which statements explain that the table does not represent a prbability distribution
A. The probability 4/3 is greater than 1.
B. The probabilities have different denominators.
C. The results are all less than 0.
D. The sum of the probabilities is 8/3 .
Answers
The sum of the probabilities is not equal to one, the table does not represent a probability distribution, so option D is the correct answer.
The statement that explains that the table does not represent a probability distribution is D. The sum of the probabilities is 8/3.
This statement explains that the probabilities do not add up to one, which is a requirement for a probability distribution. Therefore, it is not a probability distribution. If a table is given with probabilities and it is required to identify whether it represents a probability distribution or not, we must check the probabilities whether they meet the following conditions or not.
The sum of all probabilities should be equal to 1.All probabilities should be greater than or equal to zero.If any probability is greater than 1, then it is not a probability, so the probability table does not represent a probability distribution.The given probabilities have different denominators, this condition alone is not enough to reject it as probability distribution and is also a common error while creating the probability table.
An event's probability is a numerical value that reflects how likely it is to occur. Probabilities are always between zero and one, with zero indicating that the event is impossible and one indicating that the event is certain.
The sum of the probabilities of all possible outcomes for a particular experiment is always equal to one.The probabilities in the table represent the likelihood of the event happening and must add up to 1.
For example, the probability of rolling a die and getting a 1 is 1/6 because there are six possible outcomes and only one of them is a 1.The probability distribution can be used to determine the likelihood of certain outcomes. The sum of all probabilities must be equal to one.
The probability distribution function is also used in statistics to calculate the mean, variance, and standard deviation of a random variable. A probability distribution that meets the required conditions is called a discrete probability distribution. It is a distribution where the probability of each outcome is defined for discrete values.
To know more about probabilities visit:
https://brainly.com/question/32004014
#SPJ11
Related Questions
pls helppp I don't understand plsss
Answers
what is your question repet otherwise I will say you
Answer:
The third answer
Step-by-step explanation:
?+12=7
subtract 12 from 7
you get -5
then to make sure the answer is right you take -5 and add 12, then you will get 7
What’s -7 - - 1
And why?
Answers
Answer:
-8
Step-by-step explanation:
when there are two negetive numbers you add them not subtract
Which of the following is true? 1) D 5
=P 5
=Q 5
2) D 50
=P 5
=Q 25
3) D 5
=P 50
=Q 2
4) D 50
=P 5
=Q 2
Answers
Out of the given options, the statement that is true is: D50 = P5 = Q25.Therefore, the correct option is 2) D50 = P5 = Q25.
Given below are the values of P, Q, and D. D refers to the number of days to make a product, P is the number of people required to make the product, and Q is the number of products that can be made.
D5 = P50 = Q2
D50 = P5 = Q25
As per the problem statement, we need to determine which of the given statements is true.
Therefore, on comparing all the given values of P, Q, and D we can observe that the only statement that is true is
"D50 = P5 = Q25" as it satisfies the given values of P, Q, and D for producing the product.
Therefore, the correct option is 2) D50 = P5 = Q25.
Learn more about product visit:
brainly.com/question/31812224
#SPJ11
Given any integer a and any natural number n, there exists a unique integer t in the set {0, 1, 2,...,n − 1} such that a ≡ t (mod n).
Answers
The statement, known as the division algorithm, asserts that for any integer a and any natural number n, there exists a unique integer t in the set {0, 1, 2,...,n − 1} such that a ≡ t (mod n).
To prove the statement, let's consider the integer division of a by n: a = qn + r. Here, q is the quotient and r is the remainder. Since the remainder must be non-negative and less than n, it follows that 0 ≤ r < n.
Now, if we consider the congruence relation modulo n, we have a ≡ r (mod n), which means that a and r leave the same remainder when divided by n. In other words, a and r are congruent modulo n.
Since r is unique and falls in the range {0, 1, 2,...,n − 1}, we can say that there exists a unique integer t in the set {0, 1, 2,...,n − 1} such that a ≡ t (mod n).
This result is fundamental in modular arithmetic and is used to define operations such as addition, subtraction, and multiplication modulo n. It allows us to work with remainders and residues in a systematic way.
In conclusion, the statement, known as division algorithm, holds true for any integer a and any natural number n. There exists a unique integer t in the set {0, 1, 2,...,n − 1} such that a ≡ t (mod n).
To know more about division algorithm refer here:
https://brainly.com/question/29067793#
#SPJ11
The following polygons are similar find the scale factor of the small figure to the large figure 1-2
Answers
Answer:
1.5 and 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original.
1
scale factor = \(\frac{DF}{AC}\) = \(\frac{21}{14}\) = \(\frac{3}{2}\) = 1.5
2
scale factor = \(\frac{8}{2}\) = 4
Find the missing value to the nearest hundredth.
Answers
Answer:
Option (A)
Step-by-step explanation:
Let the Sine of the given angle θ is,
Sinθ = \(\frac{x}{y}\)
Then θ = \(\text{Sin}^{-1}(\frac{x}{y} )\)
From the given values in the question,
Sinθ = \(\frac{7}{29}\)
θ = \(\text{Sin}^{-1}(\frac{7}{29} )\)
θ = 13.97°
Therefore, measure of the angle 'θ' will be 13.97°.
Option (A) will be the answer.
Help me plssssss ( Geometry) answer as much as u can in the photo it would be appreciated!!)
Answers
Answer:
for 7-12 plot the points on a graph. its the rise/run. from the point farthest to the left, go down or up until you are on the same horizontal line. however many units you moved is the first number. (_/?). then from that point, go to the right until to actually land on the point. however many units you used is your second number. The slope will be in a fraction, and sometimes you can turn it into a whole number.
Step-by-step explanation:
HELP PLEASE ASAP!!!!
Answers
x+7>3 ----> x>-4
x-5< -1 -----> x<4
What quadrilateral always has 4 congruent angles and opposite sides that are congruent and parallel? Please answer it correctly.
Answers
Answer:
Square
Step-by-step explanation:
Requirements that make a square, a square;
Four sidesCongruent angles (all 90°)Opposite sides are congruent/the same.Opposite sides are also parallel because the lines of a square do not intersect.Answer:
Square
Explanation:
A square has four congruent angles as each angle measure is 90°. A square can never have an angle other than 90°. A square also has all four equal sides, and its opposite side lengths are parallel because all angles of a square must be 90°.
Please look at attached image for reference.
if f = q (v x b) and v is perpendicular to b then which is the direction of b
Answers
If f = q (v x b) and v is perpendicular to b, then the direction of b will be perpendicular to both f and v.
The cross product, also known as the vector product, is a mathematical operation performed between two vectors in three-dimensional space. The result of the cross product is another vector that is perpendicular to both original vectors.
If we have the cross product (v x b) v is perpendicular to b, then the direction of b will be perpendicular to both f and v. This is because the cross product of two vectors, v x b, will result in a vector that is perpendicular to both of the original vectors. Therefore, the direction of b will be in a direction that is perpendicular to both f and v.
See more about cross product at https://brainly.com/question/14542172.
#SPJ11
Drag each number to the correct location on the image. Each number can be used more than once, but not all numbers will be used.
Simplify or expand each expression and then classify it by its degree and number of terms.
Answers
The expression can be classified by its degree and number of terms as:
Degree=5 , number of terms = 3Degree = 6 number of terms , 4Degree= 4 , number of terms 2What is degree of a expression?The degree of a expression can be described as the highest power of the variable which can be found in the expression.
In the case, whereby there is more than one variables in an expression then the degree is the highest sum of powers of the variables .
For instance, in the third expression:
\((x^{2} + 9)(x^{2} -9)\\\\=x^{4} -9x^{2} +9x^{2} -81\\\\x^{4} -81\)
Here, the degree which is the number on the X is 4, and the term here is just 2.
This can be done for all the given expression to get the degree as well as the number of terms.
Learn more about expression on:
https://brainly.com/question/723406
#SPJ1
The triangle Inequality for vectors isdeterminant a.b < = determinant a determinant b Answer this one and the other SAME questions on the Q & A Boardto get MORE POINTS!!!!! determinant a+b^2 = (a +b).(a + b) and use property 3 of the dotproduct.] Cauchy-Schwarz Inequality: determinant a.b < = determinat a + determinant b a) Give a Geometric interpretation of the Triangle Inequality. b) Use the Cauchy-Schwarz Inequality from Exercise 49 to prove theTriangle Inequality. [Hint: Use the fact that
Answers
The Triangle Inequality states that for any two vectors a and b, the magnitude of their sum (a + b) is less than or equal to the sum of their magnitudes (|a| + |b|).
This inequality can be geometrically interpreted as follows: The length of the vector sum of two vectors is always less than or equal to the combined lengths of the individual vectors laid end to end.
The Cauchy-Schwarz Inequality states that for any two vectors a and b, the dot product of a and b is less than or equal to the product of their magnitudes (|a| * |b|).
This inequality can be used to prove the Triangle Inequality by considering the dot product of (a + b) with itself and applying the Cauchy-Schwarz Inequality.
a) Geometrically, the Triangle Inequality can be understood as follows:
If you draw vectors a and b in a coordinate system, the magnitude of their sum (|a + b|) represents the length of the diagonal of the parallelogram formed by vectors a and b. The Triangle Inequality states that this diagonal length is always less than or equal to the sum of the lengths of the two sides (|a| + |b|) of the parallelogram.
b) To prove the Triangle Inequality using the Cauchy-Schwarz Inequality, we start with the Cauchy-Schwarz Inequality: |a · b| ≤ |a| * |b|. Then, we square both sides of the inequality to get (a · b)^2 ≤ (|a| * |b|)^2. Expanding the left side of the inequality gives (a · b)^2 ≤ (a · a) * (b · b). Substituting the dot products with their corresponding magnitudes squared, we have (a · b)^2 ≤ |a|^2 * |b|^2.
Taking the square root of both sides, we get |a · b| ≤ |a| * |b|. Since |a · b| represents the magnitude of the dot product of a and b, and |a| * |b| represents the product of their magnitudes, we can conclude that the Cauchy-Schwarz Inequality implies the Triangle Inequality
Learn more about Cauchy-Schwarz Inequality here:
brainly.com/question/30402486
#SPJ11
Simplify the following rational expressions. 1) 4x3/8x2
2) (5x + 20)/(7x + 28)
3) (3x + 9)/(3x + 15)
4) (x - 3)/(x2 - 9)
5) (x2 - 2x + 1)/(x - 1)
Answers
Answer:
1) x/2
2) 5/7
3) x + 3 / x + 5
4) 1/x + 3
5) x + 1
Step-by-step explanation:
I'm assuming that the numbers right after the x's are the exponents of those x's since you didn't include the ^ symbol before the exponent number.
Steps for 1:
You can simplify the fraction 4/8 to 1/2. Now you have x³/2x². Next, simply the x's. When dividing variables of the same letter with exponents, subtract the bottom exponent from the top. In this case, it's 3 - 2 = 1. After dividing, move the x to the top. You are now left with x/2.
Steps for 2:
The first step is to factor both 5x + 20 and 7x + 28. To do this, find the greatest common factor (GCF) that you can take out for each. The GCF of 5x + 20 is 5, so you factor 5 out of 5x and 20. After doing so, for the numerator (the top), you're left with 5(x + 4).
Same thing for 7x + 28. The GCF is 7, so you factor 7 out of 7x and 28. After doing so, you're left with 7(x + 4) for the denominator (the bottom).
Now, your fraction should look like this: 5(x + 4) / 7(x + 4). Since x + 4 appears in the numerator and denominator, it cancels out (just cross both out). You're now left with 5/7.
Steps for 3:
Same steps from 2. First, factor 3x + 9. The GCF of 3x and 9 is 3, so factor 3 out of both. After doing so, you're left with 3(x + 3) for the numerator.
The GCF of 3x and 15 is also 3, so factor 3 out of both. After doing so, you're left with 3(x + 5) for the denominator. Your fraction now is 3(x + 3) / 3(x + 5). Since 3 appears on the top and bottom, it cancels out (just cross both out). You're now left with x + 3 / x + 5.
Steps for 4:
Similar steps as the ones above.
x - 3 can't be factored, but x² - 9 can be factored. After you factor x² - 9, your entire fraction is now x - 3 / (x + 3)(x - 3). Since x - 3 appears on the top and bottom, they cancel out (cross them out). You're now left with 1/x+3.
Steps for 5:
Similar steps as the ones above.
x - 1 can't be factored, but x² - 2x + 1 can be factored. After factoring, your entire fraction is now (x - 1)(x - 1) / x - 1. Since x - 1 appears on the top and bottom, they cancel out (cross them out). You're now left with the remaining x - 1.
Hope this helps!
how much of a 90 % orange juice drink must be mixed with 16 gallons of a 20% orange juice drink to obtain a mixture taht is 50%
Answers
12 gallons of 90% orange juice drink is needed to be mixed with 16 gallons of 20% orange juice drink to obtain a mixture that is 50%.
Let's first use V to represent the volume in gallons of the 90% orange juice drink that we need to mix with 16 gallons of 20% orange juice drink.
The problem is asking for the amount of the 90% orange juice drink that is required to be mixed.
Let's determine the equation for this problem.
It is given that 90% orange juice is to be mixed with 20% orange juice to obtain 50% orange juice.
Then the equation for the problem can be written as:
0.9V + 0.2(16) = 0.5(V + 16)0.9V + 3.2 = 0.5V + 8
On solving the above equation we get,
0.9V - 0.5V = 8 - 3.20.4V = 4.8V = 12 gallons
Therefore, 12 gallons of 90% orange juice drink is needed to be mixed with 16 gallons of 20% orange juice drink to obtain a mixture that is 50%.
Learn more about percentage here:
https://brainly.com/question/15221868
#SPJ11
Johnny has a jar of marbles with the following number of colored marbles in it.
If Johnny randomly pulls out a marble from the jar, what is the is the probability that he will pull out a red marble?
A. 1/4
B.1/5
C.1/3
D.1/6
Answers
Rectangle ABCD is translated and then reflected to create rectangle A'B'C'D'. Do rectangle ABCD and rectangle A'B'C'D' have the same area?
Answers
A translation is just moving the shape, and isn't changing the size in any way, so it'll still have the same area. Same goes for a reflection, the size or shape isn't being changed at all, just the location, so it still has the same area.
Rectangle ABCD and rectangle A'B'C'D' do have the same area.
The calculation of the area of a rectangle is done using the value of the height and the length of the figure, in such a way that:
\(A = L \times H\)
When the rectangle is translated, the height and length remain the same, only moving the shape, which does not affect the value of the area.
The same happen when the rectangle is reflected, just changing the location of the shape.
So, the area after a rectangle (A'B'C'D') is translated and then reflected is the same as the area before (ABCD).
Learn more about area in: brainly.com/question/9655204
Round 3, 295.351 to the nearest tenth.
3, 295.35
3, 295.3
3, 300
0 3,295.4
Answers
Answer:
3,295.4
Step-by-step explanation:
to the nearest tenth is 3,295.4
You are on a 4.7 mile run and have already 1.97 miles. How many more miles do you need to run?
Answers
Answer:
2.73
Step-by-step explanation:
You would need to run 2.73 miles to have ran 4.7 miles in all.
4.7 - 1.97
construct and interpret a 95% confidence interval for the true mean difference. does the interval provide convincing evidence of a difference in the mean price per gallon of diesel fuel and regular unleaded gasoline?
Answers
The 95% confidence interval for the mean difference in price per gallon of diesel fuel and regular unleaded gasoline is approximately (-0.209, 0.369). The interval includes zero, indicating no convincing evidence of a significant difference between the two fuel types.
To construct a 95% confidence interval for the true mean difference in the price per gallon of diesel fuel and regular unleaded gasoline, we can use the provided data. The sample mean difference is calculated by taking the average of the observed differences, and the standard error of the mean difference is calculated using the formula mentioned earlier.
From the given data, the sample mean difference is 0.08 (calculated as the average of the observed differences), and the standard error of the mean difference is 0.135.
To calculate the confidence interval, we need the critical value corresponding to a 95% confidence level. Since the sample size is not provided, we'll assume a reasonably large sample size and use the critical value of 1.96 for a two-tailed 95% confidence interval.
Using the formula for the confidence interval
Confidence Interval = D ± (t * SE(D))
Confidence Interval = 0.08 ± (1.96 * 0.135)
Calculating the confidence interval
Lower bound = 0.08 - (1.96 * 0.135) ≈ -0.209
Upper bound = 0.08 + (1.96 * 0.135) ≈ 0.369
The 95% confidence interval for the true mean difference in the price per gallon of diesel fuel and regular unleaded gasoline is approximately (-0.209, 0.369).
Since the confidence interval contains both positive and negative values, including zero, we can conclude that there is not convincing evidence of a statistically significant difference in the mean price per gallon of diesel fuel and regular unleaded gasoline.
To know more about confidence interval:
https://brainly.com/question/31482147
#SPJ4
--The given question is incomplete, the complete question is given below " Construct and interpret a 95% confidence interval for the true mean difference. Does the interval provide convincing evidence of a difference in the mean price per gallon of diesel fuel and regular unleaded gasoline? OH OH OH OH OH OH OH IN 0 IN IN Regular Unleaded 2.27 2.25 2.25 2.25 2.25 2.29 2.07 2.15 2.14 2.07 2.07 2.14 2.29 2.25 2.29 2.25 2.25 2.19 Diesel 2.15 2.35 1.85 2.47 2.45 2.47 2.28 2.28 2.28 2.29 2.28 2.28 2.26 2.24 2.26 2.27 2.25 2.39 Difference -0.12 0.1 -0.4 0.22 0.2 0.18 0.21 0.13 0.14 0.22 0.21 0.14 -0.03 -0.01 -0.03 0.02 0 0.2 2 IN IN IN HE IN IN IN 3 IN IL IN IN IN 0.14 0.22 IN IN IN IN 0.21 0.14 -0.03 -0.01 -0.03 0.02 IN IN IL 2.14 2.07 2.07 2.14 2.29 2.25 2.29 2.25 2.25 2.19 2.29 2.29 1.99 1.99 1.99 1.99 1.99 1.99 2.28 2.29 2.28 2.28 2.26 2.24 2.26 2.27 2.25 2.39 2.35 2.35 2.41 2.45 2.38 2.47 2.39 2.47 0 0.2 IL IL IL 0.06 0.06 0.42 0.46 0.39 0.48 0.4 0.48 IL IL IL IL IL IL IL ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ ΜΟ 2.25 2.19 2.35 2.19 2.19 2.17 2.17 2.17 2.17 2.19 2.19 2.06 2.15 2.04 2.04 1.89 1.87 1.99 2.35 2.38 2.39 2.06 2.06 2.06 2.06 2.07 2.09 2.06 2.06 2.13 2.13 1.99 1.95 2.05 2.25 2.07 0.1 0.19 0.04 -0.13 -0.13 -0.11 -0.11 -0.1 -0.08 -0.13 -0.13 0.07 -0.02 -0.05 -0.09 0.16 0.38 0.08 MO MO MO MO MO MO MO KS KS KS KS 1.95 1.99 1.99 1.99 1.91 1.87 1.99 2.05 2.05 1.97 1.88 1.87 1.89 1.89 1.99 2.25 1.89 2.09 2.18 2.21 2.07 2.09 2.15 2.18 2.05 2.04 2.04 2.34 2.35 2.23 2.35 2.16 2.15 2.18 2.04 2.27 0.23 0.22 0.08 0.1 0.24 0.31 0.06 -0.01 -0.01 0.37 0.47 0.36 0.46 0.27 0.16 -0.07 0.15 0.18 KS KS KS KS KS KS KS KS KS KS KS KS KS KS KS KS CO CO СО CO CO CO CO СО Co 1.96 1.99 2.09 2.11 2.09 2.09 1.93 1.93 1.97 2.14 2.21 2.05 2.05 2.15 2.05 2.19 2.09 2.07 2.15 2.33 2.23 2.19 2.29 2.34 2.24 2.39 2.15 2.18 2.18 2.37 2.35 2.28 2.09 2.09 2.35 1.99 0.19 0.34 0.14 0.08 0.2. 0.25 0.31 0.46 0.18 0.04 -0.03 0.32 0.3 0.13 0.04 -0.1 0.26 0.08 "--
Erika read 90 pages in 2 and half hours. At the same time, how many hours would it take her to read 225 pages?
Answers
Answer:
6.25 hours
Step-by-step explanation:
pages per hour
pages/hour
90/2.5 = 36
36 pages per hour
225 / 36 = 6.25 hours
Answer:
6.25 hours
Step-by-step explanation:
2 and half hours = 2.5 hours
Proportions:
90 pages ⇔ 2.5 hours
225 pages ⇔ E hours
E = 225*2.5/90
E = 6.25 hours
6.25 hours = 6 and 1 quarter hours
Use Theorem 9.11 to determine the convergence of divergence of the p-series. 1 + 1/8√2 + 1/^8√3 + 1/^8 √4+... p = ______. O converges O diverges
Answers
Using Theorem 9.11, we can determine the convergence or divergence of the p-series given by:
1 + 1/(8√2) + 1/(8√3) + 1/(8√4) + ...
The general form of this series is:
Σ (1/(8√n))
Comparing this to a p-series, we can see that the exponent p in the denominator is 1/2, as it involves a square root:
Σ (1/n^p) with p = 1/2
According to Theorem 9.11, a p-series converges if p > 1 and diverges if p ≤ 1. In this case, p = 1/2, which is less than or equal to 1. Therefore, this p-series diverges.
Theorem 9.11 states that the p-series 1/n^p converges if p > 1 and diverges if p ≤ 1.
In this case, we have a series of the form 1/√n^p, where n = 1, 2, 3, ... Since the denominator is growing exponentially with n, the terms are decreasing to zero.
To apply the theorem, we need to compare p to 1. Since the series has a square root in the denominator, we can rewrite it as 1/(n^(p/2)√n). Thus, p/2 is the exponent of the series without the square root.
If p/2 > 1, then p > 2, and the series converges by Theorem 9.11. If p/2 ≤ 1, then p ≤ 2, and the series diverges by Theorem 9.11.
So, in this case, p/2 = 1/8, which is less than 1. Thus, p ≤ 2 and the series diverges by Theorem 9.11. Therefore, the answer is "diverges".
Visit here to learn more about Divergence Theorem:
brainly.com/question/17177764
#SPJ11
Please help me with this homework!
Answers
In this case, adjacent angles are such pairs of angles that are alongside each other. Therefore, we can say that the sum of the two adjacent angles forms a bigger angle.
Part 1ii) Defining "vertical angles"In this case, vertical angles are such angles that are on opposite sides of the intersection between two lines. It is understood that vertically opposite angles are equivalent.
Part 2: SolveProblem 8:Clearly, we can see that two angles (one angle known as ∠x and the other angle) are alongside each other. Therefore, we can tell the angles are adjacent angles.
As we can see a \(\square\), we can tell that the sum of the measure of ∠x and the other angle is 90°. Therefore, we obtained;
⇒ ∠x + 35 = 90⇒ ∠x = 90 - 35⇒ ∠x = 65°Therefore, the measure of ∠x is 65°.
Problem 9:Clearly, we can see that two angles (one angle known as ∠x and the other angle) are on opposite sides. Therefore, we can tell that the angles are vertically opposite angles.
As stated in part 1ii, vertical angles are equivalent. Since ∠x and the other angles are vertically opposite angles, the measure of ∠x is 128°.
Problem 10:Clearly, we can see that two angles (one angle known as ∠x and the other angle) are alongside each other. Therefore, we can tell the angles are adjacent angles.
Since the line shown, is a straight line, we can tell that the sum of 117 and x is 180. Therefore, we obtain the following equation;
117 + ∠x = 180°When isolating x, we get;
⇒ 117 + ∠x - 117 = 180° - 117⇒ ∠x = 180° - 117⇒ ∠x = 63°Therefore, the measure of ∠x is 63°
Learn more about this topic: https://brainly.com/question/14355129
a box with a square base and open top must have a volume of . we wish to find the dimensions of the box that minimize the amount of material used. first, find a formula for the surface area of the box in terms of only , the length of one side of the square base. simplify your formula as much as possible. next, find the derivative, .
Answers
The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.
The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.
1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.
2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).
Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.
3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.
The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.
To learn more about derivative, click here: brainly.com/question/23819325
#SPJ11
“add the product of 3 and 8 to 17”
what is the expression
Answers
Answer:
41
Step-by-step explanation:
3x8=24
24+17=41
An isosceles triangle has one angle of 30 degrees. Calculate the possible sizes of the other 2 angles
Answers
Answer:
75 and 75
Step-by-step explanation:
Answer:
Hello,
Step-by-step explanation:
2 solutions:
30° is angle of the base: other angle of the base is 30° and the main angle is 180°-30°-30°=120°30° is the main angle, angles of the base are (180°-30°)/2=75° and 75°.
\( \frac{x - 9}{15} = \frac{2x - 9}{10} \)
solve the proportion. Round to the nearest hundredth if necessary.
![[tex] \frac{x - 9}{15} = \frac{2x - 9}{10} [/tex]solve the proportion. Round to the nearest hundredth](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/jlGLT2ukU0DwodEChxo1zkGlmpEnBvSk.jpeg)
Answers
Have a good day
A washer and a dryer cost 1000$ combined. The cost of the washer is three times the cost of the dryer. What is the cost of the dryer?
Answers
Answer:
$250
Step-by-step explanation:
250 x 4 is 1000 and the washer is 3 times as more as the dryer.
Answer:
The cost of the dryer is $250 and the cost of the washer is $750
Step-by-step explanation:
The ratio that is presented is Dryer 1: Washer 3 (1:3).
So, when you multiply $250x3 plus the $250 for the dryer you get $1000.
You can use the equation A+(Ax3)=$1000
which expression is equal to 4 to the power of 5 times 4 to the power of -7 divided by 4 to the power of -2
Answers
Step-by-step explanation:
4⁵ × 4^-7 / 4^-2
it is important to understand that a negative exponent means 1/...
a^-n = 1/(a^n)
in that sense we have therefore
4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)
4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1
so, "1" is the fully simplified expression equal to the original expression.
What is 4 1/6 - 8/9 step by step
Answers
Solution:
To evaluate:
\(4\frac{1}{6}-\frac{8}{9}\)we have
\(\begin{gathered} Convert\text{ to improper fraction,} \\ \frac{(6\times4)+1}{6}-\frac{8}{9} \\ \Rightarrow\frac{25}{6}-\frac{8}{9} \\ LCM\text{ is 36, thus} \\ \frac{6(25)-4(8)}{36}=\frac{150-32}{36} \\ =\frac{118}{36} \\ =3\frac{5}{18} \end{gathered}\)Hence, we have
\(3\frac{5}{18}\)The solution of the expression \(4 \dfrac{1}{6} - \dfrac{8}{9}\) in the mixed fraction is \(3 \dfrac{5}{8}\) .
The combination of a proper fraction and a whole number is called a mixed fraction.
The expression can be solved by converting the mixed fraction \(4\dfrac {1}{6}\) to an improper fraction. For this, multiply the whole number (\(4\)) by the denominator (\(6\)) and add the numerator (\(1\)):
\(4 * 6 + 1 \\= 24 + 1\\ = 25\)
The fraction can be written with the denominator as,
\(4\dfrac{1}{6} = \dfrac{25}{6}\)
The denominators are \(6\) and \(9\). The least common multiple (LCM) of \(6\) and \(9\) is \(18\).
The fractions can be written with the common denominator as,
\(\dfrac{25}{6} = \dfrac{(25 \times 3)} { (6 \times3)}\\ = \ \ \ \ \ \ \dfrac{75}{18}\)
\(\dfrac{8}{9}\) does not need to be converted since its denominator is already \(9\).
Subtract the expression as:
\(\dfrac{75}{18} -\dfrac{8}{9} = \dfrac{(75 - 16)} {18} \\ = \dfrac{59}{18}\)
Convert into a mixed fraction:
\(\dfrac{59}{18} = 3 \dfrac{5}{18}\)
Therefore, \(4 \dfrac{1}{6} - \dfrac{8}{9}\) is equal to either \(\dfrac{59}{18}\) or \(3\dfrac {5}{18}.\)
Learn more about mixed fractions here:
https://brainly.com/question/29019463
#SPJ6
Soccer team has 10 players in a tournament there are seven teams and two players on each team drop out how many are there left
Answers
Answer:
1 team = 10 players
7 teams = 7×10 players
= 70 players
drop out players:
1 team = 2 players
7 teams = 2×7
= 14 players
how many left ?
= total players - drop out players
= 70 - 14
= 56 players