Consider the system of linear equations.2y = x + 10

3y = 3x + 15

Which statements about the system are true? Check all that apply.

The system has one solution.

The system graphs parallel lines.

Both lines have the same slope.

Both lines have the same y-intercept.

The equations graph the same line.

The solution is the intersection of the 2 lines

Answers

Answer 1

Answer:

The true statements about the system are:

Both lines have the same y-intercept.

The solution is the intersection of the two lines

How to explain the equation

To determine the properties of the system, we can manipulate the equations to a standard form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

2y = x + 10

Divide both sides by 2:

y = (1/2)x + 5

3y = 3x + 15

Divide both sides by 3:

y = x + 5

Both lines have the same y-intercept. The y-intercepts of both equations are 5, so they share the same y-intercept.

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Answer 2

Answer:

Final answer:

The system has one solution, both lines have the same slope and y-intercept, and the solution is the intersection of the two lines.

Explanation:

To determine which statements about the system of linear equations are true, we can analyze the equations. Let's start by putting both equations in slope-intercept form, y = mx + b.

Equation 1: 2y = x + 10. Divide both sides by 2 to isolate y. We get y = 1/2x + 5.
Equation 2: 3y = 3x + 15. Divide both sides by 3 to isolate y. We get y = x + 5.

From the equations, we can see that both lines have the same slope, which is 1/2. Therefore, the statements that are true are:

Both lines have the same slope.
Both lines have the same y-intercept.
The solution is the intersection of the two lines. This means the system has one solution.

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Which of the following expressions represents 24C12?A) 12!/24!
B 24!/24!
C) 24!/ 12!•12!
D) 24!/12!

Answers

$24C12=(24!)/(12!12!)$

08.01)Marlow wants to know how many students in his school enjoy watching the TV news. He asks all 27 students in his art class and finds that 30% of his classmates enjoy watching the TV news. He claims that 30% of the school's student population would be expected to enjoy watching the TV news. Is Marlow making a valid inference about his population?No, it is not a valid inference because he asked all 27 students in his art class instead of taking a sample from the school

No, it is not a valid inference because his classmates do not make up a random sample of the students in the school

Yes, it is a valid inference because he asked all 27 students in his art class

Yes, it is a valid inference because his classmates make up a random sample of the students in the school



Question 2 (Multiple Choice Worth 5 points)

(08.01)Carl takes a random sample of 100 students in his school and finds that 72% of the sample prefers pizza over burgers. There are 1,500 students in the school. Based on the sample proportion, how many students in the school would be expected to prefer pizza over burgers?

72

100

1,080

1,500

Answers

Part 1 : Marlow wants to know how many students in his school enjoy watching the TV news. He asks all 27 students in his art class and finds that 30% of his classmates enjoy watching the TV news. He claims that 30% of the school's student population would be expected to enjoy watching the TV news. Is Marlow making a valid inference about his population?

No, it is not a valid inference because he asked all 27 students in his art class instead of taking a sample from the school

No, it is not a valid inference because his classmates do not make up a random sample of the students in the school

Yes, it is a valid inference because he asked all 27 students in his art class

Yes, it is a valid inference because his classmates make up a random sample of the students in the school

Answer = The correct answer is B because Marlow was supposed to ask random kids and they were not suppose to be in his class.

Part 2 : Carl takes a random sample of 100 students in his school and finds that 72% of the sample prefers pizza over burgers. There are 1,500 students in the school. Based on the sample proportion, how many students in the school would be expected to prefer pizza over burgers?

72

100

1,080

1,500

1500 / 100×72= 1080

No, it is not a valid inference because he asked all 27 students in his art class instead of taking a sample from the school.

Which of the following points is on the graph of y = log1/2x?(1, 1/2)
(1/2, 1)
(0, 1)
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Answers

Answer:

(1/2,1) is on the graph of $y=\log_(1/2)x$

B is correct.

Step-by-step explanation:

Given: $y=\log_(1/2)x$

We are given a log function whose base 1/2.

Log property:

$\log_aa=1$

If base and mantissa is same then their value is 1

We need to choose correct point from the options.

Option 1: (1,1/2)

$y=\log_(1/2)1 = 0$

$(1)/(2)\neq 1$

False

Option 2: (1/2,1)

$y=\log_(1/2)(1/2) = 1$

$1= 1$

True

Option 3:

Log is not defined for x=0.

Hence, (1/2,1) is on the graph of $y=\log_(1/2)x$

(1/2,1) is the points is on the graph of y = log1/2x?

What is the points

For (1, 1/2):

So, By Substituting x = 1 and y = 1/2 into the equation, we get:

1/2 = log₁/₂(1)

Since log of 1 to any base is always 0, the equation becomes:

1/2 is not equal to 1

In terms of Option 3: Log is not defined for x=0.

Therefore , (1/2,1) is on the graph of y = log1/2x?

Answers

Answer:

108 seconds and 0.03 hours

Find a pair of irational numbers whose sum is irational

Answers

Answer:

√2 and √3

Good Luck!!!

Final answer:

A pair of irrational numbers whose sum is irrational does not practically exist. The sum of two irrational numbers can be either rational or irrational, and this solely depends on the numbers being added together.

Explanation:

The irrational numbers can be defined as any real number that is not a rational number. However, the sum of two irrational numbers is not always irrational. It could be rational or irrational depending on the numbers you're adding. However, you've asked for a case where the sum is also irrational. Let's consider two irrational numbers √2 and -√2. √2 is irrational. Likewise, -√2 is also irrational. However, when added (√2 - √2), they result in 0 which is not irrational. Therefore, it's near impossible to find two irrational numbers whose sum is also irrational.

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A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds:f(t) = −16t2 + 48t + 100

The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____feet per second.

Answers

$f(t) = -16t^(2) +48t + 100$
Average rate of change from t = 3 seconds to t = 5 seconds = $(f(5)-f(3))/(5-3) = ((-16( 5^(2))+48(5)+100)-(-16( 3^(2))+48(3)+100 )/(2)=$ $((-16(25)+240+100)-(-16(9)+144+100))/(2) = ((-400+240+100)-(-144+144+100))/(2)=$ $(-60-100)/(2) = (-160)/(2) = -80$

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