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abruzzese [7]
3 years ago
13

Can someone help me with this exercise

Mathematics
1 answer:
Solnce55 [7]3 years ago
6 0

Answer:

Step-by-step explanation:

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A sports survey taken at THS shows that 48% of the respondents liked soccer, 66% liked basketball and 38% liked hockey. Also,30%
In-s [12.5K]

Answer:

a) The Venn diagram is presented in the attached image to this answer.

b) 0.82

c) 0.16

Step-by-step explanation:

a) The Venn diagram is presented in the attached image to this answer.

n(U) = 100%

n(S) = 48%

n(B) = 66%

n(H) = 38%

n(S n B) = 30%

n(B n H) = 22%

n(S n H) = 28%

n(S n B n H) = 12%

The specific breakdowns for each subgroup is calculated on the Venn diagram attached.

b) The probability that a randomly selected student likes basketball or hockey.

P(B U H)

From the Venn diagram,

n(B U H) = n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) = 26 + 10 + 18 + 12 + 16 + 0 = 82%

P(B U H) = 82/100 = 0.82

c) The probability that a randomly selected student does not like any of these sports.

P(S' n B' n H')

n(S' n B' n H') = n(U) - [n(S' n B n H') + n(S' n B n H) + n(S n B n H') + n(S n B n H) + n(S n B' n H) + n(S' n B' n H) + n(S n B' n H')]

n(S' n B' n H') = 100 - (26 + 10 + 18 + 12 + 16 + 0 + 2) = 100 - 84 = 16%

P(S' n B' n H') = 16/100 = 0.16

4 0
3 years ago
Find a value for x if 1/x > x
Ymorist [56]

Since x can't be zero (it sits at the denominator of the left hand side), let's split cases:

If x is positive

It this case, we can multiply both sides by x without changing the inequality sign:

\dfrac{1}{x} > x \iff 1 > x^2 \iff x \in (-1,1)

But since we're assuming that x is positive, we can only accept the numbers between 0 and 1.

If x is negative

It this case, in order to multiply both sides by x we have to change the inequality sign:

\dfrac{1}{x} > x \iff 1 < x^2 \iff x \in (-\infty,-1) \cup (1,\infty)

But since we're assuming that x is negative, we can only accept the numbers which are smaller than -1.

So, putting all the pieces together, we have that the solution is given by the following interval:

(-\infty, -1) \cup (0,1)

6 0
3 years ago
You are told that a third powered polynomial has zeroes at -1, 2, 5.
vichka [17]

Answer:

a) factors of polynomial are: (x+1)(x-2)(x-5)

b) the required polynomial in standard form is: \mathbf{x^3-6x^2+3x+10}

Step-by-step explanation:

The polynomial has zeros at -1,2,5

Part A) Write the three factors of the polynomial

we have x=-1, x=2 and x=5 as zeros of polynomial

so factors will be:

(x+1)=0, (x-2)=0, (x-5)=0

So, factors of polynomial are: (x+1)(x-2)(x-5)

Part B) Write the polynomial in standard form

For finding polynomial, we will multiply all the factors i.e

(x+1)(x-2)(x-5)

(x+1)(x-2)(x-5)\\=(x(x-2)+1(x-2))(x-5)\\=(x^2-2x+x-2)(x-5)\\=(x^2-x-2)(x-5)\\=x(x^2-x-2)-5(x^2-x-2)\\=x^3-x^2-2x-5x^2+5x+10\\=x^3-x^2-5x^2+5x-2x+10\\=x^3-6x^2+3x+10

So, the required polynomial in standard form is: x^3-6x^2+3x+10

7 0
3 years ago
Find the missing number in this proportions
iren2701 [21]

Answer:

9

Step-by-step explanation:

If 28 ends up becoming 4, 7 is what they have to divide to make 4 a numerator. That means you have to divide 63 by 7 which would make 9.

5 0
3 years ago
Square root 72 minus 3 square root 2
enot [183]

Answer:

About 4.2426

Step-by-step explanation:

5 0
3 years ago
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