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2 years ago

Is 9r+16=π5 9 r + 16 = π 5 a literal equation?

Mathematics

1 answer:

DerKrebs [107]2 years ago

3 0

Answer:

Step-by-step explanation:

9r+16=pi5

9r+16=22/7*5

9r+16=15.7

16-15.7=9r

0.3=9r

9r=0.3

r=30

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Peanut allergies among children. About 2% of children in the United States are allergic to peanuts. Choose three children at ran

Step2247 [10]

Answer:

P(X=2|X≥1) = 0.0199973.

Step-by-step explanation:

The chance that each of the three children is allergic to peanuts is independent. Each with a chance of 2% = 0.02.

X follows a binomial distribution with

3 trials, and
a chance of "success" of 2% = 0.02.

$P(X = 2|X\ge 1) = \dfrac{P(X = 2 \cap X\ge 1)}{P(X\ge 1)}$ .

The event $X \ge 1$ includes

$X = 1$
${\bf X = 2}$ , and
$X = 3$ .

In other words, $X = 2$ implies that $X\ge 1$ .

$P(X = 2 \cap X\ge 1) = P(X = 2) = \left(\begin{array}{c}3\\2\end{array}\right ) \times 0.02^{2} \times (1-0.02) = 0.001176$ .

$P(X\ge 1) = 1 - P(X< 1) \\\phantom{P(X\ge 1)}= 1 - P(X = 0) \\\phantom{P(X\ge 1)}= 1 -\left(\begin{array}{c}3\\0\end{array}\right ) \times (1-0.02)^{3} \\\phantom{P(X\ge 1)}= 0.058808$ .

$P(X = 2|X\ge 1) = \dfrac{P(X = 2 \cap X\ge 1)}{P(X\ge 1)} = \dfrac{0.001176}{0.058808} = 0.0199973$ .

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2 years ago

Three data entry specialists enter requisitions into a computer. Specialist 1 processes 42 percent of the requisitions, speciali

suter [353]

Answer:

The probabilities are 0.480;0.077 and 0.443 respectively

Step-by-step explanation:

This is a conditional probability exercise.

Let's define conditional probability :

Given two events A and B :

$P(A/B)=\frac{P(A,B)}{P(B)} \\P(B) > 0$

P(A,B) = P(A∩B) = P(B∩A) = P(B,A) : Is the probability that event A and event B occur at the same time.

We define the following events :

S1 : ''Specialist 1 processes requisitions''

S2 : ''Specialist 2 processes requisitions''

S3 : ''Specialist 3 preocesses requisitions''

I : ''Incorrect entered requisitions''

In our exercise :

$P(S1)=0.42\\P(S2)=0.27\\P(S3)=0.31\\P(I/S1)=0.04\\P(I/S2)=0.01\\P(I/S3)=0.05$

We are ask to find

$P(S1/I) ;P(S2/I);P(S3/I)$

We write the conditional equations :

$P(I/S1)=\frac{P(I,S1)}{P(S1)} \\0.04=\frac{P(I,S1)}{0.42} \\P(I,S1)=0.0168$

$P(I/S2)=\frac{P(I,S2)}{P(S2)} \\0.01=\frac{P(I,S2)}{0.27} \\P(I,S2)=0.0027$

$P(I/S3)=\frac{P(I,S3)}{P(S3)} \\0.05=\frac{P(I,S3)}{0.31} \\P(I,S3)=0.0155$

We also define

P(A∪B) = P(A) + P(B) - P(A∩B)

P(I) = P [(I,S1)∪(I,S2)∪(I,S3)]

$P(I) =P(I,S1) +P(I,S2)+P(I,S3)\\P(I)=0.0168+0.0027+0.0155\\P(I)=0.035$

There is no intersection between (I,S1);(I,S2) and (I,S3) because they are mutually exclusive events.

$P(S1/I)=\frac{P(I,S1)}{P(I)} =\frac{0.0168}{0.035} =0.480\\P(S2/I)=\frac{P(I,S2)}{P(I)} =\frac{0.0027}{0.035} =0.077\\P(S3/I)=\frac{P(I,S3)}{P(I)} =\frac{0.0155}{0.035} =0.443$

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2 years ago

one angle of a linear pair is 10 more than two thirds the other angle. find the measure if both angles

BigorU [14]

Answer:

One Angle = 110°

Other Angle = 70°

Step-by-step explanation:

A linear pair means that two angles are in a straight line (or, a straight angle).

A straight line is 180 degrees.

THey are supplementary.

We can say one angle is "a" and another one is "b".

One angle is 10 MORE THAN 2/3rds of the other, we can write:

$a=\frac{2}{3}b+10$

Also, since they are supplementary (add up to 180), we can write:

a + b = 180

We can now substitute 1st equation in this one and find b:

$a+b=180\\(\frac{2}{3}b+10)+b=180\\\frac{2}{3}b+b=180-10\\\frac{5}{3}b=170\\b=\frac{170}{\frac{5}{3}}\\b=170*\frac{3}{5}\\b=110$

Since a + b = 180, we can write:

a + 110 = 180

so,

a = 180 - 110

a = 70

Thus,

One Angle = 110°

Other Angle = 70°

8 0

1 year ago

A boy had 3 apples and gained one. How many apples does he have now?

Zigmanuir [339]

Answer: 4

step by step explanation: 3+1=4

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1 year ago

In blueprints an architects firm drew everything 1/24 of the actual size the windows will actually measure 4feet by 6 feet and t

stich3 [128]

To apply a scale to a measure, you have to follow this rule:

Real measure x Scale = Scaled measure

So the drawings will have:

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12 x 1/24 = 0'50 feet
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2 years ago

Read 2 more answers