Evaluate 21 ÷ 3 + (8 -2 ÷2) show work

Mathematics

1 answer:

san4es73 [151]2 years ago

7 0

Answer:

$21 \div 3 + (8 - 2 \div 2) \\ = 21 \div 3 + (8 - 1) \\ = 21 \div 3 + 7 \\ = 7 + 7 \\ = 14$

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The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?

klio [65]

A=(απr^2)/360=(απd^2)/1440 (r^2=d^2/4)

α=1440A/(πd^2)

s=απd/360 (where s=arc length) so

s=(1440Aπd)/(360πd^2)

s=4A/d and since A=10mi^2 and d=20mi

s=(4*10)/20

s=2 miles

8 0

3 years ago

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey

mote1985 [20]

Answer:

$P(X\geq 8)=0.0043\\\\$

It's more likely that all of the residents surveyed will have adequate earthquake supplies since it has a probability of 98.02% which is very close to 100%.

Step-by-step explanation:

-This is a binomial probability problem with the function:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}$

-Given p=0.3, n=11, the is calculated as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)+P(X=11)\\\\={11\choose 8}0.3^8(0.7)^3+{11\choose 9}0.3^9(0.7)^2+{11\choose 10}0.3^{10}(0.7)^1+{11\choose 11}0.3^{11}(0.7)^0\\\\=0.0037+0.0005+0.00005+0.000002\\\\=0.0043$

Hence, the probability that at least 8 have adequate supplies 0.0043

#The probability that non has adequate supplies is calculated as;

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= 0)={11\choose 0}0.3^{0}(0.7)^{11}\\\\=0.0198$

#The probability that all have adequate supplies is calculated as:

$P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= All)=1-{11\choose 0}0.3^{0}(0.7)^{11}\\\\=1-0.0198\\\\=0.9802$

Hence, it's more likely that all of the residents surveyed will have adequate earthquake supplies since $P(All)>P(None)\ \$ and that this probability is 0.9802 or 98.02% a figure close to 1