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3 years ago

-7p = -3p - 8 p = Help

Mathematics

2 answers:

jeka943 years ago

6 0

Answer:

p=2

Step-by-step explanation:

-7p = -3p - 8

Add 3p to each side

-7p+3p = -3p+3p - 8

-4p = -8

Divide each side by -4

-4p/-4 = -8/-4

p = 2

pentagon [3]3 years ago

6 0

Answer:

$\huge{ \fbox{ \sf{p = 2}}}$

Step-by-step explanation:

$\bigstar{ \sf{ \: - 7p = - 3p - 8}}$

$\underline{ \underline{ \mathfrak{Let's \: solve}}} :$

$\text{Step \: 1} : \sf{Move \: 3p \: to \: left \: hand \: side \: and \: change \: it's \: sign}$

$\mapsto{ \sf{ - 7p + 3p = - 8}}$

$\text{Step \: 2} : \sf{Collect \: like \: terms}$

$\sf{Like \: terms \: are \: those \: which \: have \: the \: same \: base}$

$\mapsto{ \sf{ - 4p = - 8}}$

$\text{Step \: 3} : \sf{Divide \: both \: sides \: by \: - 4}$

$\mapsto{ \sf{ \frac{ - 4p}{ - 4} = \frac{ - 8}{ - 4}}}$

$\text{Step \: 4} : \sf{Calculate}$

$\mapsto{ \sf{p = 2}}$

Hope I helped!

Best regards! :D

~ $\sf{TheAnimeGirl}$

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Find the slope of the line represented by the data on the picture

arsen [322]

Answer:

slope = - 4

Step-by-step explanation:

Calculate the slope m using the slope formula and any 2 ordered pairs from the table.

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 8) and (x₂, y₂ ) = (- 1, 4) ← 2 points from the table

m = $\frac{4-8}{-1+2}$ = $\frac{-4}{1}$ = - 4

4 0

3 years ago

A farmer had 4,999 chickens.Each chicken laid one egg.Later in the day he recieved 664 more chickens. They each laid an egg too

hammer [34]

Answer:

4'999 + 664 = 5663

Step-by-step explanation:

all chickens laid one egg so that is 4'999 then the next day 664 of them laid one egg that is how I know what it is.

your welcome for the help.

5 0

3 years ago

"In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-

creativ13 [48]

Answer:

For this case we want to find this probability:

$P(10$

And we can use the z score formula to see how many deviation we are within the mean and we got:

$z = \frac{10-37}{9}=-3$

$z = \frac{64-37}{9}=3$

And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.

Step-by-step explanation:

Previous concepts

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

Let X the random variable who represent the number of phone calls answered.

From the problem we have the mean and the standard deviation for the random variable X. $E(X)=37, Sd(X)=9$

So we can assume $\mu=37 , \sigma=9$

On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

Solution to the problem

For this case we want to find this probability:

$P(10$

And we can use the z score formula to see how many deviation we are within the mean and we got:

$z = \frac{10-37}{9}=-3$

$z = \frac{64-37}{9}=3$

And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.

3 0

3 years ago

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08

kvv77 [185]

Answer:

a) 44.93% probability that there are no surface flaws in an auto's interior

b) 0.03% probability that none of the 10 cars has any surface flaws

c) 0.44% probability that at most 1 car has any surface flaws

Step-by-step explanation:

To solve this question, we need to understand the Poisson and the binomial probability distributions.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Poisson distribution with a mean of 0.08 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

So $\mu = 10*0.08 = 0.8$

(a) What is the probability that there are no surface flaws in an auto's interior?

Single car, so Poisson distribution. This is P(X = 0).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.8}*(0.8)^{0}}{(0)!} = 0.4493$

44.93% probability that there are no surface flaws in an auto's interior

(b) If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

For each car, there is a $p = 0.4493$ probability of having no surface flaws. 10 cars, so n = 10. This is P(X = 10), binomial, since there are multiple cars and each of them has the same probability of not having a surface defect.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003$

0.03% probability that none of the 10 cars has any surface flaws

(c) If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

At least 9 cars without surface flaws. So

$P(X \geq 9) = P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{10,9}.(0.4493)^{9}.(0.5507)^{1} = 0.0041$

$P(X = 10) = C_{10,10}.(0.4493)^{10}.(0.5507)^{0} = 0.0003$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0041 + 0.0003 = 0.0044$

0.44% probability that at most 1 car has any surface flaws

5 0

3 years ago

The probability is 1 in 4,011,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an av

IrinaVladis [17]

Answer:

0.0114

Step-by-step explanation:

(a) What is the probability of a fatal accident over a lifetime?

Suppose A be the event of a fatal accident occurring in a single trip.

Given that:

P(1 single auto trip in the United States result in a fatality) = P(A)

Then;

P(A) = 1/4011000

P(A) = 2.493 × 10⁻⁷

Now;

P(1 single auto trip in the United States NOT resulting in a fatality) is:

P( $\mathbf{\overline A}$ ) = 1 - P(A)

P( $\mathbf{\overline A}$ ) = 1 - 2.493 × 10⁻⁷

P( $\mathbf{\overline A}$ ) = 0.9999997507

However, P(fatal accident over a lifetime) = P(at least 1 fatal accident in lifetime i.e. 46000 trips)

= 1 - P(NO fatal accidents in 46000 trips)

Similarly,

P(No fatal accidents over a lifetime) = P(No fatal accident in the 46000 trips) = P(No fatality on the 1st trip and No fatality on the 2nd trip ... and no fatality on the 45999 trip and no fatality on the 46000 trip)

= $[P(\overline A)] ^{46000} \ \ \ (since \ trips \ are \ independent \ events)$

= $[0.9999997507]^{46000}$

= 0.9885977032

Finally;

P(fatal accident over a lifetime) = 1 - 0.9885977032

P(fatal accident over a lifetime) = 0.0114022968

P(fatal accident over a lifetime) ≅ 0.0114

8 0

3 years ago