Exercise 4.X3 Make a reasonable conjecture about the nth term in the sequence. 5 9 15 23 33

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: 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:

0

Step-by-step explanation:

total number of balls = 3+5+2= 10

Probability of getting red P(R) = 3/10

Probability of getting white P(W) = 5/10

Probability of getting black P(B) = 2/10

for each red ball drawn you win $6 and for each black ball drawn you loose $9 dollars

E(X)= 6×3/10 +0×5/10 -9×2/10= 0

E(X)= 0

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:

[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: 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:

[tex]m=-\frac{4}{7}[/tex]

[tex]b=\frac{3}{7}[/tex]

Step-by-step explanation:

Slope intercept form of a line is

[tex]y=mx+b[/tex]             ... (1)

where, m is slope and b is y-intercept.

The given equation is

[tex]4x+7y+4=7[/tex]

We need to find the slope intercept form of given line.

Subtract 4 from both sides.

[tex]4x+7y=7-4[/tex]

[tex]4x+7y=3[/tex]

Subtract 4x from both sides.

[tex]7y=3-4x[/tex]

Divide both sides by 7.

[tex]y=\frac{3-4x}{7}[/tex]

[tex]y=\frac{3}{7}-\frac{4}{7}x[/tex]

Arrange the terms.

[tex]y=-\frac{4}{7}x+\frac{3}{7}[/tex]           .... (2)

Form (1) and (2) we get

[tex]m=-\frac{4}{7}[/tex]

[tex]b=\frac{3}{7}[/tex]

Therefore, the slope of the line is -4/7 and y-intercept is 3/7.

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:

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]}

sarah remembered scissors

please be more specific

Answer:

Qualitative and Neither

Step-by-step explanation:

Quantitative data is such a data which can be measured or calculated i.e. which is defined only in terms of numbers. In simple words we can say that numeric data is the Quantitative data.

On the other hand, qualitative data describes the characteristics, attribute or quality of the objects. This type of data is not measured or calculated.

The data which we are dealing with is "Kind of pizza". The kind/flavor of pizza is an attribute or characteristic of pizza. So from here it is clear that the data is Qualitative. Though numbers are assigned  to different flavors, these numbers are just for identification of the flavor on the order form.

The terms discrete and continuous can only be used when the data is Quantitative. Qualitative data cannot be referred to as discrete or continuous data, even if some numbers are assigned to data.

Therefore, the answers are: Qualitative and Neither

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:

Jamal received 2,880 votes

Step-by-step explanation:

In the election,

Jamal received 40% of all votes

Tran received 100% - 40% = 60% that is 4,320 votes

Let x be the number of votes Jamal received. Then

x - 40%

4,320 - 60%

Write a proportion:

[tex]\dfrac{x}{4,320}=\dfrac{40}{60}\\ \\\text{Cross multiply}\\ \\60\cdot x=40\cdot 4,320\\ \\x=\dfrac{40\cdot 4,320}{60}=\dfrac{2\cdot 4,320}{3}=\dfrac{2\cdot 1,440}{1}=2,880[/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:

The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

Step-by-step explanation:

The radius is half of the diameter. The diameter is one line going across the whole, through the midpoint. The radius starts at the midpoint and that's why it's only half of the diameter.

Answer: The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

Step-by-step explanation:

Let's check all the options.

The radius is a line segment joining two distinct points on the circle. → Wrong.

Reason :- Radius joins center and any point on circle not any two points.

The radius is the boundary of a circle. → Wrong.

Reason :- Circumference is the boundary of circle ,

Formula for circumference C= 2π r , where r is radius .

The radius is a line segment that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle.→ Wrong.

Reason :- Its diameter that starts at one point on the circle, passes through the center of the circle, and ends at another point on the circle and it is twice of radius.

So , the best answer that defines the radius of a circle is The radius is a line segment that starts at the center of the circle and ends at a point on the circle.

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:

option C the 69 businesses that returned the questionnaire.

Step-by-step explanation:

It is given in the question that only 69 businesses out of all 282 randomly chosen businesses have returned the questionnaire mailed by the committee.

Therefore,

The data available for the study by the committee is of only 69 businesses that have replied to the committee. So the study is based on this population of 69 businesses only.

Hence, option c is the correct answer.

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: 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:

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.

Answer:

14. Quadrant IV

13. Quadrant II

12. Quadrant III

11. Quadrant I

15. -17

16. -1

17. 7

Step-by-step explanation:

Answer:

8771408311 steps ( approx )

Step-by-step explanation:

Given,

The radius of the earth,

[tex]r=6.38\times 10^6[/tex]

So, the circumference of the earth,

[tex]S=2\pi (r)[/tex]

[tex]=2\times \frac{22}{7}\times (6.38\times 10^8)[/tex]

[tex]=4.0102857143\times 10^9\text{ meters}[/tex]

∵ 1 meter = 39.3701 inches

[tex]\implies S =1.578853496\times 10^{11}\text{ inches }[/tex]

Also, the length of one step = 18 inches

Hence, the total number of steps =  [tex]\frac{1.578853496\times 10^{11}}{18}[/tex]

[tex]= 8.7714083111\times 10^9[/tex]

[tex]\approx 8771408311[/tex]

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:

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:

  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°

Answer:

B. 5 rolls

Step-by-step explanation:

The areas of the room, not including the ceiling, are discriminated as follows:

Longer walls: [tex](12.5\times8)\times2=200ft^2[/tex] (6 inches equals one foot)

Shorter walls: [tex](10.5\times8)\times2 = 168ft ^ 2[/tex] (6 inches equals one foot)

Window area: [tex](4\times3)\times2 = 24ft ^ 2[/tex]

Door area: [tex](7\times3) = 21ft ^ 2[/tex]

Area that will be effectively covered:

Total area to wallpaper: [tex]200 + 168 -24 -21 = 323ft ^ 2[/tex]

Amount of paper needed: [tex]323\times1.1 = 355.3ft ^ 2[/tex]

[tex]30in = 24in + 6in = 2ft + 0.5ft = 2.5ft.[/tex] That is, the area of ​​a roll of paper is [tex]2.5\times30 = 75ft ^ 2[/tex]

Number of rolls needed:

[tex]\frac{355.3}{75} = 4.73[/tex] rolls

Answer:

Correct answer is B. 5Rolls

Step-by-step explanation:

12 inches is 1 feet

6 inches is 6/12 feet= 0,5 feet.

12 inches is 1 foot

30 inches is 30/12 feet=2,5feet.

2. Second,you have to calculate the total surface where you will wallpaper.

So you have to calculate the dimension of 2 different rectangles and substract the surfaces that you don't have to wallppaper (door and windows).

[tex]Area rectangle 1 =10.5feet*8feet=84ft^{2} \\Area rectangle2=12.5feet*8feet=100ft^{2}\\Total Area of walls=(Area rectangle 1 *2) + (Area rectangle2*2)\\Total Area of walls=(84ft^{2} *2)+(100ft^{2})\\\\Total Area of walls=368ft^{2}[/tex]

3. Now we have to calculate the area to substract from the total area, since you will not wallpaper the door and windows:

[tex]Windows=4feet*3feet*2=24ft^{2}  \\Door=7feet*3feet=21ft^{2}[/tex]

4. Total area to wallpaper is Total surface of the room minus door and windows surface:

[tex]wallpaperArea=368ft^{2} -45ft^{2}\\wallpaperArea=323ft^{2}[/tex]

5. Now you have to add 10% waste to the calculated surface:

[tex]323ft^{2} +(323*0.10)=355.3ft^{2}[/tex]

6. So, you have the real area that will wallpaper considering 10% waste, it is 326.23 square feet. To calculate how many rolls you will need, you have to calculate the surface that each roll covers and then divide total surface by roll surface.

[tex]Roll surface=2,5feet*30feet=75feet^{2}[/tex]

[tex]Rolls needed=355.3ft^{2}/75ft^{2}=4.73[/tex]

7. As the number of rolls is not integer you have to round, then the answer is you will need 5 rolls of wallpaper.

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.