(08.02 MC)

A pair of equations is shown below:

y = 2x − 1
y = 4x − 5

Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)

Part B: What is the solution to the pair of equations? (4 points)

Answer:

1/2

Step-by-step explanation:

(1/16)^x

Let x = 1/4

(1/16)^ 1/4

Rewriting 16 as 2^4

(1/2^4)^ 1/4

We know that 1 / a^b = a^-b

(2 ^ -4)^ 1/4

We know that a^b^c = a^(b*c)

2^(-4*1/4)

2^-1

We know that  a^-b = 1/ a^b

2^-1 = 1/2^1 = 1/2

Answer:

C. 1,620 in^3

Step-by-step explanation:

Thank you!

Answer:

326.8 million

Step-by-step explanation:

You just get 14% of 380 million and subtract it from 380 million

Answer:

g'(x) has a range of y ≤ −6, and its vertex is at (−6, 6)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Though you may think that u can change that piece to there, but the possibility is very less

Answer:

8 meters

Step-by-step explanation:

perimeter of a rectangular figure = 2( length + width)

=> 22 = 2 ( length + 3)

=> 11 = length + 3

=> length = 8

Answer: 9

Step-by-step explanation:

[tex]5^{2}[/tex] x [tex]5^{m}[/tex] is same as [tex]5^{2 + m}[/tex]

So, [tex]5^{2+m} = 5^{11}[/tex]

Since we have the same base we can negotiate it,

2 + m = 11

m = 11 - 2

m = 9

Answer:

52/63

Step-by-step explanation:

Given the expression;

4/7 * 13/9

WE are to take the product

= (4/9)* (13/7)

= (4*13)/(7*9)

= 52/63

Hence the required fraction is  52/63

Answer:

f(x) = (x-4)(x+2)

Step-by-step explanation:

f(x) = x^2 – 2x – 8

What 2 numbers multiply to -8 and add to -2

-4*2 = -8

-4+2 = -2

f(x) = (x-4)(x+2)

[tex]\longrightarrow{\green{ D. \:f(x)\:=\:(x - 4)(x + 2) }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \: f(x) = {x}^{2} - 2x - 8[/tex]

[tex] \:f(x) = {x}^{2} - 4x + 2x - 8[/tex]

Taking [tex]x[/tex] as common from first two terms and 2 from last two terms, we have

[tex] \:f(x) = x \: (x - 4) + 2 \: (x - 4)[/tex]

Taking the factor [tex](x-4)[/tex] as common,

[tex] \:f(x) = (x - 4)(x + 2)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

-3x³ + 44x² - 43x + 10

Step-by-step explanation:

[tex]\left[\begin{array}{ccc}&-3x&2\\x^2&-3x^3&2x^2\\-14x&42x^2&-28x\\5&-15x&10\end{array}\right][/tex]

= -3x³ + 2x² + 42x² - 28x - 15x + 10 = -3x³ + 44x² - 43x + 10

Answer:

420 unique combinations.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

One object from each set:

2 from one set, 5, 6 and 7 by others. Sets are independent, so, by the fundamental counting principle:

2*5*6*7 = 10*42 = 420

420 unique combinations.

Answer:

its 5 because of the formula

Step-by-step explanation:

Answer:

90

2

O

I can't see the last question clearly

Answer:

I don’t know

Step-by-step explanation:

Answer:

[tex]area \: of \: a \: rectangle = \: length \times width(or \: breadth) \: (unit ^{2} )[/tex]

Part B: I don't know part B :-)(•‿•)

Answer:

A

Step-by-step explanation:

Set up a ratio for the two triangles that are there.

x/(x + 10) = 20 / (20 + 8)         Combine the two terms in the right denominator

x/(x + 10) = 20/28                   Cross Multiply

28x = 20(x + 10)                      Remove the brackets on the right

28x = 20 x + 200                    Subtract 20x from both sides

8x = 200                                  Divide by 8

x = 200 /8

x = 25

Answer:

They would know a and b.

a. The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.

b. Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.

c. To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

a. The value of the mean of the sampling distribution of the sample mean.

The mean of this distribution, by the Central Limit Theorem, is the sample mean, and thus, the researches would know this after they took the sample.

b. The approximate shape of the sampling distribution of the sample mean.

Sample size is 100 > 30, and thus, by the Central Limit Theorem, they would know that the shape of the distribution is approximately normal.

c. The standard deviation of the sampling distribution of the sample mean.

To know the standard deviation of the sampling distribution of the sample mean, the researchers would have to know the population's standard deviation, which they can't get for the sample. So they would not know the standard deviation of the sampling distribution of the sample mean after they took the sample.

Answer:

a)

- the probability she will win the dinner for two is 0.016

- the probability she will not win the dinner for two is 0.984

b)

- Lisa's expected earnings is $0.57

- Money she effectively contributed to the hiking club is $11.43

Step-by-step explanation:

Given the data in the question;

fortune cookies; $1 per cookies

club sold 743

a) Lisa bought 12 cookies. What is the probability she will win the dinner for two?

P( she will win ) = Number of cookies bought / Total number of cookies

P( she will win ) = 12 / 743

P( she will win ) = 0.01615 ≈ 0.016

Therefore,  the probability she will win the dinner for two is 0.016

P( she will not win ) = 1 - P( she will win )

P( she will not win ) = 1 - 0.016

P( she will not win ) = 0.984

Therefore,  the probability she will not win the dinner for two is 0.984

b)  Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? (Round your answer to two decimal places.)$

given that value of dinner = $35

P( she will win ) = 0.01615

so

Lisa's earning = $35 × 0.01615

Lisa's earning = $0.57

Therefore, Lisa's expected earnings is $0.57

- How much did she effectively contribute to the hiking club? (Round your answer to two decimal places.)$

Lisa's contribution = Money she paid for cookies - money from expected earnings

Lisa's contribution = ( 12 × $1 ) -  $ 0.57

Lisa's contribution = $12 -  $0.57

Lisa's contribution = $11.43

Therefore, Money she effectively contributed to the hiking club is $11.43

Answer:

D.   Pink

Step-by-step explanation:

Two equation with no solutions means the lines are parallel

Answer:

500

Step-by-step explanation:

Answer:

let ? be x

every linear equation is y=mx+c

so the answer would be y=?+3

Answer:

2,3 &13

Step-by-step explanation:

78=2times39=3times13

therefore the prime factors of 78=2,3,13

Answer:

Round off the decimal to the nearest tenths.

0.82

The answer is 0.80

Step-by-step explanation:

When I learned rounding, we would round to the place value behind it then if its less than 5 than my answer would be what its rounded to. If I round 92 to the nearest tenth, it would be 90 because 2 is not greater than 5 so it would round to 90 because its the nearest tenth. If it was 95 it would be rounded to 100, any number that is 5 to 9 would be rounded to the greater tenth closer to it. So 0.82 is less than 5 nor 5 so it would round up to 0.80

Answer:

5000 students appeared in the examination.

Step-by-step explanation:

We solve this question using Venn probabilities.

I am going to say that:

Event A: Passed in Mathematics

Event B: Passed in English.

5% failed in both subjects

This means that 100 - 5 = 95% pass in at least one, which means that [tex]P(A \cup B) = 0.95[/tex]

80% passed in mathematics 75% passed in english

This means that [tex]P(A) = 0.8, P(B) = 0.75[/tex]

Proportion who passed in both:

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

Considering the values we have for this problem

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.8 + 0.75 - 0.95 = 0.6[/tex]

3000 of them were passed both subjects how many students appeared in the examination?

3000 is 60% of the total t. So

[tex]0.6t = 3000[/tex]

[tex]t = \frac{3000}{0.6}[/tex]

[tex]t = 5000[/tex]

5000 students appeared in the examination.

Answer:

3

Step-by-step explanation:

slope of line = gradient of line

= [tex]\frac{10-4}{3-1}[/tex]

= 3

Answer:

2.

Step-by-step explanation:

You don't have to mark me brainliest but, 4=22-9x. -18=-9x. 9x=18. x=2

2.

Answer:

You click on the ANSWER button and type in your answer and sometimes explanation (if necessary) and then click the blue paper airplane button on the right to post it. Hope this helps.

Answer:

Percentage = 6.8% or 7%

Explanation

cold = 25/100  

Large = 27/100

large multiplied by cold = (25/100 x 27/100) / 25 x 27 =  0.0675 x 100

= 6.75%

Percentage = 7 %

or 6.8 % to 1dp

The probability is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Here the percentage that the customer ordered a cold drink is 5.5 %.

Probability is the measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can only predict the chance of an event to occur. The probability of all the events in a sample space adds up to 1.

The value is expressed from zero to one. Here zero means the event is impossible.

Here the probability to select cold drink = 25 /100

The probability to select Large drink = 22 / 100

When we multiply both the probability, then it becomes:

25 /100 × 22 / 100 = 25 × 22 = 550 / 100 = 5.5 %

Thus the probability is  5.5 %.

To know more about probability, visit;

https://brainly.com/question/31355126

#SPJ7

Answer:

72°

Step-by-step explanation:

180-3x=2x

5x=180

x=36

Angle CBE = 2(36) = 72

Answer:

V = 217.71 in^3

Step-by-step explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h

V = 1/3 (3.14) (4)^2 ( 13)

V = 217.70666

Rounding the the nearest hundredth

V = 217.71 in^3

Answer:

x=3

Step-by-step explanation:

Since they are similar triangles, we can use ratios to solve

x           3.5

----- = -------

6           7

Using cross products

7x = 21

Divide each side by 7

7x/7 = 21/7

x = 3