GIVING BRAIN AND 30pointsWhat is the solution to the system of equations below?
y=-3x+2 and 3y =-
3
4
X-6
no solution
infinitely many solutions
(-16, 6)
O (-16, -2)

Answer:

It would increase by 1

Step-by-step explanation:

Step 1: Find the mean of the original

(9+6+1+1+3)/5 = 4

Step 2: Find the mean of the new

(9+6+1+1+8)/5 = 5

Step 3: Find the difference

5 - 4 = 1

Answer:

Step-by-step explanation:

[tex]H_0 : \texttt {null hypothesis}\\\\H_1 : \texttt {alternative hypothesis}[/tex]

The null hypothesis is the drink preferences are not changed at coffee shop.

The alternative hypothesis is the drink preferences are changed at coffee shop.

the level of significance = α = 0.05

We get the Test statistic

[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex]

Where, [tex]F_o[/tex] is observed frequencies and

[tex]F_e[/tex] is expected frequencies.

N = 6

Degrees of freedom = df = (N – 1)

= 6 – 1

= 5

the level of significance  α = 0.05

Critical value = 11.07049775

( using Chi square table or excel)

Tables for test statistic are given  below

                             F_o                F_e                 Chi square

Americanos           115                 153                9.4379

Capp.                     88                  94.5             0.447

Espresso               69                  63                 0.5714

Lattes                    59                  49.5               1.823

Macchiatos           44                   45                 0.022

Other                    75                   45                  20

Total                    450                 450                 32.30

[tex]\texttt {Chi square}=\frac{\sum (F_o-F_e)}{F_e}[/tex] = 32.30

P-value = 0.00000517

( using Chi square table or excel)

P-value < α = 0.05

So, we reject the null hypothesis

This is because their sufficient evidence to conclude that Drink preferences are changed at coffee shop.

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:

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: 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:

  5.5 in

Step-by-step explanation:

The altitude is (√3)/2 times the length of a side, so the side length is the inverse of that times the length of the altitude:

  side length = (2/√3)(4.8 in) ≈ 5.5 in

Answer: she will have 36 levels completed

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:

56

Step-by-step explanation:

to find x u add 60 and 64 which is 124

the total is 180 so u would subtract 180 by 124

hope this helps

Answer:

2 and 256

Step-by-step explanation:

Check the attachment

Answer:

2  and255

Step-by-step explanation:

look atyourquestion

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:

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. 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:

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: g(x)= -x^2

Step-by-step explanation:

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

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:

1/2 (simplified)

Step-by-step explanation:

6 numbers (that's the total probability) --> 6 denominator

3 are odd (odd numbers in the probability) --> 3 numerator

so => 3/6

--> simplify

1/2

Hope this helps!

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.

Step-by-step explanation:

-11b + 7 = 40

-11b = 40 - 7

-11b = 33

b = 33/-11

b = - 3

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:

Step-by-step explanation:

The justification of each given statements in the question are:

11) F. Definition of right angle.

12) D. Definition of supplementary <'s.

13) A. Definition of congruence.

14) C. Definition of complementary <'s.

15) L. Congruent supplementary theorem

16) H. Vertical angle theorem.

17) G. Angle addition postulate.

18) J. Supplementary theorem.

Answer:

84 x^12

Step-by-step explanation:

(4x)(-3x^8)(-7x^3)

Multiply the numbers

4*-3 *-7 = 84

x* x^8 * x^3 = Add the exponents = x^(1+8+3) = x^12

84 x^12

Answer:

C. 84x^12

Step-by-step explanation:

edge 2020

Answer:

The complete factored form of this equation is (d + 6)²

Step-by-step explanation:

The first step in factoring this equation is multiply the first term and the last term together. Out first term is d² and our last term is 36. Since d² does not have a coefficient, then we assume this number to be 1.

1 × 36 = 36

So, now we need to find two factors that multiply to 36 and add together to get 12. Two factors that best represents this is 6 and 6. So, we will plug these numbers into our equation. Replace 12d with 6d + 6d.

d² + 6d + 6d + 36

Group the first two terms together and the last two terms together.

(d² + 6d) + (6d + 36)

Now, find the greatest common factor of each parentheses and factor the terms.

d(d + 6) + 6(d + 6)

From looking at this, we can tell that this equation is a perfect squared equation. So, this means instead of writing both parentheses, we can just write one of the parentheses and square it.

So, the factored form of this equation is (d + 6)²

Answer:

[tex]y(x)==(c_1+c_2x)e^{3x}+3x^2+4x[/tex]

Step-by-step explanation:

We are given that  non-homogeneous equation

[tex]y''-6y'+9y=27x^2-18[/tex]

Particular solution of given equation is given by

[tex]y_p=3x^2+4x[/tex]

We  have to find the general solution of the non-homogeneous equation.

Auxillary equation

[tex]m^2-6m+9=0[/tex]

[tex]m^2-3m-3m+9=0[/tex]

[tex]m(m-3)-3(m-3)=0[/tex]

[tex](m-3)(m-3)=0[/tex]

[tex]m=3,3[/tex]

[tex]y_c=(c_1+c_2x)e^{3x}[/tex]

General solution is given by

[tex]y(x)=y_c+y_p[/tex]

[tex]y(x)==(c_1+c_2x)e^{3x}+3x^2+4x[/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:

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: (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:

Step-by-step explanation:

i. The parameter the manager is interested in is number of defective bulbs in a case.

ii. Null hypothesis: u <= 20

Alternative hypothesis: u > 20

iii. The critical value the manager should use to determine the rejection region is 1.645.

iv. Using the p value which is 0.021 at 0.10 significance level we will reject the null as the p value is less than 0.1. Thus, we will conclude that there is enough statistical evidence to prove that the mean number of defective bulbs per case is greater than 20.

v. Our risk of committing type one error is alpha which is the level of significance set for the hypothesis test. An alpha level of 0.1 shows that we are willing to accept a 10% chance that we are wrong when you reject the null hypothesis.

vi. With a low p value, the data has enough evidence to prove that the mean number of defective bulbs per case is greater than 20 during the morning shift

vii. The manager will conclude that there is sufficient statistical evidence to prove that mean number of defective bulbs per case is greater than 20 during the morning shift.

viii. the p value if this is a two tail test would be 0.03662

Answer:

3 - 3i

Step-by-step explanation:

The conjugate is the opposite sign i of the original. So you simply switch the sign of 3i to -3i to find your conjugate.

Answer:

3 - 3i

Step-by-step explanation:

Change the sign only of the imaginary part.

The conjugate of 3 + 3i is 3 - 3i.