A normal distribution has a mean 7 of and a standard deviation of 2. Use the​ 68-95-99.7 rule to find the percentage of values in the distribution between and .
What is the percentage of values in the distribution between 7 and 9​?

Step-by-step explanation:

8.

Let the number is x. A number minus 7 is (x-7). It is doubled to get 86. So,

[tex](x-7)^2=86\\\\x-7=\sqrt{86}\\\\x-7=\pm 9.27\\\\x-7=9.27\ and\ x-7=-9.27\\\\x=16.27\ or\ x=-2.27[/tex]

The number can be 16.27 or -2.27.

9.

The diameter of the cylindrical tank, d = 20 ft

Radius, r = 10 ft

It is filled with oil to a depth of h feet.

The volume of a cylindrical shaped object is given by :

[tex]V=\pi r^2 h[/tex]

Put the given values,

[tex]V=\pi (10)^2h\\\\V=3.14\times 100\times h\\\\V=314h\ ft^3[/tex]

So, the volume of the tank is equal to [tex]314h\ ft^3[/tex].

The required range of drivers who own 8 years car is 23years.

Given that,

The scatter plot shows the ages of drivers who attended a car show and the ages of their cars.

We have to determine,

The age range of drivers who own an 8-year-old car.

According to the question,

The Range is the difference between the lowest and highest values.

Therefore,

The age range of drivers who own 8 years old car is 17,25 and 40 years.

Then,

Range of drivers who own 8 years car = highest value of range - lowest value of age.

Range of age of drivers who own 8 years car = 40 - 17 = 23years

Hence, The required range of drivers who own 8 years car is 23years.

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The wrist circumference in relation to height tells us how big our body frames are.

The wrist circumference in relation to height tells us how big our body frames are. A man who is above 5' 5" tall and with a wrist measurement of 6" would be considered to have tiny bones.

The following chart can be used to establish whether a person has tiny, medium, or large bones by measuring their wrist with a measuring tape and comparing the results.

Women:

under 5'2" in height"

Medium wrist size is between5.5" and5.75" Small wrist size is less than5.5" "

Large is defined as a wrist size of 5.75 or greater."

between 5'2" and 5'5" tall

smaller than 6 inches around the wrist"

Bracelet size 6 is medium "Medium = wrist size between 6.25" and 6.5" Large

Over 5' 5" in height"

Small wrists measure less than 6.25", Medium wrists measure 6.25" to 6.5," and Large wrists measure over 6.5."

Example :

2(x + 3 ) + 2 (x + 4 ) = (x + 3 )( x + 4)

x² + 7x + 12 = 4x + 14

x² + 3x - 2 = 0

(x + 3 / 2 )² = 17 / 4.

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Answer:

1/4

Step-by-step explanation:

8/8=1

6/8=3/4

4/8=2/4

2/8=1/4

Answer:

the missing side is [tex]\sqrt{89}[/tex]

Step-by-step explanation:

We use Pythagoras theorem

[tex]8^{2} +5^{2} =x^{2} \\64 + 25 = x^{2} \\89=x^{2} \\\sqrt{89} =x[/tex]

the equation in the form of slope interpretation is y = 1/3x -4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.

Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c

Where m is the slope

c is constant

The slope for the given data

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 + 6 )/ (-3 + 6)

m = 1/3

Hence, the equation would be

y = 1/3x + c

for constant we would satisfy the equation with other coordinates of the line.

Substituting ( 0, -4) in the above equation

-4 = 0 + c

c = -4

thus, the equation of the line is  y = 1/3x  -4

therefore, the linear equation of the given data is y = 1/3x -4.

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Answer:

side AB

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

On solving the provided question, we can say that -  here in quadrilateral we have x + 146 + 47 + y = 360 => [tex]x= 83.5[/tex]

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

here,

x + 146 + 47 + y = 360

2x + 193 = 360

2x = 167

[tex]x= 83.5[/tex]

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Answer:

6.7 km

Step-by-step explanation:

c² = 4.9²+4.5²

= 24.01 + 20.25

= 44.26

c = √44.26 = 6.7

Answer:

The inverse function is [tex]y = -\frac{x}{4}[/tex]

Step-by-step explanation:

Inverse of a function:

To find the inverse of a function, we exchange x by y, then we isolate y.

y = -4x

Finding the inverse:

[tex]x = -4y[/tex]

[tex]4y = -x[/tex]

[tex]y = -\frac{x}{4}[/tex]

So

The inverse function is [tex]y = -\frac{x}{4}[/tex]

9514 1404 393

Answer:

  85 km/h

Step-by-step explanation:

Let s represent the speed of the slower car. Then the travel time is ...

  time = distance/speed

  2 = 360/(s +(s+10))

  4s +20 = 360 . . . . . multiply by 2s+10

  4s = 340 . . . . . . . . . subtract 20

  s = 85 . . . . . . . . . . . divide by 4

__

The rate of the slower car is 85 km/h.

Answer:

x = 1

Step-by-step explanation:

2x + 3 = 5

=> 2x = 5-3

=> 2x = 2

=> x = 2/2

=> x = 1

Therefore, the value of x is 1

Hope it helps :)

Answer:

x=1

Step-by-step explanation:

Hi there!

2x+3=5

Our goal is to isolate x on one side of the equal sign, and we can do this using inverse operations. For example, the inverse operation of addition is subtraction. Subtract both sides of the equation by 3 to isolate 2x:

2x+3-3=5-3

2x=2

The inverse of multiplication is division. Divide both sides by 2:

2x÷2=2÷2

x=1

I hope this helps!

The center of the circle is (-10,4) and the radius is 10.

The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.

All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The equation of the circle is,

( x - h )² + ( y - k )² = r²

(x+10)² + (y−4)² = 100

(x+10)² + (y−4)² = 10²

Compare the equations and find the center and radius,

Center = ( h,k) = ( -10,4)

Radius = r = 10

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Answer:

V^2 + 4V + 4

Step-by-step explanation:

Answer:

Minimum of 6 squares.

Step-by-step explanation:

The dimension of the rectangular carton = 6 by 4 inches.

The area of the carton = length x width

                                      = 6 x 4

                                       = 24 square inches

Assume that we have a square of side length 2 inches, then;

area of the square = length x length

                               = 2 x 2

                               = 4 square inches

So that since all materials is to be used,

the minimum number of squares that it can produce = [tex]\frac{24}{4}[/tex]

                                                           = 6

The minimum number of squares he can produce is 6.

What is a rectangle?

A rectangle is a 2-dimensional quadrilateral with four right angles that add up to 360 degrees. It has two diagonals which bisect each other. The diagonals are equal in length

Area of a rectangle = length x width

6 x 4 = 24 square inches.

What is a square?

A square is a quadrilateral that has four sides of equal lengths.

Possible areas of the square = 1 inches square, 4 inches square, 9 inches square, 16 inches square.

Minimum number of square = 24 / 4 = 6 squares

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Answer:

C=10

Step-by-step explanation:

Answer:

It's A

Step-by-step explanation:

I just did the test and it is A

The length of x is 6 in simplest radical form.

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given ,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = 3/x

∅ = 30°

⇒ sin30 = 3/x

⇒ 1/2 = 3/x  [ sin30 = /2  ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

Hypotenuse² = Perpendicular² + Base²

6² = 3² + Base²

6² - 3² = Base²

Base² = 25

Base = √25

Base = 5

We can conclude the value of x to be 6.

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Answer:

Angle x = 120 degrees

Angle y = 60 degrees

Step-by-step explanation: Angle x has to be equivalent to the 120 degree angle that is already given since lines l and m are parallel as well as lines p and q. To find angle y, you must realize that angles x and y are supplementary angles, so their sum is 180 degrees. Since we now know that angle x is 120 degrees, you must subtract 120 from 180 in order to find the value of angle y: 180 - 120 = 60 degrees. I'm sure that there are other methods to figuring this question out, but this is how I did it.

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

Answer:

Perpendicular line ⇒ 2x + 9y + 42 = 0

midpoint: (-1,1)

Step-by-step explanation:

Let's find the coordinates of midpoint of AB

Here, from figure, A = (-3,-2), B = (1,4)

So midpoint:

[tex]P = (\frac{-3+1}{2},\frac{-2+4}{2})[/tex]

∴ P = (-1, 1)

Now, given straight line is x - 2y = -8(x-8)

⇒x - 2y = -8x+64

⇒9x - 2y - 64 = 0

Perpendicular line to 9x - 2y - 64 = 0 is 2x + 9y + k = 0

Perpendicular line passes though (6,-6)

Putting the values, we get

2(6) + 9(-6) + k = 0

⇒12 - 54 + k = 0

⇒k = 42

∴ Perpendicular line ⇒ 2x + 9y + 42 = 0

Answer: 3 · 30= 90

Step-by-step explanation:

yes you are correct

Answer:

exponents, exponents, parenthesis, parenthesis/exponents, parenthesis.

Step-by-step explanation:

Answer:

perimeter = 70 yards

Step-by-step explanation:

⭐What is the area of a rectangle?

⭐What is the perimeter of a rectangle?

1. Make the equation for the area of the given rectangle and solve for x

2. Substitute x into the expressions of the length and width and solve for the perimeter

1. Define the expressions of the length and width of the rectangle

width: x

length: 4x

2. Make the equation for the area of the rectangle

[tex]196yd^2 = 4x * x\\196yd^2 = 4x^2[/tex]

3. Solve for x

[tex]\frac{196}{4} = x^2[/tex] . . . . . . . . . . divide both sides by 4

[tex]49 = x^2[/tex]

[tex]\sqrt{49} = \sqrt{x^2}[/tex] . . . . . . . . square root both sides to isolate x

∴ [tex]7 = x[/tex]

4. Substitute x into the expressions of the length and the width

width: x

width = 7

height: 4x

height = 4(7) = 28

5. Solve for the perimeter

[tex]perimeter = 2(length) + 2(width)[/tex]

[tex]perimeter = 2(28) + 2(7)\\perimeter = 56 + 14\\perimeter = 70[/tex]

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The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the original line.

Write in slope intercept form

2y = 8x - 6

y = 8x/2 - 6/2

y = 4x - 3

Using the slope intercept, slope m is 3.

The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.

Slope of perpendicular line = -1 / ( 4 )

Slope of perpendicular line = -1/4

Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/4)( x - (-3) )

( y - 3 ) = (-1/4)( x + 3 )

y - 3 = (-1/4)x - 3/4

y = (-1/4)x - 3/4 + 3

y = (-1/4)x + 9/4

Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.

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9514 1404 393

Answer:

  not periodic

Step-by-step explanation:

There is no value p such that f(x) = f(x+p) for all x. Hence. the function is NOT PERIODIC.

_____

It seems possible that subtracting the linear increase would result in a periodic function. Because of the linear increase, there is no left- or right-shift of the function that will map it to itself.

Answer:

−1 < y < 3

Step-by-step explanation:

Answer:

the answer is 14

Step-by-step explanation: