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Bin
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C

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Approximately 95% of data falls within 2 standard deviations (±2) of the mean. Option D is correct.

A normal distribution is a type of continuous probability distribution for a real-valued random variable such that the values are symmetric about a mean and the curve has bell shape.

Standard deviation is the measure of the randomness of the distribution. The curve has its peak at the mean.

As standard deviation increases, the peak of the curve comes lower and the distribution becomes more and more dispersed.

In a normal distribution 68% of the values falls within 1 standard deviation

and 95% of the values falls within two standard deviations. 99% of the values falls within three standard deviations.

Hence, approximately 95% of data falls within 2 standard deviations (±2) of the mean.

To learn more about normal distribution visit:

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Answer:

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . ... This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.

Step-by-step explanation:

Answer:

ax+by=c

Step-by-step explanation:

this is standard for, if that's what you'e asking for

Answer:

a = - 10

Step-by-step explanation:

3a – 8 = 5a + 12

3a – 8 + 8 = 5a + 12 + 8

3a = 5a + 20

3a - 5a = 5a + 20 - 5a

- 2a = 20

[tex]\dfrac{-2a}{-2}=\dfrac{20}{-2}[/tex]

a = - 10

Answer:

Segment DO

Step-by-step explanation:

The first option is not the radius because A is going outside of the circle and it would actually be longer than the radius.

BC is too high up, and it's considered a chord, not the radius.

DE is the diameter, not the radius.

That leaves us with 1 answer remaining.

Answer:

y = ¾x + 1

Step-by-step explanation:

Point-slope equation for line of slope ¾ that passes through (-8,-5):

y+5 = ¾(x+8)

Put into slope-intercept form:

y = ¾(x+8) - 5 = ¾x + 6 - 5 = ¾x + 1

Answer:

the slope is m= 5/31 :)

Answer:

D. (-2, 6)

Step-by-step explanation:

First, isolate a variable in one of the equations (i.e y = or x =)

The first equation already has isolated x.

x = y - 8 or y - 8 = x

5x + y = -4

Substitute the isolated variable into the second equation.

5(y-8) + y = -4

There is now only one variable, y, in the equation. Now you can solve for y.

First, use the distributive property to get the equation

5y - 40 + y = -4

Then, add 40 to both sides.

5y + y = 36

Add like-terms.

6y = 36

Divide.

36 / 6 = 6

So, y = 6.

Now that we have one coordinate, y = 6, you can substitute for y in the first equation.

x = 6 - 8

Subtract.

x = -2

Your coordinates are now x = -2 and y = 6, or (-2, 6).

Answer:

0.9

Step-by-step explanation:

can't really Explain, its simple mathamatics 6% of 15 = 0.9

Answer:

Selling the total for $ 1276, Ace lost $ 1.37 for each meter.

Step-by-step explanation:

Given that Ace earned $ 176 selling 32 meters of cloth at $ 1496, to find out his loss for each meter if he sold the total for $ 1276, the following calculation must be performed:

1496 - 176 = 1320 (stock price)

1320/32 = 41.25 (price per meter)

1276/32 = 39.87

41.25 - 39.87 = 1.37

Thus, selling the total for $ 1276, Ace lost $ 1.37 for each meter.

Answer:

2730 ways

Step-by-step explanation:

Given that,

There are 15 eligible candidates for these positions.

The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing.

It is a concept based on permutations.

[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]

Put n = 15 and r = 3

[tex]P(15,3)=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15!}{12!}\\\\=\dfrac{15\times 14\times 13\times 12!}{12!}\\\\=15\times 14\times 13\\\\=2730[/tex]

Hence, 2730 ways can the members of the cabinet be appointed

1. x+(x-26)= 180 (being corresponding angle)

2x-26=180

2x=180-26

2x=154

x=154÷ 2

∴x=77

Answer: 9m + 5y + 1

Step-by-step explanation:

3 + 6m + -2y - 2 + 3m + 7y

3 + -2 = 1

1 + 6m + -2y + 3m + 7y

-2y + 7y = 5y

1 + 6m + 5y + 3m

6m + 3m = 9m

9m + 5y + 1

Answer:

1+9m+5y

Step-by-step explanation:

(a) Applying T to p(t) = 2 - t + t ² gives

T ( p(t) ) = (t - 2) (2 - t + t ²) = -4 + 4t - 3t ² + t ³

(b) T is a linear transformation if for any p(t) and q(t) in P₂ and complex scalars a and b, the image of any linear combination of p and q is equal to the linear combination of the images of p and q. In other words,

T ( a p(t) + b q(t) ) = a T ( p(t) ) + b T ( q(t) )

Let

p(t) = α₀ + α₁ t + α₂ t ²

q(t) = β₀ + β₁ t + β₂ t ²

Compute the images of p and q :

T ( p(t) ) = (t - 2) (α₀ + α₁ t + α₂ t ²)

… = -2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³

Similarly,

T ( q(t) ) = -2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³

Then

a T ( p(t) ) + b T ( q(t) ) = a (-2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³) + b (-2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³)

… = c₀ + c₁ t + c₂ t ² + c₃ t ³

where

c₀ = -2 (a α₀ + b β₀)

c₁ = a (α₀ - 2α₁) + b (β₀ - 2β₁)

c₂ = a (α₁ - 2α₂) + b (β₁ - 2β₂)

c₃ = a α₂ + b β₂

Computing the image of a p(t) + b q(t) would give the same result; just multiply it by t - 2 and expand. This establishes that T is indeed linear.

(c) Find the image of each vector in the basis for P₂ :

T (1) = (t - 2) × 1 = t - 2

T (t ) = (t - 2) t = t ² - 2t

T (t ²) = (t - 2) t ² = t ³ - 2t ²

Then

[tex]T=\begin{bmatrix}-2&0&0\\1&-2&0\\0&1&-2\\0&0&1\end{bmatrix}[/tex]

Answer:

D. [tex](5,6)[/tex]

Step-by-step explanation:

Let [tex]R(x,y) = (1,2)[/tex], we proceed to perform all operations described on statement:

1) Dilation

[tex]R'(x,y) = O(x,y) + k\cdot [R(x,y)-O(x,y)][/tex]  (1)

Where:

[tex]O(x,y)[/tex] - Point of reference.

[tex]R(x,y)[/tex] - Original point.

[tex]R'(x,y)[/tex] - Dilated point.

[tex]k[/tex] - Scale factor.

If we know that [tex]O(x,y) = (0,0)[/tex], [tex]R(x,y) = (1,2)[/tex] and [tex]k = 3[/tex], then the dilated point is:

[tex]R'(x,y) = (0,0) +3\cdot [(1,2)-(0,0)][/tex]

[tex]R'(x,y) = (0,0) +3\cdot (1,2)[/tex]

[tex]R'(x,y) = (3,6)[/tex]

2) Translation

[tex]R''(x,y) = R'(x,y) + T(x,y)[/tex] (2)

Where:

[tex]R'(x,y)[/tex] - Original point.

[tex]T(x,y)[/tex] - Translation point.

[tex]R''(x,y)[/tex] - Translated point.

If we know that [tex]R'(x,y) = (3,6)[/tex] and [tex]T(x,y) = (2,0)[/tex], then the translated vector is:

[tex]R''(x,y) = (3,6)+(2,0)[/tex]

[tex]R''(x,y) = (5,6)[/tex]

Therefore, the correct answer is D.

Answer:d

Step-by-step explanation:

Step-by-step explanation:

Movie pricing per person is $7.75

hockey pricing per person is $7.90

The Movie pricing is less per person because 7.90<7.75

I hope it answers

Answer:

movies

Step-by-step explanation:

im adding a picture of the explination because i worked it out

Answer:

[tex]3+\frac{5i}{2}[/tex]

Step-by-step explanation:

Simplify and write the answer in the standard form, a+bi. Hope this helps!

Answer:

Graphs can only provide a limited view of the data.

b. False

Step-by-step explanation:

On the contrary, graphs present better views of the presented data.  Mathematically, graphs are methods of visually illustrating data relationships.  The main purpose of using a graph is to present complicated data that show trends or relationships between variables.  It has been an important tool for presenting data in a visual and easy-to-understand format, without using too much description.

Answer:

Graph two would be the answer because it is not curving.

Step-by-step explanation:

Answer:

a4 = -2

Step-by-step explanation:

a2 = 13 -5 = 8

a3 = 8 -5 = 3

a4 = 3 -5 = -2

Answer:

(95/12,0)

Step-by-step explanation:

Answer:

(7.916, 0)

Step-by-step explanation:

In order to find the X-intercept, let y=0

12x + 5(0) = 95

12x = 95

95/12x = 7.91666...

Therefore, the x intercept is (7.916, 0)

Answer:

drag the protactor so that the the bottom, middle line is centered in point B, and the bottom edge is flat against line BC

the angle will be whatever number AB lines up with on the outer ring (the big numbers)

Step-by-step explanation:

Answer:

About $11.88 per foot

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

5^2+12^2=13^2. It is a right triangle

Answer:

x = 8

y = 18

Step-by-step explanation:

First, it would be easiest to start by drawing a picture. To do so, draw two simple Isosceles triangles. Then, label their points. One having the points F, U, and N while the other has B, A, and T. Now, since both triangles are congruent, that means that F≅B, U≅A, and N≅T. Because of this knowledge, FN would be congruent to BT. So, you would be able to write that 52 = 14x - 60. By solving that, you would get the answer to x. Moving onto y, you would see that since the triangles are congruent, the interior angles are too. So, you would be able to use angles F and N to find A. By adding them to 180°, the equation would look like: 71° + 36° + (3y + 19)° = 180°. So, you would be able to find the answer to y. Hope this helped!