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pashok25 [27]
3 years ago
11

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the pro

bability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?
Mathematics
1 answer:
natka813 [3]3 years ago
3 0

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

Probability of passing at least one = 0.59 + 0.60 - 0.49 = 0.7 ##

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Help me asap! I will give you marks
Law Incorporation [45]

Recall the binomial theorem.

(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k

1. The binomial expansion of \left(1+\frac x3\right)^7 is

\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}

Observe that

k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x

k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2

When we multiply these by 8-9x,

• 8 and \frac73 x^2 combine to make \frac{56}3 x^2

• -9x and \frac73 x combine to make -\frac{63}3 x^2 = -21x^2

and the sum of these terms is

\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}

2. The binomial expansion is

\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k

We get the a^6b^2 term when k=2 :

k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2

6 0
1 year ago
I need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Maksim231197 [3]

Answer:

c) I think'

Step-by-step explanation:

7 0
2 years ago
Based on the given segment lengths, determine whether the segments can form a triangle.
murzikaleks [220]

For 3 sides to form a triangle two sides added together need to be greater then the 3rd side. You need to check all 3 combinations:

1. 11.5 + 10.5 = 22, 22> 6.1

11.5 + 6.1 = 17.6 17.6 > 10.5

10.5 + 6.1 = 16.6, 16.6 > 11.5

This one can make a triangle.

2. 9.5 + 3.5 > 4.5

9.5 + 4.5 > 3.5

4.5 + 3.5 < 9.5

Cannot make a triangle.

3. 8 + 6.7 > 1

6.7 + 1 < 8

Cannot make a triangle.

4. Can make a triangle

5. Can

6. Can

4 0
3 years ago
The graph of the step function g(x) = –⌊x⌋ + 3 is shown.
Blababa [14]

Using it's concept, the domain of the function is given as follows:

{x| –2 ≤ x <= 5}

<h3>What is the domain of a function?</h3>

The domain of a function is the set that contains all possible input values for the function, that is, the values for which the function is defined.

The function described in this problem is defined from x = -2 until x = 5 hence the domain of the function is given as follows, by the interval:

{x| –2 ≤ x <= 5}

More can be learned about the domain of a function at brainly.com/question/10891721

#SPJ1

3 0
1 year ago
Calculate the value of the exterior angle
aev [14]

What we know is that the sum of a triangle's internal angles are 180º, and a straight angle makes 180º.

first, we have to find the third internal angle(let's call it n) so that we can use it to find the exterior angle.

(3x + 20) + (4x + 5) + n = 180

simplify:

7x + 25 + n = 180

7x + n = 155

n = 155 - 7x

Now we can add it to the external angle to find x.

(155 - 7x) + (8x + 15) = 180

simplify:

170 + 8x - 7x = 180

170 + x = 180

x = 10

Now we can substitute it to the external angle.

8 x 10 + 15 = 95

the exterior angle is 95º.

8 0
3 years ago
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