How will the volume of the pyramid change if each side is multiplied by a factor of one-half? a rectangular pyramid. the volume will be 2 times the original volume. the volume will be 8 times the original volume. the volume will be one-fourth times the volume. the volume will be one-eighth times the volume.

Answer: The lowest common multiple of 12, 18, and 56 would be 504. Why? Well, see below for an explanation!

Step-by-step explanation: What is the lcm? Well, the lcm of two or more numbers is the lowest possible number that each number has in common as a multiple. Because we are dealing with large numbers, we can tell that the lcm will be a multiple of these numbers times at least 5. I multiplied all the numbers by 10, and it was too large and did not work. However, I backed up and tried 9.

56 x 9 = 504.

Why is this acceptable? Well, this is acceptable because I found that 504 can be divided by 12 and 18 both to get a whole number.

504 divided by 18 equals 28.

504 divided by 12 equals 42.

Using this principle, we will find that 504 is the lowest number that 12, 18, and 56 have in common.

Your final answer: 504 is the lowest common denominator. If you need extra help, let me know and I will gladly assist you.

To obtain the least common multiple (lcm) we must do it by simultaneous decomposition.

This method consist of extracting the common and uncommon prime factors, then

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left.\begin{matrix} \blue{12 \ \ \ 18 \ \ \ 56}\\ \ 6 \ \ \ \ 9 \ \ \ \ 28\\ \ 3 \ \ \ \ 9 \ \ \ \ 14\\ \ 3 \ \ \ \ 9 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 3 \ \ \ \ \ 7 \\ \ 1 \ \ \ \ 1 \ \ \ \ \ 7\\ \ 1 \ \ \ \ 1 \ \ \ \ \ 1 \end{matrix}\right|\begin{matrix} 2\\ 2\\ 2\\ 3\\ 3\\ 7\\ \: \end{matrix} \end{gathered}$}[/tex]

                        [tex]\sf{L.c.m.(12,18,56)=2\times2\times2\times3\times3\times7}[/tex]

                                        [tex]\sf{L.c.m.(12,18,56)=2^{3}\times3^{2}\times7 }[/tex]

                                            [tex]\boxed{\boxed{\sf{L.c.m.(12,18,56)=504}}}[/tex]

The lowest common multiple of 12, 18, and 56 is 504.

The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

An equation is an expression that shows the relationship between two or more variables and numbers.

For the exponential function, when f(2) = 12:

12 = ab²       (1)

Also, at f(4) = 48:

48 = ab⁴   (2)

Hence:

a = 3, b = 2

f(x) = 3(2)ˣ

For the linear function using the points (2, 12) and (4, 48):

y - 12 = [(48 - 12) / (4 - 2)](x - 2)

y = 18x - 24

The linear and exponential equation that matches f(2) = 12 and f(4) = 48 are y = 18x - 24 and f(x) = 3(2)ˣ respectively

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Answer:

Step-by-step explanation:

hello :

The graph of y =-3x+4 is the line

The 95% confidence interval of the statistics is (7.795, 8.243).

Based on the information given, the 95% confidence interval will be:

= 8.019 + (1.962 × 3.183/✓1114)

= 8.243 and

= 8.019 - (1.962 × 3.183/✓1114)

= 7.795

In conclusion, the 95% confidence interval of the statistics is (7.795, 8.243).

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This is a budgeting exercise. Based on the estimated cost of college which was set at $58,000, the following steps indicate how I intend to pay for college:

                                        $58,000

Budgeting is simply the process of outlining the total expense requirements of an individual person or a corporate entity and how those expenses will be satisfied and efficiently allocated.

From the above, the total sum of $58,000 will be satisfied from three sources:

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The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

From the information given, we have the following proofs;

Length, l = 2x + 30 - 49

Length = 2x - 19

The formula for perimeter of a rectangle is given as;

Perimeter = 2( length + width)

Substitute the expressions into the formula

Perimeter =  2 ( x+ 15 + 2x - 19 )

Perimeter = 2 (3x - 4)

Perimeter = 6x - 8

We have that the area is  162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163

Area = 27(6x-8) + 162

Expand the bracket

Area= 162x - 216 + 162

Area = 162x - 54

But we know that

Area = length × width

Substitute the expressions

Area = (x+15)(2x-19)

Area =  2x² - 19x +30x - 285

Area = 2x² + 11x - 285

Equate the two formulas for area

162x - 54 = 2x² +11x - 285

Collect like terms

2x² + 11x - 285 - 162x + 54 = 0

2x²  - 151x - 231 = 0

Solve the quadratic equation

(2x + 3)(x-77) = 0

Let's solve for x

x - 77 = 0

x = 77

The expression for the width;

Width = x+15

Width = 77 + 15

Width = 92 feet

The expression for the length

Length = 2(x+15) - 49

Length = 2 ( 77 + 15) - 49

Length = 154 + 30 - 49

Length = 184 - 49

Length = 135 feet

Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.

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Answer:

14 units

Step-by-step explanation:

Oops, I was solving for the area in the picture.  You can still use  the picture to find the perimeter.  When I change the shape into a rectangle, you can see that the top and bottom lengths are 3 and the side lengths are 4.  3+3+4+4=14

Answer:

Step-by-step explanation:

The displacement is 90.7 meter from initial point.

According to the statement

Aster first walks 70m in the direction of 37 degree north of east

Aster walks 82m 20 degree south of east

Aster finally walks 28m in the direction of 30 degree west of north

We use

β= 37 degree +(30 degree −20 degree) = 47 degree

We can use cosine law to solve for R.

R = ((A)^2 + (B)^2 + 2ABcosβ)^1/2

R = ((70)^2 + (28)^2 + 2*70*28cos47)^1/2

R = (4900 + 784 + 3920*0.682)^1/2

R = (4900 + 784 + 2673.5)^1/2

R = (8357.5)^1/2

R = 90.7 m

So, The displacement is 90.7 meter from initial point.

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In a(n) reversal design, two or more treatments are alternated relatively quickly on a regular schedule.

Reversal designs are used to observe the impact of a remedy on the conduct of a single player. The participant is observed time and again previous to remedy to establish a baseline stage of behavior.

One ought to not use a reversal layout with behaviors that aren't reversible. For instance, if you train a person to fish, that man or woman is not probable to forget about how to fish, making a reversal design a negative preference for evaluating your fishing intervention.

Reversal layout: reversing among remedies (e.g., baseline, treatment, NCR, treatment, NCR, remedy, and many others.) Withdrawal design: reversing among treatment and no treatment (e.g., baseline, remedy, baseline, treatment, etc.)

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Answer:

The answers are in the image

Step-by-step explanation:

The solution is in the attached image

Answer:

factoring

Step-by-step explanation:

The cost per person if number of students is 100 given the inverse variation is $46.75

C = k / n

where,

k = constant of proportionality

If n = 55 and C = $85

C = k / n

85 = k / 55

85 × 55 = k

4,675 = k

Find C if n = 100

C = k / n

= 4,675 / 100

C = $46.75

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Answer:

C = $46.75

Step-by-step explanation:

85 × 55 = k

4,675 = k

4675/100=46.75

therefore the answer is 46.75

Answer:

The exponent of the first term must have twice the value of the exponent of the second term.

Step-by-step explanation:

Answer:

197.82 m^2

Step-by-step explanation:

The area of a circle is

a = πr^2  The radius is half of the diameter.  They give us the diameter so we need to talk half of that number to use for the diameter.  The diameter is the length from the center of the circle to the edge of the circle.

We will find the area of the big circle and  subtract out the area of the little circle to bind the blue area.

Outer circle

a = πr^2

a = 3.14(12)^2

a = 3.14(144)

a = 452.16

Inner Circle:

a = πr^2

a = 3.14(9)^2

a = 3.14(81)

a =254.34

Lastly, subtract 254.34 from 452.16 to get  197.82

Answer: 15 square units

Step-by-step explanation:

[tex]A=(5)(3)=15[/tex]

Around 298 people can sing together with the same relative intensity to achieve a loudness of 80 decibels.

Given Information

Loudness of sound is given as, l = 10 log₁₀r

Here, r is the relative intensity.

Relative intensity of a single person when singing = 10

Loudness to be achieved, L = 10 decibels

Calculating the Number of People

Let the number of people with relative intensity 10 singing together be n decibels, then to produce a loudness of 80 decibels, we have,

80 = 10 log₁₀(r × n)

80 = 10 log₁₀(10 × n)  [∵ r = 10]

log₁₀(10 × n) = 8

10n ≈ 2980

n = 298

Therefore, 298 people, each with a relative intensity of 10 decibels can sing together to achieve a loudness of 80 decibels.

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Answer:

7.55

Step-by-step explanation:

A midpoint can be found by doing 7.2 + 7.9 then dividing by the number of points (in this case 2).

The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7

7/11 = x/9

7 × 9 = 11 × x

63 = 11x

x = 63/11

x = 5.72727272727272

Approximately,

x = 5.7

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Answer:

[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Step-by-step explanation:

Use the long division method to divide polynomials:

[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]

Therefore:

[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]

Answer:

  tan(x) = (√6)/2

Step-by-step explanation:

The tangent identity is ...

  tan = sin/cos

Substituting the given values of sine and cosine, we have ...

  [tex]\tan{x}=\dfrac{\sin{x}}{\cos{x}}=\dfrac{\dfrac{42}{55}}{\dfrac{14\sqrt{6}}{55}}[/tex]

At this point, it becomes a problem in simplifying a compound fraction. This can be done by dividing the fractions in the usual way, and cancelling common factors from numerator and denominator.

We note the denominators (55) are the same, and that 42=3·14, so we can simplify this to ...

  [tex]\tan{x}=\dfrac{3}{\sqrt{6}}=\dfrac{3\cdot\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\dfrac{3\sqrt{6}}{6}\\\\\boxed{\tan{x}=\dfrac{\sqrt{6}}{2}}[/tex]

The step of multiplying by (√6)/(√6) is for the purpose of "rationalizing the denominator," making the denominator a rational number: (√6)² = 6.

__

Additional comment

If sin(x) = 42/55, then cos(x) = (√1261)/55. There is no angle x that will have these values of its trig functions. (Another example of poor curriculum editing.)

The z-score of Kimmie is -0.625

The formula for calculating the z-score is expressed as;

z = x-η/s

where

η is the mean

s is the standard deviation

x is the Kimmie score

Substitute the given parameter

z = 85.9-88.4/4.0

z = -2.5/4.0

z = -0.625

Hence the z-score of Kimmie is -0.625

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The only set that only has rational numbers is the first one:

{1/3, -3.45, √9}

A rational number is a number that can be written as the quotient of two integers.

If we look at the first set, the elements are:

In the other sets we can see elements like:

√37, √44, or √2 which are all irrational numbers, then the only correct option is the first one.

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The given statement is True for the scoring rule in bowling.

Scoring Rule in Bowling

The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.

Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.

Rule for Spare

A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.

Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.

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Two possibilities  --- see below

Step-by-step explanation:

So it could be GREATER than 46

  .85 x = 46    x = 54.11 cm^3

Or it could be  smaller than 46

  46= (1.15)  x      x = 40 cm^3

−3/7×14/15×7/12×(−30/35)

=(−3/7×14/15)×(7/12×−30/35)

On further calculation, we get

=−2/5×−1/2

We get,

=1/5.

Property 1:

If a/b is a rational number and m is a non-zero integer then a/b =(a*m)/(b*m). In other words, we can say that the rational number remains unaltered if we multiply both the numerator and denominator with the same integer. Ex: 2/3 = 2*2/3*2 = 4/6, 2*3/3*3 = 6/9, 2*4/3*4 = 8/12.

Math Properties

Commutative Property.

Associative Property.

Distributive Property.

Identity Property.

Inverse Property.

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Answer:

d. 15√5

Step-by-step explanation:

Perimeter = 3√5 × 5 sides

= 15√5

Answer: B - 15√5

Step-by-step explanation:

As said in the question, the perimeter is the total length of all sides of a figure. The question also says that all sides are the same length, and the length of one side is 3√5 yards.

In that case, all 5 sides have length 3√5 yards, so the perimeter would be this value added 5 times, or this value multiplied by 5:

[tex]P=3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}=5*3\sqrt{5}[/tex]

[tex]P=15\sqrt{5}[/tex]

Hence, the perimeter of the chicken coop is 15√5 yards.

Answer:Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.

If either a or b equals zero, then the sums would be the same.

Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Step-by-step explanation:

The statement √a + √b = √(a + b) is not possible since a ≠ b

The operation involving surd is most likely an algebraic expression where in the case of surd the value in the square root are like the alphabets in algebraic expression.

Some surd operations are given as shown below:

Now, let us consider the question given:

Since a and b are not equal, it means

√a + √b ≠ √(a + b)

Thus, we can conclude that the statement √a + √b = √(a + b) is not possible

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The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

According to the statement

we have to explain the linear regression method and explain the way by which this method is used to predict the values.

So, For this purpose we know that the

Linear regression is the most basic and commonly used predictive analysis. Regression estimates are used to describe data and to explain the relationship.

And

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

from these definitions it is clear that the there is a presence of two types of variables which are dependent and independent variables.

So, The linear regression method seeks to predict values of a(n) dependent variable based on values of a(n)  independent variable.

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Answer:

Step-by-step explanation:

The ys have to have the same value. That allows you to equate the right side of each y to each other.

-x^2 + 4 = 2x + 1                             Subtract the right side from the left side.

-x^2 + 4 - 2x - 1 = 2x-2x +1 - 1        Combine

-x^2 - 2x + 3 = 0                            Multiply both sides by - 1

-1(-x^2 -  2x + 3) = 0*-1                    Remove the brackets

x^2 + 2x - 3                                   Factor

(x - 1)(x + 3 )

x - 1 = 0

x =   1

x + 3 = 0

x = - 3

So the line goes through x = 1 or x = - 3

x = 1

y = 2x + 1

y = 2(1) + 1

y = 3

x = - 3

y = 2(-3) + 1

y = - 6 + 1

y = - 5

Does the graph confirm this? See below.

red: y = -x^2 + 4

green: y = 2x + 1

Yes the graph is in agreement.

Answer:

75 degrees.

Step-by-step explanation:

Central angle = subtending arc.