5 points
A set of data has a normal distribution with a mean of 17.5 and a standard
deviation of 1.6. Determine which of the following values represent the
percent of the data between 15.9 and 19.1?
A 48%
B 68%
C 95%
D 99.7%

Answer:

114

Step-by-step explanation:

The question relates to the sum of an arithmetic progression, A. P.

The count of numbers added, n = 50

The sum of the numbers, Sₙ = 3,250

The formula for the sum of an A. P. is given as follows;

[tex]S_n = \dfrac{n}{2} \left[2 \cdot a + (n - 1)\cdot d\right][/tex]

[tex]S_n = \dfrac{n}{2} \left[a + a_n\right][/tex]

Where;

a = The first term of set of numbers

d = The common difference between consecutive numbers

n = The number of terms = 50

aₙ = The last term, the largest of the integers

Therefore, we get;

The common difference of consecutive even integers numbers, d = 2

Plugging in the values gives;

3,250 = (50/2) × (2·a + (50 - 1) × 2) = 25 × (2·a + 49 × 2)

2·a = (3,250/25) - 49 × 2 = 32

a = 32/2 = 16

From  [tex]S_n = \dfrac{n}{2} \left[a + a_n\right][/tex], we have;

3,250/25 = 16 + aₙ

aₙ = 3,250/25 - 16 = 114

The largest of the integers, aₙ = 114.

Answer:

He has 26 students

Step-by-step explanation:

78/3=26

Answer:

59 cm^3

Step-by-step explanation:

You can split the shape into two rectangular prisms.

3*3*1=9

10*5*1=50

9+50=59

Answer:

No, 2/3 sqrt(5) k^(11/2)

Step-by-step explanation:

Answer:

yes he simplified correctly

Step-by-step explanation:

got this question right on edg

Answer:

Step-by-step explanation:

3 + 5 +7 +9 + 11 + ....

n = 100

a = 3

d = 5 - 3 = 2

[tex]S_{n}=\frac{n}{2}(2a + (n-1)d)\\\\S_{100}=\frac{100}{2}(2*3+99*2)\\\\=50*(6+198)\\\\= 50 * 204\\= 10200\\[/tex]

Answer:

1/5

Step-by-step explanation:

20/100

Divide the top and bottom by 20

20/20 =1

100/20 =5

20/100 = 1/5

20/100

Divide the top and bottom by 20

20/20 =1

100/20 =5

20/100 = 1/5

[tex] \tt \: \verified \: \: \: \red{ \checkmark}[/tex]

Answer:

20%

Step-by-step explanation:

110-88=22

22/110=20

Answer:

125 cm

Step-by-step explanation:

[tex]V=lwh[/tex]

all cube has the same length, width, height

5 * 5 * 5 = 125

Hope this helps

Answer:

8 sides

Step-by-step explanation:

THE QUESTION IS NOT COMPLETE, SO A QUESTION OF THE SAME TYPE

Find the number of sides of a regular polygon if exterior angle of the polygon is 45°?

NOTE:

Sum of the exterior angles of any regular polygon is known as (360°)

But from the question,

Each exterior angle is given as( 45°)

Number of sides of a regular polygon can be computed as

(360°/Each exterior angle)

Then substitute the give value of exterior angle, we have

= (360°/45) = 8 sides

Answer:

tbh questions like these I just guess and I actually get them right

Answer:

x=-1, y=-4

Step-by-step explanation:

For this question, you can replace y in one equation with the second one.

This means x-3=7x+3.

From there, you subtract x from each side, giving -3=6x+3.

Subtracting 3 from each side makes it -6=6x.

Dividing both sides by 6 leaves x isolated, with a result of x=-1.

You can substitute the value of x into either equation to work out y. I'm using the first one, as it has smaller numbers.

This equation is now y=-1-3, which can be solved for y=-4.

**This content involves simultaneous equations, which you may wish to revise. I'm always happy to help!

Answer:

81.66 repeating

Step-by-step explanation:

86+72+65+82+91+94=490

490÷6=81.66 repeating

EDIT: this answer is false

Answer:

m∠QRS = 139°

Step-by-step explanation:

yes

Answer:

-9/10

Step-by-step explanation:

12/20 - 30/20

Since the denominators are the same, we can subtract the numerators

12-30 = -18

Put this over the denominator

-18/20

Simplify by dividing the top and bottom by 2

-9/10

Answer:

(-5,-15)

Step-by-step explanation:

Answer:

(-5,-15)

Step-by-step explanation:

3x=2x-5

-2x  -2x

x=-5

y=3(-5)

y=-15

Answer:

The radius is 18.3cm

Step-by-step explanation:

Given

[tex]V = 25500cm^3[/tex]

Required

The radius, r

The volume (V) of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

So, we have:

[tex]25500 = \frac{4}{3}\pi r^3[/tex]

Solve for r

[tex]\pi r^3 = 25500 * \frac{3}{4}[/tex]

[tex]\pi r^3 = 19125[/tex]

Divide by [tex]\pi[/tex]

[tex]r^3 = \frac{19125}{\pi }[/tex]

[tex]r^3 = \frac{19125}{3.14}[/tex]

[tex]r^3 = 6090.8[/tex]

Take cube roots

[tex]r = 18.3[/tex] -- approximated

x= -4

y= -7

Hope it helps you...

Answer:

The answer is 5/8

Step-by-step explanation:

Step 1 : Convert both fractions so they have the same denominator (bottom number in the fraction.)

1/4 = 2/8

So now were dealing with :

2/8 + 3/8 = ?

Step 2 : Add the numerators together to get the numerator for our answer.

2 + 3 = 5

When adding two fractions with the same denominator the denominator stays the same, so our answer is 5/8.

Hope this helps, please mark brainliest. :) Have a nice day.

Answer:

1/2

Step-by-step explanation:

1/4 +3/8

1/4 times 1/2 = 1/8

1/8 +3/8 = 4/8 = 1/2

Answer:

x=1/2

Step-by-step explanation:

x=2/4

simplification.. x=1/2

Step-by-step explanation:

I don't know whether this is correct or not

Answer:

x = 2[tex]\sqrt{35}[/tex]

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + b² = a² , that is

x² + 2² = 12²

x² + 4 = 144 ( subtract 4 from both sides )

x² = 140 ( take the square root of both sides )

x = [tex]\sqrt{140}[/tex] = [tex]\sqrt{4(35)}[/tex] = 2[tex]\sqrt{35}[/tex]

Answer:

10°

Step-by-step explanation:

the minor arc BC = 2×45 = 90°

so, the major arc BC = 360-90=270°

27x = 270°

x = 270/27 = 10°

Answer:

Ravi’s present age will be 5.

Step-by-step explanation:

From the given, Let Ravi’s present age is taken as "a" years.  

After 15 years, his age = (a+15) years.  

By the given, it is identified that the age of Ravi after 15 years is equal to the 4 times of his present age.

Given,  

[tex]a+15+4a\\4a-a+15\\3a=15\\a=15/3\\a=5[/tex]

Then, it has been found that the present age of Ravi is 5 when his age after 15 years will be 4 times of his present age.  

6 I think Sry if I wrong________

Answer:

Step-by-step explanation:

First, you should put the axis of symetry as 5, -7 because f(x)= (x-h)^2+k and h is 5 and k is -7. the axis of symetry is x=5 because that is the "folding point" of the graph. Next, you would have to plug In 4 and 6 as your helping points to tell you where the other points of the function are going to be.

Plug 4 in and you get -6. plug 6 in and you get -6. plot the points (4, -6) and (6,-6).

Hope this helps!

:)

Answer:

x = 16, y = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x = 16

----------------------------------------------------------

Using Pythagoras' identity in the right triangle

y² + 8² = 16²

y² + 64 = 256 ( subtract 64 from both sides )

y² = 192 ( take the square root of both sides )

y = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]

Answer:

Volume of air inside the cylinder = 71.6 cm³

Step-by-step explanation:

Step 1: Determine height and radius of the cylinder

Since the three tennis balls fits in closely into the cylindrical container, the height of the cylinder is equal to the sum ofnthe diameters of the three balls.

Also, the radius of the cylinder is equal to the radius of the tennis balls.

Height of cylinder = 3 × 4.5 cm = 13.5 cm

Radius of cylinder/balls = diameter of ball / 2 = 4.5 cm / 2 = 2.25 cm

Step 2: Determination of the volume of the cylinder

Volume of a cylinder = πr²h

π = 22/7; r = 2.25 cm; h = 13.5 cm

Volume of cylinder = 22/7 × (2.25 cm)² × 13.5 cm

Volume of cylinder = 214.8 cm³

Step 3: Determining the volume of the three balls

Volume of a sphere = 4πr³/3

Volume of three balls = 4πr³/3 × 3 = 4πr³

Volume of the three balls = 4 × 22/7 × (2.25 cm)³ = 143.2 cm³

Step 4: Determining the volume of air

Volume of air inside the cylinder = Volume of cylinder - volume of the three balls

Volume of air = 214.8 cm³ - 143.2 cm³ = 71.6 cm³

Therefore, volume of air inside the cylinder = 71.6 cm³

Answer:

y=2

Step-by-step explanation:

53y–16= 90

53y=90+16

53y=106

y=106/53

y=2

Answer:

y = 2

Step-by-step explanation:

If one side of a triangle inscribed in a circle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.

Therefor

53y - 16 = 90

add 16 to both sides

53y = 106

Divide both sides by 53

y = 106/53

y = 2

Answer:

y - 3 = -4 (x +2)

Step-by-step explanation:

Point slope form is

y -y1 = m(x-x1)  where m is the slope and ( x1,y1) is a point on the line

y - 3 = -4 (x - -2)

y - 3 = -4 (x +2)

Answer:

5/8

Step-by-step explanation:

The range is the largest number minus the smallest number

The largest number is 1 1/4 and the smallest number is 5/8

1 1/4 - 5/8

Getting a common denominator

1 2/8 - 5/8

Borrowing from the 1 in the form of 8/8

8/8+2/8 - 5/8

10/8 - 5/8

5/8

Answer:

5/8

Step-by-step explanation:

because 1 1/4 is 5/4 then x2 which is 10/4 so now you 10/4 - 5/8 which equals 5/8 as the difference.