given expression is,

-14.4 + x = -8.2

x = 14.4 - 8.2

x = 6.2

thus, the answer is x = 6.2

Express the interval using inequality notation(1,6)

Answers

The interval (1, 6) contains all the real numbers between 1 and 6, not including any of the endpoints.

This can be written in inequality notation as:

x >1 AND x < 6

But there is a shorter way to write the interval by combining both inequalities:

1 < x < 6

Find the set A n Φ.U = {1, 2, 3, 4, 5, 6, 7, 8, 9)A = 2, 3, 8, 9)Selectthe correct choice below and, if necessary, fill in the

Answers

Answer

Option B is the correct answer.

A n Φ = {}

A n Φ is the empty set.

Explanation

We are told to find the intersection between set A and the empty set Φ.

The intersection of two sets refers to the elements that belong to the two sets, that is, the elements that they both have in common.

Set A = (2, 3, 8, 9)

Set Φ = {}

What the elements of set A and set Φ (an empty set) have in common is nothing.

Hence, the intersection of set A and set Φ is an empty set.

A n Φ = {}

Hope this Helps!!!

the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.

Answers

the coordinates of two points on a line are (-4,8) and (2,2). Find the slope of the line.​

Applying the formula to calculate the slope

we have

m=(2-8)/(2+4)

m=-6/6

m=-1

slope is -1

Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 2ounces of rose oil at $4.36 per ounce, 5 ounces of ginger essence for $2.15 per ounce, and 4 ounces of black currant essence for $2.27 per ounce. Determine the cost per ounce of the perfume.

Answers

First, lets calculate how much the expended in the perfume:

[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]

So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:

[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]

So, about $2.6 per ounce of perfume.

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