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3 years ago

6

The sector of a circle with a 12 in. radius has a central angle measure of 60°. What is the exact area of the sector in terms of

π ? Enter your answer in the box.

1 answer:

Lana71 [14]3 years ago

3 0

That is angle/360 times area

area=pir^2
r=12 in this one
and angle=60
so
60/360 times pi12^2=1/6 times 144pi=24pi square inches

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A scuba diver swam 96 feet beneath the surface of the lake.he then climb up 49 feet .wat is the depth now?

lakkis [162]

Answer:

The depth now is 47 feet below the surface of the lake

Step-by-step explanation:

Step 1: Determine initial depth

Initial depth=surface level-depth below surface

where;

Surface level=0, since its the point of reference

depth below surface=96 feet

replacing;

Initial depth=(0-96)=-96 feet

Step 2: Final depth

Final depth=Initial depth+distance covered

where;

Initial depth=-96 feet

distance covered=+49 feet since the scuba driver moves towards the surface

replacing;

distance covered=-96+49=-47 feet

The depth now is 47 feet below the surface of the lake

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3 years ago

A prticular type of tennis racket comes in a midsize versionand an oversize version. sixty percent of all customers at acertain

svetlana [45]

Answer:

a) P(x≥6)=0.633

b) P(4≤x≤8)=0.8989 (one standard deviation from the mean).

c) P(x≤7)=0.8328

Step-by-step explanation:

a) We can model this a binomial experiment. The probability of success p is the proportion of customers that prefer the oversize version (p=0.60).

The number of trials is n=10, as they select 10 randomly customers.

We have to calculate the probability that at least 6 out of 10 prefer the oversize version.

This can be calculated using the binomial expression:

$P(x\geq6)=\sum_{k=6}^{10}P(k)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\geq6)=0.2508+0.215+0.1209+0.0403+0.006=0.633$

b) We first have to calculate the standard deviation from the mean of the binomial distribution. This is expressed as:

$\sigma=\sqrt{np(1-p)}=\sqrt{10*0.6*0.4}=\sqrt{2.4}=1.55$

The mean of this distribution is:

$\mu=np=10*0.6=6$

As this is a discrete distribution, we have to use integer values for the random variable. We will approximate both values for the bound of the interval.

$LL=\mu-\sigma=6-1.55=4.45\approx4\\\\UL=\mu+\sigma=6+1.55=7.55\approx8$

The probability of having between 4 and 8 customers choosing the oversize version is:

$P(4\leq x\leq 8)=\sum_{k=4}^8P(k)=P(4)+P(5)+P(6)+P(7)+P(8)\\\\\\P(x=4) = \binom{10}{4} p^{4}q^{6}=210*0.1296*0.0041=0.1115\\\\P(x=5) = \binom{10}{5} p^{5}q^{5}=252*0.0778*0.0102=0.2007\\\\P(x=6) = \binom{10}{6} p^{6}q^{4}=210*0.0467*0.0256=0.2508\\\\P(x=7) = \binom{10}{7} p^{7}q^{3}=120*0.028*0.064=0.215\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\\\P(4\leq x\leq 8)=0.1115+0.2007+0.2508+0.215+0.1209=0.8989$

c. The probability that all of the next ten customers who want this racket can get the version they want from current stock means that at most 7 customers pick the oversize version.

Then, we have to calculate P(x≤7). We will, for simplicity, calculate this probability substracting P(x>7) from 1.

$P(x\leq7)=1-\sum_{k=8}^{10}P(k)=1-(P(8)+P(9)+P(10))\\\\\\P(x=8) = \binom{10}{8} p^{8}q^{2}=45*0.0168*0.16=0.1209\\\\P(x=9) = \binom{10}{9} p^{9}q^{1}=10*0.0101*0.4=0.0403\\\\P(x=10) = \binom{10}{10} p^{10}q^{0}=1*0.006*1=0.006\\\\\\P(x\leq 7)=1-(0.1209+0.0403+0.006)=1-0.1672=0.8328$

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3 years ago

Consider the equations 15x + 9y = 45 and 9x + 8y = 12. Solve the system of equations using elimination. Give your solution to th

True [87]

Answer:

(-5.77, 6.46)

Step-by-step explanation:

15x + 9y = 45 ----------- i

9x + 8y = 12----------------ii

Multiply equation i by 9 the coefficient of x in equ ii

And equation ii by 15 the coefficient of x in equ I

9 x 15x + 9y = 45 ----------- i

15 x 9x + 8y = 12----------------ii

135x+81y = 405

135x+120y= 180

Subtract equation ii from I

135x-135x+81y-(+120y)= 405-180

-39y=225

y = 225/-39 = -5.77

Insert the value of y in equ i

15x + 9y = 45

15x+9(-5.77) = 45

15x-51.92=45

15x = 45+51.92

15x= 96.92

x = 96.92/15= 6.46

(x,y) = (-5.77, 6.46)

x = 6.92/15

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3 years ago

Use the four-step method in problem-solving to solve the problem.

svp [43]

Answer:

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Step-by-step explanation:

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$43834 + $12348= $56,182

$56,182 x 1= $56,182

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3 years ago

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Inessa [10]

have you ask your teacher yet?

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2 years ago