(m-3)/(7)=(m)/(m+8) Solve the proportion.

Answer: 1/8

Step-by-step explanation:

Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.

Hope this helps! Please mark as brainliest!

The unit fraction of the cake is 1/8

A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.

A unit fraction is therefore the reciprocal of a positive integer, 1/n.

Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.

Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake

Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.

Hence, the unit fraction of the cake is 1/8

Learn more about unit fractions, click;

https://brainly.com/question/15326565

#SPJ3

Answer:

There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.

Step-by-step explanation:

We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.

Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000      {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000      {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}

The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;

                              T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean market value = $259,860

            s = sample standard deviation = $24,922

            n = sample of houses = 35

So, the test statistics  =  [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex]  ~ [tex]t_3_4[/tex]

                                     =  2.34

The value of t-test statistic is 2.34.

Also, P-value of the test statistics is given by;

            P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137

Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.

Answer:

0.0579

Step-by-step explanation:

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

Probability of obtaining a success is 0.0579 .

Here,

Binomial distribution formula:

P(x:n,p) = nCx px (1-p)n-x Or P(x:n,p) = nCx px (q)n-x

Substituting the values of n and p

n = 5

p = 0.8

So,

P(X≤2) = P(X=0) + P(X=1) + P(X=2)

P(X≤2) = ₅C₀ (0.8)⁰ (0.2)⁵ + ₅C₁ (0.8)¹ (0.2)⁴ + ₅C₂ (0.8)² (0.2)³

P(X≤2) = 0.00032 + 0.0064 + 0.0512

P(X≤2) = 0.0579

Know more about binomial distribution,

https://brainly.com/question/29163389

#SPJ3

Answer: g(x)= -x^2

Step-by-step explanation:

BRO THIS IS THE MOST BASIC ALGEBRA 1 !?!?!?!?!?!?!?!

Answer:

I believe it is Inductive Reasoning.

Step-by-step explanation:

Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.

Deductive Reasoning is a basic form of valid reasoning.

Answer:

5/6

Step-by-step explanation:

10/12

Divide the top and bottom by 2

10/2 = 5

12/2 =6

the fraction becomes 5/6

Answer :

10/12

Reduce the fraction

= 5/6

Answer:825cm

Step-by-step explanation:550cm/2=275cm

275*3=825cm

Answer:

0.5 gallon

Step-by-step explanation:

let x refer to students

5 = 8x + 1

8x = 4

x= 0.5 gallon

Answer: (fоg)(24)=5

Step-by-step explanation:

(fоg)(24) is f of g of 24. This means you plug in g(24) into f(x).

[tex]g(24)=\sqrt{24-8}[/tex]

[tex]g(24)=\sqrt{16}[/tex]

[tex]g(24)=4[/tex]

Now that we know g(24), we can plug it into f(x).

f(4)=2(4)-3

f(4)=8-3

f(4)=5

Answer:

(a) P(Millennial | Read a Book) = 0.3086

(b) P( Not Millennial | Did Not Read a Book) = 0.8421

(c)

P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)

0.25 = 0.81 × 0.28

0.25 ≠ 0.2268

Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.

Step-by-step explanation:

The probability a person has read a book in the past year is 0.81.

P(Read a Book) = 0.81

The probability a person is considered a millennial is 0.28.

P(Millennial) = 0.28

The probability a person has read a book in the past year and is considered a millennial is 0.25.

P(Millennial and Read a Book) = 0.25

(a) Find P(Millennial | Read a Book)

Recall that Multiplicative law of probability is given by

P(A ∩ B) = P(B | A) × P(A)

P(B | A) = P(A ∩ B) / P(A)

For the given case,

P(Millennial | Read a Book) = P(Millennial and Read a Book) / P(Read a Book)

P(Millennial | Read a Book) = 0.25 / 0.81

P(Millennial | Read a Book) = 0.3086

(b) Find P(Not Millennial | Did Not Read a Book)

P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)

Where

∵  P(A' and B') = 1 - P(A or B)

P(Not Millennial and Did Not Read a Book) = 1 - P(Millennial or Read a Book)

∵  P(A or B) = P(A) + P(B) - P(A and B)

P(Millennial or Read a Book) = P(Read a Book) + P(Millennial) - P(Millennial and Read a Book)

P(Millennial or Read a Book) = 0.81 + 0.28 - 0.25

P(Millennial or Read a Book) = 0.84

So,

P(Not Millennial and Did Not Read a Book) = 1 - 0.84

P(Not Millennial and Did Not Read a Book) = 0.16

Also,

∵  P(A') = 1 - P(A)

P(Did Not Read a Book) = 1 - P(Read a Book)

P(Did Not Read a Book) = 1 - 0.81

P(Did Not Read a Book) = 0.19

Finally,

P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)

P( Not Millennial | Did Not Read a Book) = 0.16/0.19

P( Not Millennial | Did Not Read a Book) = 0.8421

(c) Are being considered a millennial and having read a book in the past year independent events? Justify your answer mathematically.

Mathematically, two events are considered to be independent if the following relation holds true,

P(A and B) = P(A) × P(B)

For the given case,

P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)

0.25 = 0.81 × 0.28

0.25 ≠ 0.2268

Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.

Answer:

1/9

Step-by-step explanation:

Since each next term is 1/9 of the last, the common ratio is 1/9. This can be confirmed by the fact that 243*1/9=27, 27*1/9=3, 3*1/9=1/3, and so on. Hope this helps!

Answer:

71.25 - 22.50 = d

Step-by-step explanation:

To find how much she earned yesterday, we subtract how much she earned today by the amount more she earned.

Answer:

A

Step-by-step explanation:

Answer:

Step by step solution:

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

So

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that [tex]P(B) = \frac{1}{3}[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667[/tex]

So

[tex]P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714[/tex]

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that [tex]P(B) = 0.7[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25[/tex]

So

[tex]P(B|A) = \frac{0.7*0.1}{0.25} = 0.28[/tex]

28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

-11b + 7 = 40

-11b = 40 - 7

-11b = 33

b = 33/-11

b = - 3

Answer:

yes

Step-by-step explanation:

not every person is going to have the same opinion, so it is yes.

// have a great day //

Answer:

Yes, because if Pedro asked them the question "what do you think of public transportation?" the majority would probably say that they like it or something along those lines. This is biased because there may be other city inhabitants who don't think very highly of public transportation. Basically, what I'm trying to say is that not everyone will have the same opinion.

Answer: she will have 36 levels completed

Answer: he can make 21 different numbers.

Step-by-step explanation:

If he uses only one card, the numbers are:

1, 2 and 6, so here we have 3 combinations.

If he uses two cards, for the first digit he has 3 options (because he has 3 cards) and for the second digit he has two options (because he already selected one of the cards) then he has:

3*2 = 6 different options

If uses the 3 cards, then he has 3 options for the first card, 2 options for the second card and one option for the third card, then the number of combinations is:

c = 3*2*1 = 6 combinations.

Adding all together we have C = 3 + 6 + 6 = 21 combinations.

Answer:

Step-by-step explanation:

The claim here is that the brand name aspirin is more consistent in the amount of active ingredient used than the generic aspirin.

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean amount of active ingredients in brand name aspirin and μ2 be the mean amount of active ingredients in generic name aspirin

The random variable is μ1 - μ2 = difference in the mean amount of active ingredients between the brand name and generic aspirin

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 ≥ μ2 H0 : μ1 - μ2 ≥ 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 325.01

x2 = 323.47

s1 = 10.12

s2 = 11.43

n1 = 200

n2 = 180

t = (325.01 - 323.47)/√(10.12²/200 + 11.43²/180)

t = 1.24

1.237877

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [10.12²/200 + 11.43²/180]²/[(1/200 - 1)(10.12²/200)² + (1/180 - 1)(11.43²/180)²] = 1.53233946713/0.00537245359

df = 285

We would determine the probability value from the t test calculator. It becomes

p value = 0.108

Since alpha, 0.025 < than the p value, 0.108, then we would fail to reject the null hypothesis. Therefore, at 2.5% level of significance, these data support the brand name producers claim

Answer:

b: a over b divided by do over c

Step-by-step explanation:

You can solve this by plugging in numbers for each variable.

For example: a=1, b=4, c=1, d=2

1/4 ÷ 1/2 = 0.125

If you plug in the numbers for all the equations listed, only 1/4 ÷ 2/1 = 0.125.

Answer:

Step-by-step explanation:

In constructing a confidence interval about the mean, the central limit theorem is usually applied. This makes it possible to use the normal distribution. As the number of samples is increasing, the distribution tends to be normal. This would require using the z distribution. In the case where the sample size is small, we assume a normal distribution and use the t distribution. Therefore, the given statement is true.

Answer: A. This is a discrete probability distribution.

hours             probability

  1                      0.09        

 2                      0.16

 3                      0.23

 4                      0.17

 5                      0.09

 6                      0.05

 7                      0.04

 8                      0.16

B. E(X) = 4.12; σ = 2.21

C. μ = 12.75; s = 6.11

Step-by-step explanation: Probability Distribution is an equation or table linking each outcome of an experiment with its probability of ocurrence. For this case, since the experiment is performed a high number of times and in a long run, the relative frequency of the event is its probability. Therefore:

A. To convert to a probability distribution, find the probability through the frequency by doing:

Hour 1

P(X) = [tex]\frac{21}{228}[/tex] = 0.09

Hour 2

P(X) = [tex]\frac{36}{228}[/tex] = 0.16

Hour 3

P(X) = [tex]\frac{53}{228}[/tex] = 0.23

Hour 4

P(X) = [tex]\frac{40}{228}[/tex] = 0.17

Hour 5

P(X) = [tex]\frac{22}{228}[/tex] = 0.09

Hour 6

P(X) = [tex]\frac{11}{228}[/tex] = 0.05

Hour 7

P(X) = [tex]\frac{9}{228}[/tex] = 0.04

Hour 8

P(X) = [tex]\frac{36}{228}[/tex] = 0.16

The table will be:  

hours             probability

  1                      0.09        

 2                      0.16

 3                      0.23

 4                      0.17

 5                      0.09

 6                      0.05

 7                      0.04

 8                      0.16

This is a discrete distribution because it lists all the possible values that the discrete variable can be and its associated probabilities.

B. Mean for a probability distribution is calculated as:

E(X) = ∑[[tex]x_{i}[/tex].P([tex]x_{i}[/tex])]

E(X) = 1*0.09 + 2*0.16+3*0.23+4*0.17+5*0.09+6*0.05+7*0.04+8*0.16

E(X) = 4.12

Standard Deviation is:

σ = √∑{[x - E(x)]² . P(x)}

σ = [tex]\sqrt{(1-4.12)^{2}*0.09 + (2-4.12)^{2}*0.16 + ... + (7-4.12)^{2}*0.04 + (8-4.12)^{2}*0.16}[/tex]

σ = [tex]\sqrt{4.87}[/tex]

σ = 2.21

The average number of hours parked is approximately 4h with a standard deviation of approximately 2 hours, which means that a typical costumer parks between 2 to 6 hours.

C. Mean for a sample is given by: μ = ∑[tex]\frac{x_{i}}{n}[/tex] , which is this case is:

μ = [tex]\frac{4+6+9+13+14+16+18+22}{8}[/tex]

μ = 12.75

Standard Deviation of a sample: s = √[tex]\frac{1}{n-1}[/tex]∑([tex]x_{i}[/tex] - μ)²

s =  [tex]\sqrt{ \frac{(4-12.75)^{2} + (6-12.74)^{2} + ... + (18-12.75)^{2} + (22-12.75)^{2} }{8-1}}[/tex]

s = 6.11

The average amount charged is 12.75±6.11.

Answer:

-3

Step-by-step explanation:

You find the difference between the numbers, which is 3. Then you make it negative since 24 is less than 27.

Answer:

h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.

Answer:

D

Step-by-step explanation:

the height of the rock 3.2 seconds before it reaches the ground

the time it takes the rock to reach the ground, or 3.2 seconds

the time it takes the rock to reach a height of 3.2 meters

the height of the rock 3.2 seconds after it is propelled

Answer:

See explanation below

Step-by-step explanation:

1) Prove or disprove that if [tex] x^y[/tex] is an irrational number, then x or y is also an irrational number.

Let's take the following instances:

i) When x= 2 and y=[tex] \sqrt{2} [/tex] we have: [tex] 2^\sqrt^{^2^} [/tex]

ii) When [tex] x=2\sqrt{2} [/tex] and y=3, we have: [tex] (x=2\sqrt{2})^3 [/tex]

iii) When [tex] x=2\sqrt{2} [/tex] and [tex] y = \sqrt{2}[/tex], we have: [tex] (2\sqrt{2})^\sqrt^{^2^}[/tex]

It is proven because, in scenario

i) x is rational and y is irrational

ii) x is irrational and y is rational

iii) x and y are irrational

2) Prove tha x² is irrational, then x is irrational.

Use contradiction here.

Thus, x² is irrational and x is rational.

[tex] x =\frac{b}{a} [/tex] when x is rational, a & b are integers.

Therefore, [tex] x^2 =\frac{b^2}{a^2} [/tex]. This x² is rational.

This contradicts the statement that x² is irrational.

Therefore, if x² is irrational, x is also irrational.

Answer:

a) 13/25

b) 12/15

Step-by-step explanation:

a) Since it is with replacement, the chance of them being both the same colour will be

P(both red) + P(both black) = (6/15*6/15) + (9/15*9/15)

                                              = 13/25

b) If they are both different colours, then we will be working out

P(both colours) = (6/15*9/15)*2 = 12/25   (Its *2 because the other way of pulling both colours is 9/15*6/15 which is the same but flipped)

Another way of working this question out is

P(1-All red or all blue) which from above we know that All red or all blue is 13/25 so

P(1-All red or all blue) = 1 - 13/25 = 12/25

Step-by-step explanation:

[tex] \boxed{3!} + \boxed{9 }+ \boxed{15} = 30 \\ \because \: 3! = 3 \times 2 \times 1 = 6 \\ \therefore \: 6 + 9 + 15 = 30[/tex]

Answer:

Step-by-step explanation:

a. The hypotheses are:

Null hypothesis: the average test scores are the same for the different teaching methods.

Alternative hypothesis: the average test scores are different for the different teaching methods.

b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample

c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.

Answer:

90

Step-by-step explanation:

1/1111= 0. (0009) cycles of 0009 after decimal point (one 9 per 4 digits)

Number of digits 9:

Answer:

90

Step-by-step explanation: