Why do we divide by 3 when finding the volume of a square pyramid?

Answer:

Step-by-step explanation:

Your question asks what is  -[tex]3^{2}[/tex] / 2    but,  since it's on the Unit circle, I know you meant   - [tex]\sqrt{3}[/tex] /2    Also, it's one of those known angles on the unit circle.

note that the angles can all be put in the form of  [tex]\sqrt{x}[/tex] / 2 , where x = 0,1,2,3,4 ,  for the five special points on the unit circle.  

as the attached pic shows,   Cos(t) for the given point would be 180-150°= 30 and sin(t) would be 90 - 30 = 60 °

it's not easy to understand how I got those angles,  just ask if you don't get it.  :)

Answer:

45, 60, 75

Difference between the largest and smallest angles

75 - 40 = 35

Step-by-step explanation:

First solve for x.  The sum of the interior angles of a triangle is 180

3x + 4x + 5x =180  Combine like terms

12x + 180  Divide both sides by 12

[tex]\frac{12x}{12}[/tex] = [tex]\frac{180}{12}[/tex]

x = 15

3x = 3(15) = 45

4x = 4(14) = 60

5x  = 5(15) = 75

Step-by-step explanation:

please, burn this into your brain for life :

the sum of all angles in a triangle is always (yes, no exceptions) 180°.

so,

3x + 4x + 5x = 180

12x = 180

x = 180/12 = 15

3x = 3×15 = 45°

4x = 4×15 = 60°

5x = 5×15 = 75°

the difference between largest and smallest angle is therefore

75 - 45 = 30°

By using the property of combination, it can be calculated that -

This is a problem of combination.

There are 15 ways to choose the students who will go to the meeting

What is combination?

Combination is the process of selection some objects from a group of items where the order of the selection do not matter

This is a problem of combination

Number of seniors = 6

Number of students will go to the all district meeting = 2

Number of ways to choose the students who will go to the meeting =

                                                                                                       [tex]{6 \choose 2}[/tex]

                                                                                                = [tex]\frac{6!}{(6 - 2)! \times 2!}[/tex]

                                                                                                = 15

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According to good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats.

It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home.

Every paint has a spread rate that controls how many square feet may be covered each gallon. A good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats. Choosing the proper quantity of paint for steel is a tough matter because high-quality paint is expensive and you don't want to overbuy. To avoid overbuying paint, we advise simply purchasing 80% of the projected amount at first and the remaining 20% after you are nearly completed.

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Answer:

Slope

Angle (degrees) Gradient Grade (%)

Therefore, the correct answer is 5.24

Answer:0.5x - y -7.5 = 0

Step-by-step explanation:

The property that represents the commutative law of sets is given as follows:

d. (A ∪ B) ∪ C = A ∪ (B ∪ C)

The cumulative law of sets states that the order in which the union operation is made does not change the resulting set of these multiple union operations.

The symbol that represents the union operation is given as follows:

∪.

Hence statement d is the correct statement of the commutative law of sets, as:

For both cases, the resulting set is the same.

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The number of two-points and three points shot The Cruisers scored are 24 and 19 points respectively.

The Cruisers scored a total of 105 points in a basketball game. They also had a total of 43 baskets, of which some were two-point shots and some of were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

x = number of two-points

y = number of three-points

So;

x + y = 43 -------1

Also;

2x + 3y = 105 -----2

Multiplying equation(1) by 2

2x + 2y = 86

2x + 3y = 105

Subtract equation(i) from equation(ii)

y = 19

To find x:

x = 43 - 19

x = 24

Therefore,

number of two-points = 24

number of three-points = 19

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Answer:

0

Step-by-step explanation:

Rise over run.

Difference between y is 0.

Difference between x is 5.

0/5 = 0.

Answer:

m = 0

Step-by-step explanation:

Slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y stay the same, and the x decrease by 5, so the slope is

m = 0/5

The statement regarding the correlation coefficient (r) that is true is b) "the correlation coefficient describes the direction of the association between two variables."

The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 1 implies a strong positive correlation between the variables, meaning that as one variable increases, the other variable also tends to increase.

A correlation coefficient of -1 implies a strong negative correlation between the variables, meaning that as one variable increases, the other variable tends to decrease. A correlation coefficient of 0 implies no correlation between the variables. The sign of the correlation coefficient (positive or negative) indicates the direction of the association between the variables, while the magnitude of the coefficient (closer to 1 or -1) indicates the strength of the association.

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Answer: 10

Step-by-step explanation:

Because 0.25 or 25%

We take 40 times 0.25 =  10

To find horizontal line,its equation is y=b where b is constant.Horizontal line is parallel to x-axis of the coordinate plane.To find vertical ,its equation is x=b where b is constant.Vertical line is parallel to y-axis.

A horizontal line is a line extending from left to right and right to left.The slope of horizontal line is always zero.Horizontal lines are always parallel to x-axis.The y-intercepts of a horizontal line y=b is the point (0,b).

A vertical line is a line extending from up to down and downward to upward.Its never moves left to right.Vertical lines are always parallel to y-axis.The equation of a vertical line is x=a and x=-a where x is the x-coordinate of ant point on the line and a is the point where he line crosses the x-intercepts.

Hence we can find horizontal and vertical lines on the graph or paper easily.

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The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

What is Standard Deviation?

It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.

The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.

The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.

To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.

Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.

So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

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Answer: You are correct, because negative number don't have real square roots

Step-by-step explanation:

Answer:

The tree is 10.77 meters tall.

Step-by-step explanation:

The given diagram is an example of similar triangles. Look at the image I attached to my response to see this problem in terms of triangles.

The triangle that is formed by Alyssa and her shadow and the triangle that is formed by the tree and its shadow is an example of similar triangles because they both share an internal angle.

As per the similar triangles theorem, the ratios of the corresponding sides of both sides are proportional.

Thus, we have to make a proportion of the corresponding sides of both triangles to solve for the height of the tree. Let x = the height of the tree.

Proportion: [tex]\frac{BE}{BC} = \frac{DE}{AC}\\[/tex]

BE = 4.25 meters

BC = 27.75 meters

DE = 1.65 meters

AC = x meters

[tex]\frac{4.25}{27.75} = \frac{1.65}{x}[/tex]

Now, cross multiply to solve for x.

[tex]4.25x = 1.65(27.75)\\4.25x = 45.7875\\x = 10.77[/tex]

∴ The tree is 10.77 meters tall!

The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

We have to given that;

Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree.

Now, we can make a proportion of the corresponding sides of both triangles to solve for the height of the tree.

And,  Let us assume that,

x = the height of the tree

Hence, We get;

⇒ (27.75 - 23.5) / 27.75 = 1.65 / x

Solve for x;

⇒ 4.25 / 27.75 = 1.65 / x

Cross multiply we get;

⇒ 4.25x = 1.65 x 27.75

⇒ 4.25x = 45.78

⇒ x = 10.77 meters

Thus, The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

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Therefore , the 2 year old children can able to count to 1 to 100 counting by making them learn.

The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number,

variable then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."

Here,

Every child is different in how they grow and learn, yet many

Children as young as two years old may count past ten and learn their numbers from 1 to 100.

They could be ready to try numbering in fives or using other skip counting strategies (5, 10, 15, 20, and so on).

As soon as you can, begin teaching your child how to recognise

numbers.

As a result, by making the toddlers study, two-year-olds can count to one hundred.

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Answer:

increase 10.5 percent

Step-by-step explanation:

..

The denominator of a fraction represents the number of equal parts in a whole, while the numerator represents the number of parts considered.

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The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.

Every point in a circle is equally distance from the center. Similar to a sphere, every point on a sphere is equally distance from the center.

Two equal chords on a circle indicate that they are equally spaced from the circle's center.

The incenter of a triangle is the point that is equally far from each of its sides. A median is a line segment that has one of its endpoints in the vertex of a triangle and the other endpoint in the midpoint of the side opposite the vertex. The three medians of a triangle meet in the centroid.

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Answer: The mean is less than the median IQ

Step-by-step explanation:

When a distribution is skewed left (there is an obvious tail going in the left direction, which is true in this case), then the mean is drawn down because it is not resistant to any outliers, or unusual data points.

The median, however, is resistant to outliers and will not move as much.

Therefore, the mean will be less than the median.

The relationship between the mean and median of a data set is determined by whether the data is symmetrically distributed, positively skewed, or negatively skewed. However, without a visual representation or specific values, we cannot definitively compare the mean and median of the IQ scores.

In order to determine the relationship between the mean and the median of a data set, we need to know the nature of its distribution. If the data is symmetrically distributed, the mean and the median will be equal. If the data is positively skewed (has a long right tail), the mean will be larger than the median. If the data is negatively skewed (has a long left tail), the mean will be less than the median.

However, in the absence of the actual histogram in your question, the correct answer would be 'It cannot be determined because we cannot tell the exact values of the IQ scores in the sample.' This is because without a visual representation or specific values, we cannot determine the distribution's skewness, and by extension, cannot compare the mean and median.

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The Answer Is 1,837 cm

If the polygon has four right angles , then it is a square when all four sides are equal and a rectangle when the opposite sides are equal .

The Polygon is defined as closed object that is made of line segments rather than curves on a 2 - D plane .

A square is defined as a polygon in which all the angles are right angles and pair of opposite sides are equal .

A rectangle is defined as polygon that have all the angles as right angles and all four sides are equal .

From above definitions , we can say that ,

A polygon that has four right angles , is a square when all four sides are equal and it is a rectangle when pair of opposite sides are equal .

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The roots of the quadratic equation 4x2 − 7x + 0 are -7/4 and 0.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Quadratic equations are used to solve problems involving areas, lengths, and other geometric figures, as well as to find unknown values. Such equations are often used in calculus and physics.
To find the roots, you can use the quadratic formula, which is x = -b ± √b2 - 4ac/2a. In this case, a = 4, b = -7, and c = 0, so the roots are -7/4 and 0.
Another way to find the roots is to use the factoring method. To factor 4x2 − 7x + 0, you can factor out 4x and then group the terms to get 4x(x − 7) + 0. Then you can set each factor equal to zero to get x = 0 and x = 7. Therefore, the roots of the equation 4x2 − 7x + 0 are -7/4 and 0.
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According to question,

Given data,

We know that;

Zero product property,

ab =0

either a or b or both must be zero.

(x-5) (x+7) = 0

Where a=(x-5)

b= (x+7)

then,

x-5=0(both side equation adding +5)

 +5=+5

So,

x = 5

therefore,

x+7=0(both side equation substrate -7)

 -7=-7

So,

x=7

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Completing the table using equivalent ratios Willka can cover 4.5 m² of the area with 1 - liter paint.

Given :

What are equivalent ratios?

Equivalent ratios are the ratios that express same relation or numbers that are equivalent.

so area covered for 1 paint

13.5 / 3 = 4.5

4.5 for 1 paint

for 10 paint :

Area covered = 4.5 * 10

= 45

Table :

Area covered  ( m^2 )        paint ( L )

13.5                                      3

4.5                                        1

45                                         10

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[tex]y=2[/tex] ± [tex]\sqrt{28+4x}[/tex] is the equation that equals 2(x - 2)2 = 8(7 + y).

Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other. In most cases, a number's inverse refers to its reciprocal, or x - 1 = 1 / x. When a number is combined with its reciprocal, or inverse, the result is 1, or 1.

Considering the equation:

[tex]2(x-2)^2=8(7+y)[/tex]

Change the x and y variables.

[tex]2(y-2)^2=8(7+x)[/tex]

In terms of x, solve for y.

We have two sides, therefore divide them by two.

[tex](y-2)^2=4(7+x)[/tex]

Using the distribution property, [tex]a.(b+c)=a.b+a.c[/tex]

[tex](y-2)^2=28+4x[/tex]

Square-rooting both sides yields:

[tex]y-2=[/tex]±[tex]\sqrt{28+4x}[/tex]

our two sides plus two;

[tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex]

As a result, equation [tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex] is the opposite of [tex]2(x-2)^2=8(7+y)[/tex]

The complete question is:-

Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?

Options:

–2(x – 2)^2 = –8(7 + y)

y= 1/4 x^2 -x -6

y= -2 +/- sqrt of 28+4x

y= 2 +/- sqrt of 28+4x

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The equation to form 5 with 4 2s is 2 + 2+ (2/2).

Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.

The formation of 5 with 4 2s is -

= 2 + 2+ (2/2)

= 2 + 2 + 1

= 5

Thus, the expression to form 5 with 4 2s is 2 + 2+ (2/2).

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The required solution would be h = 3Vr²/3.14 for h, where V is the volume of a cone.

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

The volume of the cone (V ) = 1/3πhr²

We have been given that the volume of a cone is (1/3)3.14r²h

We have to determine the solution for h

As per the given question, we have

⇒ V = (1/3)3.14r²h

Multiply by 3 into the above equation,

⇒ 3V = 3.14r²h

Divided by 3.14 into both sides

⇒ 3V/3.14 = r²h

⇒ h = 3Vr²/3.14

Therefore, the required solution would be h = 3Vr²/3.14.

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For the given observation 5,6,7,8,9,11 the Median is 7.5

The median is one of the metrics of central tendency. The middle value in a group of numbers is known as the median. It divides a given data sample into the higher half and the lower half. At least half of the observations fall below the median and at least half of the observations fall above the median.

If a data collection contains an even number of observations, the median can be determined as follows:

Sort the information either by ascending or by descending.

Identify the (n/2)nd and [(n/2) + 1] th observations if there are an even number of observations (let's say n).

The median of the provided data is equal to the average of the top two observations (as determined in step 2).

Here n = 6, So [6/2 + (6/2)+1}/2

=>  Median = 7.5.

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