Write the ratio 70:80 in its simplest form

Answer:

His pay for 4 hours of work is $106.67.

Step-by-step explanation:

2:1, full rate : reduced rate.

This means that for each 2+1 = 3 hours that he works, 2 he has full pay and 1 he has reduced pay.

4 hours

How much are full pay?

For each 3, 2 are full pay. For four?

3 hours - 2 full pay

4 hours - x full pay

[tex]3x = 8[/tex]

[tex]x = \frac{8}{3}[/tex]

So for [tex]\frac{8}{3}[/tex] hours he makes the full pay($30) and for [tex]4 - \frac{8}{3} = \frac{12}{3} - \frac{8}{3} = \frac{4}{3}[/tex] he makes reduced pay($20).

Calculate his pay for 4 hours of work

[tex]30*\frac{8}{3} + 20*\frac{4}{3} = 106.67[/tex]

His pay for 4 hours of work is $106.67.

Answer:

The answer is option c

x = 1 y = - 1 z = 1

Hope this helps.

Answer:

Step-by-step explanation:

Wheres the question??

Answer:

100

Step-by-step explanation:

When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.

Answer:

100

Step-by-step explanation:

:3

Answer:

a) The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

c)

Step-by-step explanation:

a) Let p be  the probability of winning each ticket be = 0.1

Then q which is the probability of failing each ticket  = 1 - p = 1  - 0.1 = 0.9

Assume X represents the  number of failure preceding the 5th success in x + 5 trials.

The last trial must be success whose probability is p = 0.1 and in the remaining (x + r- 1) ( x+ 4 ) trials we must have have (4) successes whose probability is given by:

[tex]\binom{x+r-1}{r-1}*p^{r-1}*q^{x} = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

Then, the probability distribution of random variable X is

[tex]P(X=x) = \binom{x+4}{4}0.1^{4}*0.9^{x} ; x =0, 1, .........[/tex]

where;

X represents the  negative binomial random variable.

K= X + 5 = number of ticket buy up to and including fifth winning ticket.

Since K =X+5 this signifies that  X = K-5

as X takes value 0, 1 ,2,...

K takes value 5, 6 ,...

Therefore:

The probability mass function of K = [tex]P(K=k) = \binom{k-1}{4}0.1^{4}*0.9^{k-5} ; k =5,6,...[/tex]

b)

Let p represent the probability of getting a tail on a flip of the coin

Thus p = 0.5 since it is a fair coin

where L = number of flips of the coin including 33rd occurrence of  tails

Thus; the negative binomial distribution of L can be illustrated as:

[tex]P(X=x) = \binom{x-1}{r-1}(1-p)^{x-r}p^r[/tex]

where

X= L

r = 33  &

p = 0.5

Since we are looking at the 33rd success; L is likely to be : L = 33,34,35...

Thus; the PMF of L = [tex]P(L=l) = \binom{l-1}{33-1}(1-0.5)^{l}(0.5)^{33} \\ \\ \\ \mathbf{P(L=l) = \binom{l-1}{33-1}(0.5)^{l} }[/tex]

c)  

Given that:

Let  M be the random variable which represents  the number of tickets need to be bought to get the first success,

also success probability is 0.01.

Therefore, M ~ Geo(0.01).

Thus, the PMF of M is given by:

[tex]P(M = m) = (1-0.01)^{m-1} * 0.01 , \ \ \ since \ \ \ (m = 1,2,3,4,....)[/tex]

[tex]P(M=m) = (0.99)^{m-1} * 0.01 , m = 1,2,3,4,....[/tex]

Answer:

Height = 12 inches

Step-by-step explanation:

Volume = Area × Height

1080 = 90 × H

H = 1080/90

H = 12 inches

Answer:

x+(x+2) = 156

Step-by-step explanation:

Let x = 1st odd integer

x+2 = next odd integer

x+(x+2) = 156

2x+2 =156

Subtract 2

2x= 154

Divide by 2

x = 77

x+2 = 79

Answer:

5 / (x+4)      x ≠2 x≠-4

Step-by-step explanation:

5(x-2)/(x-2)(x+4)

The denominator cannot be zero so x ≠2 x≠-4

Cancel like terms in the numerator and denominator

5 / (x+4)      x ≠2 x≠-4

Answer:

[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]

The area is given by:

[tex]A= \pi r^2[/tex]

And replacing we got:

[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]

So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2

Step-by-step explanation:

For this case we know that we have a coin with a diamter of [tex] D =18mm[/tex], and by definition the radius is given by:

[tex] r =\frac{D}{2}=\frac{18mm}{2}= 9mm[/tex]

The area is given by:

[tex]A= \pi r^2[/tex]

And replacing we got:

[tex] A=\pi (9mm)^2 =81\pi mm^2[/tex]

So then we can conclude that the area of the coin is [tex] 81\pi[/tex] mm^2

Answer:

a= 2/5

b= -3/5

Step-by-step explanation:

We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator

[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]

This simplifies to:

[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]

This further simplifies to:

[tex]\frac{-3i +2}{5}[/tex]

Can be rewritten as:

[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]

a = 2/5

b = -3/5

Answer: this is a guess but 7.69 percent chance that you will pick a blue candy

Step-by-step explanation:

Answer:

Choosing 1 blue and 1 green candy

Step-by-step explanation:

There are no red candies and there is only 1 blue candy.

Answer:

[tex]7.9584 \times 10^8[/tex]

Step-by-step explanation:

[tex]8.05 \times 10^8 - 9.16 \times 10^6[/tex]

[tex]805000000-9160000[/tex]

[tex]=795840000[/tex]

Answer:

16. A

17. D

Step-by-step explanation:

16. By saying that a line intersects one plane and then another, you are saying that a line is existing on two planes. This is a direct contradiction to the statement.

17. The triangle is equilateral because syllogism is basically connecting the dots. If the angles in the triangle are all equal, it has all equal sides, and if it has all equal sides, then it is equilateral, therefore, it is D, not C.

Answer:

Car: 60%

Motorcycle: 30%

Truck: 10%

Step-by-step explanation:

Car: [tex]\frac{12}{12+6+2} =\frac{12}{20} =\frac{60}{100}[/tex] or 60%

Motorcycle: [tex]\frac{6}{12+6+2} =\frac{6}{20} =\frac{30}{100}[/tex] or 30%

Truck: [tex]\frac{2}{12+6+2} =\frac{2}{20} =\frac{10}{100}[/tex] or 10%

Answer:

A: 97π/18 m

Step-by-step explanation:

Central Angle = 97°

In radians:

97° = 97π/180

Now

S = r∅

S = (10)(97π/180)

S = 97π/18 m

Answer:

The answer is option 1.

Step-by-step explanation:

Given that the formula for length of Arc is Arc = θ/360×2×π×r when r represents the radius of circle. Then, you have to substitute the following values into the formula :

[tex]arc = \frac{θ}{360} \times 2 \times \pi \times r[/tex]

Let θ = ∠VCW = 97°,

Let r = 10m,

[tex]arc = \frac{97}{360} \times 2 \times \pi \times 10[/tex]

[tex]arc = \frac{97}{360} \times 20 \times \pi[/tex]

[tex]arc = \frac{97}{18} \pi \: m[/tex]

Answer: What what my you explain shorter please

Step-by-step explanation:

Answer:

a. P(X>695)=0.026

b. P(X<485)=0.44

Step-by-step explanation:

The question is incomplete:

a. higher than 695 on the test.

b. at most 485 on the test.

We have a normal distribution with mean 500 and standard deviation of 100 for the test scores. We will use the z-scores to calculate the probabilties with the standard normal distribution table.

a. We want to calculate the probability that a randomly selected student scores higher than 695.

We calculate the z-score and then we calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{695-500}{100}=\dfrac{195}{100}=1.95\\\\\\P(X>695)=P(z>1.95)=0.026[/tex]

a. We want to calculate the probability that a randomly selected student scores at most 485.

We calculate the z-score and then we calculate the probability:

[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{485-500}{100}=\dfrac{-15}{100}=-0.15\\\\\\P(X<485)=P(z<-0.15)=0.44[/tex]

Answer:

Oil

Step-by-step explanation:

Car engine needs oil to avoid friction.

Answer:

[tex]oil \\ [/tex]

Answer C is correct

Step-by-step explanation:

car engine needs oil to avoid the friction .

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer: The graph is

The graph is plotted and attached.

A function is a law that relates a dependent and an independent variable.

The function is y = 3/4 x + 5

The slope of the line is (3/4)

and the y intercept is 5.

The graph is plotted and attached with the answer.

To know more about Function

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Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 30.7, \sigma = 23[/tex]

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 30.7}{23}[/tex]

[tex]Z = -0.03[/tex]

[tex]Z = -0.03[/tex] has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

[tex]n = 36[/tex]

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is [tex]s = \frac{23}{\sqrt{36}} = 3.83[/tex]

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 30.7}{3.83}[/tex]

[tex]Z = 1.12[/tex]

[tex]Z = 1.12[/tex] has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Answer:

C

Step-by-step explanation:

The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.

Answer:

c) The Z-score = - 1.90 unusual

Step-by-step explanation:

Explanation:-

Let 'X' be the random variable in normal distribution

Given student received a score X = 50

Mean of the Population x⁻ = 69

standard deviation of the Population 'σ' = 10

now

[tex]Z = \frac{x^{-}-mean }{S.D}[/tex]

[tex]Z = \frac{x^{-}-mean }{S.D} = \frac{50 -69}{10} = - 1.90[/tex]

The Z-score = - 1.90

Conclusion:-

The Z-score = - 1.90 unusual

Answer: The Z-score = - 1.90 unusual

Step-by-step explanation:

Answer:

hey mate,

here is your answer. Hope it helps you.

C-(3,3)

Step-by-step explanation:

An equilateral triangle, which has three equal sides, has three lines of symmetry. This is because you can fold an equilateral triangle in  three halves and the are equal. Hence an equilataral triangle has three vertices and 3 lines of symmetry.

Answer:

to cm it's still 200 if you mean to metre 2m

Step-by-step explanation:

Answer:

It would still be 200

Step-by-step explanation:

Answer:

The probability that either Alex or Bryan get an A is 0.9

Step-by-step explanation:

Before we proceed to answer, we shall be making some important notation;

Let A = event of Alex getting an A

Let B = event of Bryan getting an A

From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1

We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)

We can use the addition theorem here;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)  .......................(i)

Also,

P(A) = P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)   .........................(ii)

We can insert ii into i and we have;

P(A ∪ B) =  P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)  + P(B) - P(A ∩ B) =   P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9

Answer:

  see below

Step-by-step explanation:

The first subtraction has a zero result (blue) from the thousands digit, so we know the dividend has 4 in that place. The 5 in the 1s place of the dividend is brought down to fill the space on the bottom line. 6 goes into that number 0 times, so the final quotient digit is 0.

  4,925 = 6×820 +5

or

  4,925 ÷ 6 = 820 r5

Answer:

Are there any choices?..

The correct statement the describes the equation is The lines intersect at (1, 0) and the lines are parallel.

x - y = 1.............equation 1

y - x = 1.............equation 2

Add equations (1) and (2):

(x - y) + (y - x) = 1 + 1

Simplifying

0 = 2

Since 0 = 2, the system is inconsistent, meaning there is no solution. The lines represented by the equations are parallel and will never intersect.

The system of equations has no solution, as the lines represented by the equations are parallel and will never intersect.

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The complete question is- Which statement describes the graph of the system of equations?

[x-y=1

Ly- X= 1

The lines are parallel.

The lines are coinciding.

The lines intersect at(1, 0).

The lines intersect at (-1,0).

Answer:

yall the answer is B for 2020 edge

Step-by-step explanation:

I took the test

Answer:

I do agree its B.

Step-by-step explanation:

Why i think this is because my average grade was a 100%

Answer:

A score of 1920 has a z-score of 1.27.

A score of 1290 has a z-score of -0.74.

A score of 2220 has a z-score of 2.23.

A score of 1420 has a z-score of -0.32.

The score of 2220 is more than two standard deviations from the mean, so it is unusual.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If X is 2 or more standard deviations from the mean, it is considered unusual.

In this question, we have that:

[tex]\mu = 1521, \sigma = 314[/tex]

Score of 1920:

X = 1920. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1920 - 1521}{314}[/tex]

[tex]Z = 1.27[/tex]

A score of 1920 has a z-score of 1.27.

Score of 1290:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1290 - 1521}{314}[/tex]

[tex]Z = -0.74[/tex]

A score of 1290 has a z-score of -0.74.

Score of 2220:

X = 1290. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2220 - 1521}{314}[/tex]

[tex]Z = 2.23[/tex]

A score of 2220 has a z-score of 2.23.

Since it is more than 2 standard deviations of the mean, the score of 2220 is unusual.

Score of 1420:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1420 - 1521}{314}[/tex]

[tex]Z = -0.32[/tex]

A score of 1420 has a z-score of -0.32.

Answer:

140

Step-by-step explanation:

Because the lines are parallel:

[tex]\dfrac{DE}{35}=\dfrac{60}{15} \\\\DE=4\cdot 35=140[/tex]

Hope this helps!