Experimental vs. Theoretical Probability:
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?

The increase of Omar's mass from 6000kg to 7000kg will raise the mean mass of the elephants because the mean involves all values. However, it won't affect the median mass because the position of the middle value in the set won't change.

The correction of Omar's mass from 6,000 kilograms to 7,000 kilograms will affect both the mean and the median mass of the elephants. However, the effect on each measure of central tendency will be different.

The mean is the average, calculated by adding up all values and then dividing by the number of values. If Omar's weight is increased, the total mass of the elephants will increase, leading to an increase in the mean mass of the elephants.

However, the median, which is the middle value when all values are arranged in ascending order, will not change because it only depends on the arrangement of values, not their actual size. Since Omar's mass is already the largest value, an increase in his mass will not change the position of the middle value.

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Answer:

c

Step-by-step explanation:

Answer:

C. (11,-23)

Step-by-step explanation:

The given equations are

[tex]3a+b=10[/tex].....................equation 1

[tex]-4a-2b=2[/tex]...................equation 2

Multiply first equation by 2

[tex]6a+2b=20[/tex]

Now add this new equation to 2nd equation

[tex]6a-4a +2b-2b = 20+2[/tex]

[tex]2a = 22[/tex]

Divide both sides by 2

[tex]a=11[/tex]

We got a=11 , plug this value in anyone equation

3(11)+b=10[tex][/tex]

[tex]33+b=10[/tex]

Subtract 33 from both sides

[tex]b=-23[/tex]

So solution is (a,b) = ( 11,-23)

Solution :

Give that, a 72° sector in a circle ,

Area of Sector in a circle =

[tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]

Suppose radius of circle is r .

then Volume of sector of circle

[tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]

Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]

Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]

Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]

given, [tex] \pi =3.14 [/tex]

[tex] volume =82 \times 3.14 = 257.48 [/tex]

Hence, Area of circle= 257.48

Answer:257.48 yd sq

Step-by-step explanation: took de quiz

Answer:

D. [tex]y=-2x-1[/tex]

Step-by-step explanation:

We have been given a line on coordinate plane. We are asked to find the equation of our given line.

First of all, we will find slope of our given line using points [tex](-2,3)[/tex] and [tex](0,-1)[/tex] in slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,

[tex]y_2-y_1[/tex] = Difference between two y-coordinates,

[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.

Upon substituting our given values in slope formula, we will get:

[tex]m=\frac{-1-3}{0--2}[/tex]

[tex]m=\frac{-4}{0+2}[/tex]

[tex]m=\frac{-4}{2}[/tex]

[tex]m=-2[/tex]

Now, we will use slope-intercept form of equation [tex]y=mx+b[/tex], where,

m = Slope of line,

b = The y-intercept.

Upon looking at our given graph, we can see that y-intercept is [tex]-1[/tex].

Therefore our required equation would be [tex]y=-2x-1[/tex] and option D is the correct choice.

Answer:

The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.

Step-by-step explanation:

Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.

For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:

[tex] y = (x-3) + 2 [/tex]

[tex] y = x-3 + 2 [/tex]

[tex] y = x-1 [/tex]

Answer:

Hence, A radius is half the diameter.

Step-by-step explanation:

The question is asked as:

A radius is [tex]a_0[/tex] the diameter.

i.e. what is the value of the constant [tex]a_0[/tex] such that the radius and the diameter are related to each other.

We know that:

The Radius is the length of the line through the center that touches a point on the edge of the circle.

The diameter is the length of the line through the center that touches two points on the edge of the circle.

Hence Radius is half the diameter.

so the value of [tex]a_0=\dfrac{1}{2}[/tex]

( Or we can say Diameter is twice the radius of the circle.

[tex]d=2r\\\\r=\dfrac{1}{2}d[/tex]

where d denotes the diameter of the circle and r denotes the radius of the circle ).

Final answer:

The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

Explanation:

The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.

Here are the steps:

Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.

Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.

Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).

Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.

The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

Answer:

[tex]\text {Area of figure is }44 units^2[/tex]

Step-by-step explanation:

Given the figure and we have to find the area of given figure.

Area of figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(GHF)

From the figure, dimensions according to square boxes can be written as

AE=HF=8 units, EF=3 units, BI=3 units, GH=2 units, AC=CE=4 units.

[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\timesAC\times BI=\frac{1}{2}\times4\times3=6 units^2[/tex]

[tex]ar(AEFH)=HF\times EF=8\times 3=24 units^2[/tex]

[tex]ar(GHF)=\frac{1}{2}\timesHF\timesGH=\frac{1}{2}\times8\times 2=8units^2[/tex]

∴ [tex]\text {Area of figure is }44 units^2[/tex]

Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.

This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.

Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.

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Answer:

f(52) = 32,951,280,099

Step-by-step explanation:

In Fibonacci sequence, the sum of the two preceding sequence of the sequence is always equivalent to the next sequence.

For example, this is a Fibonacci sequence 1,2,3,5,8... As you can see that the sum of the two preceding sequence gave the next sequence i.e 1+2 = 3, 2+3 = 5, 3+5 = 8 etc and the chain continues like that.

If we are now given two large numbers of. Fibonacci sequence to bef(50)=12,586,269,025 and f(51)= 20,365,011,074

The next sequence f(52) will be the sum of the preceding sequences f(50) and f(51) that is;

f(52) = f(50) + f(51)

f(52) = 12,586,269,025 + 20,365,011,074

f(52) = 32,951,280,099

The resulting numbers if they are added is 32,951,280,099.

The area of the given sectors of circles is required.

The area of the sector is [tex]8.79\ \text{in}^2[/tex]

The area of the sector is [tex]151.98\ \text{cm}^2[/tex]

[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]

d = Diameter = 5.6 in

r = Radius = 2.8 in

Area of a sector is given by

[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]

[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]

r = 11 cm

[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]

Learn more about area of sector:

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Answer: The answer is 101!

Step-by-step explanation:

Call the first number in the sequence x

The next integer in the sequence is x + 1

The sum of the 5 consecutive integers is:

x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505

5x + 10= 505

5x = 495

x = 99

Since x is the first number, x + 2 is the third integer.

Thus, the third number in the sequence is 101

Answer:

it is 6 so have a merry christmas

Step-by-step explanation:

To use synthetic division to divide a polynomial by a linear expression, follow the steps: arrange the terms, change the sign of the linear expression, bring down the coefficient, multiply and add, write the result, and determine the quotient and remainder.

To use synthetic division to divide a polynomial by a linear expression, follow these steps:

In this case, the quotient is[tex]9x^3 + 4x^2 + 5x + 2[/tex].

Answer: 12 different combinations were possible.

Step-by-step explanation:

Given: At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza.

i.e. The number of types of pizza = 3

They also served cups of milk, orange juice, apple juice, or lemonade.

i.e. The number of  types of drinks = 4

Now, if each guest at the party chose one slice of pizza and one type of drink, then the number of different possible combinations are :

[tex]3\times4=12[/tex]

Hence, there were 12 different combinations .