Jaden buys a raffle ticket. Each ticket has a 1% chance of being drawn. How likely is it that Jaden's ticket will be drawn? It definitely will be drawn.

It likely won't be drawn.

It likely will be drawn.

It definitely won't be drawn.

Answer:

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Step-by-step explanation:

Final answer:

To multiply 5 by the expression (2a-7b-2), each term inside the parentheses is multiplied by 5, resulting in the final expression 10a - 35b - 10.

Explanation:

To use the distributive property to multiply 5(2a-7b-2), multiply each term inside the parentheses by 5.

Multiply 5 by 2a which gives 10a.

Multiply 5 by -7b which gives -35b.

Multiply 5 by -2 which gives -10.

Now, combine these results to get the final expression: 10a - 35b - 10.

Which expression represents the area of the triangle drawn below?

Base of the triangle=4x+2

Height of the triangle=2x+1

Area of triangle=[tex] \frac{1}{2} [/tex]*b*h

Area=[tex] \frac{1}{2} [/tex]*(4x+2)(2x+1)

Simplifying 4x+2 we get, 2(2x+1)

So, we have, Area=[tex] \frac{1}{2} [/tex]*2(2x+1)(2x+1)

Area=[tex] \frac{1}{1} [/tex]*1(2x+1)(2x+1)

=(2x+1)(2x+1)

FOILing the two we get, 2x*2x +2x*1 +1*2x+1*1

(2x+1)(2x+1)=4x²+2x+2x+1

Area=4x²+4x+1

So, Area of the triangle=4x²+4x+1

Answer:Option C

Answer:

It is C

Step-by-step explanation:

I just took the same quiz. I saw that this was the answer.

Hope this helps!

The required number of lunch that contains 55% of ham sandwich is given as 23.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The total number of lunches is given as,
= 3 × 14
= 42 lunch in the 3 ice chests,

Now, 55% of the lunch consists the ham sandwich,
The number of lunch that contains the ham sandwich is given as,
= 0.55 × 42
= 23.1
≈ 23

Thus, the required number of the lunch that contains 55% of the ham sandwich is given as 23.

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The correct answer is option B: [tex]\( y = -2x + 7 \).[/tex] To write the equation of a line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation.

The point-slope form is given as:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Where [tex]\( (x_1, y_1) \)[/tex] is a point on the line and [tex]\( m \)[/tex] is the slope.

Given that the point is [tex]\( (2, 3) \)[/tex] and the slope is [tex]\( -2 \)[/tex], we can substitute these values into the point-slope form:

[tex]\[ y - 3 = -2(x - 2) \][/tex]

Now, we can simplify and rewrite the equation in various forms to match the options provided:

Option A: [tex]\( 2x + y = 7 \)[/tex]

To match this option, let's rearrange the equation:

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ 2x + y = 7 \][/tex]

So, option A is equivalent to the given equation.

Option B: [tex]\( y = -2x + 7 \)[/tex]

Let's solve the equation for [tex]\( y \):[/tex]

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ y = -2x + 7 \][/tex]

This matches option B.

Option C: [tex]\( y - 3 = -2(x - 2) \)[/tex]

This is already in point-slope form and matches the given equation.

Option D: [tex]\( y = -\frac{1}{2} x + 5 \)[/tex]

Let's solve the equation for [tex]\( y \):[/tex]

[tex]\[ y - 3 = -2(x - 2) \][/tex]

[tex]\[ y - 3 = -2x + 4 \][/tex]

[tex]\[ y = -2x + 7 \][/tex]

This does not match option D.

Therefore, the correct answer is option B: [tex]\( y = -2x + 7 \).[/tex]

The complete question is:

A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?

A) 2x + y = 7

B) y = -2x + 7

C) y - 3 = -2(x - 2)

D) y = - 1 2 x + 5.

11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.

Make them equal to each other in an equation.

5x = x + 20

Subtract x from both sides.

4x = 20

Divide both sides by 4.

x = 5

12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:

x + x + 50 = 180

Combine like terms.

2x + 50 = 180

Subtract 50 from both sides.

2x = 130

Divide both sides by 2.

x = 65

Now make the base angle plus x equal 180, because they form a straight line.

65 + x = 180

Subtract 65 from both sides.

x = 115

13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.

x + x + 90 = 180

Combine like terms.

2x + 90 = 180

Subtract 90 from both sides.

2x = 90

Divide both sides by 2.

x = 45

the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).

To solve the quadratic equation[tex]\( x^2 - 7x - 8 = 0 \)[/tex]by completing the square, we follow these steps:

1. Move the constant term to the other side of the equation:

[tex]\[ x^2 - 7x = 8 \][/tex]

2. To complete the square, take half of the coefficient of ( x ) (which is -7), square it, and add it to both sides of the equation:

[tex]\[ x^2 - 7x + \left( \frac{-7}{2} \right)^2 = 8 + \left( \frac{-7}{2} \right)^2 \]\[ x^2 - 7x + \frac{49}{4} = 8 + \frac{49}{4} \][/tex]

3. Simplify the right side of the equation:

[tex]\[ x^2 - 7x + \frac{49}{4} = \frac{32}{4} + \frac{49}{4} \]\[ x^2 - 7x + \frac{49}{4} = \frac{81}{4} \][/tex]

4. Write the left side of the equation as a perfect square:

[tex]\[ \left( x - \frac{7}{2} \right)^2 = \frac{81}{4} \][/tex]

5. Take the square root of both sides to solve for ( x ):

[tex]\[ x - \frac{7}{2} = \pm \sqrt{\frac{81}{4}} \]\[ x - \frac{7}{2} = \pm \frac{9}{2} \][/tex]

6. Solve for ( x ) by adding [tex]\( \frac{7}{2} \)[/tex]to both sides:

[tex]\[ x = \frac{7}{2} \pm \frac{9}{2} \][/tex]

This gives us two solutions:

[tex]\[ x = \frac{7}{2} + \frac{9}{2} = \frac{16}{2} = 8 \]\[ x = \frac{7}{2} - \frac{9}{2} = \frac{-2}{2} = -1 \][/tex]

So, the solutions to the equation [tex]\( x^2 - 7x - 8 = 0 \)[/tex] are ( x = 8 ) and ( x = -1 ).

Given that all helmets in the bin are red, the probability of randomly selecting a red helmet is 1, which corresponds to answer C.

The question is asking for the probability that a randomly selected helmet from a bin of four is red. Since all the helmets in the bin are red, no matter which one you pick, it will be red. In probability, this is represented as the total number of favorable outcomes divided by the total number of outcomes. In this scenario, both favorable outcomes (red helmets) and total outcomes (helmets in the bin) are four. Mathematically, 4/4 results in 1. So, the correct answer is C which symbolize the probability to be 1.

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The length of one side of Colin's square garden, which has an area of 97 square feet, is approximately 9.85 feet.

Colin has a square garden with an area of 97 square feet. The area of a square is calculated by squaring the length of one side (Side length * Side length = Area). Therefore, to find the length of one side of the square when you know the area, you would take the square root of the area.

In Colin's case, the area of the garden is 97 square feet, so the length of one side would be the square root of 97, which is approximately 9.85 feet.

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1. The student that wrote a statistical question is Lisa. This is because there can be many answers to the question

2. The score of each student is: 4.5 points.

A statistical question is a question whose answer can be gotten by collecting data that has variability. That is, the answers to the question may be many.

1. The question that is more statistical in nature is Lisa's. This is because there can be many answers to the question

2. The average of a data is the mean, which is the sum of all data points divided by the number of data points.

Therefore, if all students had the same score and the mean score was 4.5, it means the score of each student is: 4.5 points.

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