Answer:
64
Step-by-step explanation:
10 ft is 4 times 2 1/2 ft, so the larger container has dimensions of 4 crates in every direction. That is, it will hold 4^3 crates, or 64 crates.
A police report shows that 82% of drivers stopped for suspected drunk driving receive a breath test, 34% receive a blood test, and 24% receive both tests. What's the probability that a randomly selected DWI suspect receives neither test
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%.
26 POINTS!!! BRAINLIEST TOO.
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.
Grandma's bakery sells single crust apple pies for $6.99 in double crust cherry pies for $10.99. The total number of pies sold on a busy Friday was 36. If the amount collected that day was $331.64 how many of each type were sold
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
An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What’s the probability the airline will not have enough seats, so someone gets bumped?
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.
which of the following is the product of the rational expressions shown below? 7x/x-4•x/x+7
Step-by-step explanation:
We have,
[tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
To find, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = ?
∴ [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
= [tex]\dfrac{7x.x}{(x-4)(x+7)}[/tex]
= [tex]\dfrac{7x^2}{(x(x+7)-4(x+7)}[/tex]
= [tex]\dfrac{7x^2}{x^2+7x-4x-28}[/tex]
= [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]
Thus, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}[/tex].
A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation 5. A e 95 percent confidence level? (A) with 100 confidence intervals, we can be95% co nfident that the sample proportion of citizens of the (B) We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the (C) We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of (D) Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from (E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sample United States who are optimistic about the economy
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:
Triangle L N M is shown. Angle L N M is 90 degrees, angle N M L is 48 degrees, and angle M L N is 42 degrees. Consider △LMN. m∠L + m∠M = ° sin(L) = sin(M) =
Answer:
m∠L + m∠M = 90° sin(L) = 0.66913sin(M) = 0.74314Step-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.
Mr. C is such a mean teacher! The next time Mathias gets in trouble, Mr. C has designed a special detention for him. Mathias will have to go out into the hall and stand exactly meters away from the exit door and pause for a minute. Then he is allowed to walk exactly halfway to the door and pause for another minute. Then he can again walk exactly half the remaining distance to the door and pause again, and so on. Mr. C says that when Mathias reaches the door he can leave, unless he breaks the rules and goes more than halfway, even by a tiny amount. When can Mathias leave?
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.
Explanation: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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Help please
Find the area of the following figure: (Do NOT include the units in your answer...only type the numerical portion of your answer!)
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
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 7 to 2?
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%.
Which interval is the solution set to 0.35x - 4.8<5.2- 0.9x
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
The legs of a right triangle are x and 15 while the hypotenuse is 17.
Which equation can be used to determine the value of x using the Pythagorean Theorem?
Answer:
Since the Option of equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Step-by-step explanation:
Given:
Length of One leg = x
Length of other Leg= 15
Hypotenuse = 17
We need to find the equation used to determine the value of x.
Solution:
Assuming Triangle to right angled triangle.
So we will apply Pythagoras theorem which sates that;
"The square of sum of two legs of right angle triangle is equal to square of the length of hypotenuse."
so we can say that;
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Since the equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Answer:
b
Step-by-step explanation:
What is the best answer
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.
Aliens have injected Ana with mathematical nanobots. These nanobots force Ana to think about math more and more. Initially, there were only five nanobots. The population of the nanobots doubles every hour. The population of the nanobots follows the equations p(t) = 5·2^t. After there are 106nanobots, Ana will cease thinking of anything other than math. How many hours will it take for math to take over Ana's brain?
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.
Explanation: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:
p(t) = 5·[tex]2^t[/tex] = 160Dividing both sides by 5 gives:
[tex]2^t = 32[/tex]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.
50 POINTS
A two-sided coin is flipped and a six-sided die is rolled. 'Die' is the singular version of the plural word 'dice.' How many ways can one coin flip and one die roll be done?
12 ways can one coin flip and one die roll be done.
What does a math probability mean?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur.'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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Let w represent Henry's weight in pounds. Eric weighs 12 pounds less then Henry. Write an algebraic expression that represents Eric's weight in pounds.
Answer:
Step-by-step explanation:
w = Henry's weight
e = Eric's weight
e = w - 12
The algebraic expression that represents Eric's weight in pounds is [tex]\( w - 12 \)[/tex].
1. We're given that [tex]\( w \)[/tex] represents Henry's weight in pounds. This means we're using the variable [tex]\( w \)[/tex] to stand for whatever Henry's weight is.
2. The problem states that Eric weighs 12 pounds less than Henry. So, if Henry weighs [tex]\( w \)[/tex] pounds, then Eric's weight would be [tex]\( w - 12 \)[/tex] pounds because he's 12 pounds lighter than Henry.
3. Therefore, the expression [tex]\( w - 12 \)[/tex] represents Eric's weight in pounds. We subtract 12 from Henry's weight [tex]\( w \)[/tex] to get Eric's weight. This expression tells us Eric's weight in terms of Henry's weight.
A statistician proposed a new method for constructing a 90 percent confidence interval to estimate the median of assessed home values for homes in a large community. To test the method, the statistician will conduct a simulation by selecting 10,000 random samples of the same size from the population. For each sample, a confidence interval will be constructed using the new method. If the confidence level associated with the new method is actually 90 percent, which of the following will be captured by approximately 9,000 of the confidence intervals constructed from the simulation? a. The sample mean b. The sample median c. The sample standard deviation d. The population mean e. The population median
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.
Which choice is equivalent to the quotient shown here when x>0?
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
A vertical pole is supported by a wire that is 26 feet long. If the wire is attached to the ground 24 feet away from the base of the pole, how many feet up the pole should the wire be attached?
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.
Samuel wants to eat at least 15 grams of protein each day. Let x represent the amount of protein he should eat each day to meet his goal. Which inequality represents this situation?
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
There was 1/4 watermelon in the refrigerator. Mom brought home 1/2 watermelon from the grocery store. What fractional part of the watermelon did the family have for supper
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.
Six friends are going to the state fair. The cost of one admission is $9.50, and the cost for one ride on the Ferris wheel is $1.50. Write two equivalent expressions and then find the total cost.
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.
Determine what type of observational study is described. Explain. Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with opteoperosis and an equal number of women without osteoperosis. The two groups were matched in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. a.cohort; Individuals are observed over a long period of time. b.cross-sectional; Information is collected at a specific point in time. c.retrospective; Individuals are asked to look back in time Question 15 4 pts
Answer:
thats too long to read but good luck!
Step-by-step explanation:
What is the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang?
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.
An isosceles triangle in which the two equal sides, labeled x, are longer than side y. The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
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.
Racheal has a board that is 1 7/12 feet long and another board that is 2 11/12 feet long. Write an expression Racheal can use to find the total length I feet of the two boards
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.
GEOMETRY HELP !!!!!!!!!What is the sequence of transformations that
maps A ABC to A A'B'C' ?
Select from the drop-down menus to correctly
identify each step.
Step 1: Choose ...
Reflect across the y-axis
Reflect across the line y = x.
Rotate 180 degrees about to origin.
Rotate 90 degrees clockwise about the origin.
Step 2: Choose...
Translate 1 units right.
Translate 2 units right.
Translate 4 units down.
Reflect across the x-axis.
The sequence of transformations is: reflect across the x-axis, rotate 180 degrees about the origin, and translate 4 units down.
Explanation:The sequence of transformations that maps triangle ABC to triangle A'B'C' is:
Reflect across the x-axisRotate 180 degrees about the originTranslate 4 units downLearn more about Sequences of Transformations here:https://brainly.com/question/27885960
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The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1515 and a standard deviation of 15. Approximately what percentage of buckets contain between 1470 and 1560 pieces of popcorn?
Approximately 68%
Approximately 75%
Approximately 95%
99.7%
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%
How is percentage mean?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.
How do you calculate percentages?The following formula is a common strategy to calculate a percentage:
Determine the total amount of what you want to find a percentage. Divide the number to determine the percentage.Multiply the value by 100To learn more about percentage, refer
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PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !!!
Ms Nelson will be teaching a group math lesson with counters frist she dumps out 4 bags that have 20 counters each then she divides the counter among 6 group of students
Answer:
13 r 3
Step-by-step explanation: