After calculating, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is: 3 log²2 (5 - 3 log 3)
We can start by simplifying the logarithmic expressions inside the parentheses:
log²(2^18) + log²(4) = (18 log 2)^2 + (2 log 2)^2 = 324 log²2 + 4 log²2 = 328 log²2
log²(32) + log²(216) = (5 log 2)^2 + (3 log 6)^2 = 25 log²2 + 27 log²3
Now, we can express the original expression as:
HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) = HCF(328 log²2, 25 log²2 + 27 log²3)
To find the highest common factor of these two terms, we can factor out the common factor of log²2:
HCF(328 log²2, 25 log²2 + 27 log²3) = log²2 HCF(328, 25 + 27 log²3)
Now, we need to find the highest common factor of the two integers 328 and 25 + 27 log²3.
We can factor out 3 from 25 and 27, and then use the difference of squares formula to write:
25 + 27 log²3 = (5 + 3 log 3)(5 - 3 log 3)
So, the highest common factor of 328 and 25 + 27 log²3 is the product of the common factors, which is:
HCF(328, 25 + 27 log²3) = 3(5 - 3 log 3)
Therefore, the value of the expression HCF(log²(2^18) + log²(4))(log²(32) + log²(216)) is:
log²2 HCF(328, 25 + 27 log²3) = log²2 * 3(5 - 3 log 3) = 3 log²2 (5 - 3 log 3)
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Construct triange ABC, in which AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. Measure the length of BC. Give your answer to 1 d. P
From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm
To construct triangle ABC, we can follow these steps:
Draw a line segment AB of length 6 cm.Draw an angle of 96 degrees at point A using a protractor.Draw an angle of 35 degrees at point B using a protractor.The intersection point of the two lines that were drawn in step 2 and 3 will be point C, which is the third vertex of the triangle.To measure the length of BC in triangle ABC, we can use the law of sines.
The law of sines states that in any triangle ABC:
a / sin(A) = b / sin(B) = c / sin(C)
Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.
In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:
angle ACB = 180 - angle BAC - angle ABC
= 180 - 96 - 35 = 49 degrees
Now, we can apply the law of sines to find the length of BC:
BC / sin(35) = 6 / sin(96)
BC = 6 × sin(35) / sin(96)
Using a calculator, we can evaluate this expression to get:
BC ≈ 4.22 cm
Therefore, the length of BC in triangle ABC is approximately 4.22 cm.
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Kate is x years old. Lethna is 3 times as old as Kate. Mike is 4 years older than Lethna. write down an expression, in terms of x for Mike's age
Answer: Mike is ( 3x + 4 ) years old
Step-by-step explanation:
K -> x y/o
L -> 3x y/o
M -> (3x + 4) y/o
8.2 / m = tan(17).
What is m?
Answer:
26.82 (2 d.p.)
Step-by-step explanation:
tan(17)*m=8.2
8.2/tan(17) = m
= 26.82
20. Assertion(A): The sides of a triangle are 5cm, 12cm and 13cm and its area is 30 cm². Reason(R): Area of a triangle is base x height. (a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion, (b) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion. (c) Assertion is true but the Reason is false. (d) Assertion is false but the Reason is true.
if x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?
Option (A) x+1 is a positive odd integer.
Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.
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Which of the following algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order? A Heap Sort B Quick Sort Merge Sort (D Radix Sort
B) Quick Sort is algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order
What is Merge Sort Algorithm?Merge Sort is an effective algorithm for sorting the data items of a list or an array. This algorithm's fundamental idea is to break the unsorted list into many sub-lists until every sub-list contains only one item.
The merging procedure then recombines all of the sublists, resulting in a sorted list. Divide-and-conquer is the name given to this merging process. Merge Sort divides the original list into N sublists, each of which contains one element.
The Merge Sort algorithm is faster than other sorting algorithms when it comes to time complexity. The time complexity of Merge Sort is O (n log n), which is better than Bubble Sort and Insertion Sort.
It is a more efficient sorting algorithm than other algorithms, such as bubble sort, which has a higher time complexity of O (n²).
Therefore, we can say that Merge Sort is the most efficient algorithm to sort an array in ascending or descending order.
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stuck on this question need some help
Answer:
1. The graphs of f(x) and h(x) are both quadratic functions with a minimum point. However, the minimum point of f(x) is located at (6,0), while the minimum point of h(x) is located at (2,3).
2. The graphs of g(x) and h(x) both open upwards and are quadratic functions. However, the vertex of g(x) is located at the origin (0,0), while the vertex of h(x) is located at (2,3).
3. The graph of g(x) is a simple parabola that opens upwards, while the graphs of f(x) and h(x) are more complex parabolas with a minimum point and an upward opening. The graph of f(x) is centered at (6,0), while the graph of h(x) is centered at (2,3).
Solve for x and y.
8
7
X
y
By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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The solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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the national football league (nfl) records a variety of performance data for individuals and teams. to investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 nfl teams for one full season.
The National Football League (NFL) is an American football league that is based in the United States. The NFL records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (conf), average number of passing yards per attempt (yds/att), the number of interceptions thrown per attempt (int/att), and the percentage of games won (win%) for a random sample of 16 NFL teams for one full season.The data collected by the NFL shows that passing has a significant impact on the percentage of games won by a team. Teams that have a higher average number of passing yards per attempt tend to win more games than those with a lower average. Additionally, teams that have a lower number of interceptions thrown per attempt also tend to win more games than those with a higher number of interceptions thrown per attempt.The data also shows that the conference a team plays in does not have a significant impact on the percentage of games won by a team. This means that a team's conference is not a good indicator of its performance.The NFL should continue to record data on passing to help teams improve their performance. Coaches can use this data to identify areas for improvement and develop strategies to help their teams win more games.
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I am in need of some help with this
The required volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
What is volume?A measurement of three-dimensional space is volume. It is frequently expressed mathematically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are linked.
First, let's find the volume of the cylinder:
[tex]$$V_{cylinder} = \pi r^2 h = \pi (5)^2 (8) = 200\pi$$[/tex]
Next, let's find the volume of the hemisphere:
[tex]$V_{hemisphere} = \frac{2}{3}\pi r^3 = \frac{2}{3}\pi (5)^3 = \frac{250\pi}{3}$$[/tex]
To find the volume of the entire shape, we simply add the volume of the cylinder and hemisphere:
[tex]$$V_{shape} = V_{cylinder} + V_{hemisphere} = 200\pi + \frac{250\pi}{3} = \frac{850\pi}{3}$$[/tex]
Therefore, the volume of the shape is [tex]\frac{850\pi}{3}$[/tex] cubic units.
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phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?
Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.
What is p-value?The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.
The ratio of seniors bringing a bag lunch= 78/104 or 0.75,
while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.
This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.
Further, the difference between the proportions is
0.75-0.65 = 0.1,
which is a large enough difference to be considered significant.
The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.
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Show using the value x=2 that
5x³ are not equivalent.
20x^6/4x²
and 5x^3 are not equivalent
Answer:
5x³ = 40
20x^6/4x² = 80
100 is not equal to 80
Step-by-step explanation:
5x³ = 5*2^3
= 40
20x^6/4x² = 20*2^6/4*2^2
= 20*64/16
= 80
if the measure of and acute angle is represented by x, then the measure of the angle that it is complementary which is represented by 90-x
The measure of the angle that it is complementary which is represented by 90-x is always true. Option A
What is an acute angle?An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.
It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.
What is a complementary angle?A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.
From the information given, we have that;
x is the acute angle
The complementary angle is 90 - x
We can see that the angle x must be complementary to be subtracted from 90 degrees.
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The complete question:
If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.
always true
sometimes true
never true
PLSS HELP IVE TRIED EVERYTHING
Answer:
Step-by-step explanation: To obtain the function g(x) that represents the indicated transformations of the graph of f(x) = 2, which are a translation 1 unit up followed by a horizontal stretch by a factor of 2, we can follow these steps:
To translate f(x) = 2 one unit up, we can add 1 to the function: f(x) + 1.
To horizontally stretch f(x) + 1 by a factor of 2, we can multiply the input (x) by 1/2: f(1/2 x) + 1.
Therefore, the function g(x) that represents the indicated transformations of f(x) is:
g(x) = f(1/2 x) + 1
g(x) = 2(1/2 x) + 1
g(x) = x + 1
Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?
Answer:11
Step-by-step explanation:
The hanger image below represents a balanced equation.
Write an equation to represent the image
HELP THIS IS DUE TODAY
Answer:
2 + r = 6
Step-by-step explanation:
2 + r = 6
r = 6 - 2 = 4
6 on the left balanced by 2 plus r on the right
Caleb observed the costumes that people wore to a costume party. The themes of the costumes and the number of people who wore them are shown in the following table.
Costume Theme Superhero Decades Scary TV & Movie Characters Animals Career
Number of People 128 96 72 52 24 28
A circle graph was drawn from the data in the table. What percentage would be on the Decades slice of the circle graph?
24%
26.7%
86.4%
96%
Question 4(Multiple Choice Worth 2 points)
Answer: 24
Step-by-step explanation:
Urgent Help! 100 points to whoever is willing ^-^
Noise-canceling headphones have microphones to detect the ambient, or background, noise. They interpret those noises as sinusoidal functions. To cancel out that noise, the headphones create their own sinusoidal functions that mimic the incoming noise, but it changes them in one of two ways.
1. The mimic function is the negative of the noise's function.
2. The mimic function is the noise function shifted one-half period.
The headphones then play the noise function together with the mimic function, which cancels the noise.
Instructions
• Find the frequency of any musical note in hertz (Hz).
• Use the frequency to write f(x), the sine function for the note. For example, [tex]A_4[/tex] has a frequency of 440 Hz. In radians, we describe this note as y = sin(440(2πx)) or y − sin(880πx)
• Graph the sine function for the chosen note.
• Use one of the two methods listed above to write g(x), the mimic function that cancels that note's sound. Graph that function.
• Write a third function, h(x), that is the sum of f(x) and g(x). Graph it.
• Use your three graphs to explain why g(x) cancels out f(x).
I NEED HELP ON THIS ASAP!!
In response to the stated question, we may state that x + y < 380 (the variable corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)
What is a Variable?A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. The letters x, y, and z are often used as generic variables symbols.
To indicate the amount of boards of each type of wood sold, consider the following variables:
Let x be the number of mahogany boards sold.
Let y represent the number of black walnut boards sold.
The system of inequalities representing the restrictions of this issue scenario may therefore be represented as follows:
[tex]x < 260[/tex] (the corporation has 260 boards of mahogany) (the company has 260 boards of mahogany)
y ≤ 320 (the corporation has 320 boards of black walnut) (the company has 320 boards of black walnut)
x + y < 380 (the corporation plans to sell at most 380 boards of wood) (the company expects to sell at most 380 boards of wood)
Furthermore, we know that the profit on the sale of the wood is $20 per board for mahogany and $6 per board for black walnut. Let P represent the total profit from the sale of the wood. Then: P = 20x + 6y
We may display the three boundary lines x = 260, y = 320, and x + y = 380 to graph this system of inequalities, and shade the feasible region that meets all three inequalities. The triangle bordered by the x-axis, y-axis, and the line x + y = 380 will be the viable region. Here's a basic idea of how the graph may look:
|
380 - * - - - - - - - - - - - - - - - - - -
| /\
| / \
|/ \
260 - *-------* - - - - - - - - - - - - - - -
0 320
Mahogany Black Walnut
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Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let x= the number of free throws faith makes out of 20 shots. Calculate and interpret the standard deviation of x
If at practice, each player shoots 20 free throws, the standard deviation of x is 0.975.
To calculate the standard deviation of x, we need to first determine the variance. The variance is the average of the squared differences of each observation from the mean.
In this case, Faith is a 95% free throw shooter, so she is expected to make 19 out of 20 shots on average. The probability of making a free throw is 0.95, and the probability of missing a free throw is 0.05. Therefore, the mean of x is:
mean(x) = 20 * 0.95 = 19
To calculate the variance, we need to find the expected value of (x - mean(x))^2. Since Faith's free throw shooting is independent, we can use the binomial distribution to find the probability of making x shots out of 20.
The formula for the variance of a binomial distribution is np(1-p), where n is the number of trials and p is the probability of success. Therefore, the variance of x is:
var(x) = 20 * 0.95 * 0.05 = 0.95
Finally, the standard deviation is the square root of the variance:
sd(x) = √(var(x)) = √(0.95) = 0.975
This means that on average, Faith is expected to make 19 out of 20 free throws, but there is a standard deviation of 0.975, which indicates the degree of variability or spread around the mean. In other words, we can expect Faith to make between 18 and 20 free throws in most cases, but there is a small chance that she may make fewer or more than that.
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Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
Answer:
C. (0, –5) and (2, –1)
please help me !!!!!!
The equation representing total fraction strip is ³/₃ + ¹/₃ = ⁴/₃.
option B.
What is a fraction?
A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.
For this case, 1 is divided into, and 1 divide into 3.
To obtain the total fractions, we will add the individual fractions as shown below;
For this first fraction = ¹/₃ + ¹/₃ + ¹/₃
For the second fraction = ¹/₃
Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃
Total fraction = ³/₃ + ¹/₃ = ⁴/₃
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A box contains some green and yellow counters. 7/9of the box is green counters. Are 24 yellow counters. There How many green counters are there?
If 7/9 of the box is green counters, and there are 24 yellow counters in the box, then there are 84 green counters .
Let's assume that the total number of counters in the box is x.
We are given that 7/9 of the box is filled with green counters, which means that the remaining 2/9 of the box must be filled with yellow counters. We are also given that there are 24 yellow counters in the box.
We can set up an equation to represent the relationship between the number of yellow counters and the total number of counters:
2/9 x = 24
To solve for x, we can multiply both sides of the equation by the reciprocal of 2/9, which is 9/2:
(2/9) x * (9/2) = 24 * (9/2)
x = 108
This means that there are a total of 108 counters in the box. To find out how many of these are green counters, we can use the fact that 7/9 of the box is filled with green counters:
(7/9) * 108 = 84
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what is the target domain for a poisson distribution?
The target domain for a Poisson distribution is given the term (0, inf) which can be seen correct in option B.
A Poisson distribution's target domain is (0, inf). This means that the Poisson distribution can only be specified for non-negative integer values of the random variable it is modelling.
The Poisson distribution is a discrete probability function, which indicates that the variable may only take particular values from a finite list of integers. A Poisson distribution estimates how many times an event will occur in "x" amount of time. In other words, it is the probability distribution resulting from the Poisson experiment.
A Poisson experiment is a statistical experiment that categorises the experiment as either successful or unsuccessful. A limiting process of the binomial distribution is the Poisson distribution.
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Complete question:
What is the target domain for a Poisson distribution?
1) (-inf, inf)
2) (0, inf)
3) (-inf, 0]
4) [0, inf)
What is the measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠C= ° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
The measure of angle C is 53.13 degrees.
What are trigonometric functions?
Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Calculating the value of angle C :
The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.
To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.
Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:
[tex]5^2 = 3^2 + 4^2[/tex]
[tex]25 = 9 + 16[/tex]
[tex]25 = 25[/tex]
So, the triangle is a right triangle.
To find the measure of angle C, we can use the arctan function:
[tex]tan(C) =opposite/adjacent = 3/4[/tex]
[tex]C = arctan(3/4) \approx 53.13[/tex] degrees
Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).
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Emily needs enough fabric for 3½ hats, since she has half done already. If each hat requires1 2/7 feet of fabric how much will she need to make the 3½ hats
Using simple mathematical operations we know that 4.5 ft of fabric is needed.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, to find the fabric needed:
1 2/7 feet of fabric
Then, 3 1/2 hands will need:
= 9/7 * 7/2
= 9/2
= 4.5 ft of cloth
Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.
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Correct question:
Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
* 24% of the students purchased their lunch
* 190 students brought their lunch from home.
How many students are in the sixth grade?
24% of the students bought their lunch on Monday. Therefore, the number of students in the 6th grade is 190
Step-by-step explanation:
I travel 480 km in 4 hours what is my speed in km/h
Answer:
120 km/h.
Step-by-step explanation:
480 km / 4h
Divide top and bottom by 4 to get the desired km/h.
We have 120 km/h.
Hope this helps!
What formula is used to find the side lengths?
ANSWER:
The Pythagorean theorem is used to find the hypotenuse of a triangle.
=> AC² = AB² + BC²
In squares, the length of the side can be calculated by finding the square root of the area.
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 3y + 4z = 9_______.
The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.
To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.
Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.
The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:
yz + λ = 0
xz + 3λ = 0
x*y + 4λ = 0
x + 3y + 4z - 9 = 0
Solving these equations simultaneously, we get:
x = 1.5, y = 1, z = 2.25, and λ = -0.5625
Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.
To learn more about coordinate planes
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