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seraphim [82]
3 years ago
8

Among a group of 100 people, 68 can speak English, 45 can speak French, 42 can speak Spanish. 27 can speak both English and Fren

ch, 25 can speak both English and Spanish, 16 can speak both French and Spanish, and 9 can speak all three languages. Pick a person at random from this group, what is the probability that this person can speak at least 1 of these languages?
Mathematics
1 answer:
Nat2105 [25]3 years ago
8 0

Answer:

Step-by-step explanation:

Given

No of People who can speak English is n(E)=68

No of People who can speak French is n(F)=45

No of People who can speak Spanish is n(S)=42

No of People who can speak both English and French n\left ( E\cap F\right )=27

No of People who can speak both English and Spanish n\left ( E\cap S\right )=25

No of People who can speak both French and Spanish n\left ( F\cap S\right )=16

No of people who can speak all languages is n\left ( E\cap F\cap S\right )=9

no of People who can Speak at least one Language is

n\left ( E\cup F\cup S\right )=n\left ( E\right )+n\left ( F\right )+n\left ( S\right )-n\left ( E\cap F\right )-n\left ( E\cap S\right )-n\left ( F\cap S\right )+n\left ( E\cap F\cap S\right )

n\left ( E\cup F\cup S\right )=68+45+42-27-25-16+9=96

Probability that Randomly selected can speak at least 1 of these languages

P=\frac{96}{100}=0.96

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1.3. If Sara draws a red ball and DOES NOT RETURN it, and then she goes to draw a green
dimulka [17.4K]

Answer:

Dependent Event

Step-by-step explanation:

Assume that are 10 balls, such that:

Red = 6

Green = 4

If the balls are replaced after taken, the probability is:

Pr(Red) = 6/10

Pr(Green) = 4/10

This is referred to as independent event; because each selection do not affect the next or previous selection

However, if the balls are not replaced, the probability is:

Pr(Red) = 6/10

Pr(Green) = 5/(10 - 1) = 5/9

We subtracted 1 because there is a reduction in the number of balls when the red ball is not returned.

This is referred to as independent event; because a selection affects the next selection

3 0
3 years ago
A: l = h - 7.0<br> B: l= 9/16h<br> C:h = 9/16L<br> D:h = L - 7.0
Georgia [21]

Answer:

A

Step-by-step explanation: The answer is A

3 0
3 years ago
Paul deposited $95,000 in a savings account that pays 4% interest compounded daily. What is his balance at the end of six months
Arada [10]

Answer:

\$96,919.02  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=6/12=0.5\ years\\ P=\$95,000\\ r=4\%=4/100=0.04\\n=365  

substitute in the formula above  

A=95,000(1+\frac{0.04}{365})^{365*0.5}  

A=95,000(1+\frac{0.04}{365})^{182.5}=\$96,919.02  

5 0
3 years ago
Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b,
nataly862011 [7]

Answer:

b = -9.

Step-by-step explanation:

The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

(12 - 3) / (7 - 4) = 9 / 3 = 3.

Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

3 = 3 * 4 + b

b + 12 = 3

b = -9.

Hope this helps!

4 0
3 years ago
Read 2 more answers
Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*
Veronika [31]

Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

<u>Area of a Triangle:</u>

A triangle of base B and height H (both must be perpendicular) has an area of:

\displaystyle A=\frac{BH}{2}

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

\displaystyle A=\frac{5*4}{2}=10

The area of the triangle DEF is 10.

4 0
3 years ago
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