Find the perimeter of a rectangle whose width is 16 and whose length is 12 square feet

Answer:

See below

Step-by-step explanation:

5x + y = 9      re-arrange  to    y = 9-5x  

   use this value of 'y' in the second equation:

    10x - 7(9-5x) = - 18

       solve for x = 1

  sub in this value of 'x' into one of the equations to compute 'y'

5 (1) + y = 9

  y = 4

Answer:

What is the best choice for the equation of the line of best fit shown?

b) y = -1.5x + 23

What would the value of y be for a point at x = 8?

b) 11

Did this on EDGE!

The best choice for the equation of the line shown in the graph is y = -1.5x + 23. the correct option is B.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

In the given graph the data is varying along the line y = -1.5x + 23. Where y is the dependent variable and x is the independent variable.

Therefore, the correct option is B.

To know more about equations follow

https://brainly.com/question/2972832

#SPJ5

Answer:

neither

Step-by-step explanation:

Answer:

False.

Inflation occurs in an economy when there is an increase in the overall price level of goods and services over time. It is usually caused by factors such as an increase in the money supply, higher demand for goods and services, or a decrease in the supply of goods and services. Therefore, a reduction in the total amount of money in an economy would generally lead to deflation, which is the opposite of inflation.

Answer:

1: C =69.3 m2

2: F = ll units

3. C:  3 in.

4. G =65 units

Step-by-step explanation:

1: C =69.3 m2

We see from the figure that height of the parallelogram ABCD is not known and the base is 10 m

Taking the right angled triangle the height is given by

Sine theta= height/hypotenuse

height = hypotenuse* sine theta

         = 8* sine 60

         = 8* 0.866= 6.928

Area of parallelogram= base * height

                   = 10 * 6.928

                   = 69.28

                  =69.3 m²

2: F = ll units

We see from the figure that height of the parallelogram DEFG is not known and the base is 13 cm

Area of parallelogram= base * height

                  143 = 13 * height

           Height = 143/13= 11 units

3. C:  3 in.

The area of the triangle = 1/2 * base * height

Let the height be x then the base is 3x

54= 1/2*x*3x

54= 3x²/2

27= 3x²

x²=27/3

x²= 9

x= 3

The height is 3 inches

4. G =65 units

Area of the quadrilateral = 1/2 *PR*QO + 1/2 *PR*OS

                                      = 1/2*13*4+ 1/2*13*6

                                        =26+ 39

                                        = 65 units

These measurements are given in the diagram .

1) Number sense, arithmetic operations, algebra, geometry, data analysis, and probability are some of the topics that are commonly covered in math classes.

The need of developing problem-solving and procedural fluency skills is underlined. To ensure they have a solid basis for future learning, students may also receive training on arithmetic concepts they missed in earlier grades.

2) The use of real-world issues, direct education, cooperative learning, and the use of technology to aid learning are some particular methods of mathematical instruction that are encouraged.

Additionally, emphasis is placed on encouraging a growth mentality and a positive attitude toward mathematics.

3) Direct instruction, visual aids like graphs and diagrams, manipulatives and hands-on activities, scaffolding, and systematic review and practice are some specific techniques used to teach fundamental mathematical instruction.

In order to promote critical thinking and the growth of students' problem-solving abilities, teachers may also employ questioning strategies.

Learn more about mathematics at:

brainly.com/question/929808

#SPJ1

Answer:

(i) The surface(sheet) of a conical tent is circular so we must use the formula for the area of a circle to find out;

Given the diameter 14, we must find the radius.

To find the radius we must do 1/2 of the diameter to get the radius.

14 x 1/2 = 7, is the radius

Formula for area of a circle;

a = πr^2

where pi is 3.14 or 22/7, r is the radius which is being squared

Plug in the actual values:

a = πr^2

a = 3.14 x 7^2

a = 3.14 x 49

a = 153.86 square meters, is the area of the conical tent's sheet.

(ii) Since there are 153.86 meters in one sheet, we should multiply that by         $12(because $12 per meter) to get the total cost.

So,

153.86 meters x $12 = $1,846.32, it would cost 1,846.32 dollars.

The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

To know more about equivalent visit :

https://brainly.com/question/25197597

#SPJ11

The tank with the smallest surface area will take the least amount of time to build. The tank's radius is 4.72 feet and its height is 22.72 feet.

The formula for the surface area of a cylinder is 2πrh + 2πr2 where r is the radius and h is the height. Since the tank has a free space of 500 cubic feet, the formula for its volume is V=πr2h = 500. Using trial and error to calculate the possible dimensions, we get the radius of 4.72 feet and the height of 22.72 feet, which result in the least surface area, 419.67 square feet.

Willy will take 15 minutes per square foot of material required to build the tank, so he will take a total of 6,295.05 minutes or approximately 105 hours to build the tank. Therefore, the cylindrical water tank with the least surface area will take the least amount of time to build and its radius is 4.72 feet and height is 22.72 feet.

Learn more about cylinder here:

https://brainly.com/question/28575608

#SPJ11

The potential function ϕ for the given conservative vector field F and its line integral along the curve C can be determined as ϕ(x, y, z) = (1/3) x^3 + xy + (1/3) y^3 + (z - 1) e^z, and the line integral ∫C F · dr evaluates to 2π(1/2 eπ - 1/2 e^(-π) + 1/6).

Given the conservative vector field F(x, y, z) = (x^2 + y)i + (y^2 + x)j + (ze^z)k. To determine a potential function ϕ such that F = ∇ϕ, the potential function ϕ can be found as follows:

ϕ(x, y, z) = ∫ Fx(x, y, z) dx + G(y, z) ...............(1)

ϕ(x, y, z) = ∫ Fy(x, y, z) dy + H(x, z) ...............(2)

ϕ(x, y, z) = ∫ Fz(x, y, z) dz + K(x, y) ...............(3)

Here, G(y, z), H(x, z), and K(x, y) are arbitrary functions of the given variables, which are constants of integration. The partial derivatives of ϕ(x, y, z) are:

∂ϕ/∂x = Fx

∂ϕ/∂y = Fy

∂ϕ/∂z = Fz

Comparing the partial derivatives of ϕ(x, y, z) with the given components of the vector field F(x, y, z), we can write:

ϕ(x, y, z) = ∫ Fx(x, y, z) dx + G(y, z) = ∫ (x^2 + y) dx + G(y, z) = (1/3) x^3 + xy + G(y, z) ...............(4)

ϕ(x, y, z) = ∫ Fy(x, y, z) dy + H(x, z) = ∫ (y^2 + x) dy + H(x, z) = xy + (1/3) y^3 + H(x, z) ...............(5)

ϕ(x, y, z) = ∫ Fz(x, y, z) dz + K(x, y) = ∫ z*e^z dz + K(x, y) = (z - 1) e^z + K(x, y) ...............(6)

Comparing Equations (4) and (5), we have:

G(y, z) = (1/3) x^3

H(x, z) = (1/3) y^3

K(x, y) = constant

Evaluating the line integral ∫C F · dr along the curve C with parameterization r(t) = (cos t)i + (sin t)j + (t/2π)k, 0 ≤ t ≤ 2π, we substitute the given values in the equation and apply the derived value of the potential function:

ϕ(x, y, z) = (1/3) x^3 + xy + (1/3) y^3 + (z - 1) e^z + K(x, y)

Along the curve C with parameterization r(t) = (cos t)i + (sin t)j + (t/2π)k, we get:

F(r(t)) = F(x(t), y(t), z(t)) = [(cos^2(t) + sin(t))i + (sin^2(t) + cos(t))j + [(t/2π) e^(t/2π)]k

∴ F(r(t)) · r′(t) = [(cos^2(t) + sin(t))(-sin t)i + (sin^2(t) + cos(t))cos

Learn more about conservative vector field: https://brainly.com/question/33068022

#SPJ11

Given:

f(x≤2)=4x+2

f(x>2)=3x+4

Function is continuous:

lim(x→2) =10 from either piece.

Each piecewise function is differentiable alone, but we see the f(x) is not differentiable because the derivatives are not the same:

(Depending on your calculus experience, you can use the definition of a derivative or the power rule to find the derivative)

For x≤2

f’=lim(h→0) {[4(x+h)+2]-[4x+2]}/h def. of derivative

f’=lim(h→0) (4x+4h+2-4x-2)/h   expand and cancel terms

f’=lim(h→0) (4h/h) simplify

f’=4

or:

f’=4  power rule

For x>2

f’= lim(h→0){[3(x+h)+4]-[3x+4]}/h def. of derivative

f’=lim(h→0)(3x+3h+4-3x-4)/h expand and cancel terms

f’=lim(h→0)3h/h simplify

f’=3

or

f’=3 via power rule

HOPE THIS IS HELP FUL PLEASE FOLLOW ME

Answer:

Step-by-step explanation:

Answer to #5: is T, F, F, F, T I'm pretty sure that's correct.

Answer:

Point T is on a line segment SU. Given SU=4x+1, TU=3x, and ST=3x-1, determine the numerical length of SU

Step-by-step explanation:

By the segment addition rule, length of ST + length TU equals length of SU so 3x -1 + 3x = 4x + 1 6x - 1 = 4x + 1 2x = 2 x = 1 substituting value of x back into formula for length of SU: 4 (1) + 1 = 5

Answer:

16a^4

Step-by-step explanation:

Answer:

16a^4

Step-by-step explanation:

The expression (2a)^4 can be written in exponential form as 2^4 * a^4. Using the laws of exponents, we can simplify this to:

2^4 = 2 * 2 * 2 * 2 = 16

a^4 = a * a * a * a

So, (2a)^4 = 16a^4

The conclusion regarding the mayor's claim is:

There is not sufficient evidence at the 0.01 level of significance to say that the percentage of residents who support the construction is not 62%.

In other words, based on the hypothesis test conducted by the community group, they did not find enough evidence to reject the null hypothesis, which suggests that the true percentage of residents who favor the construction could still be 62% as claimed by the mayor.

Learn more about null hypothesis here:

https://brainly.com/question/30821298

#SPJ11

Answer:

slope = -2

Step-by-step explanation:

rise/run: y2-y1/x2-x1 .

=12-18/4-1 = -6/3 = -2

To find an equation of a plane through a given point and perpendicular to a given line, you can follow these steps:

1. Find the direction vector of the given line. This can be done by subtracting the coordinates of any two points on the line. Let's denote this vector as "d".

2. Find the normal vector of the plane. Since the plane is perpendicular to the line, its normal vector will be the same as the direction vector of the line. So, the normal vector of the plane is "d".

3. Use the coordinates of the given point on the plane to find the equation of the plane. Let's denote the coordinates of the point as (x₀, y₀, z₀).

The equation of the plane can be written as:

Ax + By + Cz = D,

where A, B, C are the components of the normal vector "d", and x, y, z are the variables representing any point on the plane.

To find the values of A, B, C, and D, substitute the coordinates of the given point into the equation:

A(x₀) + B(y₀) + C(z₀) = D.

Therefore, the equation of the plane through the given point and perpendicular to the line is:

d₁(x - x₀) + d₂(y - y₀) + d₃(z - z₀) = 0,

where (d₁, d₂, d₃) are the components of the direction vector "d" of the line, and (x₀, y₀, z₀) are the coordinates of the given point.

to know more about perpendicular here:

brainly.com/question/12746252

#SPJ11

Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

Answer:

C

Step-by-step explanation:

The add to 180 because that's a straight line    

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

Know Further about "statistical tests" then: https//brainly.com/question/14128303

#SPJ4

We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

Learn more about Kruskal Wallis test here:

https://brainly.com/question/28329564

#SPJ4

Answer:

A. You need to draw a straight line that increases from left to right. Try and get the same amount of plots on the top and bottom of the line and go through one or two of the plots. Don't connect the dots, though.

B. This scatter plot demonstrates a positive association between a person's height and weight because the trendline increases from left to right. According to this data, as weight increases, so does height. The more someone weighs, the more likely they are to be tall.

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

Learn more about Fourier transform

brainly.com/question/29063535

#SPJ11

Ar of triangle = 3b , Ar of triangle = 6a a = 12/root3

An orthogonal basis of the plane containing vectors and in is: { , }.

To find an orthogonal basis of the plane containing vectors and in , we can use the Gram-Schmidt process.

First, we normalize the first vector :

Next, we find the projection of the second vector onto the first vector :

Then, we subtract the projection from the second vector to obtain a new vector that is orthogonal to the first vector :

Finally, we normalize the new vector :

Therefore, an orthogonal basis of the plane containing vectors and in is { , }.

To learn more about orthogonal basis, click here: brainly.com/question/29578595

#SPJ11

Answer:

B. 180 degrees

Step-by-step explanation:

They are exactly across from one another. Here, this will make more sense.

               0 (starting point)

               |

 270--            -- 90

               |

             180 (where you ended up)

Now till the screen towards the right. The zero and the 180 should be pointing in the same direction as the squares.

Degrees was ABCD rotated or transformed  to form A'B'C'D' is  180 degrees about the origin .

In geometry, a transformation  is an operation that moves, flips, or changes a shape to create a new shape. A rotation is an example of a transformation where a figure is rotated about a specific point (called the center of rotation), a certain number of degrees.

According to the question

ABCD is rotated counterclockwise about the origin.  

Degrees was ABCD transformed to form A'B'C'D' is

180 degrees about the origin

As when we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.

So, as per figure ABCD which is in first quadrant were x and y both are positive and  figure A'B'C'D' third quadrant were x and y both are negative.

Hence, Degrees was ABCD rotated or transformed  to form A'B'C'D' is  180 degrees about the origin .

To know more about rotation in graph here:

https://brainly.com/question/12091224

#SPJ2

Answer:

1312 miles

Step-by-step explanation:

To solve this, we simply need to subtract the distance she traveled in her trips to Chicago from the distance she traveled in her trips to Louisville.

She made 4 round trips to​ Chicago, Illinois​. Each of the trips is a distance of 218 miles. This means that the total distance she traveled is:

4 * 218 = 872 miles

She made 6 round trips to​ Louisville, Kentucky​/ Each of the trips is a distance of 364 miles. This means that the total distance she traveled is:

6 * 364 = 2184 miles

Therefore, the difference between the distances she traveled is:

2184 - 872 = 1312 miles

She traveled 1312 miles more in her trips to Louisville than in her trips to Chicago.

Answer:

a = 7.5

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{opposite}{hypotenuse}\) = \(\frac{a}{15}\) = \(\frac{1}{2}\) ( cross- multiply )

2a = 15 ( divide both sides by 2 )

a = 7.5

Answer:

Step-by-step explanation:

(a) To find the height that represents the 90th percentile, we would need to use a standard normal distribution table and a Z-score. We need to first find the Z-score corresponding to the 90th percentile by solving for Z using the formula:

Z = (x - μ) / σ

Where x is the height at the 90th percentile, μ is the mean height (64.7 inches), and σ is the standard deviation (2.9 inches).

Z = (x - 64.7) / 2.9

Since the 90th percentile corresponds to a Z-score of 1.28, we can use the above formula to find x:

x = μ + Zσ

x = 64.7 + (1.28)(2.9)

x = 68.9 inches

So, the height that represents the 90th percentile is 68.9 inches.

(b) To find the first quartile (25th percentile), we would use a Z-score of -0.67.

x = μ + Zσ

x = 64.7 + (-0.67)(2.9)

x = 62.3 inches

So, the height that represents the first quartile is 62.3 inches.