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3 years ago

9

Here is the histogram of a data distribution. All class widths are 1. Which of the following numbers is closest to the mean of t

his distribution?
A. 6
B. 9
C. 4
D. 3
E. 5

2 answers:

ozzi3 years ago

3 0

Answer:

The answer is A

It is 6 on apex

Alina [70]3 years ago

3 0

Answer: A. 6

Step-by-step explanation:

From the given histogram we got the following table of frequency distribution:-

X f

1 5

2 4

3 4

4 1

5 1

7 5

8 4

9 4

10 5

Now, $\sum f=5+4+4+1+1+4+4+5=28$

$\sum Xf=2\cdot5+3\cdot4+4\cdot4+5\cdot1+7\cdot1+8\cdot4+9\cdot4+10\cdot5=168$

Now, $\text{Mean=}\dfrac{\sum xf}{\sum f}=\dfrac{168}{28}=6$

Hence, the mean of this distribution = 6

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The graph of this function is shifted downwards and the axis of symmetry remains x=1. Which function below the equation of the n

Natali5045456 [20]

Answer:

$y=-x^{2}+2x$

$y=-x^{2}+2x-4$

$y=-x^{2}+2x-3$

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

The axis of symmetry is equal to the x-coordinate of the vertex

so

$x=h$

If a> 0 then the parabola open upward (vertex is a minimum)

If a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

$y=-x^{2} +2x+3$

The vertex is the point $(1,4)$ ------> observing the graph

The axis of symmetry is $x=1$

If the graph of this function is shifted downwards and the axis of symmetry remains x=1

then

The x-coordinate of the vertex of the new graph must be equal to 1

The y-coordinate of the vertex of the new graph must be less than 4

The parabola of the new graph open downward

therefore

<u>Verify each case</u>

case a) $y=-x^{2}+2x$

Convert to vertex form

$y=-(x^{2}-2x)$

$y-1=-(x^{2}-2x+1)$

$y-1=-(x-1)^{2}$

$y=-(x-1)^{2}+1$

The vertex is (1,1)

therefore

The function could be the equation of the new graph

case b) $y=-x^{2}-2x+3$

Convert to vertex form

$y-3=-(x^{2}+2x)$

$y-3-1=-(x^{2}+2x+1)$

$y-4=-(x+1)^{2}$

$y=-(x+1)^{2}+4$

The vertex is (-1,4)

therefore

The function cannot be the equation of the new graph

case c) $y=-x^{2}+2x-4$

Convert to vertex form

$y+4=-(x^{2}-2x)$

$y+4-1=-(x^{2}-2x+1)$

$y+3=-(x-1)^{2}$

$y=-(x-1)^{2}-3$

The vertex is (1,-3)

therefore

The function could be the equation of the new graph

case d) $y=-x^{2}+2x+4$

Convert to vertex form

$y-4=-(x^{2}-2x)$

$y-4-1=-(x^{2}-2x+1)$

$y-5=-(x-1)^{2}$

$y=-(x-1)^{2}+5$

The vertex is (1,5)

therefore

The function cannot be the equation of the new graph

case e) $y=-x^{2}+2x-3$

Convert to vertex form

$y+3=-(x^{2}-2x)$

$y+3-1=-(x^{2}-2x+1)$

$y+2=-(x-1)^{2}$

$y=-(x-1)^{2}-2$

The vertex is (1,-2)

therefore

The function could be the equation of the new graph

8 0

3 years ago

Help please guys I need help

omeli [17]

Answer:

= 3 + 6/15 + 10/15

Step-by-step explanation:

To make 2/5 into a fifteenth, you have to multiply the 5 by 3 to get 15. Whatever you do to the top you have to do to the bottom, meaning that you have to multiply 2 by 3 to get 6 on top.

To make 2/3 into a fifteenth, you have to multiply the 3 by 5 to get 15. Whatever you do to the top you have to do to the bottom, meaning that you have to multiply 2 by 5 to get 10 on top.

This is the same rule for all equations involving fractions.

7 0

3 years ago

Convert Each Equation To Slope-Intercept Form. (1/2)

kotykmax [81]

Hey there, Mandoguy!

To convert each equation to slope-intercept form, first we need to distribute everything that's on the parenthesis (if it has one)
So, number one would be

1) y + 3 = 4x + 24 (I multiplied 4 times x and 4 times 6)
Now, we need to isolate y and since they are adding 3 to it, we need to subtract 3 to cancel it out. Remember what we do on one side we have to do it in the other side.
So, it would be y + 3 - 3 = 4x + 24 - 3
Number 1 would be
y = 4x + 21
$y=4x+21$

2) 6x + 2y = 12
Goes to
2y = 12 - 6x (I subtracted 6x from both sides to leave 2y alone)
y = 6 - 3x (I divided both sides by 2 since y it's being multiplied by 2)
y = -3x + 6 (Now, I just rearranged to make it y = mx + b
$y=-3x+6$

3) y = -2 + 1/3 (x + 9) In this case y is already isolated but we have parenthesis and we can't have that.
So, we distribute the number that's in front of the parenthesis to the numbers inside.
y = -2 + 1/3x + 3 (I multiplied 1/3 times x and 1/3 times 9 which is 3)
y = 1/3x + 1 (I combined like terms and rearranged to make it y=mx+b)
$y= \frac{1}{3} x+1$

4) 2x - 5y = -15 (Same as always. Isolate y. Subtract 2x from both sides)
-5y = -15 - 2x (Did you see that? We have a negative value on y and we can't have that. To fix it, we multiply both sides by -1 or just change the sign of every term)
Once you do that you will get
5y = 15 + 2x
y = 3 + 2/5 x (I divided both sides by 5 to isolate y)
y = 2/5x + 3 (Rearranged it to y = mx + b)
$y = \frac{2}{5}x + 3$

5) -x - 2y = 2 (Since the x it's being subtracted, we added to both sides)
-2y = 2 + x (See again? We have a negative value on y, so we multiply by -1 on both sides or change every sign to the opposite of itself)
So we get
2y = -2 - x (Now, we divide both sides by 2 to isolate y)
y = -1/2x - 1 (Rearranged to y = mx + b)
$y = - \frac{1}{2} x - 1$

Thanks for using Brainly!
See you soon.

7 0

3 years ago

HARDEST QUESTION IN THE ENTIRE WORLD. CAN YOU SOLVE?

makvit [3.9K]

Hello, there!

The distance from Mia to Eva is 15 feet, and the distance from Mia to Abigail is 25 feet. A triangle is drawn connecting the positions of Mia, Abigail, and Eva. How far is Eva from Abigail if the angle marking Mia’s position is 50°?

Let's pretend that:

Mia is point A

Abigail is point B

Eva is point C.

The answer is 19.2 feet.

That means that the answer is C

I have drawn the triangle to scale, and attached it below. That way, you can see how I got this answer.

I hope I helped!

Let me know if you need anything else!

~ Zoe

6 0

3 years ago

An artist receives 20% royalty on the retail price of his recordings. If he receives $36,000 in royalties, what is the dollar am

Mariulka [41]

Answer:

$180,000

Step-by-step explanation:

Because the artist gets 20% of the retail price, and 20% is equal to 1/5, the artist gets 1/5 of the retail price. So you do 36,000 times 5 to get the whole, original price.

4 0

4 years ago