Choose the point-slope form of the equation of this line.​

Answer:

Step by step solution:

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:

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: 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

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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: she will have 36 levels completed

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:

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

Step-by-step explanation:

-11b + 7 = 40

-11b = 40 - 7

-11b = 33

b = 33/-11

b = - 3

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:

66.7%

Step-by-step explanation:

The numbers less than 7 on the list are 3, 4, 5, and 6.

4 numbers are less than 7 out of total 6 numbers.

4/6 = 2/3 = 0.667 = 66.7%

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:825cm

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

275*3=825cm

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:

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

Answer: g(x)= -x^2

Step-by-step explanation:

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

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:

2 and 256

Step-by-step explanation:

Check the attachment

Answer:

2  and255

Step-by-step explanation:

look atyourquestion

Answer:

9 1/2

Step-by-step explanation:

Answer:

[tex]\frac{3x}{32}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}\times \frac{1}{4}x[/tex]

[tex]\frac{3\times \:1\times \:x}{8\times \:4}[/tex]

[tex]=\frac{3x}{32}[/tex]

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:

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.

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:

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

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Answer:

c. (280+ 0.050d)w

Step-by-step explanation:

Owen gets paid $280 per week

=$280 per week

Plus 5% commission on all sales of electronic equipment

=0.05

If he sells the dollar(d) worth of electronic equipment in one week

=(0.05d)w

Total earnings

=280w+0.05(d)w

Factorise

=(280+0.05d)w

Owen=(280+0.05d)w

c. (280+ 0.050d)w

*0.050=0.05

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

Answer:

Denver got 72 inches of snow over three days.

Step-by-step explanation:

Since it has snowed consistently for 3 days, accumulating an inch of snow per hour, over that number of days at least 72 inches of snow would have accumulated.

This is so because, since each day has 24 hours, in the event of a 3-day snowfall, it would have lasted 72 hours. Thus, while every hour a new inch of snow would accumulate, at the end of the storm the city of Denver would have accumulated 72 inches of snow (1 x 24 x 3 = 72).

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:

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: 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.