A student committee of 4 is formed by randomly drawing people (without replacement) from a collection of 4 sophomores, 4 juniors and 3 seniors. What is the probability the committee thus formed will have at least one representative from all three groups of students?

Answer:

2

Step-by-step explanation:

1+1=2

Answer:

\(\begin{aligned}SA &= 7.125\pi \text{ in}^2\\& \approx 22.4 \text{ in}^2 \end{aligned}\)

Step-by-step explanation:

We can find the Surface Area of the can by adding the areas of each of its parts:

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

First, we can calculate the area of the circular base:

\(A_{\text{circle}} = \pi r^2\)

\(A_{\text{base}} = \pi (0.75 \text{ in})^2\)

\(A_{\text{base}} = 0.5625\pi \text{ in}^2\)

Next, we can calculate the area of the rectangular side:

\(A_\text{rect} = l \cdot w\)

\(A_\text{side} = (4\text{ in}) \cdot C_\text{base}\)

Since the width of the side is the circumference of the base, we need to calculate that first.

\(C_\text{circle} = 2 \pi r\)

\(C_\text{base} = 2 \pi (0.75 \text{ in})\)

\(C_\text{base} = 1.5 \pi \text{ in}\)

Now, we can plug that back into the equation for the area of the side:

\(A_\text{side} = (4\text{ in}) (1.5\pi \text{ in})\)

\(A_\text{side} = 6\pi \text{ in}^2\)

Finally, we can solve for the surface area of the can by adding the area of each of its parts.

\(SA = 2( A_{\text{base}}) + A_\text{side}\)

\(SA = 2(0.5625\pi \text{ in}^2) + 6\pi \text{ in}^2\)

\(\boxed{SA = 7.125\pi \text{ in}^2}\)

\(\boxed{SA \approx 22.4 \text{ in}^2}\)

Answer:

42 or 4^2

hope this helps

Answer:

4^12

Step-by-step explanation:

Answer:

What number is represented by point B = -1  

Which point represents the number 2? = C

On solving the provided question, by the help of BODMAS we can say that - Subtract 22 from both sides is the answer to the given question.

BODMAS and PEDMAS are both names for it in various places. This stands for exponents, parenthesis, division, multiplication, addition, and subtraction. The BODMAS rule states that parentheses must be answered before powers or roots (that is, of), divisions, multiplications, additions, and lastly subtractions. The BODMAS rule states that the degree (52 = 25), parenthesis (2 + 4 = 6), any division or multiplication (3 x 6 (bracket response) = 18), and any addition or subtraction (18 + 25 = 43) come before any other operations.

\(f/3 +22 = 17\)

\(f/3 +22 -22 = 17 -22\) Subtracting the same value from both sides keeps the equation equal.  

Then simplify. The \(+22 and -22= 0\) They "cancel"   \(17-22 = -5\)

\(f/3 = -17 f/3\) is now isolated-- by itself-- in the equation.

If we have to solve  f, the next step we to take is to multiply on the both sides by  3.

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The percentage decrease would be 70 percent.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

The price of an item has dropped to 27$ today. Yesterday it was 90.

90 - 27 = 63

The percentage decrease;

63 / 90 x 100= 70%

Hence, The percentage decrease would be 70 percent.

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Answer:

y = 120

Step-by-step explanation:

y = 4x (corresponding angles)

y + 2x = 180

substitute the value of y into the second equation

4x + 2x = 180

6x = 180

x = 30

now that we have the value of x, plug it into either equation and solve for y

y = 4 (30)

y = 120

The definition of a ray is a part of a line that has one endpoint and extends indefinitely in one direction

A ray is part of a line that has one endpoint and extends indefinitely in one direction and has the folowing properties.

So, the definition of a ray is a part of a line that has one endpoint and extends indefinitely in one direction.

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The minimum side length of the triangle needed to complete the triangle is 5 feet.

A polygon that has three sides and three vertices is called a triangle.

The sum of all the angles of the triangle is 180°.

Given:

The two sides of the triangle are 7 feet and 3 feet.

Let a = 7 and b = 3.

The minimum possible value,

= Max(a, b) - Min(a, b) + 1

= 7 - 3 + 1

= 5 feet.

Therefore, the minimum length is 5 feet.

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Answer:

0.5256

Step-by-step explanation:

X ~ B(10,0.75)

q = 1 - 0.75 = 0.25

The images best represents the result is image W.

We have, the image is rotated about the x-axis.

Now, rotating around x axis can give the other half of the image.

Also, rotating about x axis gives the mirror image of the figure.

So, the rotation leads to a circle.

and, In three dimensional we can say that Sphere.

Thus, the required image is W.

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The exact area of the circle with a radius of 9 cm is 81π cm².

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr².

Given, The radius of the circle is 9 cm.

Therefore, The area of the circle with a radius of 9 cm is,

= π(9)² cm².

= 81π cm².

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Answer:

$20 million.

Step-by-step explanation:

Amir is buying tickets for the $120 million lotteries. If he buys tickets with his brother, then they will split the money equally. But he is also considering buying tickets with his brother’s four friends, and they will each get

The illustration provided in the question is an example of an inverse variation.

When there is an inverse proportion, as one of the variable increases, the other variable decreases. As the number of people who share the money increases, the amount of money each person would get would become smaller.

The formula used to represent inverse proportion is:

y =  k/x

• y = dependent variable

• x = independent variable

• k = constant of proportionality

Here is the complete question: Amir is buying tickets for the  million lottery. If he buys tickets with his brother, then they will split the money equally. But he is also considering buying tickets with his brother's four friends, and they will each get  million. Is this an example of direct, inverse, or joint variation?Joint variationInverse variationDirect variation

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Answer:

70.48% probability that it was infected with Dummy

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Fixed by Bob

Event B: Infected with Dummy

65% of the customers with virus problems are bothered by Dummy

This means that \(P(B) = 0.65\)

If the computer is infected by Dummy, Bob has a 90% chance of fixing the problem.

This means that \(P(A|B) = 0.9\)

Probability of Bob Fixing

90% of 65%(fixing a Dummy-infected virus)

70% of 35%(fixing a Smarty-infected virus).

So

\(P(A) = 0.9*0.65 + 0.7*0.35 = 0.83\)

What is the probability that it was infected with Dummy

\(P(B|A) = \frac{0.65*0.9}{0.83} = 0.7048\)

70.48% probability that it was infected with Dummy

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer:

ps is perpendicular to line ur.

angle pvr is 90°

12x+3x=90°

15x=90°

x=90°/15

x=6

by putting value of x

12x=72°

Answer:

ok it is best answer very very very best

Answer:

Step-by-step explanation:look it up

Answer:

Step-by-step explanation:

We know from the property of 30°x60°x90° right triangle:

We see AC = 2*BC, therefore:

Correct choice is B

The ratio of angles is directly proportional to the ratio of sides

The ratio of sides here is 1:1/2:1

Now

\(\\ \sf\longmapsto 2x+x=90°\)

\(\\ \sf\longmapsto 3x=90\)

\(\\ \sf\longmapsto x=30\)

Answer:

AB =  4.9cm

Step-by-step explanation:

We know

AC is 9.1 centimeters, and BC is 4.2 centimeters.

Find AB

We take

9.1 - 4.2 = 4.9cm

So, AB = 4.9cm

Answer: The result can be shown in multiple forms.

Exact Form:

− √ 3 /2

Decimal Form:

− 0.86602540 …

Step-by-step explanation:

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

− sin ( π/3 )

The exact value of  

sin ( π /3 )  is  √ 3 /2 .

− √ 3 /2

Answer:

40800

Step-by-step explanation:

4 weeks = 1 month

So we use,

850 * 4 = 3400 (monthly)

12 months = 1 year

So we use,

3400 * 12 = 40800 (annually)

Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:

P = Proportion of red candies in the large bag

R = Red candies in the small bag

R × (33/9) = P

12 × (33/9) = P

P = 40 red candies in the large bag

Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

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Answer: 0.75

Step-by-step explanation:

The scale factor of the perimeters from figure A to figure B is 1.5. Scale factor is the ratio of any two corresponding lengths in two similar figures.

Here, the two figures are similar, that is why we can find the scale factor by dividing corresponding sides of one figure by the corresponding sides of another figure. We will find the scale factor for the perimeter of figures A and B below:Perimeter of figure A = 12 + 10 + 18 = 40 unitsPerimeter of figure B = 15 + 15 + 15 = 45 unitsTo find the scale factor of the perimeters, we divide the perimeter of figure B by the perimeter of figure

A:Scale factor of the perimeters = (Perimeter of figure B)/(Perimeter of figure A) = 45/40 = 1.125To simplify any fractional answer, we have to convert it to the lowest terms, which is 9/8. The decimal answer 1.125, when rounded to the nearest tenth is 1.1. Therefore, the scale factor of the perimeters from figure A to figure B is 1.5.

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The payment amount rate required to pay off the loan in 2 years is k = $4,266.67 and the total interest paid during the two-year period is $2,142.66. This is calculated by using the formula for continuous compounding to solve for k and the formula for calculating interest to solve for I.

1. Calculate the payment rate required to pay off the loan in 2 years:

k = P/(1 - e^(-rt))

= 7506/(1 - e^(-0.15*2))

= 7506/(1 - 0.8698)

= 4,266.67

2. Calculate the total interest paid during the two-year period:

I = P(e^(rt) - 1)

= 7506(e^(0.15*2) - 1)

= 7506(1.3302 - 1)

= 2,142.66

Payment rate required to pay off the loan in 2 years: K = $5,062.89. The amount of interest paid during the 2-year period is $1,506.11. The borrower pays back a total of $9,012.89 over the 2-year period. The interest rate of 15% is continuously compounded and the payments are made at a continuous rate of K dollars per year.

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Answer: 14.8

Step-by-step explanation: If the number in the hundredths place is less than 5, you must round down. On the contrary, if that number is 5 or greater, you must round up. This applies for rounding to any place not just the tenths place. For example, if you were to round it to the ones place, the answer would be 15.

Answer:

14.8

Step-by-step explanation:

The hundredth is smaller than 5, therefore you have to round down.

hope it helps