Find the volume of the sphere.
Either enter an exact answer in terms of t or use 3.14 for it and round your final answer to the nearest
hundredth.

Each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

To find the scale factor of the dilation, we can divide the length of each side of the dilated triangle by the length of the corresponding side of the original triangle.

For example, for the side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

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The side of length 5 inches in the dilated triangle, the scale factor is 5 inches / 15 inches = 1/3.

We can do the same for the other two sides and we will get the same scale factor for all three sides, since the dilation is uniform.

In this case, the scale factor is 1/3 for all three sides, so the scale factor for the dilation is 1/3.

This means that each side of the dilated triangle is 1/3 of the length of the corresponding side of the original triangle.

The value of "i" squared results in:

(-1) = i²

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:

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Answer:

Option D. No solution

Step-by-step explanation:

There is no value of x that makes the equation be true since an absolute value can never be negative.

No solution

Answer:

OptionD)

Step-by-step explanation:

[tex]x + 4 = -6\\x=-6-4\\x=-10\\[/tex]

Since there is no options with -10 only

The correct answer is OptionD)

C) 2x+y=10 is the line has an X intercept of 5 and Y intercept of 10

To find the eqaution of line whose X intercept and Y intercept is given we will use line intercept form of line

The equation of line with A units of X intercept and  B units of

Y intersect is given by:

  [tex]\frac{x}{A} + \frac{y}{B} =1[/tex]   ----(i)

 given that A= 5 (X intercept) and B= 10 (Y intercept)

 so equation (i) reduces to

  [tex]\frac{x}{5}+\frac{y}{10} =1[/tex]

so 2x + y = 1*10

so the equation of the line is 2x+y=10

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Complete question:

Which equation has an X intercept of 5 and a Y intercept of 10?

A) 3x+2y=10

B) 5x+7y=2

C) 2x+y=10

D) 11x+7y=9

Answer:

1/256

Step-by-step explanation:

-4 times -4 times -4 times -4 = 256

A negative exponent means it's a fraction!

So, the answer is 1/256

answer :

1/256

steps:

negative exponent means it's a fraction

4^-4 =

1/4^4 :

4^4 =

4 * 4 * 4 * 4 =

256

again negative exponent means it's a fraction so

1/256

The variability in your data collection is measured by the standard deviation. It reveals the average distance between each score and the mean.

How to interpret a standard deviation?

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

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Therefore , the given expression of this problem of square root

 2√2  not equal to √2.

The value that results from multiplying the square root of an integer by itself is the number.

Example: Since 5* 5 = 25, 5 is the square root of 25. Observe that (5) (5) also equals 25, proving that (5) is a square root of 25.

Here,

In this case, the mathematical symbol for Root 2 is 2.

Root 2 then multiplied by Root 2.

√2 + √2 = 2√2

If we take the estimated value of 2 = 1.4142

Then

=> 2√2 = 1.4142 x 2

=> 2.8284 (approximately)

Please take note that 2 is an irrational number.

Alternatively, root2* root 2

√2 * √2 = 2

Because 2 is just the square root of 2,

Therefore,

what happens when root 2 + root 2 and root2 root 2 are different

2√2 - 2 = 2.8284 - 2 = 0.8284 (approx)

Therefore , the given expression of this problem of square root

 2√2  not equal to √2.'

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Therefore , the solution to the problem is  factors of the given equation comes out be (x-14)(x+3).

By joining two expressions with the equivalent sign, a mathematical statement known as an equation is produced. The equation 3x - 5 = 17 is an illustration. By solving this equation, we can determine that the value of the variable x is 4.

Here,

In the given question the equation is given as  [tex]x^{2}[/tex]-11x-42.

Given  polynomial : [tex]x^{2}[/tex]-11x-42

Thus we factorise the given equation

First:

=> [tex]x^{2}[/tex]-14x+3x-42

Second:

=> x(x-14)+3(x-14)

=> (x-14)(x+3)

thus factors comes out to be

(x-14) and (x+3)

Therefore , the solution to the problem is  factors of the given equation comes out be (x-14)(x+3).

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The equation of line in slope intercept form passing through (-5,-2) and parallel to  y = -2x+1 is  y = -2x -12 .

The Slope intercept form of the line is written as " y = mx + c " , where c is the y intercept and m is the slope of line .

the required line is parallel to the line with equation ⇒ y = -2x+1 ,

on comparing it with slope intercept form of line ,

we get the slope(m) as "-2"  .

the required line is passing through (-5,-2).

substituting the values , we get ;

-2 = (-2)(-5) + c ,

-2 = 10 + c ,

c = -10 -2

c = -12 .

So , the equation is ⇒ y = -2x -12 .

Therefore , the slope intercept form of the required line is y = -2x -12  .

The given question is incomplete , the complete question is

How do you write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation ?  the point is (-5,-2); and is parallel to y = -2x + 1   .

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Answer: Strong Negative Correlation

Step-by-step explanation:

For a w10×15 cantilevered beam of A - 36 steel subjected to loading as in the attached image, slope at B is 0.0042rad and displacement at B is 0.034ft.

For w10×15, moment of inertia I = 68.9in⁴ and for A - 36 steel, Young's modulus E = 29e3 ksi

Slope at B

θB = P₂x³/ (2EI) + P₁l³/ (2EI)

θB = (5 × 6³ + 9 × 12³)/ (2 × 29 × 10³ × 68.9)

θB = 0.0042rad

Displacement at B

yB = P₂x³(3l - x)/ (6EI) + P₁l³(3l - l)/ (6EI)

yB = ( 5 × 6³ × (3 × 12 - 6) + 9 × 12³ × 2 × 12)/ (6 × 29 × 10³ × 68.9)

yB = 0.034ft

--The question is incomplete, answering to the question below--

"The W10×15 cantilevered beam is made of A - 36 steel and is subjected to the loading shown.

1. Determine the displacement at B, if P1 = 9kip and P2 = 5kip

2. Determine the slope at B, if P1 = 9kip and P2 = 5kip"

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Answer:

17

Step-by-step explanation:

(9+25)/2 = 34/2 = 17

when finding a mean, you have to add all the numbers and divide the sum by the number of values given.

Answer:

13

Step-by-step explanation:

Divide 500 by 40 to find the amount of buses you need

500 ÷ 40 = 12.5

BUT, you cannot have .5 of a bus! So you need ONE extra bus to hold the remaining people

you'll need 13 buses

Answer:

13 buses

Step-by-step explanation:

12 buses but 20 people left so they need 12 buses, and the 13th bus will be half filed.

Examples of inverse relationships are :  As the speed of the car increases the time taken to cover certain distance decreases and  More buses on the road less space on the road.

inverse relationships

An inverse relationship, also known as a negative relationship, is a contrary correlation between two variables such that they move in opposite directions. For example, we have two variables X and Y. As X increases, Y decreases and as Y increases, X decreases .The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

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The solution is Option B.

The rate of change of population at time t = T when the population has doubled from its initial time is P' = 2P₀ ln ( 1.09 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The formula for the population at time t is

P ( t ) = P₀ ( 1 + 9/100 )^t

P ( t ) = P₀ ( 1 + 0.09 )^t

P ( t ) = P₀ ( 1.09 )^t

Now , when population is doubled from the initial population ,

P ( t ) = 2P₀

Substituting the values in the equation , we get

2P₀ = P₀ ( 1.09 )^t

Taking logarithm on both sides of the equation , we get

log ( 2 ) = t x  log ( 1.09 )

Divide by log ( 1.09 ) on both sides of the equation , we get

t = log ( 2 ) / log ( 1.09 )

To find the rate of change , take the derivative

P'( t ) = P₀ ( 1.09 )^t ln ( 1.09 )

Now ,  we find P'(log(2)/log(1.09))

So , the equation will be

P′ ( log( 2 ) / log( 1.09 ) ) = 2P₀ln( 1.09 )

Hence , the equation will be A = 2P₀ln( 1.09 )

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The median of 1 to 99 is 50.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.

The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.

Median= 99+1/2 = 100/2 = 50th term, which in this case is 50.

Thus, the median of 1 to 99 is 50.

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More than 50 in mathematical expression is written as >50.

Any two integers can be compared using the greater than and less than symbols. Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than sign (>) is used when the first number exceeds the second number. The less than sign (<) is used when the first number is less than the second number.

The quantity on the left of the > sign is the greater quantity. It could be a variable or expression [like 3x - 2 > 50].

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Whole numbers are closed under addition and multiplication. If we add and  multiply any two whole numbers, the result will be a whole number.

What are Whole numbers ?
The numbers that include natural numbers and zero. Not a fraction or decimal. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Whereas Integer: A counting number, zero, or the negative.

If we add any two whole numbers, the result will be a whole number. For example, 2 + 4 = 6 and 6 is a whole number.

Therefore, whole numbers are closed under addition.

If we multiply any two whole numbers, the result will be a whole number. For example, 2 × 4 = 8 and 8 is a whole number.

Therefore, whole numbers are closed under multiplication.

Also , Whole numbers are not closed under Subtraction and division.

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.

Here,

A quadratic function is one where an equation has two roots.

A quadratic function's two roots are equal if D=0.

D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.

As a result, if an equation has two roots, a quadratic function is what it is.

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The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in an unequal way.  By comparing the sizes of two numbers on the number line, it is most frequently utilized. Different types of inequalities are represented by a variety of different notations, including:

The symbol a b indicates that an is less than b.

A bigger value for a than a lesser value for b is indicated by the notation a > b.

A is not equal to b in either situation. These relationships are referred to as stringent inequalities, which means that an is strictly less than or strictly bigger than b. Equivalence is not included.

There are two kinds of inequality relations that are not strict, in contrast to strict inequalities:

When something is written with an an or b, it signifies that.

A is smaller than or equal to b when a notation like a ≤ b is used (or, equivalently, at most b, or not greater than b).

A greater or equal value for a indicates that b is greater than it (or, equivalently, at least b, or not less than b).

The symbol for "greater than" that is divided in half by a slash, "not," can also be used to express the connection not greater than. The same applies to and not less than and a b.

Hence, The notation a ≤ b denotes a value that is less than or equal to b (or, equivalently, at most b, or not larger than b), while the notation a ≥ b denotes a value that is greater than or equal to b (or, equivalently, at least b, or not less than b).

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It signifies that the supplied variable or number must have a value that is larger than or equal to the specified limit. It is the opposite of less than or equal to.

The phrase "more than or equal to" denotes that the variable is either greater than or equal to a specific value. When a quantity is bigger than another, the phrase "more than" is used to indicate this. Two quantities are said to be equal when the phrase "is equal to" is used. It is possible for the quantity or amount value limit to be equal to or larger than the stated limit when these phrases are combined to form the new term Greater Than Or Equal To.

The phrase "less than or equal to" denotes that a variable is either less than or equal to another quantity, number, or variable. Other ways to say "less than or equal to" include at most, no more than, a maximum of, and not surpassing.

Inequalities like less than or equal to and greater than or equal to are represented in a different way on a number line. To denote these, we use the closed circle to mark the limit value and point the arrow towards the given condition of inequality.

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Answer:

a_n = -15 (n - 4) (for all terms given)

Step-by-step explanation:

a_n = -15 (n - 4) (for all terms given)

45, 30, 15, 0, -15, -30, -45, -60, -75, -90, -105, -120, -135, -150, -165, ...

To search for the nth sequence, replace n with the desired term.

The height of pyramid when given the volume and area is estimated as; H = 3 * V / a²

How is the height of the a square pyramid determined?

H = 3 * V / A_b

In which,

H - height of pyramid;

V- volume of pyramid

A_b - base area of pyramid; A_b = a²,

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The function representing the area to paint as a function of time is A(t) = 52 - 8t, where A(t) represents the area left to paint after t hours.

The area to paint, A(t), can be represented as a linear function based on the given information. Initially, Hiro had the entire room to paint, which can be represented as A(0) = A₀, where A₀ is the total area of the room.

Given that Hiro painted at a rate of 8 square meters per hour, after t hours, he would have painted 8t square meters.

Therefore, the remaining area to paint after t hours can be expressed as A(t) = A₀ - 8t.

We are told that after 3 hours, Hiro had 28 square meters left to paint. Substituting t = 3 and A(t) = 28 into the equation, we can solve for A₀:

28 = A₀ - 8 x 3

28 = A₀ - 24

A₀ = 52

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The complete question:

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?

The operation 1+15 would result in integer overflow, because the result of this operation (16) cannot be represented with 4 bits.

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Systems of linear equations in two variables can be solved in one of four ways: by graphing; by the substitution approach; or by the elimination method and by matrix approach.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." Because a straight line emerges when we attempt to display the graph of the provided linear function, a linear equation is known as linear.

Given,

The four methods of solving linear equations are:

The Substitution Method

The Graphing Method.

The Addition Method, also known as the Linear Combination Method, and the Elimination Method.

The Matrix Approach

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The similarity ratio of first polygon to second polygon is 4 : 1.

If two figures have the same shape, they are said to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio. The ratio of any pair of corresponding sides is the ratio of any two similar figures. Simply put, when two figures are found to be similar, all of their associated side pairs have the same ratio.

Given,

Two polygons given,

Ratio of PQRS polygon = 20

Ratio of EFGH polygon = 5

Similarity ratio,

20 : 5

Simplifying,

4 : 1

The similarity ratio of first polygon to second polygon is 4 : 1.

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Answer:

⭐ AAS = Angle-Angle-Side

⭐ I don't know what AES is.

Step-by-step explanation:

AAS is a triangle congruence statement you use to say that 2 triangles are congruent ≅ (the same).

Here's how to determine if 2 triangles are congruent by AAS:

Congruent side lengths and congruent angles are often denoted by tick marks.

⭐ Example:

The dimensions of the rectangle is length = 5ft and width = 3ft

Define System of equation

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.

Let,

x = length of rectangle

y = width of rectangle

Next, set up system of equation

We have given, the length of a rectangle is 5 ft more than twice its width.

x = 2y + 5    --------(a)

Next,  The area of the rectangle is 33 ft²

xy = 33      ----------(b)

x = 33/y

substitute the value of x in eq(a)

x = 2y + 5

33/y = 2y + 5

33 = 2y² + 5y

2y² + 5y - 33 = 0

Factor it,

2y² + 11y - 6y - 33 = 0

y( 2y + 11) - 3( 2y + 11) = 0

(y - 3) (2y + 11) = 0

Split the values,

y - 3 = 0               and         2y + 11 = 0

y = 3                 and             y = -11/2 (ignore this as width cannot be -ve)

Substitute y = 3 in eq(b)

x * 3 = 33

x = 11

So, we get

length = 11 ft and width = 3 ft

Hence, the dimensions of the rectangle is length = 5ft and width = 3ft

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The range is an absolute value functions is

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function.

Remember that a number's distance from 0 on the number line represents its absolute value.

A number can never have a negative absolute value. hence the negative values will never be in the range

This makes the range to start possibly from zero, from the graph explained 0 is among the values that are in the range

Considering that absolute values are non zero and option B is the only option that does not have a negative value. This is the best option

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Answer:

The range is an absolute value functions is

B. 0 ≤ y < ∞

Step-by-step explanation: