MATHEMATICS HIGH SCHOOL

Which of the following shows 27/54 written in prime factored form to help in reducing the fraction to simplest form? A. 9x3/9x6
B. 27x1/27x2
C. 3x3x3/3x3x3x2
D. 1/2

Answers

Answer 1

Answer:

Answer: C. 27/54 .

Step-by-step explanation:

Here, given number, 27/54

Since the prime factor form of 27 = $3* 3* 3$

And, the prime factor form of 54 = $3* 3* 3* 2$

putting the prime factor form of both 27 and 54 in the given numbers.

we get, $(27)/(54) =(3* 3* 3)/(3* 3* 3* 2) = 1/2$

Thus, by putting the prime factor form by C we get the simplest form of the given fraction.

Therefore, Option C is correct.

Answer 2

Answer: C. 3x3x3/3x3x3x2

27 splits into 3 and 9, the 9 splits into 2 3's. You can't split the threes.
54 splits into 2 and 27, the 27 is the same as above.

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At a 25% off sale, a shirt cost $36.00. what was the regular price of the shirt?

Answers

36.00 / 75% = 0.48

0.48 x 100% =$48.00

Since the shirt is 75% of the regular price you would divide 36/75 which gives you .48 and then you times that by 100 which equals
48 dollars

Rathan thinks all factors of even numbers are even. Which explains whether Rathan is correct? He is correct because the product of 2 and any number is even.
He is correct because the product of two even numbers is even.
He is incorrect because the product of an even number and an odd number is even.
He is incorrect because the product of two odd numbers is odd

Answers

The answer to this would be C, the third of the options. This is the only response that fully answers the question. For example, two factors of 42 would be 6 and 7, and both are not even, so given the absolute nature of Rathan's belief, there is no exception that can be made to make him correct. I hope this helps, and if it was sufficient to make you understand fully set it to the brainliest answer. Have a nice day! =)

The correct answer is:

He is incorrect because the product of an even number and an odd number is even.

Explanation:

When you multiply any number by an even number, whether it is even or odd, the product will be even.

This means that an even number can have an odd factor, and Rathan is incorrect.

A car insurance company has determined that 7% of all drivers were involved in an accident last year. If 11 drivers are selected at random, what is the probability that 3 or more were involved in an accident last year?

Answers

Using the binomial distribution, it is found that there is a 0.0369 = 3.69% probability that 3 or more were involved in an accident last year.

For each driver, there are only two possible outcomes, either they were involved in an accident, or they were not. The probability of a driver being involved in an accident is independent of any other driver, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$C_(n,x) = (n!)/(x!(n-x)!)$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

7% of all drivers were involved in an accident last year, hence $p = 0.07$ .

11 drivers are selected at random, hence $n = 11$ .

The probability is:

$P(X \geq 3) = 1 - P(X < 3)$

In which:

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

Then

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 0) = C_(11,0).(0.07)^(0).(0.93)^(11) = 0.4501$

$P(X = 1) = C_(11,1).(0.07)^(1).(0.93)^(10) = 0.3727$

$P(X = 2) = C_(11,2).(0.07)^(2).(0.93)^(9) = 0.1403$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.4501 + 0.3727 + 0.1403 = 0.9631$

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.9631 = 0.0369$

0.0369 = 3.69% probability that 3 or more were involved in an accident last year.

To learn more about the binomial distribution, you can check brainly.com/question/24863377

Answer:

Therefore the probability that 3 or more were involved in an accident last year is 0.376.

Step-by-step explanation:

Binomial distribution:

A discrete random variable X having the set {0,1,2.....,n} as the spectrum, is said to have binomial distribution with parameter n= the number of trial and p = probability of getting successes in one trial if the p.m.f of X is give by

$P(X=x)=C(n,x)p^x(1-p)^(n-x)$ for x=0,1,2,....,n

=0 elsewhere

where $C(n,x)= (n!)/(x!(n-x)!)$ , n is a positive integer and 0<p<1.

Given that,

7% of all drivers were involved in an accident last year that was determined by a car insurance company.

p= 7%=0.07, n=11, x=3

P(X≥3)

= 1-P(X≤2)

= 1- P(X=0)-P(X=1)-P(X=2)

$=1- C(11,0)(0.07)^0(1-0.07)^(11)- C(11,1)(0.07)^1(1-0.07)^(10)- C(11,2)(0.07)^2(1-0.07)^(9)$

$=1- C(11,0)(0.07)^0(0.93)^(11)- C(11,1)(0.07)^1(0.93)^(10)- C(11,2)(0.07)^2(0.93)^(9)$

=1-0.624

≈0.376

Therefore the probability that 3 or more were involved in an accident last year is 0.376.

Simplify the rational expressions into lowest forms. (x²-5x)/(2x-10)

Answers

Answer: $(x)/(2)$

Step-by-step explanation:

In order to simplify, I want to see if there is anything we can factor out.

$(x^2-5x)/(2x-10)$ [factor out x in numerator and factor out 2 in denominator]

$(x(x-5))/(2(x-5))$ [notice that there is (x-5) in numerator and denominator, these divide to equal 1]

Therefore the remaining expression is $(x)/(2)$ .

Final answer:

The question involves simplifying a rational expression. This is done by factoring the numerator and denominator, then cancelling out common factors. The simplified form of (x²-5x)/(2x-10) is x/2.

Explanation:

The process of simplifying rational expression such as (x²-5x)/(2x-10) involves factoring both the numerator and the denominator and cancelling out any common factors. Therefore, in this case:

Factor the numerator: x² - 5x = x(x - 5)
Factor the denominator: 2x - 10 = 2(x - 5)
Next, as both expressions have a common factor of (x - 5), cancel these out.

So, the simplified expression is x/2.

Learn more about Simplifying Rational Expressions

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Which is the choice to the inequality below? -x/9>4
A. x<4
B:x<-36
C.x<-0.44
D. x>-36

Answers

Answer:

x < -36

Step-by-step explanation:

-x/9>4

Multiply each side by -9, remembering to flip the inequality

-x/9 * -9 < 4*-9

x < -36

The table below shows the relationship between the number of miles traveled, x, and the number of gallons of gas used, y.х
35
70
105
140
175
Y
1
2
3
4
5
Which of the following equations best represents the relationship?
A. y = 3.5x
B. y = 35x
C. y = 1/35x
D. 35 = 1x

Answers

The relationship between the number of miles traveled, x, and the number of gallons of gas used, y is, y = 35x . So Option B is correct

What is the equation of line?

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

the number of miles traveled x, the number of gallons of gas used, y

35, 1

70, 2

105, 3

140, 4

175, 5

For 1 mile distance, 35 gallons of gas is required,

And for 2 mile distance, 70 gallons gas is required

So, the number of gallons y = 35 times the number of miles traveled

Now it can be write as,

Y = 35X

Hence, the equation is Y = 35X

To know more about Line check:

brainly.com/question/17188072

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Answer: (y = 35x)

Step-by-step explanation: you get your answer to y which is the number of gallons used and x is the number of miles traveled; Meaning 35x (35 miles traveled) is y (1 gallon used).

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Russell conducted an experiment where he collected snow in a container, measured it, and then measured the amount of water in the container after the snow had melted. He created the graph below to display his findings.Based on the graph, what does the point (0, 0) represent?A. The collection of 0 inches of snow results in no water.B. The collection of 0 inches of water results in no snow.C. The amount of snow was not proportional to the amount of water.D. The rate of inches of rain to inches of snow was 0.1125.