Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.
<span>
<u><em>Answer:</em></u>sin (C)
<u><em>Explanation:</em></u><u>In a right-angled triangle, special trig functions can be applied. These functions are as follows:</u>
sin (theta) = </span>

<span>
cos (theta) = </span>

<span>
tan (theta) = </span>

<span>
<u>Now, let's check the triangle we have:</u>
<u>We have two options:</u>
<u>First option:</u>5 is the hypotenuse of the triangle
4 is the side adjacent to angle B
Therefore, we can apply the <u>cos function</u>:
cos (B) = </span>

<span>
<u>Second option:</u>5 is the hypotenuse of the triangle
4 is the side opposite to angle C
Therefore, we can apply the <u>sin function</u>:
sin (C) = </span>

<span>
Among the two options, the second one is the one found in the choices. Therefore, it will be the correct one.
Hope this helps :)
</span>
Answer:
<em><u>3. Last year, the numbers of calculators produced per day at a certain factory were normally distributed with a mean of 560 calculators and a standard deviation of 12 calculators.</u></em><em><u>(</u></em><em><u>C</u></em><em><u>)</u></em>
Step-by-step explanation:
<em><u>please click the heart and rate excellent and brainleist to </u></em><em><u>❤</u></em><em><u>☺️</u></em><em><u>☻</u></em><em><u>♨️</u></em><em><u>☻</u></em><em><u>☺️</u></em><em><u>❤</u></em>
<h3>
Answer: $2400</h3>
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Explanation:
x = Mason's salary in dollars for that month
x/6 = one-sixth of his salary
x/6+800 = total amount spent (the x/6 dollars and $800 combined)
In total, he spent half his salary. This means he spent x/2 dollars for the month overall.
Set the two items equal to one another. Solve for x.
x/6 + 800 = x/2
6(x/6 + 800) = 6*(x/2) ... see note at the bottom of the page
x+4800 = 3x
4800 = 3x-x
4800 = 2x
2x = 4800
x = 4800/2
x = 2400
His monthly salary is $2400
1/6 of this is (1/6)*2400 = 2400/6 = 400 dollars. Add on the $800 he also spent to get a total of 400+800 = 1200 dollars spent, which is exactly one half of the $2400. The answer is confirmed.
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Note: I multiplied both sides by 6 to clear out the fractions. The value 6 is the LCD in this case.
The answer is 2/8. Hope this helps.