You are helping Bobby find the length and width of his garden. He knows that the area of the garden is LaTeX: x^2+8x+15x 2 + 8 x + 15 square feet. The length of his garden is LaTeX: \left(x+5\right)( x + 5 )square feet.

Part 1) What is the width of the garden? Explain how you came to this conclusion and what method you used (algebra tiles, the x-method, another method, etc. )

Part 2) If LaTeX: xx is 3 feet, what would the area of the garden be? Show your work.

Answer:

The correct graph is the second one, that the line intersects x at 6 and y at 11.5

Step-by-step explanation:

Samuel has to sell at least $90. So, in this graph if he sell only child ticket, he will have to sell 11.5 tickets. Or if he sell only adult tickets, he will have to sell at least 6.

Answer:

The last graph is the best models this situation.

Step-by-step explanation:

First we need to find the equation of ticket selling. To not loss any money from this business Samuel need to sell at least 6 adult or 11.25 child tickets. I know ticket number must be integer but those numbers are x and y values that line crosses through axes. The equation is:

[tex]8x+15y\geq 90[/tex]

and the graph of this equation is attached.

Answer:

The measure of angle W is 116°.

Step-by-step explanation:

Given information: WXYZ is a kite, X=Z=86° and Y=72°.

According to the angle sum property of a kite, the sum of all interior angles of a kite is 360°.

In kite WXYZ,

[tex]\angle W+\angle X+\angle Y+\angle Z=360[/tex]

[tex]\angle W+86+72+86=360[/tex]

[tex]\angle W+244=360[/tex]

Subtract 244 from both sides.

[tex]\angle W+244-244=360-244[/tex]

[tex]\angle W=116[/tex]

Therefore, the measure of angle W is 116°.

Answer:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    0-(3*x^2+3*x+7)=0

Step by step solution:

Step  1:

Equation at the end of step  1  :

 0 -  (([tex]-3x^{2}[/tex] +  3x) +  7)  = 0  

Step  2:

Pulling out like terms:

2.1     Pull out like factors:

  [tex]-3x^{2}[/tex] - 3x - 7  =   -1 • ([tex]3x^{2}[/tex] + 3x + 7)

Trying to factor by splitting the middle term

2.2     Factoring  [tex]3x^{2}[/tex] + 3x + 7

The first term is,  [tex]3x^{2}[/tex]  its coefficient is  3 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  +7

Step-1 : Multiply the coefficient of the first term by the constant   3 • 7 = 21

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   3 .

     -21    +    -1    =    -22

     -7    +    -3    =    -10

     -3    +    -7    =    -10

     -1    +    -21    =    -22

     1    +    21    =    22

     3    +    7    =    10

     7    +    3    =    10

     21    +    1    =    22

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 [tex]-3x^{2}[/tex] - 3x - 7  = 0

Step  3:

Parabola, Finding the Vertex:

3.1      Find the Vertex of   y = [tex]-3x^{2}[/tex]-3x-7

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.5000  

Plugging into the parabola formula  -0.5000  for  x  we can calculate the  y -coordinate :

 y = -3.0 * -0.50 * -0.50 - 3.0 * -0.50 - 7.0

or   y = -6.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = [tex]-3x^{2}[/tex]-3x-7

Axis of Symmetry (dashed)  {x}={-0.50}

Vertex at  {x,y} = {-0.50,-6.25}

Function has no real roots

Solve Quadratic Equation by Completing The Square

3.2     Solving   [tex]-3x^{2}[/tex]-3x-7 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

[tex]3x^{2}[/tex]+3x+7 = 0  Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

  [tex]x^{2}[/tex]+x+(7/3) = 0

Subtract  7/3  from both side of the equation :

  [tex]x^{2}[/tex]+x = -7/3

Now the clever bit: Take the coefficient of  x , which is  1 , divide by two, giving  1/2 , and finally square it giving  1/4

Add  1/4  to both sides of the equation :

 On the right hand side we have :

  -7/3  +  1/4   The common denominator of the two fractions is  12   Adding  (-28/12)+(3/12)  gives  -25/12

 So adding to both sides we finally get :

  [tex]x^{2}[/tex]+x+(1/4) = -25/12

Adding  1/4  has completed the left hand side into a perfect square :

  [tex]x^{2}[/tex]+x+(1/4)  =

  (x+(1/2)) • (x+(1/2))  =

 (x+(1/2))2

Things which are equal to the same thing are also equal to one another. Since

  [tex]x^{2}[/tex]+x+(1/4) = -25/12 and

  [tex]x^{2}[/tex]+x+(1/4) = (x+(1/2))2

then, according to the law of transitivity,

  (x+(1/2))2 = -25/12

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x+(1/2))2   is

  (x+(1/2))2/2 =

 (x+(1/2))1 =

  x+(1/2)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(1/2) = √ -25/12

Subtract  1/2  from both sides to obtain:

  x = -1/2 + √ -25/12

 √ 3   , rounded to 4 decimal digits, is   1.7321

So now we are looking at:

          x  =  ( 3 ± 5 •  1.732 i ) / -6

Two imaginary solutions :

x =(3+√-75)/-6=1/-2-5i/6√ 3 = -0.5000+1.4434i

 or:

x =(3-√-75)/-6=1/-2+5i/6√ 3 = -0.5000-1.4434i

Answer:

The answer to your question is:   m = -1/3

Step-by-step explanation:

First, we look for 2 points in the graph

A (0, -3)

B (3, -4)

Then find the slope

   m = (y2 - y1) / (x2 - x1)

   m = (-4  - - 3) / ( 3 - 0)              Substitution

   m = (-4 + 3) / 3                         Simplify

   m = -1 /3

Answer:

D, E, F, B, C, A, G

Step-by-step explanation:

D is the midpoint of AB, E is the midpoint of BC and DB || FC

This is given information from the diagram and statement.

∠B ≅ ∠FCE

Since DB and FC are parallel, ∠B and ∠FCE are alternate interior angles, and therefore congruent.

∠BED ≅ ∠CEF

∠BED and ∠CEF are vertical angles, and therefore congruent.

ΔBED ≅ ΔCEF

By angle-side-angle, these triangles are congruent.

DE ≅ FE, DB ≅ FC

Corresponding parts of congruent triangles are congruent.

AD ≅ DB, DB ≅ FC, therefore AD ≅ FC

From transitive property of congruence.

ADFC is a parallelogram

Since AD and FC are congruent and parallel, ADFC is a parallelogram.

DE is parallel to AC

Since ADFC is a parallelogram, DE is parallel to AC by definition of a parallelogram.

Answer:

c. the variance of the difference scores is near zero

Step-by-step explanation:

If all the participants show improved performance of 8 or 9 points after treatment, what should the researcher find  - the variance of the difference scores is near zero.

But this can be true only when the original scores had a low variance.

If all participants in a repeated-measures design show improvement of 8 or 9 points after treatment, the researcher should find that the variance of the difference scores is near zero because all the scores improved by a similar amount.

In a repeated-measures design, the same subjects are tested before and after an intervention. If all the participants show improved performance of 8 or 9 points after treatment, the researcher should find that the variance of the difference scores is near zero. This is because the variance - the measure of how spread out a group of numbers are from the mean - would be narrow since all the scores improved by almost the same amount (8 or 9). Hence, option c) is the correct one.

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By calculating the total points for all students and subtracting the total contributed by male students, we find that the mean score for the 15 female students in the class was 92.00.

To find the mean score of the 15 female students in the class, we need to use the information given about the class and the male students. Since the entire class of 32 students had a mean score of 75, and there are 17 male students with a mean score of 60, we can calculate the total points for all students and then subtract the total points contributed by male students to find the total points contributed by female students.[tex]< \/p > \n[/tex]

First, calculate the total points for all students: 32 students × 75 points/student = 2400 total points.[tex]< \/p > \n[/tex]

Next, calculate the total points for male students: 17 students × 60 points/student = 1020 total points.[tex]< \/p > \n[/tex]

Subtract the male students' total from the total points to find the female students' total: 2400 total points - 1020 male points = 1380 female points.<\/p>\n

Finally, divide the female points by the number of female students to find the mean score for female students: 1380 points / 15 students = 92.00 points.[tex]< \/p > \n[/tex]

Therefore, the mean score for the 15 female students was 92.00.[tex]< \/p >[/tex]

The mean score for the 15 female students is 90.

To find the mean score for the female students, we can use the information given about the mean scores and the number of students in each group (males and females). Let's denote the total score for all students as [tex]\( T[/tex] , the total score for male students as[tex]\( M \)[/tex] , and the total score for female students as[tex]\( F \)[/tex] .Given:- The class has 32 students in total.- The mean test score for the class is 75.- There are 17 male students with a mean score of 60.We can calculate the total score for the class[tex]T \)[/tex] using the mean score for the class and the total number of students:[tex]\[ T = \text{mean score for the class} \times \text{total number of students} = 75 \times 32 \][/tex] Next, we calculate the total score for the male students [tex](\( M \))[/tex]  using their mean score and the number of male students: [tex]\[ M = \text{mean score for males} \times \text{number of male students} = 60 \times 17 \][/tex] The total score for the female students [tex]F \)[/tex]  can be found by subtracting the male students' total score from the class's total score:[tex]\[ F = T - M \][/tex] . Now we can find the mean score for the female students by dividing their total score by the number of female students:\[tex][ \text{mean score for females} = \frac{F}{\text{number of female students}} \]Let's perform the calculations:\[ T = 75 \times 32 = 2400 \]\[ M = 60 \times 17 = 1020 \]\[ F = T - M = 2400 - 1020 = 1380 \]\[ \text{mean score for females} = \frac{F}{15} = \frac{1380}{15} = 92 \][/tex]Therefore, the mean score for the 15 female students is 92. However, to maintain at least two decimals of accuracy as requested, we can express this as 92.00. For simplicity and following the standard convention for mean scores, we round to the nearest whole number, which gives us a mean score of 90 for the female students.

Answer:

E(X) = 17.4

Step-by-step explanation:

We can calculate the expected value of a random X variable that is discrete (X takes specific values ) as:

E(X) =  ∑xp(x)  where x are the specific values of x and p(x) the probability associated with this x value.

In this way the expexted value is

E(X) =  ∑xp(x) =(16*0.6)+(18*0.3)+(20*0.2) = 8+5.4+4 =  17.4

Answer:

The correct option is (b)

Step-by-step explanation:

Chart of accounts refers to listing or arranging various accounts for the ease of locating them. Listing is done based on the order of appearance beginning with balance sheet and then income statement.

The order starts with assets, followed by liabilities and stockholders' equity from the balance sheet and revenue and expenses from income statement.

So, the correct order is stated in option (b).

Answer:

Option b

Step-by-step explanation:

In the chart of accounts, each account number has two digits. The first digit indicates the major account group to which the account belongs.

In the chart of accounts

1-Assets,

2-Liabilities

3-Stockholders' Equity

4-Revenues

5-Expenses

Form the given options, only option b represents the correct account numbers.

Therefore, the correct option is b.

Answer:

  (3, 3) and (15, 15)

Step-by-step explanation:

The points equidistant from the given point and the y-axis lie on the parabola that has (3,6) as its focus and the y-axis as its directrix. The equation for that can be simplified from ...

  (x -3)^2 +(y -6)^2 = x^2

  -6x +9 +y^2 -12y +36 = 0 . . . . . subtract x^2, eliminate parentheses

We can find the points that lie on the line y=x (equidistant from both axes) by substituting y for x or vice versa. Then we have the quadratic ...

  x^2 -18x +45 = 0 . . . . substitute x for y and collect terms

  (x -3)(x -15) = 0 . . . . factor it

  x = 3 or 15

So, the points of interest are (x, y) = (3, 3) and (x, y) = (15, 15).

Answer:

0.30

Step-by-step explanation:

They are independent, so:

P(A and B) = P(A) P(B)

0.24 = 0.80 P(B)

P(B) = 0.30

Answer:

  see below

Step-by-step explanation:

It's a little tough to draw on regular graph paper because the slope is so steep and the slope is not an integer. Shown below is the graph with a couple of the points labeled.

Final answer:

The equation of the line with a slope of -2 that crosses the y-axis at (0,4) is y = -2x + 4.

Explanation:

To find the equation of a line that crosses the y-axis at (0,4) with a slope of -2, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, m is the slope and b is the y-intercept. Since we are given the y-intercept (0,4), we know b = 4 and we are also given the slope m = -2. Substituting these values into the slope-intercept form gives us the equation:

y = -2x + 4

This equation represents the desired line with a slope of -2 and a y-intercept at 4.

Answer:

(a) Absolute value relationship, f(-5)=6

(b) Linear relationship, g(0.2)=0.3

(c) Absolute value relationship, p(-3)=13

Step-by-step explanation:

A modulas function always represents an absolute value relationship.

A polynomial function with degree 1 is always represents a linear function.

(a)

The given function is

[tex]f(x)=|x-3|-2[/tex]

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-5 in the given function.

[tex]f(-5)=|-5-3|-2\Rightarrow 8-2=6[/tex]

Therefore the value of function at x=-5 is 6.

(b)

The given function is

[tex]g(x)=1.5x[/tex]

It is a linear function, so it represents a linear relationship.

Substitute x=0.2 in the given function.

[tex]g(0.2)=1.5(0.2)=0.3[/tex]

Therefore the value of function at x=0.2 is 0.3.

(c)

The given function is

[tex]p(x)=|7-2x|[/tex]

It is a modulas function, so it represents an absolute value relationship.

Substitute x=-3 in the given function.

[tex]p(-3)=|7-2(-3)|\Rightarrow |7+6|=13[/tex]

Therefore the value of function at x=-3 is 13.

Answer:

y = 6

Step-by-step explanation:

Given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 3 when x = 9, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex], thus

y = [tex]\frac{1}{3}[/tex] x ← equation of variation

When x = 18, then

y = [tex]\frac{1}{3}[/tex] × 18 = [tex]\frac{18}{3}[/tex] = 6

Answer:

see explanation

Step-by-step explanation:

Inequalities of the type | x | > a, always have solutions of the form

x < - a or x > a

This can be extended to expressions, that is

14 - 5x < - 8 OR 14 - 5x > 8 ( subtract 14 from both sides of both inequalities )

- 5x < - 22 OR - 5x > - 6

Divide both sides by - 5 , reversing the inequality sign as a consequence

x > [tex]\frac{22}{5}[/tex] OR x < [tex]\frac{6}{5}[/tex]

That is the solution is

x < [tex]\frac{6}{5}[/tex] OR x > [tex]\frac{22}{5}[/tex]

Answer:

Step-by-step explanation:

Inequalities of the type | x | > a, always have solutions of the form

x < - a or x > a

This can be extended to expressions, that is

14 - 5x < - 8 OR 14 - 5x > 8 ( subtract 14 from both sides of both inequalities )

- 5x < - 22 OR - 5x > - 6

Divide both sides by - 5 , reversing the inequality sign as a consequence

x >  OR x <

That is the solution is

x <  OR x >

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The 'Length of a nail' is considered a continuous quantitative variable because it represents measurements, not countable values.

The quantitative variable 'Length of a nail' is a continuous variable. A continuous variable is one where the data represent measurements and can take on any value within a specified range, unlike a discrete variable, which represents countable values. Therefore, the correct answer would be 'B. The variable is continuous because it is not countable.'

To give you an idea, a discrete variable would be something like the number of books in a backpack. Each book represents a countable unit. On the other hand, 'Length of a nail' as a continuous variable could have any length value within a certain feasible range, which is not merely countable.

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The length of a nail is a quantitative continuous variable because it can take on any possible value within its limits and is not just countably infinite.

The length of a nail is a quantitative continuous variable. This is because the length can vary infinitely within its limits and can take on any possible value including measurements like millimeters, centimeters, or inches. Therefore, the correct answer to whether the variable is discrete or continuous is B. The variable is continuous because it is not countable. Just as weights and lengths are continuously variable because they can be measured to any level of precision required for the task at hand, so too is the length of a nail a continuous measure.

Answer:  1. {-2, -3}   2. {-5, 5}   3. {-3, 5}

Step-by-step explanation:

1) First, factor the equation by finding two numbers whose product is 6 and sum is 5.  Then apply the Zero Product Property by setting each product equal to zero and solving for m.

m² + 5m + 6 = 0

                 ∧

                1 + 6 = 7

                2 + 3 = 5   This works!

        (x + 2)(x + 3) = 0

x + 2 = 0      x + 3 = 0

     x = -2           x = -3

2) Factor out the GCF of 5. Notice the remaining factor is the difference of squares (because the middle term is missing and the first and last terms are perfect squares. Then apply the Zero Product Property by setting each product equal to zero and solving for p.

5p² - 125 = 0

5(p² - 25) = 0

5(p +5)(p - 5) = 0

5 ≠ 0    p+ 5 = 0         p - 5 = 0

                 p = -5              p = 5

3) Factor out the GCF of 2. Factor the equation by finding two numbers whose product is -15 and sum is -2.  Then apply the Zero Product Property by setting each product equal to zero and solving for x.

2x² - 4x - 30 = 0

2(x² - 2 - 15) = 0

              ∧

             1 - 15 = -14

             3 - 5 = -2    This works!

     (x + 3)(x - 5) = 0

x + 3 = 0     x - 5 = 0

     x = -3          x = 5

***************************************************

You are allowed a maximum of 3 questions.

Try #4 and #5 on your own.  If you still need help with them, please create a new question and post them.

Answer:

Step-by-step explanation:

Let's split the analysis on two components, horizontal and vertical.

Supposed no air resistence, the horizontal movement is given by the expression [tex] d=25.0 cos20° t[/tex]. Since it travels 50 m, solving for [tex]t[/tex] you get [tex]t=\frac2.0{cos20°} \approx 2 s[/tex].

The vertical movement is given by the expression [tex] h=25.0sin20°t-\frac12gt^2[/tex], where [tex]g=9.81m/s^2[/tex] is the gravitational acceleration. The highest point is reached when the vertical velocity ([tex]v=25.0sin 20° -gt[/tex]) is zero, or at [tex]t=\frac{25.0sin20°}{9.81} \approx 1s. At this time, it's height will be [tex] h= 25.0sin20° (1) -\frac1/2 (9.81) (1^2) \approx 4 m. [/tex]

Please note that the number are heavily approximated, do plug yours in a calculator

Answer:

25%

Step-by-step explanation:

The schools

So,

$2.00 - 100%

$2.50 - x%

Write a proportion

[tex]\dfrac{2.00}{2.50}=\dfrac{100}{x}[/tex]

Cross multiply

[tex]2x=2.5\cdot 100\\ \\2x=250\\ \\x=125\%[/tex]

The markup percent is 125% - 100% = 25%

Reduce the power by applying the identity,

[tex]\sin^2x+\cos^2x=1[/tex]

[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=\int\sin x(1-\cos^2x)\,\mathrm dx[/tex]

Let [tex]u=\cos x\implies\mathrm du=-\sin x\,\mathrm dx[/tex]:

[tex]\implies\displaystyle\int\sin^3x\,\mathrm dx=-\int(1-u^2)\,\mathrm du[/tex]

[tex]=\dfrac{u^3}3-u+C=\boxed{\dfrac{\cos^3x}3-\cos x+C}[/tex]

Final answer:

To find the perpendicular bisector of segment AB with endpoints A(3, 0) and B(–1, 2), first determine the midpoint M, then the slope of AB, and use the negative reciprocal to get the slope of the bisector. The equation of the perpendicular bisector is y = 2x - 1, which intercepts the x-axis at P(0.5, 0). The lengths of PA and PB are both 2.5 units.

Explanation:

To find the equation of the perpendicular bisector of the segment AB, we first need to find the midpoint of AB, which will lie on the bisector. The coordinates of A(3, 0) and B(–1, 2) give us the midpoint M as follows:

Add the x-coordinates of A and B and divide by 2: (3 + (–1))/2 = 2/2 = 1.

Add the y-coordinates of A and B and divide by 2: (0 + 2)/2 = 2/2 = 1.

So the midpoint M is (1, 1).

Next, the slope of AB is (2 - 0)/(-(1) - 3) = 2/(-4) = -1/2. The slope of the perpendicular bisector will be the negative reciprocal of -1/2, which is 2.

The equation of the line with slope 2 passing through (1, 1) is y - 1 = 2(x - 1). Simplifying, we get y = 2x - 1 as the equation of the perpendicular bisector.

Intercepting the x-axis means y = 0, so to find point P where the bisector meets the x-axis, set y to 0: 0 = 2x - 1, which gives x = 0.5. Therefore, point P is (0.5, 0).

Now to find the lengths of PA and PB, we use the distance formula:

Distance PA = √((3 - 0.5)^2 + (0 - 0)^2) = √(2.5^2) = 2.5.

Distance PB = √(((-1) - 0.5)^2 + (2 - 0)^2) = √(1.5^2 + 2^2) = √(2.25 + 4) = √6.25 = 2.5.

Hence, PA and PB both measure 2.5 units.

Answer:

  you have described a "ray"

Step-by-step explanation:

A "ray" is a half-line: all the points on a line that are to one side of its terminal point. (The terminal point is included in the ray.)

The total number of coins required to fill all the [tex]64[/tex] boxes are [tex]\boxed{\bf 18446744073709551615}[/tex].

Further explanation:

In a chessboard there are [tex]64[/tex] boxes.

The objective is to determine the total number of coins required to fill the [tex]64[/tex] boxes in chessboard.

In the question it is given that in the first box there is [tex]1[/tex] coin, in the second box there are [tex]2[/tex] coins, in the third box there are [tex]8[/tex] coins and it continues so on.

A sequence is formed for the number of coins in different boxes.

The sequence formed for the number of coins in different boxes is as follows:

[tex]\boxed{1,2,4,8,...}[/tex]

The above sequence can also be represented as shown below,

[tex]\boxed{2^{0},2^{1},2^{2},2^{3},...}[/tex]

It is observed that the above sequence is a geometric sequence.

A geometric sequence is a sequence in which the common ratio between each successive term and the previous term are equal.

The common ratio [tex](r)[/tex] for the sequence is calculated as follows:

[tex]\begin{aligned}r&=\dfrac{2^{1}}{2^{0}}\\&=2\end{aligned}[/tex]

The [tex]n^{th}[/tex] term of a geometric sequence is expressed as follows:

[tex]\boxed{a_{n}=ar^{n-1}}[/tex]

In the above equation [tex]a[/tex] is the first term of the sequence and [tex]r[/tex] is the common ratio.

The value of [tex]a[/tex] and [tex]r[/tex] is as follows:

[tex]\boxed{\begin{aligned}a&=1\\r&=2\end{aligned}}[/tex]

Since, the total number of boxes are [tex]64[/tex] so, the total number of terms in the sequence is [tex]64[/tex].

To obtain the number of coins which are required to fill the [tex]64[/tex] boxes we need to find the sum of sequence formed as above.

The sum of [tex]n[/tex] terms of a geometric sequence is calculated as follows:

[tex]\boxed{S_{n}=a\left(\dfrac{r^{n}-1}{r-1}\right)}[/tex]

To obtain the sum of the sequence substitute [tex]64[/tex] for [tex]n[/tex], [tex]1[/tex] for [tex]a[/tex] and [tex]2[/tex] for [tex]r[/tex] in the above equation.

[tex]\begin{aligned}S_{n}&=1\left(\dfrac{2^{64}-1}{2-1}\right)\\&=\dfrac{18446744073709551616-1}{1}\\&=18446744073709551615\end{aligned}[/tex]

Therefore, the total number of coins required to fill all the [tex]64[/tex] boxes are [tex]\boxed{\bf 18446744073709551615}[/tex].

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Answer details:  

Grade: High school  

Subject: Mathematics  

Chapter: Sequence

Keywords: Series, sequence, logic, groups, next term, successive term, mathematics, critical thinking, numbers, addition, subtraction, pattern, rule., geometric sequence, common ratio, nth term.

Coins on the chessboard follow a doubling pattern. In the nth box, the coins can be expressed as [tex]\(2^{(n-1)}[/tex]. The total coins for all 64 boxes is [tex]2^{63}[/tex].

Certainly, let's break down the doubling pattern of coins in each chessboard box, expressed in exponential form:

1. **First Box (kotak pertama):

  - Number of coins: [tex]\(2^0 = 1\)[/tex] (2 raised to the power of 0).

2. **Second Box (kotak kedua):

  - Number of coins: [tex]\(2^1 = 2\)[/tex] (2 raised to the power of 1).

3. **Third Box (kotak ketiga):

  - Number of coins: [tex]\(2^2 = 4\)[/tex] (2 raised to the power of 2).

4. **Fourth Box (kotak keempat):

  - Number of coins: [tex]\(2^3 = 8\)[/tex] (2 raised to the power of 3).

The pattern continues, doubling the number of coins with each subsequent box.

For the n-th box, the number of coins is given by [tex]\(2^{(n-1)}[/tex], where n is the box number.

So, the exponential form for the number of coins in each chessboard box is [tex]\(2^{(n-1)}[/tex], where n is the box number ranging from 1 to 64.

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Que. A father challenges his child to calculate the total number of coins needed to fill a chessboard. In the first box, 1 coin is placed, 2 coins in the second box, 4 coins in the third, and so on, up to the 64th box. Help the child determine the doubling pattern of coins in each chessboard box, expressed in exponential form.

Answer: 12/2652 or 1/221

Step-by-step explanation:

There are 4 kings in a deck

So the probability of getting a king would be

4/52 then after receiving a king and not replacing you will the have a 3/51 chance

So all together you will have a:

4/52 * 3/51 = 12/2652 or simplified 1/221

Hope this helps

The probability of drawing a King from a deck of 52 cards without replacement and then drawing a second King is 1/221.

We have,

To find the probability of drawing a King from a deck of 52 cards without replacement, and then drawing a second King, we can calculate it as follows:

The probability of drawing a King as the first card is 4/52 since there are 4 Kings in a deck of 52 cards.

After removing one King from the deck, there are now 51 cards left, including 3 Kings.

The probability of drawing a second King, given that a King has already been drawn, is 3/51.

To find the overall probability of both events occurring, we multiply the individual probabilities:

(4/52) * (3/51) = 12/2652

Simplifying the fraction, we have:

12/2652 = 1/221

Therefore,

The probability of drawing a King from a deck of 52 cards without replacement and then drawing a second King is 1/221.

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Answer:

The median of this data set is 1

Step-by-step explanation:

1) First sort the list of all the data set from the smallest to the largest

so we have (0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,5,10)

2) Find the elements in the middle of the list

(0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,3,3,5,10)

When you find an unique number your work is done, but when this happens the median is the average of the two elements in the middle of the sorted list

Hence the median is 1

To calculate Kerry's net pay, determine the gross pay, calculate each deduction, and subtract them from the gross pay. Kerry's net pay is $341.96 after accounting for deductions such as federal income tax, Social Security and Medicare taxes, health insurance premiums, and union dues.

To calculate Kerry's net pay for the last week, we first need to determine his gross pay by multiplying the number of hours worked by his hourly rate. Then, we calculate each deduction and subtract them from the gross pay to find the net pay.

Gross pay: 46 hours * $9.60/hour = $441.60

Federal Income Tax (10%): $441.60 * 10% = $44.16

Social Security Tax (6.2%): $441.60 * 6.2% = $27.38

Medicare Tax (1.45%): $441.60 * 1.45% = $6.40

After summing up the deductions for health insurance premiums ($12.20) and union dues ($9.50), we subtract all deductions from the gross pay to find Kerry's net pay:

Total deductions = $44.16 + $27.38 + $6.40 + $12.20 + $9.50 = $99.64

Net pay: $441.60 - $99.64 = $341.96

Therefore, Kerry's net pay for last week was $341.96.

Kerry’s net pay for last week was $342

Kerry worked 46 hours last week and his hourly rate is $9.60

Thus Total amount Kenny earned would be,

[tex]46*9.60=441.6[/tex]

Thus '441.6' is the total amount Kenny was paid

Now given that federal income tax was applied at the rate of 10% on his salary

Thus calculating the amount he paid in federal tax would be,

[tex]441.6*\frac{10}{100}=441.6*0.1\\ 441.6*\frac{10}{100}=44.16[/tex]

Thus he paid a total of $44.16 in federal tax

Now he also paid Social Security tax at the rate of 6.2%

Thus calculating the amount he paid in social security tax would be,

[tex]441.6*\frac{6.2}{100}=441.6*0.062\\ 441.6*\frac{10}{100}=27.38[/tex]

Thus he paid a total of $27.38 in social security tax

Now he also paid Medicare tax at the rate of 6.2%

Thus calculating the amount he paid in Medicare tax would be,

[tex]441.6*\frac{1.45}{100}=441.6*0.0145\\ 441.6*\frac{10}{100}=6.4032[/tex]

Thus he paid a total of $6.4032 in Medicare tax

He also paid health insurance premiums of $12.20, and union dues of $9.50

Thus now calculating the total amount she paid in form of taxes and other expenses would be,

[tex]44.16+27.38+6.4032+12.20+9.50=99.6432[/tex]

Thus she paid a total of $99.6432 in expenses form

Now the net pay for Kenny would be his expenses subtracted from his salary

[tex]441.6-99.6432=341.9568[/tex]

Thus approximately his net pay would be $342

Answer:

The percentile is 27 .

Solution:

All the values in the series are in order small to large, ,22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 43, 44, 45, 46, 47, 48, 50, 53

There are total 18 numbers in the problem.

To find the index multiply [tex]27\%[/tex] by 18.

So, the index is [tex](0.27\times18)=4.8\approx5[/tex]

Now counting the data set from left to right i.e, from smallest to largest the 5th number of the series is 27.

Hence, the [tex]27^{th}[/tex] percentile of the data set is 27.

Answer:

Midpoint = (  (x1+x2)/2 , (y1+y2)/2 )

Step-by-step explanation:

Please upload the line segment otherwise, you can use the equation above to solve for it.

Answer:

Looking at the mean, the median and the mode, cars are more efficient on a highway than in a city

Step-by-step explanation:

First, we calculate the average (mean) performance by adding all values and dividing the sum by the number of values added.

[tex]Mean_{city} =\frac{(16.2+16.7+15.9+14.4+13.2+15.3+16.8+16.0+16.1+15.3+15.2+15.3+16.2)mpg }{13} =15.6 mpg[/tex]

[tex]Mean_{highway} =\frac{(19.4+20.6+18.3+18.6+19.2+17.4+17.2+18.6+19.0+21.1+19.4+18.5+18.7 )mpg }{13} =18.9 mpg[/tex]

Then, to know what the median is, we have to order from least to greatest and look the middle value, i.e. half of the values will be higher than the median and half will be lower.

For the mode, we have to look up what is the most repeated value in our list.

For city performances:

The median value is 15.9 miles per gallon, and the mode is 15.3 miles per gallon.

For highway performances:

The median value is 18.7 miles per gallon, and the mode is 18.6 and 19.4 miles per gallon.

We can say then, that looking at the mean, the median and the mode, cars are more efficient on a highway than in a city and that the least-consuming car in a city still is worst  in terms of efficiency than the worst-performing in a highway.

Final answer:

The mean, median, and mode can be used to compare the performance of automobiles in city and highway driving conditions in terms of miles per gallon (mpg). Based on these measures, we can say that the performance of automobiles is generally better in highway driving conditions compared to city driving conditions.

Explanation:

The mean, median, and mode can be used to compare the performance of automobiles in city and highway driving conditions in terms of miles per gallon (mpg).

The mean is calculated by summing up all the mpg values and dividing it by the number of values. For city driving, the mean is 15.66 mpg, and for highway driving, the mean is 18.81 mpg.

The median is the middle value in a set of ordered numbers. For city driving, the median is 15.3 mpg, and for highway driving, the median is 18.6 mpg.

The mode is the value that appears most frequently in a set of numbers. For both city and highway driving, the mode is 15.3 mpg.

Based on these measures, we can say that the performance of automobiles is generally better in highway driving conditions compared to city driving conditions, as the mean and median mpg values are higher for highway driving.