To win the jackpot, 4 different numbers are randomly selected from 1 to 46 and one number from 1 to 22. The order of the first 4 numbers does not matter. What is the probability of winning the jackpot on one try?

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:

Part a) 9*5+2

Part b) 7*6+4

Part c) Lena is correct

Part d) see the explanation

Step-by-step explanation:

The complete question in the attached figure

Part a) Write a numerical expression to represent Lena’s way of counting

To represent Lena’s way of counting, multiply the number of stacks by the number of pennies in each stack plus the number of pennies left over

Let

x -----> the number of stacks

y ----> the number of pennies in each stack

z ----> the number of pennies left over

so

[tex]xy+z[/tex]

we have

x=9 stacks

y=5 pennies

z=2 pennies

substitute

[tex]9*5+2[/tex]

Part b) Write a numerical expression to represent her mother's way

To represent her mother’s way of counting, multiply the number of stacks by the number of pennies in each stack plus the number of pennies left over

Let

x -----> the number of stacks

y ----> the number of pennies in each stack

z ----> the number of pennies left over

so

[tex]xy+z[/tex]

we have

x=7 stacks

y=6 pennies

z=4 pennies

substitute

[tex]7*6+4[/tex]

Part c) Lena thinks her mother must have been working with fewer pennies than she was.  Is Lena correct? 

we have that

Lena’s expression

[tex]9*5+2[/tex]

Simplify

[tex]9*5+2=47[/tex]

Her mother’s expression

[tex]7*6+4[/tex]

Simplify

[tex]7*6+4=46[/tex]

therefore

Lena’s expression is more.

Lena is correct

Part d) Use a  < ,  > , or  =  symbol to show how the two expressions compare

[tex]9*5+2 > 7*6+4[/tex]

[tex]47 > 46[/tex]

The number 47 is greater than the number 46

therefore

The symbol is  " >"

Answer:

Lee has more pizza

Lee has 2.24 in^2 more than John

Step-by-step explanation:

step 1

Find the area of each slice of pizza

[tex]A=\frac{1}{8}\pi r^{2}[/tex]

we have

[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=\frac{1}{8}\pi 8^{2}[/tex]

[tex]A=8\pi\ in^{2}[/tex]

step 2

Find the area of John's part (area of shaded triangle)

The measure of the central angle of each slice of pizza is equal to

[tex]360\°/8=45\°[/tex]

so

the height of triangle is equal to the base

Let

x ---->the base of the shaded triangle

[tex]cos(45\°)=\frac{x}{r}[/tex]

[tex]cos(45\°)=\frac{x}{8}[/tex]

Remember that

[tex]cos(45\°)=\frac{\sqrt{2}}{2}[/tex]

substitute

[tex]\frac{\sqrt{2}}{2}=\frac{x}{8}[/tex]

solve for x

[tex]x=4\sqrt{2}\ in[/tex]

Find the area of shaded triangle

[tex]A=(1/2)(4\sqrt{2})(4\sqrt{2})=16\ in^2[/tex]

step 3

Find the area of Lee's part

The area of Lee's part is equal to the area of two slices of pizza minus the area of two triangles

so

[tex]2(8\pi)-2(16)=(16\pi-32)\ in^2[/tex]

assume

[tex]\pi =3.14[/tex]

[tex](16(3.14)-32)=18.24\ in^2[/tex]

so

Lee's part is greater than John part's

Find the difference

[tex]18.24-16=2.24\ in^2[/tex]

therefore

Lee has more pizza

Lee has 2.24 in^2 more than John

Without exact dimensions of Lee's cut, we can't calculate the precise difference in area after he cuts off an edge, but John likely has more pizza since his slice is unmodified.

The student's question involves comparing areas of pizza slices after one has been modified by cutting off an edge. To answer who has more pizza and by how much, we need to calculate the area of the pizza slices. The original pizza is 16 inches in diameter, and when divided into 8 equal slices, each slice is a sector of a circle with a central angle of 45 degrees. If Lee cuts off an edge and John takes an unmodified triangular slice, John would likely have more pizza because Lee's slice has been reduced in size. However, without knowing the exact dimensions of the removed edge, we can't calculate the precise difference in area.

]

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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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.

Step-by-step explanation:

t=2+5×j

j=5

t=2+5×5

t=27

Tom has 2 more than 5 times what Jane has, so you would multiply the amount Jane has by 5, then add 2 to that:

Tom  = 5(5) +2

Tom = 25 +2

Tom = 27 CD's.

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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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:

Rachel's score is 2.3333 standard deviations above the mean

Step-by-step explanation:

GRE scores are normally distributed

Let be G the random variable ''Gre scores''

G  ~ N (mean,standard deviation)

G ~ N (600,30)

Rachel scored 670 on the analytic portion of the GRE.

670 - 600 will be the score above the mean

670 - 600 = 70

To find this in terms of standard deviation we divide by the standard deviation

70/standard deviation = 70/30 = 7/3 = 2.33333333 standard deviations

Rachel's GRE score is approximately 2.33 standard deviations above the mean. The calculation is made by subtracting the mean from the observed score and dividing this by the standard deviation.

The subject of this question pertains to the mathematical concept of Z-scores, used in statistics to measure how many standard deviations an element is from the mean. In the case of Rachel's GRE score, we can calculate the number of standard deviations her score is above the mean using the formula z = (X - μ) / σ where:

By substituting these values into the formula, we get:

z = (670 - 600) / 30 = 70 / 30 = 2.33

This means that Rachel's score is approximately 2.33 standard deviations above the mean.

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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:

sorry  can you write it down and take a pic of it

please that is the only way i can answer it

Step-by-step explanation:

Final answer:

To calculate the volume of a cylinder with a radius of (x+4) cm and height of 5 cm, substitute the values into the formula V = πr²h, resulting in V = 5π(x² + 8x + 16), which gives the volume in standard form.

Explanation:

The question is about finding the volume of a cylinder with a given radius of (x+4) cm and a height of 5 cm. The formula to calculate the volume of a cylinder is V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder.

To find the volume with the given dimensions, we substitute 'r' with (x + 4) and 'h' with 5. This results in:

V = π(x + 4)² × 5 = π(x² + 8x + 16) × 5

Simplifying this expression gives us:

V = 5π(x² + 8x + 16)

This is the volume of the cylinder in standard form, expressed as a function of x. Therefore, the volume depends on the value of x, and this expression allows us to calculate it for any given 'x'.

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 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:

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:

  see below for the stretched graph; see the second attachment for the functions

Step-by-step explanation:

The transformation ...

  g(x) = f(x/a)

represents a horizontal stretch of f(x) by a factor of "a". You want a stretch by a factor of 4, so you can use a=4:

  g(x) = f(x/4)

_____

Horizontal stretch by a factor of 4 means all the points on the graph of g(x) are 4 times as far from they y-axis as they are on the graph of f(x). That is, x must be 4 times as large to give the same y-value.

The graphs of f(x) and g(x) are shown in the second attachment, along with their equations.

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.

Answer:

Let's replace the h(x) function in g(x) and then use 74 as a result on the axis y. The correct answer is 4 .

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.)

Answer:

a) ∀x∃y ¬∀zT(x, y, z)

∀x∃y ∃z ¬T(x, y, z)

b) ∀x¬[∃y (P(x, y) ∨ Q(x, y))]

∀x∀y ¬ [P(x, y) ∨ Q(x, y)]

∀x∀y [¬P(x, y) ^ ¬Q(x, y)]

c) ∀x ¬∃y (P(x, y) ^ ∃zR(x, y, z))

∀x ∀y ¬(P(x, y) ^ ∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ¬∃zR(x, y, z))

∀x ∀y (¬P(x, y) v ∀z¬R(x, y, z))

d) ∀x¬∃y (P(x, y) → Q(x, y))

∀x∀y ¬(P(x, y) → Q(x, y))

∀x∀y (¬P(x, y) ^ Q(x, y))

Answer:

a) ∃x∀y∃z~T(x, y, z)

b) ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∃x∀y(P(x, y) → ~Q(x, y))

Step-by-step explanation:

The negation of a is written as ~a.

Note the following properties that are going to be applied in the problems here :

~(P → Q) = P → ~Q

De Morgan's Laws

~(P ∨ Q) = ~P ∧ ~Q

~(P ∧ Q) = ~P ∨ ~Q

~∃xP = ∀xP

~∀xP = ∃xP

So back to the original problem.

a) ∀x∃y∀zT(x, y, z)

We have the negation as

~[∀x∃y∀zT(x, y, z)]

= ∃x~∃y∀zT(x, y, z)

= ∃x∀y∀~zT(x, y, z)

= ∃x∀y∃z~T(x, y, z)

b) ∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)

Negation is:

~[∀x∃yP(x, y) ∨ ∀x∃yQ(x, y)]

= ~∀x∃yP(x, y) ∧ ~∀x∃yQ(x, y)

= ∃x~∃yP(x, y) ∧ ∃x~∃yQ(x, y)

= ∃x∀y~P(x, y) ∧ ∃x∀y~Q(x, y)

c) ∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

Negation is:

~[∀x∃y(P(x, y) ∧ ∃zR(x, y, z))]

= ~∀x∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x~∃y(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y~(P(x, y) ∧ ∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ~∃zR(x, y, z))

= ∃x∀y(~P(x, y) ∨ ∀z~R(x, y, z))

d) ∀x∃y(P(x, y) → Q(x, y))

Negation is:

~[∀x∃y(P(x, y) → Q(x, y))]

= ~∀x∃y(P(x, y) → Q(x, y))

= ∃x~∃y(P(x, y) → Q(x, y))

= ∃x∀y~(P(x, y) → Q(x, y))

= ∃x∀y(P(x, y) → ~Q(x, y))

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:

The sampling technique used here is Cluster Sampling.

Step-by-step explanation:

Since here Population is divided into different parts called grid and whole elements of some selected grid is taken as sample. So, Cluster Sampling is used here.

Further the different types of sampling we have are:

Simple Random Sampling is the sampling where samples are chosen randomly, where each unit has an equal chance of being selected in a sample.

If the population is divided into a different group called cluster and all elements of clusters are selected as a sample then it is Cluster Sampling.

In Convenience sampling, observers collect the sample as his\her convenience.

In Systematic Sampling sample is chosen by some criteria like he\she is taken every 10th unit as a sample from the population.

In Stratified Sampling population is divided into several groups such that within the group it is homogeneous and between the group it is heterogeneous. And now a selection of each stratum and unit has an equal chance of selection.

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:

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.

Answer:

144 malt balls will fit in the carton

Step-by-step explanation:

* Lets explain how to solve the problem

- To solve the problem we must to know each dimensions of the

 cartoon will fit how many balls

- To do that divide each dimension by the diameter of the ball

∵ The diameter of the chocolate malt ball is 0.75 inches

∵ The dimensions of the carton are 3 inches , 3 inches , 7 inches

* Lets find how many balls will fit in the side of 3 inches

∵ 3 ÷ 0.75 = 4

∴ There are 4 balls will fit in the side of 3 inches

∵ Two dimensions of the carton are 3 inches

∴ There 4 × 4 balls fit in the base of the carton

∵ The height of the carton is 7

* Lets find how many balls can fit in the height

∵ 7 ÷ 0.75 = 9.3333

∴ 9 balls can fit the height of the carton

∴ There are 4 × 4 × 9 balls will fit in the carton

∴ The number of the balls = 4 × 4 × 9 = 144 balls

* 144 malt balls will fit in the carton

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].

Learn more:

1. A problem on greatest integer function https://brainly.com/question/8243712  

2. A problem to find radius and center of circle https://brainly.com/question/9510228  

3. A problem to determine intercepts of a line https://brainly.com/question/1332667  

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.

For more such questions on chessboard:

https://brainly.com/question/29504883

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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: we can use the folowing polynomial.

P(x) = [tex]\frac{y1 (x - x2)(x -x3)}{(x1 - x2)(x1-x3)}[/tex] + [tex]\frac{y2 (x - x1)(x -x3)}{(x2 - x1)(x1-x3)}[/tex] + [tex]\frac{y3 (x - x2)(x -x1)}{(x3 - x2)(x3-x1)}[/tex]

you can see that P(x1) = y1

                          P(x2) = y2

                          P(x3) = y3

this is a Lagrange polynomial.

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.

Explanation:

The term containing the variable, e^-t has a range from 0 to infinity, as all exponential terms do.

For t → -∞, e^-t → ∞ and the value of the rational expression becomes 5/∞ ≈ 0. That is, there is a horizontal asymptote at f(t)=0 for large negative values of t.

For t → ∞, e^-t → 0 and the value of the rational expression becomes approximately 5/2. That is, there is a horizontal asymptote at f(t) = 5/2 for large positive values of t.

Essentially, the curve is "S" shaped, with a smooth transition between 0 and 5/2 for values of t that make 3e^-t have values within an order of magnitude of the other term in the denominator, 2.

At t=0, 3e^-t = 1 and the denominator is 2+3=5. That is, f(0) = 5/5 = 1. Of course, the curve will cross the line f(t) = 5/4 (halfway between the asymptotes) when 3e^-t = 2, or t=ln(3/2)≈0.405. The curve is symmetrical about that point.

You can sketch the graph by finding values of t that give you points on the transition. Typically, you would choose t such that 3e^-t will be some fraction or multiple of 2, say 1/10, 1/3, 1/2, 1, 2, 3, 10 times 2.

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f(t) is called a "logistic function." It models a situation where growth rate is proportional both to population size and the difference between population size and carrying capacity. In public health terms, it models the spread of disease when that is proportional to the number of people exposed and to the number not yet exposed.