The height of Mountain P is 1,086 feet.The height of Mountain Q is 4 times the height of Mountain P.The area model shown below represents one way to find the height of Mountain Q. What are missing values for a,b,c in the model?

Answer:

The answer to your question is letter A

Step-by-step explanation:

The first inequality is a circle with center (0,0) and radius 4, the inequality indicates that the solution must be greater than the radius (4) so the solutions are letters A and D.

The second inequality is the line, the solutions must be the numbers below the line, areas A and B.

The region where both inequalities cross is the solution  letter A.

Answer:

Correct option (B).

Step-by-step explanation:

A 95% confidence interval for a population parameter implies that there is 0.95 probability that the population parameter is contained in that interval.

Or, if 100, 95% confidence intervals are created then 95 of those intervals would contain the population parameter with probability 0.95.

In this question the 95% confidence interval was created for population proportion of all United States citizens who were optimistic about the economy.

Then this 95% confidence interval implies that if 100 such confidence intervals were created then 95 of those would consist of the true proportion of US citizens who were optimistic about the economy..

Thus, the correct option is (B).

Answer:

We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

Step-by-step explanation:

Answer:

The family would have [tex]\frac34[/tex] of the watermelon for supper.

Step-by-step explanation:

Given:

Amount of watermelon in refrigerator = [tex]\frac14[/tex]

Amount of water melon brought form grocery store =[tex]\frac12[/tex]

We need to find the fraction of water melon family have for supper.

Solution:

Now we can say that;

the fraction of water melon family have for supper is equal to sum of Amount of watermelon in refrigerator and Amount of water melon brought form grocery store.

framing in equation form we get;

the fraction of water melon family have for supper = [tex]\frac14+\frac12[/tex]

Now taking LCM to make the denominator common we get;

the fraction of water melon family have for supper = [tex]\frac{1\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{1}{4}+\frac24[/tex]

Now denominators are common so we will solve for numerator we get;

the fraction of water melon family have for supper = [tex]\frac{1+2}{4}=\frac34[/tex]

Hence the family would have [tex]\frac34[/tex] of the watermelon for supper.

Answer:

Solution set {x|x<8}

Step-by-step explanation:

0.35x - 4.8<5.2- 0.9x

0.35x+0.9x<5.2+4.8

1.25x<10

x<10/1.25

x<8

Solution set {x|x<8}

Answer:

x < 8

Step-by-step explanation:

0.35x - 4.8 < 5.2- 0.9x

0.35x + 0.9x < 5.2 + 4.8

1.25x < 10

x < 10/1.25

x < 8

Answer:

X is greater than or equal to 15

Step-by-step explanation:

Final answer:

The inequality x >= 15 represents Samuel's goal of eating at least 15 grams of protein each day. Protein-rich foods like chicken breast and Greek yogurt are good sources of protein.

Explanation:

The inequality representing the situation is: x >= 15

To meet his goal of eating at least 15 grams of protein each day, Samuel should eat at least 15 grams of protein daily.

Examples of protein-rich foods include:

3 ounces of chicken breast: about 25 grams of protein

1 cup of Greek yogurt: approximately 20 grams of protein

Answer:

thats too long to read but good luck!

Step-by-step explanation:

Answer:

d: 99.7

Step-by-step explanation:

We know the mean is 1515. we know the standard devation is 15. both of 1560 and 1470 are both 3 standar devations away from the mean. on a table this would show almost all of the table. hence 99.7. Now im not 100% on this as i ahve the same question on a quiz but if i get it write i will add an answer or comment to this.

Percentage of buckets contain between 1470 and 1560 pieces of popcorn= 99.7%

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

The following formula is a common strategy to calculate a percentage:

To learn more about percentage, refer

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Answer:

The two equivalent expression are  [tex]T=6(9.5+1.5)[/tex] and [tex]T=6\times9.5+6\times1.5[/tex].

The Total cost at state fair will be $66.

Step-by-step explanation:

Given:

Number of friends = 6

Cost for admission for each at the fair = $9.50

Cost of each person ride on Ferris wheel = $1.50

We need to find the two equivalent expressions and then find the total cost.

Solution:

Let the Total Cost be denote by 'T'.

So we can say that;

Total Cost will be equal to Number of friends multiplied by sum of Cost for admission for each at the fair and Cost of each person ride on Ferris wheel.

framing in equation form we get;

[tex]T=6(9.5+1.5)[/tex]

Now Applying Distributive property we get;

[tex]T=6\times9.5+6\times1.5[/tex]

Hence The two equivalent expression are [tex]T=6(9.5+1.5)[/tex] and [tex]T=6\times9.5+6\times1.5[/tex].

On Solving the above equation we get;

[tex]T=57+9= \$66[/tex]

Hence The Total cost to state fair will be $66.

Answer:

C. x>0

Step-by-step explanation:

The given quotient is

[tex] \frac{ \sqrt{7 {x}^{2} } }{ \sqrt{3x} } [/tex]

Recall that the expression in the denominator should not be equal to zero.

Also the expression under the radical should be greater than or equal to zero.

This means that we should have:

[tex] \frac{7 {x}^{2} }{3x} \: > \: 0[/tex]

This implies that:

[tex]x \: > \: 0[/tex]

Option C is correct

Answer:

84

Step-by-step explanation:

Area of a rectangle : A = bh

5 x 6 = 30

Area of a trapezoid : A = 1/2 (b1 + b2) h

b1: 7 + 5 = 12

b2:  15

h: 10 - 6 = 4

12 + 15 = 27

27 x 4 x .5 = 54

Add the areas up:

30 + 54 = 84

Answer: 16 single crust apple pies and double crust apple pies were sold.

Step-by-step explanation:

Let x represent the number of single crust apple pies sold on a Friday.

Let y represent the number of double crust apple pies sold on a Friday.

The total number of pies sold on a busy Friday was 36. This means that

x + y = 36

Grandma's bakery sells single crust apple pies for $6.99 in double crust cherry pies for $10.99. The total amount that was collected that Friday was $331.64. This means that

6.99x + 10.99y = 331.74- - - ---- - - - -1

Substituting x = 36 - y into equation 1, it becomes

6.99(36 - y) + 10.99y = 331.74

251.64 - 6.99y + 10.98y = 331. 74 - 3 31.74

251.64 - 331.74

4y = 80

y = 80/4 = 20

x = 36 - y i= 36 - 20

x = 16

Answer:

13 r 3

Step-by-step explanation:

Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.

To find the total length of the two boards, Racheal needs to add the lengths of the two boards together.

The length of the first board is [tex]\(1 \frac{7}{12}\)[/tex] feet, and the length of the second board is [tex]\(2 \frac{11}{12}\)[/tex] feet.

To add these lengths together, we first need to convert them to improper fractions:

[tex]\[ 1 \frac{7}{12} = \frac{12}{12} + \frac{7}{12} = \frac{19}{12} \][/tex]

[tex]\[ 2 \frac{11}{12} = \frac{24}{12} + \frac{11}{12} = \frac{35}{12} \][/tex]

Now, to find the total length, we add the lengths of the two boards:

[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} \][/tex]

To add fractions, we need a common denominator, which in this case is [tex]\(12\)[/tex].

[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} = \frac{19 + 35}{12} = \frac{54}{12} \][/tex]

Now, we simplify the fraction:

[tex]\[ \text{Total length} = \frac{54}{12} = 4 \frac{1}{2} \][/tex]

So, Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.

Final answer:

To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight. The probability is 0.1525.

Explanation:

To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight.

First, we need to calculate the probability that a passenger shows up for the flight. Since the airline believes that 5% of passengers fail to show up, the probability that a passenger shows up is 1 - 0.05 = 0.95.

Next, we can use the binomial distribution to calculate the probability that more than 265 passengers show up. The formula for the binomial distribution is P(X > k) = 1 - P(X <= k), where X is the number of passengers who show up and k is the maximum number of passengers the plane can hold (265).

Using the binomial distribution, we can calculate the probability that more than 265 passengers show up as P(X > 265) = 1 - P(X <= 265) = 1 - binomcdf(275, 0.95, 265) = 0.1525.

The sequence of transformations is: reflect across the x-axis, rotate 180 degrees about the origin, and translate 4 units down.

The sequence of transformations that maps triangle ABC to triangle A'B'C' is:

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Answer:

Therefore option A.) 0 is correct.

Step-by-step explanation:

The graph is attached.

The solution of the equations as seen from the intersection of the equations in the graph is (0,2).

Therefore x  = 0 is the solution which gives y = 2 for both equations.

Therefore option A.) 0 is correct.

The answer is in the attachment

Final answer:

Using the Pythagorean theorem, the calculation shows that the wire should be attached 10 feet up the pole to support it if the wire is 26 feet long and attached to the ground 24 feet away from the base of the pole.

Explanation:

The question asks how high up the pole a wire should be attached if the pole is supported by a wire that is 26 feet long and is attached to the ground 24 feet away from the base of the pole. This scenario forms a right triangle with the ground and the pole as the perpendicular sides, and the wire as the hypotenuse. To solve for the height of the pole where the wire should be attached (the vertical side of the triangle), we can use the Pythagorean theorem which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): [tex]a^2 + b^2 = c^2[/tex].

Given that the distance from the pole to the point where the wire is attached to the ground (b) is 24 feet and the length of the wire (c) is 26 feet, we can set up the equation as follows:

[tex]24^2 + a^2 = 26^2[/tex]
576 + [tex]a^2[/tex] = 676
[tex]a^2[/tex] = 676 - 576
[tex]a^2[/tex] = 100
a = [tex]\sqrt{100}[/tex]
a = 10
Thus, the wire should be attached 10 feet up the pole.

This is based on the mathematical concept of geometric series, where in theoretical terms Mathias would never reach the door because he keeps moving half the remaining distance each time. Although, in practical terms, there comes a point where the remaining distance becomes negligible.

The situation you're describing is an example of a geometric series scenario in mathematics. In this case, where Mathias walks half the distance to the door each time, is often referred to as Zeno's paradox.

Zeno's paradox poses the question, how can one ever reach a destination if they are always traveling halfway there? Theoretically, Mathias is never able to fully reach the door, because no matter how small the remaining distance becomes, he is only allowed to cover half. Therefore, there will always technically be some distance remaining.

However, in practical terms, there would come a point where the distance remaining is so minuscule, it could be considered as Mathias having reached the door. For instance, if he started 10 meters away, after the first step he is 5 meters away, then 2.5 meters, then 1.25 meters, and so on. Eventually, this distance becomes negligible.

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The equation to find the value of x in an isosceles triangle with a perimeter of 7.5 m and a side y measuring 2.1 m is 2x + 2.1 = 7.5. Solving for x, we find that x equals 2.7 meters.

To find the value of x for an isosceles triangle with a perimeter of 7.5 meters and the shortest side y measuring 2.1 meters, we can set up an equation. Since it's an isosceles triangle, the two equal sides are both x, and the perimeter is the sum of all sides: x + x + y = 7.5.

We can substitute y with 2.1 m to get 2x + 2.1 = 7.5. Solving for x, we subtract 2.1 from both sides to obtain 2x = 5.4, and then divide both sides by 2 to find x = 2.7 meters. This is the length of the two equal sides of the triangle.

Answer:

Math will take over Ana's brain at 4.4 hours

Step-by-step explanation:

Exponential Grow

The population of the nanobots follows the equation  

[tex]p(t) = 5\cdot 2^t[/tex]

We must find the value of t such that the population of nanobots is 106 or more, that is

[tex]5\cdot 2^t\geq 106[/tex]

We'll solve the equation

[tex]5\cdot2^t= 106[/tex]

Dividing by 5

[tex]2^t= 106/5=21.2[/tex]

Taking logarithms

[tex]log(2^t)= log(21.2)[/tex]

By logarithms property

[tex]t\cdot log(2)= log(21.2)[/tex]

Solving for t

[tex]\displaystyle t=\frac{log21.2} {log2}[/tex]

[tex]t=4.4 \ hours[/tex]

Math will take over Ana's brain at 4.4 hours

It will take 5 hours for the nanobot population to reach 160, utilizing the equation p(t) = 5·[tex]2^t[/tex] and solving for t.

The problem involves determining how long it will take for the population of nanobots, which doubles each hour, to reach a specific number. The equation given for the population of nanobots at any time t is p(t) = 5·[tex]2^t[/tex], where t is the time in hours. We are tasked with finding the value of t when the population reaches or exceeds 160 nanobots.

To solve this, we set the equation equal to 160 and solve for t:

Dividing both sides by 5 gives:

To find t, we need to determine the power of 2 that equals 32. This can be expressed as 2⁵ = 32. Therefore, t = 5. It will take 5 hours for the population of nanobots to reach 160, at which point Ana will think of nothing but math.

Answer:

Step-by-step explanation:

The sum of the two angles is ...

  m∠L + m∠M = 42° +48° = 90°

__

A calculator can show you the sines of these angles.

  sin(42°) ≈ 0.66913

  sin(48°) ≈ 0.74314

_____

The two acute angles of a right triangle always have a sum of 90°.

In triangle LNM, the sum of angles L and M is 90°. The sine values for angles L and M are approximately 0.6691 and 0.7431 respectively.

The sum of the measures of angles L and M can be calculated as follows:

m∠L + m∠M = 42° + 48°

                      = 90°

For a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, using trigonometry:

sin(L) = sin(42°)

         ≈ 0.6691

sin(M) = sin(48°)

           ≈ 0.7431

Thus, the sum of angles L and M is 90°, and the sine values are approximately 0.6691 and 0.7431 respectively.

Answer: e. The population median

Step-by-step explanation:

If repeated intervals are taken for each sample then the 90% of the intervals would actually have the population median in them. The other options like the sample mean, the sample median and the sample standard deviation and population will not be captured as only the population median is captured and confidence intervals can be interpreted in this way.

Answer:

Grand coffee cup = 1469 gm

Jumbo coffee cup = 60 gm

Step-by-step explanation:

Let x be the grande coffee cup and y be the jumbo coffee cup.

Solution:

From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.

So, the equation is.

[tex]23x+51y = 36846[/tex] ---------(1)

From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.

[tex]58x+68y=59460[/tex] ----------(2)

Solve the equation 1 for x.

[tex]23x = 36846-51y[/tex]

[tex]x=\frac{36846}{23}-\frac{51}{23}y[/tex]

[tex]x=1602-\frac{51}{23}y[/tex] ---------(3)

Substitute [tex]x=1602-\frac{51}{23}y[/tex] in equation 2.

[tex]58(1602-\frac{51}{23}y)+68y=59460[/tex]

[tex]92916-\frac{51\times 58}{23}y+68y=59460[/tex]

[tex]-\frac{2958}{23}y+68y=59460-92916[/tex]

[tex]\frac{-2958+1564}{23}y=-33456[/tex]  

[tex]\frac{-1394}{23}y=-33456[/tex]

Using cross multiplication.

[tex]y=\frac{-23\times 33456}{-1394}[/tex]

[tex]y = 55.99[/tex]

y ≅ 60 gram

Substitute y = 60 in equation 3.

[tex]x=1602-\frac{51}{23}\times 60[/tex]

[tex]x=1602-\frac{3060}{23}[/tex]

[tex]x=1602-133.04[/tex]

[tex]x = 1469[/tex] grams

Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm

Final answer:

The answer explains how to calculate the amount of coffee required to make each size (grande and jumbo cups) based on the given information. Answer is 722 grams

Explanation:

The coffee required to make each size:

To ascertain the amount of coffee needed for a jumbo cup, we look at the data indicating 51 jumbo cups utilizing the same 36,846 grams. Dividing this total by the number of jumbo cups, we find that each jumbo cup requires approximately 722 grams of coffee.

Thus, the calculation yields 722 grams of coffee for each jumbo cup, confirming the final answer.

12 ways can one coin flip and one die roll be done.

'Die' is the singular version of the plural word 'dice.'

when we flip coin we got

Heads: 1,2,3,4,5,6

Tails:1,2,3,4,5,6

so total flips are 12 ways.

or  we can do in other way 6 × 2 = 12 ways

Therefore , 12 ways can one coin flip and one die roll be done.

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Answer:

0.08

Step-by-step explanation:

If 8% of drivers receive neither test, then the probability = 8/100 = 0.08

Final answer:

The probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%, determined by subtracting the combined probability of receiving at least one test (92%) from 1.

Explanation:

Calculating the Probability of Receiving Neither Test

To determine the probability that a DWI (driving while intoxicated) suspect receives neither a breath test nor a blood test, we can use the principle of inclusion-exclusion from probability theory. According to the police report, 82% receive a breath test, 34% receive a blood test, and 24% receive both tests.

Firstly, we need to find the probability of a suspect receiving at least one test. We add the probabilities of receiving each test and subtract the probability of receiving both tests to avoid double-counting:

P(Breath or Blood Test) = P(Breath) + P(Blood) - P(Both)
= 0.82 + 0.34 - 0.24
= 0.92

This means that 92% of DWI suspects receive at least one test. To find the probability that a suspect receives neither test, we subtract this value from 1 since the sum of the probabilities of all possible outcomes must equal 1:

P(Neither) = 1 - P(Breath or Blood Test)
= 1 - 0.92
= 0.08 or 8%

Hence, the probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%.

Average speed: 8 feet/second. Total distance traveled: 32 feet. Total time: 4 seconds (from[tex]\( t = 1 \)[/tex] to[tex]\( t = 5 \)).[/tex]

To find the average speed of the car over the interval from[tex]\( t = 1 \) to \( t = 5 \),[/tex] we need to find the total distance traveled by the car during this time interval and then divide it by the total time taken.

Given the formula [tex]\( d = t^2 + 2t \)[/tex] for the distance from the crosswalk in terms of time [tex]\( t \),[/tex]  we'll find the distance at [tex]\( t = 1 \)[/tex]  and[tex]\( t = 5 \),[/tex]  and then subtract to find the total distance traveled:

1. At  [tex]\( t = 1 \):[/tex]

 [tex]\[ d_1 = (1)^2 + 2(1) = 1 + 2 = 3 \text{ feet} \][/tex]

2. At[tex]\( t = 5 \):[/tex]

 [tex]\[ d_5 = (5)^2 + 2(5) = 25 + 10 = 35 \text{ feet} \][/tex]

Now, the total distance traveled is [tex]\( d_5 - d_1 = 35 - 3 = 32 \)[/tex] feet.

The total time taken is [tex]\( t = 5 - 1 = 4 \)[/tex] seconds.

To find the average speed, divide the total distance by the total time:

[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{32 \text{ feet}}{4 \text{ seconds}} = 8 \text{ feet/second} \][/tex]

So, the average speed of the car over the interval from [tex]\( t = 1 \) to \( t = 5 \) seconds is \( 8 \) feet per second.[/tex]

Answer:

The answer to your question is letter C.

Step-by-step explanation:

[tex]\sqrt{50x^{3}}[/tex]     Find the prime factors of 50

                          50   2

                          25   5

                            5   5

                             1

               50 = 2 5²

[tex]\sqrt{5^{2} 2 x^{2} x} = 5 x\sqrt{2x}[/tex]

[tex]\sqrt{32x^{2}}[/tex]    Find the prime factors of 32

                         32   2

                          16   2

                           8   2

                           4   2

                           2   2

                            1

              32 = 2⁴2[tex]\sqrt{32x^{2}} = 2^{2} x\sqrt{2} = 4x\sqrt{2}[/tex]

Division                            [tex]5x\sqrt{2}\sqrt{x} / 4x\sqrt{2}[/tex]

Simplification                  [tex]\frac{5\sqrt{x}}{4}[/tex]

Answer:

C

Step-by-step explanation:

A P E x

Answer:

The required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].

Step-by-step explanation:

Consider the provided information.

A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis,

The probability of yea or nay vote is equal, = [tex]\frac{1}{2}[/tex]

So, we can say that [tex]p=q=\frac{1}{2}[/tex]

Use the formula: [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]

Where n is the total number of trials, x is the number of successes, p is the probability of getting a success and q is the probability of failure.

We want proposal wins by a vote of 7 to 2, that means the value of x is 7.

Substitute the respective values in the above formula.

[tex]P(x)=\binom{9}{7}(\frac{1}{2})^7(\frac{1}{2})^{9-7}[/tex]

[tex]P(x)=\frac{9!}{7!2!}(\frac{1}{2})^7(\frac{1}{2})^{2}[/tex]

[tex]P(x)=\frac{8\times9}{2}\times(\frac{1}{2})^9[/tex]

[tex]P(x)=\frac{4\times9}{2^9}[/tex]

[tex]P(x)=\frac{9}{2^7}[/tex]

[tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex]

Hence, the required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].

Final answer:

The probability that a proposal wins by a 7 to 2 vote in a committee with 9 members is calculated using the binomial probability formula and is approximately 7.03%.

Explanation:

The question posed involves calculating the probability that a proposal wins by a vote of 7 to 2 in a committee with 9 members. We need to consider each vote as an independent 'yea' or 'nay' and find out the number of ways to get exactly 7 'yea' votes out of 9. This is a problem that can be solved using the binomial probability formula:

Binomial Probability Formula: P(X=k) = (n! / (k! * (n-k)!)) * p^k * (1-p)^(n-k), where 'n' is the total number of trials (or votes), 'k' is the number of successful outcomes need (yea votes), and 'p' is the probability of getting a yea vote. Since the voting is random, p = 0.5 assuming each member has an equal likely chance to vote yea or nay.

Plugging the values in, we get P(X=7) = (9! / (7! * 2!)) * 0.5^7 * 0.5^2. Calculating the factorials and powers of 0.5, the probability is:

P(X=7) = 36 * 0.5^9 = 36/512 = 0.0703125.

So, the probability that the proposal wins by a vote of 7 to 2 is approximately 7.03%.

Answer:

17 cm is the side length of the smallest square plate.

Step-by-step explanation:

Length of the square = l

Length of the diagonal = d

Length of chopstick = s = 24 cm

If chopstick is to be fitted along a diagonal . then length of the diagonal will be:

d = s = 24 cm

Applying Pythagoras Theorem :

[tex]l^2+l^2=(24 cm)^2[/tex]

[tex]2l^2=576 cm[/tex]

[tex]l^2=\frac{576}{2} cm^2[/tex]

[tex]l=\sqrt{\frac{576}{2} cm^2}=16,97 cm \approx 17 cm[/tex]

17 cm is the side length of the smallest square plate.

Final answer:

To determine the size of the smallest square plate that a 24-cm chopstick can fit diagonally on without overhang, the Pythagorean theorem is used, yielding a side length of approximately 16.97 cm.

Explanation:

The question asks for the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang. To find this, we can use the Pythagorean theorem in the context of a square. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the hypotenuse is the diagonal, and the other two sides are equal, each being the side length of the square.

Let's denote the side length of the square as s. The diagonal (d) is then given as d = 24 cm. According to the Pythagorean theorem applied to a square, this can be written as √(2*s²) = d, because the diagonal divides the square into two equal right-angled triangles. Solving for s, we get s = √(d² / 2). Substituting 24 cm for d gives:

s = √(24² / 2)

s = √(576 / 2)

s = √(288)

s = 16.97 cm (approximately)

Therefore, the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang is approximately 16.97 cm.