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Mamont248 [21]
3 years ago
5

14 3/5 - 3 ÷ 5 11/12​

Mathematics
1 answer:
dalvyx [7]3 years ago
5 0

Answer:

33/355

not sure though

Step-by-step explanation:

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At a college, 69% of the courses have final exams and 42% of courses require research papers. Suppose that 29% of courses have a
laila [671]

Answer:

a) 0.82

b) 0.18

Step-by-step explanation:

We are given that

P(F)=0.69

P(R)=0.42

P(F and R)=0.29.

a)

P(course has a final exam or a research paper)=P(F or R)=?

P(F or R)=P(F)+P(R)- P(F and R)

P(F or R)=0.69+0.42-0.29

P(F or R)=1.11-0.29

P(F or R)=0.82.

Thus, the the probability that a course has a final exam or a research paper is 0.82.

b)

P( NEITHER of two requirements)=P(F' and R')=?

According to De Morgan's law

P(A' and B')=[P(A or B)]'

P(A' and B')=1-P(A or B)

P(A' and B')=1-0.82

P(A' and B')=0.18

Thus, the probability that a course has NEITHER of these two requirements is 0.18.

3 0
3 years ago
1. The equation of a circle is x^2 + y^2 + 6x - 4y + 4 = 0. What are the center and the radius of the circle? Show ALLLLLL your
Novosadov [1.4K]

Answer:

(2, -3) and r = 3.

Step-by-step explanation:

you can also plug this equation in desmos but I guess it's good to know how to do it also:

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2

Now in order to make a perfect square on both sides, we need to do this:

First add 9 to both sides:

x^2 + 6x + 9 + y^2 -4y +4 = 9.

I purposely shifted it to show the perfect square created when you add 9 to both sides. Factor:

(x+3)^2 + y^2 - 4y + 4 = 9.

now the second bolded part is allso a perfect square. Factor:

(x+3)^2 + (y-2)^2 = 9

Based on the equation of a circle, the center must be at (2, -3) and the radius is the square root of 9 which is 3.

:)

8 0
3 years ago
A) -40÷5(2) <br> B) (-2) + 3(12) ÷ 4<br> C) -2(3+4)
Furkat [3]
Always do brackets first

a) -40/10 = -4
b) 36/4 -2 = 7
c) -2 x 7 = -14
5 0
3 years ago
Read 2 more answers
Johanna can jog 24 feet in 5 seconds. If she jogs at the same rate, how many feet can she jog in 8 seconds? PLSS help!
Fynjy0 [20]
38.4? Since if she runs 24 feet in five seconds add that two times she would run 48 feet in ten second so.. divide 24 with 5 and get 4.8. So 48 minus 9.6 makes 38.4.
6 0
3 years ago
Are exponential function one to one. How can you tell? What does this tell you about their inverses
aleksandrvk [35]

See in the explanation

<h2>Explanation:</h2>

<h3>1. Are exponential function one to one. How can you tell?</h3>
  • A function f is one-to-one if each value of x corresponds to exactly one value of y.

To demonstrate this, we take the Horizontal Line Test that states:

<em>A function f has an inverse function if and only if there is no any horizontal line that intersects the graph of f at more than one point.</em>

As you can see in the first figure, the horizontal line y=3 (the green one) intersects the graph of the exponential function y=e^x (the red one) in just one point. If you take every horizontal line y=y_{0} with y_{0} any real number, you will find that every line intersects the exponential function in just one point. Therefore, this function is one-to-one

<h3>2. What does this tell you about their inverses?</h3>

Another important thing is that:

  • A function has an inverse function if and only if is one-to-one.  

As we have demonstrated that exponential functions are one-to-one by Horizontal Line Test, then we conclude exponential functions have inverse functions. The domain of the inverse function is the range of the original one and the range of the inverse function is the domain of the original one. The inverse of y=e^x is y=ln(x) whose graph is the second figure below.

<h2>Learn more: </h2>

How to find the inverse of a function? brainly.com/question/9980183

#LearnWithBrainly

5 0
3 years ago
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