The area of a surface can be measured in units of square meters (m^2). Which of the following combinations of units could not be used to measure area?

a)m.cm

b)ft^3/m^2

c)in^2

d)m.ft

e)ft^3/m

Answer:

Step-by-step explanation:

Assume a solution

Assume that 60 is the length. The width is then 1/4 less, or 60 -60/4 = 45.

The diagonal of this rectangle is found using the Pythagorean theorem:

  d = √(60² +45²) = √5625 = 75

Make the adjustment

This is a factor of 75/40 larger than the actual diagonal, so the actual dimensions must be 40/75 = 8/15 times those we assumed.

  length = (8/15)×60 = 32

  width = (8/15)×45 = 24

The length and width of the rectangle are 32 and 24, respectively.

_____

Comment on this solution method

This method is suitable for problems where variables are linearly related. If we were concerned with the area, for example, instead of the diagonal, we would have to adjust the linear dimensions by the square root of the ratio of desired area to "false" area.

Final answer:

This detailed answer explains how to use the Babylonian method of false position to find the length and width of a rectangle.

Explanation:

The Babylonian method of false position involves making an initial assumption about the solution and then iteratively honing in on the correct answer.

Step-by-step:

Let's start with an assumption: Length = 60. Then calculate the width based on the given conditions.

Adjust your assumption based on the calculated width until you reach the correct solution.

By using this method, you can find the length and width of the rectangle described in the problem.

Answer:

  x ≈ 181/128 ≈ 1.41406

Step-by-step explanation:

The attached table shows the iterations. At each step, the interval containing the root is bisected and the function value at the midpoint of the interval is found. The sign of it relative to the signs of the function values at the ends of the interval tell which half interval contains the root. The process is repeated until the interval width is less than 10^-2.

Interval: [0, 2], signs [+, -], midpoint: 1; sign at midpoint: +

             [1, 2]                                      3/2                           -

             [1, 3/2]                                   5/4                           +

...

the rest is in the attachment. The listed table values are the successive interval midpoints.

The final midpoint is 181/128 ≈ 1.41406. This is within 0.0002 of the actual root.

_____

The actual solution in the interval [0, 2] is √2 ≈ 1.41421.

To find a solution utilizing the Bisection Method, one needs to establish the function and verify it satisfies the bisection condition. The process is iteratively repeated by adjusting the interval to the midpoint until the error tolerance is reached or the function value of the midpoint is within the desired accuracy.

The subject of your question concerns utilizing the Bisection method to solve a certain polynomial equation from a given interval [0, 2] with an accuracy of within 10^-2. The Bisection Method is a root-finding method in numerical analysis to solve for roots in given intervals.

This is an example of how the Bisection Method would be applied in solving for roots of polynomial equations. Do take note that this method only provides approximate solutions and it can be a lengthy process for equations with multiple roots.

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Answer:

The equation for this line, in slope-intercept form, is given by:

[tex]y = - 9[/tex]

Step-by-step explanation:

The equation of a line in the slope-intercept form has the following format:

[tex]y = ax + b[/tex]

In which a is the slope of the line and b is the y intercept.

Solution:

The line has the same y-intercept as [tex]y + 1 = 4 (x - 2)[/tex].

So, we have to find the y-intercept of this equation

[tex]y + 1 = 4 (x - 2)[/tex]

[tex]y = 4x - 8 - 1[/tex]

[tex]y = 4x - 9[/tex]

This equation, has the y-intercept = -9. Since this line has the same intercept, we have that [tex]b=-9[/tex].

Fow now, the equation of this line is

[tex]y = ax - 9[/tex]

The line contains the point [tex](9,-9)[/tex]

This means that when [tex]x = 9, y = -9[/tex]. We replace this in the equation and find a

[tex]y = ax - 9[/tex]

[tex]-9 = 9a - 9[/tex]

[tex]9a = 0[/tex]

[tex]a = \frac{0}{9}[/tex]

[tex]a = 0[/tex]

The equation for this line, in slope-intercept form, is given by:

[tex]y = - 9[/tex]

Answer:

23 chalkboards

Step-by-step explanation:

Given:

Mean length = 5 m

Standard deviation = 0.01

Number of units ordered = 1000

Now,

The z factor = [tex]\frac{\textup{x - Mean}}{\textup{standard deviation}}[/tex]

or

The z factor = [tex]\frac{\textup{4.98 - 5}}{\textup{0.01}}[/tex]

or

Z = - 2

Now, the Probability P( length < 4.98 )

Also, From z table the p-value = 0.0228

therefore,

P( length < 4.98 ) = 0.0228

Hence, out of 1000 chalkboard ordered (0.0228 × 1000) = 23 chalkboard are likely to have lengths of under 4.98 m.

Answer:

An unknown variable by reversing the process used to form the original equation.

Step-by-step explanation:

The opposite process rule says to solve for - an unknown variable by reversing the process used to form the original equation.

If an equation indicates an operation such as addition, subtraction, multiplication, or division, solve for the unknown variable by using the opposite process.

For example:

Lets say we have to find [tex]x+25=35[/tex]

Here 25 is subtracted from both sides of the equation to isolate x.

[tex]x+25-25=35-25[/tex]

we get x = 10

Check this : [tex]10+25=35[/tex]

Final answer:

The opposite process rule is a technique used to solve for an unknown variable by reversing the operations that were used to create the equation. It is a key concept in algebra for finding values of unknown variables.

Explanation:

The opposite process rule refers to solving for an unknown variable by reversing the process used to form the original equation. This is a fundamental technique in solving algebraic equations, necessary for determining the value of the unknown.

To solve for an unknown variable, you follow several steps. Initially, identify the unknowns and known variables. Then, find an equation that expresses the unknown in terms of the knowns. If more than one unknown is present, multiple equations may be needed.

To find the numerical value of the unknown, substitute known values, including their units, into the equation and solve. In algebra, this could mean performing operations such as addition, subtraction, multiplication, or division inversely to isolate the variable.

Answer:

a) False b) False c) True d) True e) True

Step-by-step explanation:

a) If A is a subset of B, and x∈B, then x∈A. False

Suppose A is Z (Set of Integers), and B is R (Set of Real Numbers). Then A is a subset of B. x ∈ B, let's say x equals π. If x ∈ B (B = Real Numbers) and x=π then x ∉ A (Z).

We could call A, any other subset of Real numbers (Q, I,..) and we both would come up to the same conclusion when it comes to Real numbers the Set.

So this conclusion is False. Not always an element of a subset is an element of a set.

b) False

For this one, I've drawn some lines, and it is useful to work with them.

Given the set {(x,y) ∈ R²| 0<x<0} then all negative and positive numbers but zero belong to this set.

c) If A and B are square matrices, then AB is also square. True

Taking into account the rules for multiplying matrices. The number of columns of A must be the same number of lines of B to there can be a matrix product.

Whenever we multiply square matrices, we'll always get square matrices. Then this conclusion is true.

d) A and B are subsets of a set S, then A∩B and A∪B are also subsets of S. True

Suppose A= Z (Integer Numbers) and B=Q (Rational Numbers) and S= R (Real Numbers)

A∩B = Z∩Q=∅ and A∪B =Z∪Q = subset

Since the ∅ empty set ⊂ in every set and ZUQ is another Subset of R this is a True conclusion.

e) True. For a matrix A, we define A²= AA

For any Power of Matrices, all we have to do is multiply any given matrix by itself for a given number of times.

M²=M*M

M³=M*M*M

Answer:

equation of plane, 5x+3y-z-36=0

Distance of point (2,2,2) from plane = 4.05 units

Step-by-step explanation:

Given,

Plane passing through the point = (8, -2, 0)

Let's say, [tex]x_1\ =\ 8[/tex]

               [tex]y_1\ =\ -2[/tex]

                [tex]z_1\ =\ 0[/tex]

Plane perpendicular to the vector, a= 5i + 3j- k

Since, the vector is perpendicular to the plane, hence the equation of plane can be given by

[tex](5i + 3j- k).((x-x_1)i+(y-y_1)j+(z- z_1)k)=\ 0[/tex]

[tex]=>(5i + 3j- k).((x-8)i+(y+2)j+(z-0)k)=\ 0[/tex]

[tex]=>\ 5(x-8)+3(y+2)-z=0[/tex]

[tex]=>\ 5x\ -\ 40\ +\ 3y\ +\ 6\ -\ z\ =\ 0[/tex]

[tex]=>\ 5x\ +\ 3y\ -\ z\ -\ 36\ =\ 0[/tex]

Hence, the equation of plane can be given by, 5x+3y-z-36=0

Now, we have to calculate the distance of the point O(2,2,2) from the plane 5x+3y-z-36=0

Let's say,

a= 5, b= 3, c= -1, d=-36

[tex]x_0=2,\ y_0=2,\ z_0=2[/tex]

So, distance of a point from the plane can be given by,

[tex]d=\dfrac{ax_0+by_0+cz_0+d}{\sqrt{a^2+b^2+c^2}}[/tex]

 [tex]=\dfrac{\left |5\times 2+3\times 2+(-1)\times 2-36\right |}{\sqrt{5^2+3^2+(-1)^2}}[/tex]

 [tex]=\dfrac{24}{\sqrt{35}}[/tex]

  = 4.05 units

So, the distance of the point O(2,2,2) from the given plane will be 4.05 units.

sarah remembered scissors

please be more specific

Answer: I'm sure its 2/21

Step-by-step explanation: you just need to multiply cross sides then divide by any number that works on both of them.

I hope that I answer your question.

Answer:

4 rows

Step-by-step explanation:

It is given that two statements two be connected with AND, the statements may be either true or false.

The output of the AND will be true if both the statements will be true otherwise false.

We can construct the table as follows:

statement 1            statement 2         output

false                        false                        false

false                         true                         false

true                          false                        false

true                          true                          true

Hence, the number of rows the truth will have = 4

Answer:

Step-by-step explanation:

As per the given question,

In a manufacturing operation, a part is produced by machining, polishing, and painting.

Number of machine tools = 3

Number of polishing tools = 4

Number of painting tools = 3

Now,

For finding the different routing consisting of machining, followed by polishing, and followed by painting, we have to simply multiply the number of machine tools, polishing tools and painting tools.

Therefore,

The different routing (consisting of machining, followed by polishing, and followed by painting) for a part are possible = 3 × 4 × 3 = 36.

Hence, the required answer is 36.

Number of ways a process can be done is the count of total distinguished ways that process can be done. The count of different routings possible for a part is 36

Suppose that a process A can be done in 'a' different ways.
And there is a process following A, call it B, can be done in 'b' different ways. Then, the process A then B can be done in a×b different ways.

This is called rule of product in combinatorics.

Since there are 3 processes to be done subsequently(machining, polishing, then painting), and each of them can be done in 3, 4, and 3 ways respectively, thus,

Total number of routings possible for a part is [tex]3 \times 4 \times 3 = 36[/tex] ways.

Thus, The count of different routings possible for a part is 36

Learn more about rule of product here:

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Answer:

Maximum height of the arrow is 203 feets

Step-by-step explanation:

It is given that,

The height of the arrow as a function of time t is given by :

[tex]h(t)=-16t^2+64t+11[/tex]..........(1)

t is in seconds

We need to find the maximum height of the arrow. For maximum height differentiating equation (1) wrt t as :

[tex]\dfrac{dh(t)}{dt}=0[/tex]

[tex]\dfrac{d(-16t^2+64t+11)}{dt}=0[/tex]

[tex]-32t+64=0[/tex]

t = 2 seconds

Put the value of t in equation (1) as :

[tex]h(t)=-16(2)^2+64(2)+11[/tex]

h(t) = 203 feet

So, the maximum height reached by the arrow is 203 feet. Hence, this is the required solution.

Answer:

The basis for the null space of A is [tex]{\left[\begin{array}{c}-1&-1&1&0\end{array}\right],\left[\begin{array}{c}-1&1&0&1\end{array}\right]}[/tex]

Step-by-step explanation:

[tex]\left[\begin{array}{cccc}1&0&1&1\\3&2&5&1\\0&4&4&-4\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}1&0&1&1\\0&2&2&-2\\0&4&4&-4\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}1&0&1&1\\0&2&2&-2\\0&0&0&0\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}1&0&1&1\\0&1&1&-1\\0&0&0&0\end{array}\right][/tex]

    2. Convert the matrix equation back to an equivalent system and solve the matrix equation

[tex]1x_{1} +x_{3} +1x_{4}=0\\ 1x_{2} +x_{3} -1x_{4}=0\\0=0[/tex]

[tex]\left[\begin{array}{cccc}1&0&1&1\\0&1&1&-1\\0&0&0&0\end{array}\right] \left[\begin{array}{c}x_{1} &x_{2} &x_{3}&x_{4} \end{array}\right]=\left[\begin{array}{c}0&0&0\end{array}\right][/tex]

If we take [tex]x_{3}=t, x_{4}=s[/tex] then [tex]x_{1}=-s-t,x_{2}=s-t,x_{3}=t,x_{4}=s[/tex]

Therefore,

[tex]\boldsymbol{x}=\left[\begin{array}{c}-s-t&s-t&t&s\end{array}\right]=\left[\begin{array}{c}-1&-1&1&0\end{array}\right]t+\left[\begin{array}{c}-1&1&0&1\end{array}\right]s\\\boldsymbol{x}=\left[\begin{array}{c}-1&-1&1&0\end{array}\right]x_{3} +\left[\begin{array}{c}-1&1&0&1\end{array}\right]x_{4}[/tex]

The null space has a basis formed by the set {[tex]{\left[\begin{array}{c}-1&-1&1&0\end{array}\right],\left[\begin{array}{c}-1&1&0&1\end{array}\right]}[/tex]}

Step-by-step explanation:

We will prove by mathematical induction that, for every natural n,  

[tex](x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}[/tex]

We will prove our base case (when n=1) to be true:

Base case:

[tex](x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=(x-y)(x^{1}+y^{1})=x^2-y^2=x^{1+1}-y^{1+1}[/tex]

Inductive hypothesis:  

Given a natural n,  

[tex]x^{n+1}-y^{n+1}=(x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})[/tex]

Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.

Inductive step:

Observe that, for y=0 the conclusion is clear. Then we will assume that [tex]y\neq 0.[/tex]

[tex](x-y)(x^{n+1}+x^{n}y+...+xy^{n}+y^{n+1})=(x-y)y(\frac{x^{n+1}}{y}+x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+(x-y)y(x^{n}+...+xy^{n-1}+y^{n})=(x-y)y(\frac{x^{n+1}}{y})+y(x^{n+1}-y^{n+1})=(x-y)x^{n+1}+y(x^{n+1}-y^{n+1})=x^{n+2}-yx^{n+1}+yx^{n+1}-y^{n+2}=x^{n+2}-y^{n+2}\\[/tex]

With this we have proved our statement to be true for n+1.    

In conlusion, for every natural n,

[tex](x-y)(x^{n}+x^{n-1}y+...+xy^{n-1}+y^{n})=x^{n+1}-y^{n+1}[/tex]

Answer: 1503

Step-by-step explanation:

Given : Significance level : [tex]\alpha:1-0.98=0.02[/tex]

Critical value : [tex]z_{\alpha/2}=2.326[/tex]

Margin of error : [tex]E=\pm0.03[/tex]

We know that the formula to find the sample size (the prior true proportion is not available) is given by :-

[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]

i.e. [tex]n=0.25(\dfrac{2.326}{0.03})^2=1502.85444444\approx1503[/tex]

Hence, the minimum sample size should be 1503.

Answer:

[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given differential equation is,

     y"+y'-2y=1

[tex]=>\ (D^2+D-2D)y\ =\ 1[/tex]

To find the complementary function we will write,

    [tex]D^2+D-2=0[/tex]

[tex]=>\ D\ =\ \dfrac{-1+\sqrt{1^2+4\times 2\times 1}}{2\times 1}\ or\ \dfrac{-1-\sqrt{1^2+4\times 2\times 1}}{2\times 1}[/tex]

[tex]=>\ D\ =\ -2\ or\ 1[/tex]

Hence, the complementary function can be given by

[tex]y(t)\ =\ C_1e^{-2t}\ +\ C_2e^t[/tex]

Let's say,

[tex]y_1(t)\ =\ e^{-2t}\ \ =>y'_1(t)\ =\ -2e^{-2t}[/tex]

[tex]y_2(t)\ =\ e^{t}\ \ =>y'_2(t)\ =\ e^{t}[/tex]

[tex]g(t)\ =\ 1[/tex]

Wronskian can be given by,

[tex]W\ =\ y_1(t).y'_2(t)\ -\ y_2(t).y'_1(t)[/tex]

     [tex]=\ e^{-2t}.e^{t}\ -\ e^{t}.(-2e^{-2t})[/tex]

     [tex]=\ e^{-t}\ +\ 2e^{-t}[/tex]

     [tex]=\ 3.e^{-t}[/tex]

Now, the particular integral can be given by

[tex]y_p(t)=\ -y_1(t)\int\dfrac{y_2(t).g(t)}{W}dt\ +\  y_2(t)\int\dfrac{y_1(t).g(t)}{W}dt[/tex]

        [tex]=\ -e^{-2t}\int\dfrac{e^t.1}{3.e^{-t}}+e^t\int\dfrac{e^{-2t}.1}{3.e^{-t}}dt[/tex]

       [tex]=\ -e^{-2t}\int\dfrac{1}{3}dt+\dfrac{e^t}{3}\int e^{-t}dt[/tex]

       [tex]=\ \dfrac{-e^{-2t}}{3}.t\ -\ \dfrac{e^t}{3}.e^{-t}[/tex]

        [tex]=\ -t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Hence, the complete solution can be given by

[tex]y(t)\ =\ C_1.e^{-2t}+C_2e^t-\ t.\dfrac{e^{-2t}}{3}-\dfrac{1}{3}[/tex]

Answer:

The rabbit should be fed:

[tex]6 + 2z[/tex] grams of food A

[tex]12 - 3z[/tex] grams of food B

[tex]z[/tex] grams of food C

For [tex]z \leq 4[/tex].

Step-by-step explanation:

This can be solved by a system of equations.

I am going to say that x is the number of grams of food A, y is the number of grams of food B and z is the number of grams of Food C.

The problem states that:

A researcher wants to provide a rabbit exactly 162 units of ​protein:

There are 5 units of protein in each gram of food A, 11 units of protein in each gram of food B and 23 units of protenin in each gram of food C. So

[tex]5x + 11y + 23z = 162[/tex]

A researcher wants to provide a rabbit exactly 72 units of carbohydrates:

There are 2 units of carbohydrates in each gram of food A, 5 units of carbohydrates in each gram of food B and 11 units of carbohydrates in each gram of food C. So:

[tex]2x + 5y + 11z = 72[/tex]

A researcher wants to provide a rabbit exactly 30 units of Vitamin A:

There is 1 unit of Vitamin A in each gram of food A, 2 units of Vitamin A in each gram of food B and 4 units of Vitamin A in each gram of food C. So:

[tex]x + 2y + 4z = 30[/tex].

We have to solve the following system of equations:

[tex]5x + 11y + 23z = 162[/tex]

[tex]2x + 5y + 11z = 72[/tex]

[tex]x + 2y + 4z = 30[/tex].

I think that the easier way to solve this is reducing the augmented matrix of this system.

This system has the following augmented matrix:

[tex]\left[\begin{array}{cccc}5&11&23&162\\2&5&11&72\\1&2&4&30\end{array}\right][/tex]

To help reduce this matrix, i am going to swap the first line with the third

[tex]L_{1} <-> L_{3}[/tex]

Now we have the following matrix:

[tex]\left[\begin{array}{cccc}1&2&4&30\\2&5&11&72\\5&11&23&162\end{array}\right][/tex]

Now i am going to do these following operations, to reduce the first row:

[tex]L_{2} = L_{2} - 2L_{1}[/tex]

[tex]L_{3} = L_{3} - 5L_{1}[/tex]

Now we have

[tex]\left[\begin{array}{cccc}1&2&4&30\\0&1&3&12\\0&1&3&12\end{array}\right][/tex]

Now, to reduce the second row, i do:

[tex]L_{3} = L_{3} - L_{2}[/tex]

The matrix is:

[tex]\left[\begin{array}{cccc}1&2&4&30\\0&1&3&12\\0&0&0&0\end{array}\right][/tex]

This means that z is a free variable, so we are going to write y and x as functions of z.

From the second line, we have

[tex]y + 3z = 12[/tex]

[tex]y = 12 - 3z[/tex]

From the first line, we have

[tex]x + 2y + 4z = 30[/tex]

[tex]x + 2(12 - 3z) + 4z = 30[/tex]

[tex]x + 24 - 6z + 4z = 30[/tex]

[tex]x = 6 + 2z[/tex]

Our solution is: [tex]x = 6 + 2z, y = 12 - 3z, z = z[/tex].

However, we can not give a negative number of grams of a food. So

[tex]y \geq 0[/tex]

[tex]12 - 3z \geq 0[/tex]

[tex]-3z \geq -12 *(-1)[/tex]

[tex]3z \leq 12[/tex]

[tex]z \leq 4[/tex]

The rabbit should be fed:

[tex]6 + 2z[/tex] grams of food A

[tex]12 - 3z[/tex] grams of food B

[tex]z[/tex] grams of food C

For [tex]z \leq 4[/tex].

Answer: option (C)

Step-by-step explanation: The slope of a linear function is undetermined when the line is parallel respect to the y-axis. In the current problem there is no way to observe such geometrical issue, but if we consider how to derive the slope using the following expression; [tex]m=\frac{\Delta y}{\Delta x}= \frac{y_{2}-y_{1}}{x_2-x_{1}}[/tex].

With the previous equation, we have

[tex]a) for P_{1}(-1,1), P_{2}(1,-1)   m=\frac{\Delta y}{\Delta x}= \frac{-1-1}{1-(1)}=\frac{-2}{2}=1\\[/tex], therefore the slope is defined

[tex]b) for P_{1}(-2,2), P_{2}(2,2)   m=\frac{\Delta y}{\Delta x}= \frac{2-2}{2-(2)}=\frac{0}{4}=0\\[/tex], therefore the slope is defined

[tex]c) for P_{1}(-3,3), P_{2}(-3,3)   m=\frac{\Delta y}{\Delta x}= \frac{3-(-3)}{-3-(-3)}=\frac{6}{0}=undetermined\\[/tex]

[tex]d) for P_{1}(-4,4), P_{2}(4,4)   m=\frac{\Delta y}{\Delta x}= \frac{4-(-4)}{4-(-4)}=\frac{8}{8}=1\\[/tex]

In this case, the option (C) shows that is not possible to divide over zero. Given such issue, the slope is undetermined and therefore it is a vertical line parallel to y-axis.

Answer: 0.0475

Step-by-step explanation:

Given : The amount of money spent on red balloon in a certain college town when the football team is in town is a normal random variable with

[tex]\mu=\$50000[/tex] and [tex]\sigma=\$3000[/tex]

Let x be the random variable that represents the  amount of money spent on red balloon.

Using formula [tex]z=\dfrac{x-\mu}{\sigma}[/tex], the z-score corresponding to x= 45000 will be :_

[tex]z=\dfrac{45000-50000}{3000}\approx-1.67[/tex]

Now, by using the standard normal distribution table for z, we have

P value : [tex]P(z<-1.67)=1-P(z<1.67)=1-0.9525=0.0475[/tex]

∴The proportion of home football game days in this town is less than $45000 worth of red balloons sold = 0.0475

Answer:

[tex]f(x) = 4sin(\frac{\pi}{2}x) - 3[/tex], the third one

Step-by-step explanation:

Explaining the sine function:

The sine function is defined by:

[tex]S = Asin(p(x - x_{0})) + V[/tex]

In which A is the amplitude, [tex]p = \frac{2\pi}{N}[/tex] is the period, [tex]x_{0}[/tex] is the horizontal shift and V is the vertical shift.

So, in your problem:

The amplitude is 4, so A = 4.

The period is [tex]\frac{\pi}{2}[/tex], so [tex]p = \frac{\pi}{2}[/tex].

There is no horizontal shift, so [tex]x_{0} = 0[/tex].

The vertical shift is −3, so V = -3.

The sine function that represents these following conditions is

[tex]f(x) = 4sin(\frac{\pi}{2}x) - 3[/tex], the third one

Answer:  21

Step-by-step explanation:

Given : A bag containing five red marbles, two green ones, one transparent one, four yellow ones, and two orange ones .

Total marbles other than red or green = 1+4+2=7

Now, the number of combinations to select five marbles from the set of 7 will be :-

[tex]7C_5=\dfrac{7!}{5!(7-5)!}=\dfrac{7\times6\times5!}{5!\times2!}=21[/tex]

Hence, the number of  possible sets of five marbles are there in which none of them are red or green =21

Answer:

A simple random sample.

Step-by-step explanation:

A simple random sample is an statistical sample in which each member of a group has the same probability of being chosen. Since the researcher doesn't really have specific characteristics added to the sample other than being from public or private universities, this would be a simple random sample.

Answer:

[tex]y(t)=-\frac{1}{t+C}[/tex]

Step-by-step explanation:

We are given that

[tex]\frac{dy}{dt}=y^2[/tex]

We have to find the value of y(t).

[tex]\frac{dy}{dt}=y^2[/tex]

[tex]\frac{dy}{y^2}=dt[/tex]

Integrating on both sides

[tex]\int y^{-2}dy=\int dt[/tex]

We know that [tex]\int x^n dx=\frac{x^{n+1}}{n+1}+C[/tex]

Using the formula

[tex]\frac{y^{-1}}{-1}=t+C[/tex]

[tex]-\frac{1}{y}=t+C[/tex]

[tex]a^{-1}=\frac{1}{a}[/tex]

Taking the reciprocal on both side then , we get

[tex]-y=\frac{1}{t+C}[/tex]

[tex]y(t)=-\frac{1}{t+C}[/tex]

Answer: 0.4729%

Step-by-step explanation:

The formula to find the percent of a part in total amount :-

[tex]\%=\dfrac{\text{Part}}{\text{Total}}\times100[/tex]

Given : Total amount = 1,1050.00

Part of total amount = 52.25

Now, substitute all the values in the formula , we get

[tex]\%=\dfrac{52.25}{11050}\times100\\\\\Rightarrow\ \%=\dfrac{5225}{1105000}\times100=\dfrac{5225}{11050}=0.472850678733\approx0.4729\%[/tex]

Hence, 52.25 is 0.4729% of 1,1050.00.

Answer: 39.308 pounds

Step-by-step explanation:

We assume that the given population is normally distributed.

Given : Significance level : [tex]\alpha: 1-0.98=0.02[/tex]

Sample size : n= 12, which is  small sample (n<30), so we use t-test.

Critical value (by using the t-value table)=[tex]t_{n-1, \alpha/2}=t_{11,0.01}=2.718[/tex]

Sample mean : [tex]\overline{x}=50[/tex]  

Standard deviation : [tex]\sigma= 20[/tex]

The lower bound of confidence interval is given by :-

[tex]\overline{x}-t_{(n-1,\alpha/2)}\dfrac{\sigma}{\sqrt{n}}[/tex]

i.e. [tex]55-(2.718)\dfrac{20}{\sqrt{12}}[/tex]

[tex]=55-15.6923803166\approx55-15.692=39.308[/tex]

Hence, the lower bound for the 98%  confidence interval for the mean yearly sugar consumption= 39.308 pounds

Answer:

5 + 2          

Step-by-step explanation:

We have to rewrite the given statement in addition form.

The integers have  property of:

Negative(-)  Negative(-) = Positive(+)

Positive(+)  Positive(+)  = Positive(+)

Positive(+)  Negative(-) = Negative(-)

Negative(-) Positive(+)  = Negative(-)

The given statement is:

5-(-2)

Since we have two negative together, it is converted into a positive.

Thus, the given statement can be written in positive form as

5 + 2

Answer:

$5265.71

Step-by-step explanation:

We have been given that you deposit $3000 into a money-market savings account which pays 4.8% compounded quarterly.

We will use future value formula to solve our given problem.

[tex]FV=C_0\times (1+r)^n[/tex], where,

[tex]C_0=\text{Initial amount}[/tex],

r = Rate of return in decimal form,

n = Number of periods.

[tex]4.8\%=\frac{4.8}{100}=0.048[/tex]

[tex]n=3\times 4=12[/tex]

[tex]FV=\$3,000\times (1+0.048)^{12}[/tex]

[tex]FV=\$3,000\times (1.048)^{12}[/tex]

[tex]FV=\$3,000\times 1.7552354909370114[/tex]

[tex]FV=\$5265.7064\approx \$5265.71[/tex]

Therefore, there will be $5265.71 in your account at the end of those 3 years.

Answer:

  see below for the working

Step-by-step explanation:

Dividing by a number is the same as multiplying by the inverse of that number.

[tex]\displaystyle\frac{\left(\frac{1}{4}\right)}{\left(-\frac{2}{3}\right)}=-\frac{1}{4}\cdot\frac{3}{2}=-\frac{3}{4\cdot 2}=-\frac{3}{8}[/tex]

Answer:

  D.  14°

Step-by-step explanation:

The Law of Sines tells you sides are in proportion to the sine of the opposite angle:

  sin(A)/BC = sin(B)/AC

  sin(A) = BC/AC·sin(B)

  A = arcsin(BC/AC·sin(B)) = arcsin(7/28·sin(75°)) ≈ 13.974° ≈ 14°