A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?

a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)

Answer:

  18√91 +54√3

Step-by-step explanation:

Name the point at the top of the pyramid "A", the point at the left front corner "B", and the one in the center of the hexagonal base "C". Then right triangle ABC is shown. The "base" BC of that triangle is the same measure as the front edge (6), because the diameter of a regular hexagon is equal to twice the side length.

Using the Pythagorean theorem, we can find the face edge length to be ...

  AB^2 = BC^2 +AC^2

  AB^2 = 6^2 +8^2 = 100

  AB = √100 = 10

If we call the midpoint of the front edge "D", then we need to find the length of AD in order to determine the face area. Again, we can use the Pythagorean theorem.

  AB^2 = BD^2 +AD^2

  AD^2 = AB^2 -BD^2 = 10^2 -3^2 = 91

  AD = √91

The area of one of the 6 lateral faces is ...

  A = (1/2)bh = (1/2)(6)√91 = 3√91

The area of one of the 6 equilateral triangles that make up the base is ...

  A = (√3)/4·s^2 = (√3)/4(6^2) = 9√3

Then the total area of the pyramid is ...

  total area = 6 × (face area + partial base area)

  = 6(3√91 +9√3)

  total area =  18√91 +54√3

Answer:

  6

Step-by-step explanation:

Jana had a total of 3+3+3+3 = 12 muffins. Half that number is 3+3 = 6 muffins.

Jana put 6 muffins on the plate.

Answer:

[tex]\bold{\dfrac{11}{16}}[/tex]

Step-by-step explanation:

Given four tiles with numbers:

1, 4, 5 and 8

Tile chosen once and then replaced, after that another tile chosen:

All possibilities are:

{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)

(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)

(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Total number of possibilities = 16

When the sum is greater than 7, the possibilities are:

{(1, 8)

(4, 4) ,(4, 5) ,(4, 8)

(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Number of favorable cases = 11

Formula for probability of an event E is:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Hence, the required probability is:

[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]

Answer:11/16

Step-by-step explanation:i took the test

Answer:

[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]

Step-by-step explanation:

The domain is all possible values for x.

[tex]f(x)=(\frac{1}{4} )^x[/tex]

There are no restrictions on x.

The domain is all real numbers.

Answer:

B.All real number

hope you have unterstand

[tex] 1.2\times3.5\times4.1=[(1+0.2)(3+0.5)](4+0.1)[/tex]

$=[1\times3+1\times0.5+0.2\times3+0.2\times0.5](4+0.1)$

$=(3+0.5+0.6+0.1)(4+0.1)$

$=(4.2)(4+0.1)=(4+0.2)(4+0.1)$

$=4\times4+4\times0.1+0.2\times4+0.2\times0.1$

$=16+0.4+0.8+0.02=17.22$

Answer:

The cost of 3 magnets is $1

The cost of 9 magnets is $3

The cost of 6 magnets is $2

Step-by-step explanation:

The cost of magnets is calculated using the equivalent ratio. If 3 magnets cost  $ then the multiple used for the calculations of more magnets is 3. The ratio for every magnet price is 1 : 3 which means every dollar will be equal to 3 magnets. The cost of 3 magnets is $1, the cost of 6 magnets is $2 and cost of 9 magnets is $3.

Answer:

Step-by-step explanation:

You must multiply the first two equation which is 5x+1 and x this will give you

5x^2 + x. The bold goes in the first box.

Then do the same thing for 2x+1 and x+1 which will give you 2x^2+2x+x+1 or 2x^2+3x+1. This goes in the second box.

In the last box you will add 5x^2 +x and 2x^2 +3x +1, which gives you 7x^2 +4x +1.

Goes in the last box.

Hope this helps you.

Answer:

Put 25 in the box.

Step-by-step explanation:

Apply the exponent rule: (ax)^n = a^n × x^n

So we have:

(5x)^2 = 5^2 × x^2

= 25x^2

Best Regards!

Answer:

[tex]\frac{784}{15} \pi[/tex]

Step-by-step explanation:

According to the given situation, the calculation of volume of the solid is shown below:-

Here we will consider the curves that is

[tex]x = 7y^2, x = 7[/tex]

Now, rotating the line for the line x which is equals to 7

[tex]7y^2 = 7\\\\y^2 = 1\\\\ y = \pm1[/tex]

So, the inner radio is

7 - 7 = 0

and the outer radius is

[tex]7y^2 - 7\\\\ = 7(y^2 - 1)[/tex]

Now, the area of cross section is

[tex]A(y) = \pi(7(y^2 - 1))^2\\\\ = 49\pi(y^4 - 2y^2 + 1)[/tex]

The volume is

[tex]V = \int\limits^1_{-1} A(y)dy[/tex]

now we will put the values into the above formula

[tex]= \int\limits^1_{-1} 49\pi(y^4 - 2y^2 + 1)dy\\\\ = 49\pi(\frac{y^5}{5} - \frac{2y^3}{3} + y)^{-1}\\\\ = 49\pi(\frac{1}{5} - \frac{2}{3} + 1 + \frac{1}{5} - \frac{2}{3} + 1)\\\\ = 49\pi(2 + \frac{2}{5} - \frac{4}{3} )\\\\ = 49\pi(\frac{30+6-20}{15} )\\\\ = \frac{49\pi}{15} (16)[/tex]

After solving the above equation we will get

[tex]= \frac{784}{15} \pi[/tex]

Hi there! :)

Answer:

y = -2x + 3

Step-by-step explanation:

We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in values from the table:

[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]

Simplify:

m = -2 (rate of change)

Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:

7 = -2(-2) + b

7 = 4 + b

7 -4 = b

b = 3

Rewrite:

y = -2x + 3 is the equation for the linear function.

Answer:

2x^2 + x - 6 = rectangular garden: length = 2x – 3 feet; width = x + 2 feet

Step-by-step explanation:

(2x - 3)(x + 2) = 2x^2 + x - 6 =

2x^2 + 4x - 3x - 6 = 2x^2 + x - 6 =

2x^2 + x - 6

You get the original equation from the two sides multiplied. :)

Hope this helps, have a good day.

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The area is 2x² + x – 6 square feet. Then the factor of the equation is given as,

A = 2x² + x – 6

A = 2x² + 4x – 3x – 6

A = 2x(x + 2) – 3(x + 2)

L × W = (2x – 3)(x + 2)

The length and width of the rectangle will be (2x – 3) and (x + 2). Then the correct option is D.

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

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Answer:

finding the value of x first

2x + 3x + 10 = 180 (linear pair)

5x = 180 - 10

x = 170 / 5

x = 34

3x = 102

Answer: x>3

Step-by-step explanation:

x-5>2

x>+5-2

x>3

Answer:

Question 18: B. 104

Question 19: [tex] x = \frac{3}{2} [/tex]

Step-by-step Explanation:

Question 18:

Step 1: express the inverse relationship with an equation

[tex] y = \frac{k}{x^2} [/tex] ,

where k is constant

y = 26 when x = 4,

Constant, k, = [tex] y*x^2 = k [/tex]

[tex] k = 26*4^2 = 416 [/tex]

The equation would be [tex] y*x^2 = 416 [/tex]

Step 2: use the equation to find y when X = 2.

[tex] y*x^2 = 416 [/tex]

[tex] y*2^2 = 416 [/tex]

[tex] y*4 = 416 [/tex]

Divide both sides by 4

[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]

[tex] y = 104 [/tex]

Question 19:

[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]

Cross multiply

[tex] x(7) = 3(x + 2) [/tex]

[tex] 7x = 3x + 6 [/tex]

Subtract 3x from both sides

[tex] 7x - 3x = 3x + 6 - 3x [/tex]

[tex] 4x = 6 [/tex]

Divide both sides by 4

[tex] \frac{4x}{4} = \frac{6}{4} [/tex]

[tex] x = \frac{3}{2} [/tex]

Answer: D.) 52

Explanation: I guessed and got it right lol

Answer:

3.75

Step-by-step explanation:

[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]

The volume of the rectangular prism will be 3.75 cubic meters.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A box is 1 m high, 2.5 m long, and 1.5 m wide.

Then the volume of the rectangular prism will be

V = L x W x H

V = 1 x 2.5 x 1.5

V = 3.75 cubic meters

Thus, the volume of the rectangular prism will be 3.75 cubic meters.

More about the volume of the rectangular prism link is given below.

https://brainly.com/question/21334693

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Answer:

Step-by-step explanation:

Let the speed of Frank be x and speed of Gregory be y. If Gregory drives 22 miles per hour faster than Frank, then y = 22+x. SInce they they are 216miles apart after 2.25 hours,

Speed = Distance/Time

Total time travelled by them = 2.25hours

Total distance = 216 hours

Total speed = x+y = x+22+x

Substituting this parameters into the formula given to get x we will have;

x+22+x = 216/2.25

2x+22 = 96

2x = 96-22

2x = 74

x = 74/2

x = 37

Hence the speed of Frank is 37miles per hour while that of gregory is 37+22 = 59miles/hour

Answer:

[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

To simplify the fraction [tex]\frac{24}{64}[/tex], we need to find its greatest common factor.

Both 24 and 64 are divisible by 2, but that's not the biggest.

Both 24 and 64 are divisible by 4, but that's not the biggest either.

Both 24 and 64 are divisible by 8, and that's the highest we can go.

So:

[tex]\frac{24\div8}{64\div8} = \frac{3}{8}[/tex].

Hope this helped!

Answer:

The ball first bounces up to a height of 2 meters, and then falls 2 meters towards the ground

Step-by-step explanation:

Answer:

To find the volume of this cube, you would have to multiply 1.08 by 5.25 by 3.3 feet. If you did this, you would get: 18.711 feet^3. This is the volume of the rectangular prism.

Hope this helped!

Answer:

2^11

Step-by-step explanation:

since the bases are the same, we can add the exponents

a^b * a^c = a^(b+c)

2^6 * 2^5

2^(6+5)

2^11

Looks like either [tex]f''(x)=4x^2[/tex] or [tex]f''(x)=\frac4{x^2}[/tex]...

In the first case, integrate both sides twice to get

[tex]f''(x)=4x^2\implies f'(x)=\dfrac43x^3+C_1\implies f(x)=\dfrac13x^4+C_1x+C_2[/tex]

Then the initial conditions give

[tex]f'(1)=2\implies 2=\dfrac43\cdot1^3+C_1\implies C_1=\dfrac23[/tex]

[tex]f(1)=5\implies 5=\dfrac13\cdot1^4+C_1\cdot1+C_2\implies C_2=4[/tex]

so that the particular solution is

[tex]f(x)=\dfrac{x^4}3+\dfrac{2x}3+4[/tex]

If instead [tex]f''(x)=\frac4{x^2}[/tex], we have

[tex]f''(x)=\dfrac4{x^2}\implies f'(x)=-\dfrac4x+C_1\implies f(x)=-4\ln|x|+C_1x+C_2[/tex]

[tex]f'(1)=2\implies 2=-\dfrac41+C_1\implies C_1=6[/tex]

[tex]f(1)=5\implies 5=-4\ln|1|+C_1\cdot1+C_2\implies C_2=-1[/tex]

[tex]\implies f(x)=-4\ln|x|+6x-1[/tex]

Answer:

their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster

Subtracting a negative is the same as adding a positive. So 2-(-8) is really 2+8 = 10.

With something like 2-8, we start at 2 and move to the left 8 units to arrive at -6 on the number line. When we do 2-(-8), we start at 2 and move 8 units in the opposite direction since -8 is the opposite of 8.

In terms of money, you can think of a negative number as an IOU or it represents the amount of debt. Writing -8 means you are 8 dollars in debt. If we subtract away debt, then we have less of it and effectively its the same as adding dollars to your pocket. Subtracting away 8 dollars of debt is the same as adding 8 dollars to your pocket, which is one interpretation of how 2-(-8) is the same as 2+8.

Answer:

C.

On a coordinate plane, a line goes through (negative 2, 2) and (negative 1, negative 2).

The line parallel to the line 8x + 2y = 12 will be a line that goes through (-2, 2) and (-1, -2). The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

Given that the equation of the line is 8x + 2y =12. First, calculate the slope of the line if the slope of the line is the same as the equation of the given line then the two lines will be parallel.

8x + 2y = 12

2y = -8x + 12

y =-4x + 6

Take points (-2, 2) and (-1, -2) and find the slope of the line.

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2 - 2 ) / ( -1 + 2 )

Slope = -4

Therefore, the line parallel to the line 8x + 2y = 12 will be a line that goes through (-2, 2) and (-1, -2). The correct option is C.

To know more about an equation of the line follow

brainly.com/question/18831322

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Answer:

249.14 mm³

Step-by-step explanation:

r = diameter/2

= 7.8 /2

volume = 4/3 π r³

= 4/3 * 3.15 * (7.8/2)³

= 249.14 mm³

Hey there! I'm happy to help!

To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.

We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.

∛91.125=4.5

Therefore, the side length of the sandbox is 4.5 inches.

I hope that this helps! Have a wonderful day! :D

Answer:

Step-by-step explanation:

Distance walked by Arthur = 5/8 miles

Distance ride  by Jonathan = 8 times that of Arthur

it means that Distance rode on bus by Jonathan is 8 multiplied by Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * Distance walked by Arthur

Distance rode on bus by Jonathan = 8 * 5/8 = 5 Miles Answer

Step-by-step explanation:

Let minimum score on the final exam to earn an A be X

[tex]mean \: = \frac{sum \: of \: observation}{number \: of \: observation} [/tex]

[tex]90 = \frac{83 + 97 + 89 + 82 + x}{5} [/tex]

Further solving :

X = 99 marks

Answer:

30 31 64 59 58 33 54 77 56 41 (arrange it)

30 31 33 41 54 56 58 59 64 77 (done!)

Mean: Find the number in the middle (54+56)/2= 110/2 = 55

Mode: None

Mean: (30+31+33+41+54+56+58+59+64+77)/10=503/10= 50,3