find the two square roots of 400

The height of the pyramid is 16 feet.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the height of the pyramid.

The slant height of the pyramid is the hypotenuse of a right triangle whose legs are the height of the pyramid and half the length of the base of the pyramid. Since the base is a square, half the length of the base is 12 feet.

Using the Pythagorean theorem:

height² + 12² = 20²

height² = 20² - 12²

height² = 256

height = 16 feet

Therefore, the height of the pyramid is 16 feet.

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Answer

9a-5

Step-by-step explanation:

5a - 8+ 4a +3 or 5a -5 +4a

If you combine it 5a - 5 + 4a

(sorry if wrong)

The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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Answer:

4x & 7x

and

3 & 7

(hope this helps <3 )

Step-by-step explanation:

hope this helps you

..................

If A is an m × n matrix. The following are true regarding it: 1. The number of pivot positions in A is called the rank of A.2. A pivot column of A is a column that contains a pivot position.3. A pivot position of A is a location in A that corresponds to a leading 1 in the reduced echelon form of A.4. Free variables of a linear system are variables corresponding to the non-pivot columns of A.

The rank of a matrix is the number of pivot positions in the matrix after it has been reduced to a reduced echelon form. In the reduction procedure, the rows and columns of the matrix are manipulated to convert the matrix into a reduced echelon form.

A pivot column of matrix A is one that contains at least one pivot position, according to the definition. These are columns that have a leading 1 in a reduced echelon form. These columns contain the variables in the equation system that correspond to the pivot rows.

In matrix A, a pivot position is the location of a leading 1 in the matrix's reduced echelon form. The reduced echelon form of a matrix is the one in which the matrix has been transformed so that it satisfies certain criteria for ease of use.

The variables that do not correspond to pivot columns in matrix A are referred to as free variables. These variables are not bound to specific values in a solution to the associated equation system. They can take on any value and therefore provide an infinite number of solutions.

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Answer:

\(y=\frac{1}{2}x+6\) and \(y=5x+8\)

Step-by-step explanation:

The big thing to remember with this is that parallel lines have the same slopes. We can isolate the y-variable in both of these to get the slope-intercept form, which just makes it easier to see the slope.

a. 3x-6y=12

\(-6y=-3x+12\\y=\frac{1}{2}x-2\\\)

Now that we know the slope, we can have any y-intercept except for the original one, they just need to have the same slope. So an equation that could work is \(y=\frac{1}{2}x+6\).

b. 5x-y=10

This equation can be solved in the exact same way.

\(-y=-5x+10\\y=5x-10\)

Parallel line: \(y=5x+8\)

Again, it does not matter what the y-intercept is, they just can't have the same one. The slopes have to be the same.

Hope this helps!

Answer:

9

Step-by-step explanation:

13 - 5 = 8

8 / 2 = 4

13 - 4 = 9

Answer:

1/-2

Step-by-step explanation:

To find the slope:

rise/run

From point to point

So....

From (-1,0)

you go up 2(2)

then left 4(-4)

to get to (-5,2)

so 2/-4 reduced is 1/-2

490

472 <490<500

it fits the criteria

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

5, first subtract then multiply divide by two and last divided by 3

Answer:

y = -25x + 170

Step-by-step explanation:

For the graph equation y = ax + b, we have to find a and b.

Pick two points that are on the grid for best accuracy.

e.g., (2,120) and (6,20)

Then a = (20-120)/(6-2) = -25

b is the y coordinate of the line with the y axis: 170

So the formula is:

y = -25x + 170

If the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

Given that the speed of the ball after kicking is 48 feet per second and the function that represents the height of the ball is \(-16t^{2} +48t\).

We are required to find the time that the ball took to travel before returning the ground.

We know that speed is the distance a thing covers in a particular time period.

The height of the ball after t seconds is as follows:

h(t)=\(-16t^{2} +48t\)

It is at ground at the instants of t.

Hence,

\(-16t^{2} +48t\)=0

-16t(t-3)=0

We want value of t different of 0, hence :

t-3=0

t=3.

Hence if the speed of the ball after kicking is 48 feet per second then the ball will return on the ground after 3 seconds.

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Answer:

B. t=3

Step-by-step explanation:

i took the test and got it right

225 students taking the biology course are neither computer science nor biology majors.

To find out how many students taking the biology course are neither computer science nor biology majors, we can use the following steps:
Determine the total number of students majoring in computer science, biology, or both.
- Computer science majors: 50 students
- Biology majors: 213 students
- Double majors (both computer science and biology): 44 students
Subtract the double majors from the individual major counts to find the unique number of students in each major.
- Unique computer science majors: 50 - 44 = 6 students
- Unique biology majors: 213 - 44 = 169 students.

Add the unique number of students in each major.
- Total unique majors: 6 (computer science) + 169 (biology) = 175 students
Subtract the total unique majors from the total number of students taking the biology course to find the number of students who are neither of these majors.
- Neither major: 400 (total students) - 175 (unique majors) = 225 students.

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To determine if a line is parallel or perpendicular, we can place each line on a sloped intersection shape (y = mx + b) and observe the slope m of each line. Equal slopes result in parallel lines. If the slope is multiplied by -1, then the line is vertical.

Parallel Lines:

Two or more lines that lie in the same plane and do not intersect are called parallel lines. They are equidistant from each other and have the same slope. A straight line equation is usually written in the form of a slope intercept represented by the equation y = mx + b. where "m" is the slope and "b" is the y-intercept. The "m" value defines the slope and tells how steep the line is.

Perpendicular Lines:

A vertical line or perpendicular line is two separate lines that intersect at an angle of 90° to each other. These are straight lines known as perpendiculars that meet each other at certain angles (right angles).

We have already seen what a vertical line looks like. If a shape has an "L" shape, its vertex angles are right angles. Vertical lines always intersect each other, but not all intersecting lines are always perpendicular to each other.

Two main properties of vertical lines:

1. Perpendicular lines always intersect or intersect each other.

2. The angle between two vertical lines is always 90°.

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Answer:

Correct so far.

The median score must be between positions 32 and 33 on the table.

The median score is 72.

Step-by-step explanation:

Correct so far.

The median score must be between positions 32 and 33 on the table.

The median score is 72.

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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The probability that both spins are red is 1/16

from the question, we have the following parameters that can be used in our computation:

Sections = 8

Red sections = 2

So, we have

P(Red) = 2/8

Simplify

P(Red) = 1/4

Using the above as a guide, we have the following:

P(Red, Red) = 1/4 * 1/4

Evaluate the products

So, we have

P(Red, Red) = 1/16

Hence, the probability that both spins are red is 1/16

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Answer:

The expression cannot be factored

Step-by-step explanation:

got it correct

Answer:

Factor analysis

Step-by-step explanation:

A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion.

The statistical technique that would allow a researcher to cluster is called Cluster Analysis. It is a statistical technique that enables researchers to cluster groups of objects that share certain similarities based on their attributes, observations, or characteristics.What is cluster analysis?Cluster analysis is a data-driven technique that helps in grouping similar objects based on the data provided. It is often used in many fields, including data mining, machine learning, and bioinformatics. Cluster analysis is used to find the natural groupings of objects, which have similar attributes or characteristics. For instance, it is used to group customers based on their behavior, cluster genetic markers in DNA, cluster galaxies in the universe, and much more. Cluster analysis helps in analyzing large datasets by grouping similar objects into smaller groups that are easier to understand.The Cluster analysis technique is a valuable tool in statistical analysis and it is used in different fields like market research, bioinformatics, genetics, etc. It is a method of statistical data analysis that helps researchers identify groups or clusters of data. It is a commonly used technique that is used to identify natural patterns within large datasets.

Answer:

She saw the letter K, and other letters Are X and Y

Step-by-step explanation:

Answer:

m<1=120

Step-by-step explanation:

A linear pair adds up to 180 degrees.

So <1+<2=180

Let <2=X, that would make <1=2X because <1 is 2 times more.

So substitute that into the equation.

2x+x=180.

Combine like terms and get 3x=180

Divide both sides by 3 and get x=60.

Substitute that into <1 and get <1=120

Answer:

a=1/3m

Step-by-step explanation:

Divide each side by 12m and then you simplify it

The real world situation that can be modelled with the given  expression can be modelled as shown below.

Given is the expression as -

D/3

A real world situation that can be modelled with this expression can be written as follows -

Amanda has a total of {D} bananas. She divides the bananas into 3 of her childrens equally. Write an expression that would represent the amount of bananas recieved by each of her child.

Therefore, the real world situation that can be modelled with the given  expression can be modelled as shown above.

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Scout says the class is suspicious of their first-grade teacher, Miss Caroline Fisher, because she comes from a county in North Alabama that supported the secession of the Confederate States from the Union during the Civil War.

The secession of the Confederate States from the Union during the Civil War refers to the act of Southern states, including Alabama, separating from the United States in order to form their own independent nation. Scout's statement suggests that Miss Caroline Fisher comes from a county in North Alabama that actively supported this secession.

During the Civil War, Alabama was a Confederate state, meaning it sided with the Southern states that seceded from the Union. Many counties within Alabama showed support for the Confederate cause and were known for their allegiance to the Confederacy.

Scout's statement implies that the class views Miss Caroline Fisher's background from a county in North Alabama as a reason for suspicion. The historical context of the Civil War and the divide between the Union and Confederate states likely contribute to the class's skepticism or concern regarding their teacher's origins and potential biases.

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