MATHEMATICS COLLEGE

In a large Introductory Statistics lecture hall, the professor reports that 55% of the students enrolled have never taken a Calculus course, 32% have taken only one semester of Calculus, and the rest have taken two or more semesters of Calculus. The professor randomly assigns students to groups of three to work on a project for the course. What is the probability that the first groupmate you meet has studied a) two or more semesters of Calculus?
b) some Calculus?
c) no more than one semester of Calculus?

Answers

Answer 1

Answer:

Answer:

a) There is a 13% probability that a student has taken 2 or more semesters of Calculus.

b) 45% probability that a student has taken some calculus.

c) 87% probability that a student has taken no more than one semester of calculus.

Step-by-step explanation:

We have these following probabilities:

A 55% that a student hast never taken a Calculus course.

A 32% probability that a student has taken one semester of a Calculus course.

A 100-(55+32) = 13% probability that a student has taken 2 or more semesters of Calculus.

a) two or more semesters of Calculus?

There is a 13% probability that a student has taken 2 or more semesters of Calculus.

b) some Calculus?

At least one semester.

So there is a 32+13 = 45% probability that a student has taken some calculus.

c) no more than one semester of Calculus?

At most one semester.

So 55+32 = 87% probability that a student has taken no more than one semester of calculus.

Answer 2

Answer:

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A line passes through the point (4,-6) and has the slope of -3/4. Which is the equation of the line? y=-3/4x-3 y=-3/4x-6 y=-3x-3/4 y=-6x-3/4
Simplify the following expression by using the distributive property 6(3a-4)

Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Answers

Answer:

The answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

Step-by-step explanation:

$\bold{\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]}$

Solve the L.H.S part:

$\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right]\n\n\n\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]$

After calculating the L.H.S part compare the value with R.H.S:

$\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]} \n\n$

$\to a+2c =6....(i)\n\n\to b+2d =5....(ii)\n\n\to 3a+4c =19....(iii)\n\n\to 3b+4d = 8 ....(iv)\n\n$

In equation (i) multiply by 3 and subtract by equation (iii):

$\to 3a+6c=18\n\to 3a+4c=19\n\n\text{subtract}... \n\n\to 2c = -1\n\n\to c= - (1)/(2)$

put the value of c in equation (i):

$\to a+ 2 (- (1)/(2))=6\n\n\to a- 2 * (1)/(2)=6\n\n\to a- 1=6\n\n\to a =6 +1\n\n\to a = 7\n$

In equation (ii) multiply by 3 then subtract by equation (iv):

$\to 3b+6d=15\n\to 3b+4d=8\n\n\text{subtract...}\n\n\to 2d = 7\n\n\to d= (7)/(2)\n$

put the value of d in equation (iv):

$\to 3b+4 ((7)/(2))=8\n\n\to 3b+4 * (7)/(2)=8\n\n\to 3b+14=8\n\n\to 3b =8-14\n\n\to 3b = -6\n\n\to b= (-6)/(3)\n\n\to b= -2$

The final answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

Consider the quadratic function f(x) = x2 – 8x – 4. What is the value of the leading coefficient?8 оооо
4

Answers

Answer:

x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)

thus :

Step-by-step explanation:

Solve for x over the real numbers:

x^2 - 8 x - 4 = 0

Hint: | Solve the quadratic equation by completing the square.

Add 4 to both sides:

x^2 - 8 x = 4

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 16 to both sides:

x^2 - 8 x + 16 = 20

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 4)^2 = 20

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 4 = 2 sqrt(5) or x - 4 = -2 sqrt(5)

Hint: | Look at the first equation: Solve for x.

Add 4 to both sides:

x = 4 + 2 sqrt(5) or x - 4 = -2 sqrt(5)

Hint: | Look at the second equation: Solve for x.

Add 4 to both sides:

Answer: x = 4 + 2 sqrt(5) or x = 4 - 2 sqrt(5)

Answer:

-8 or option A

Step-by-step explanation:

2023

-3 < 5 true or false

Answers

Answer:

true

Step-by-step explanation:

Answer:

true?

Step-by-step explanation:

A) Kenyans went elections and they had to choose between three coalitions; JubileeCord and Amani. They must choose one, if they have no preference, can choose
all the three or, if against one option, they choose for the two they prefer. A
sample of 200 voters revealed the following information
30 chose Jubilee and Amani but not Cord
130 chose Cord only
102 chose Amani only
30 chose Jubilee and Cord
234 chose for either Jubilee or Cord, or both Jubilee and Cord, but not Amani
256 chose for either Cord or Amani, or both Cord and Amani, but not Jubilee
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many
students chose
i) All the three options
(2 marks
ii) Only one option
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iii) Jubilee irrespective of Cord or Amani
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Answers

Answer:

iii is right..................

PLZ HURRY IT'S URGENT!!!What is the slope of the line?

y=3
options:

0

1

3

undefined

Answers

Answer:

There is no x or number with an x (example: y= 2x+3, the 2 would be the slope)

Answer:

Step-by-step explanation:

The perimeter of a rectangle is 52 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 120 square feet. I need to find the solution set for this.

Answers

Answer:

2x+2y=52

x*y=120

Step-by-step explanation:

Final answer:

The possible lengths of a side of the rectangle are 22, 21, 20, 19, 18, 17, 16 feet.

Explanation:

To find the possible lengths of a side of the rectangle, let's use the formula for the perimeter of a rectangle, which is 2(length + width). We can set up an equation using the given information:

2(length + width) = 52

Dividing both sides by 2, we get:

length + width = 26

Now, to find the possible lengths, we need to consider the area. The formula for the area of a rectangle is length x width. We are given that the area is not to exceed 120 square feet, so we can set up the inequality:

length x width <= 120

Using the relationship length + width = 26, we can substitute length = 26 - width into the inequality:

(26 - width) x width <= 120

Simplifying the inequality, we get:

-width^2 + 26width - 120 <= 0

Now, we can solve this quadratic inequality to find the range of possible widths. Once we have the widths, we can substitute them back into the equation length + width = 26 to find the corresponding lengths.

By solving the quadratic inequality, we find that the possible widths are 4 <= width <= 10. Substituting these widths back into the equation length + width = 26, we get the corresponding lengths:

If width = 4, then length = 22

If width = 5, then length = 21

If width = 6, then length = 20

If width = 7, then length = 19

If width = 8, then length = 18

If width = 9, then length = 17

If width = 10, then length = 16

The possible lengths of a side of the rectangle are {22, 21, 20, 19, 18, 17, 16} feet.

Learn more about rectangle side lengths here:

brainly.com/question/16605856

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