Answer:
We can start by using conservation of momentum and conservation of energy to solve this problem.
Conservation of momentum:
Before the explosion, the momentum of the projectile is:
p = mv = (228 kg)(146 m/s) = 33312 kg·m/s
After the explosion, the momentum is still conserved, so the momentum of each piece must be equal to 1/3 of the initial momentum:
p = (1/3) mv1 + (1/3) mv2 + (1/3) mv3
where v1, v2, and v3 are the velocities of the three pieces after the explosion.
Conservation of energy:
At the highest point of the arc, the projectile has no kinetic energy and all of its energy is in the form of potential energy. Therefore, we can use conservation of energy to find the potential energy at this point and use that to find the initial kinetic energy of the projectile.
mgh = (1/2) mv²
where h is the maximum height of the projectile and v is the initial velocity of the projectile.
Solving for v, we get:
v = sqrt(2gh)
where g is the acceleration due to gravity (9.81 m/s²).
Substituting the given values, we get:
v = sqrt(2(9.81 m/s²)(h)) = 146 m/s
Now we can use the conservation of momentum equation to solve for the velocity of the third fragment:
p = (1/3) mv1 + (1/3) mv2 + (1/3) mv3
33312 kg·m/s = (1/3)(228 kg)(146 m/s) + (1/3)(228 kg)(146 m/s) + (1/3)(228 kg)(v3)
Simplifying and solving for v3, we get:
v3 = 306.23 m/s
Therefore, the magnitude of the velocity of the third fragment immediately after the explosion is 306.23 m/s.
To determine the direction of the velocity of the third fragment immediately after the explosion, we can use the fact that two of the fragments move with the same speed right after the explosion as the entire projectile had just before the explosion. This means that the horizontal component of the velocity of the third fragment must be equal in magnitude to the horizontal component of the velocity of the original projectile (146 m/s), and the vertical component must be opposite in sign to the vertical component of the velocity of the fragment that moves vertically downward.
Since the fragment that moves vertically downward has a velocity that is purely vertical, its vertical component is equal in magnitude to its total velocity. Therefore, the vertical component of the velocity of the third fragment must also be equal in magnitude to 306.23 m/s.
Using the Pythagorean theorem, we can find the magnitude of the horizontal component of the velocity of the third fragment:
sqrt((146 m/s)² - (306.23 m/s)²) = 259.31 m/s
Therefore, the velocity of the third fragment immediately after the explosion has a magnitude of 306.23 m/s and is directed at an angle of arctan(-306.23 m/s / 259.31 m/s) = -51.4° below the horizontal.
Answer:
Step-by-step explanation:
To solve this question, we need to use conservation of momentum.
1. The problem tells us that is breaks into 3 pieces of equal mass. So each piece weighs: [tex]\frac{228}{3}=76kg[/tex]
2. This problem also tells us that the projectile breaks up into 3 parts at the highest point of its arc. This tells us that the initial momentum of the system in the y-direction is 0.
3. Before we solve, we need to clear something up. The velocity of each fragment is NOT [tex]146\frac{m}{s}[/tex]. Since we launch at an angle, the velocity of the fragments will be [tex]146cos(70)=49.93[/tex], because each fragment move with the same speed after the explosion, and our speed after the explosion only has an x-component to it, as the y-component is 0.
4. To solve we need the equations:
[tex]m_{1}v_{1_{x}}+m_{2}v_{2_{x}}+m_{3}v_{3_{x}}=m_{1}v'_{1_{x}}+m_{2}v'_{2_{x}}+m_{3}v'_{3_{x}}[/tex]
[tex]m_{1}v_{1_{y}}+m_{2}v_{2_{y}}+m_{3}v_{3_{y}}=m_{1}v'_{1_{y}}+m_{2}v'_{2_{y}}+m_{3}v'_{3_{y}}[/tex]
NOTE: fragment 1 is going to be the one that travels horizontally. Fragment 2 will be the one traveling vertically downward. 3 will be our unknown
5. Solving for x:
[tex]m_{1}v_{1_{x}}+m_{2}v_{2_{x}}+m_{3}v_{3_{x}}=m_{1}v'_{1_{x}}+m_{2}v'_{2_{x}}+m_{3}v'_{3_{x}}[/tex]
[tex]228(146)cos(70)=76(49.93)cos(0)+76(50)cos(270)+76v'_{3_{x}} = > v'_{3_{x}} \approx 100[/tex]
6. Solving for y:
[tex]m_{1}v_{1_{y}}+m_{2}v_{2_{y}}+m_{3}v_{3_{y}}=m_{1}v'_{1_{y}}+m_{2}v'_{2_{y}}+m_{3}v'_{3_{y}}[/tex]
[tex]0=76(49.93)sin(0)-76(50)sin(270)+76v'_{3_{y}} = > v'_{3_{y}} \approx 50[/tex]
7. Solve for v:
[tex]v'_{3}=\sqrt{100^2+50^2}=111.8\frac{m}{s}[/tex]
8. Solve for theta:
[tex]\theta=tan^{-1}(\frac{50}{100} )=26.57[/tex]
Hope this helped. :)
Find the surface area of the pyramid. The side lengths of the base are equal.
10 m
6.9 m
8m
Answer:
147.6 m²
Step-by-step explanation:
You want the surface area of a triangular pyramid with base sides of length 8 m and a slant height of 10 m. (The altitude of the base triangle is approximately 6.9 m.)
Surface areaThe surface area is the sum of the areas of the triangular faces.
SA = 1/2(8 m)(6.9 m) + 3 × 1/2(8 m)(10 m)
= 1/2(8 m)(6.9 m + 3×10 m) = (4)(36.9) m² = 147.6 m²
The surface area of the pyramid is 147.6 square meters.
Compute the average (mean) from the given information.
• Number of data values: 106
• Sum of data values: 2,332
Responses
Step-by-step explanation:
The average = sum of data value ÷ number of data value = 2332 ÷ 106 = 22
what is the length of AB
the length of side AB of triangle ABC is 6 units.
How to find the length?
To find the length of side AB of triangle ABC, we can use the distance formula which is given by:
distance = sqrt((x2 - x1)² + (y2 - y1)²)
Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment.
Using the distance formula, we can calculate the length of side AB as follows:
AB = sqrt((2 - (-4))²+ (3 - 3)²)
AB = sqrt((6)²+ (0)²)
AB = sqrt(36)
AB = 6
Therefore, the length of side AB of triangle ABC is 6 units.
We can also visualize the triangle on the graph and see that side AB is a horizontal line segment between the points (-4,3) and (2,3), which have the same y-coordinate. This makes the length of AB equal to the horizontal distance between these two points, which is simply 2 - (-4) = 6.
It is important to note that the distance formula can be applied to find the length of any line segment in the coordinate plane, as long as we know the coordinates of its endpoints.
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on thurday, lisa had 5$ in her bank account. she went to target to purchase stickers for her class. each pack of stickers cost 2$
write an inequality that represents s, the number of stickers purchased that resulted in her account ending in -10.
Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. The inequality can be written as: s ≥ 8
What is fractiοn?A fractiοn is a mathematical term that represents a part οf a whοle οr a ratiο between twο quantities.
Let's start by defining the variables and the inequality. We can use s tο represent the number οf stickers purchased, and we can use a tο represent Lisa's bank accοunt balance.
Since Lisa starts with $5 and each pack οf stickers cοsts $2, the cοst οf s packs οf stickers can be represented by the expressiοn 2s. Therefοre, Lisa's bank accοunt balance after purchasing s packs οf stickers can be represented by the expressiοn:
a = 5 - 2s
Tο represent the scenariο where Lisa's accοunt ends up with a balance οf -10, we can write the fοllοwing inequality:
a = 5 - 2s ≤ -10
Simplifying the inequality:
5 - 2s ≤ -10
-2s ≤ -15
s ≥ 7.5
Since we can't purchase a fractiοn οf a pack οf stickers, the smallest number οf packs Lisa wοuld have tο buy tο end up with a balance οf -10 is 8. Therefοre, the inequality can be written as:
s ≥ 8
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What is the solution to this equation? -12x - 7 = 53 Responses a) -5 a) -5 b) 5 b) 5 c) -3.83 c) -3.83 d) 3.83
Answer:
D
Step-by-step explanation:
Marcus is reading a 80-page book. He read the first 20 pages in 30 minutes. If Marcus continues to read a the same rate, how long will it take him to finish the book? Set up the table to represent the information from the problem. Pages Minutes 20 30 You got it! How long will it take Marcus to read his book? Pages Minutes 20 30 80
Using division, we can find that Marcus will take 2 hours or 120 minutes to read the book.
Define division?Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. By dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers.
Marcus is reading a book with 80 pages.
He reads first 20 pages in 30 mins.
So, to read 1 page time taken
= 30/20
= 3/2
= 1.5 mins
Now to read 80 pages, time taken will be:
80 × 1.5
= 120 mins.
Therefore, Marcus will take 2 hours or 120 minutes to read the book.
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Maria's grandmother gave her a gift of $2,000 for her birthday in November 2015. She deposited this into a savings account on January 2, 2016, after the holidays. The savings bank offered 0.725% interest at the time. Over the next year, the inflation rate averaged 1.3%. Now consider the following statements:
Statement I: In 2016, the buying power of Maria's gift decreased by about 0.6%.
Statement II: Maria's gift earned around $14.50 in interest during 2016, but this amount did not keep up with inflation.
Statement III: Maria's savings account had less than $2000 in it by the end of 2016.
Statements I and II are correct, but not Statement III.
None of the statements are correct.
All the statements are correct.
Statements I and III are correct, but not Statements II.
Statements II and III are correct, but not Statements I.
According to the given question we can conclude that statement I and statement II are correct but not statement III.
Define interest?Interest is the cost incurred when lending and borrowing a specific amount of money from a financial standpoint. It is crucial to note that interest is calculated as a percentage.
given,
Statement I is correct because the inflation rate averaged 1.3%, and Maria's savings account earned interest at a rate of 0.725%, which is lower than the inflation rate. This means that the buying power of her gift decreased by approximately 1.3% - 0.725% = 0.575% or 0.6% (rounded).
Statement II is also correct because Maria's savings account earned interest on the deposit of $2,000 for one year at a rate of 0.725%. The interest earned can be calculated as:
Interest = Principal x Rate x Time
Interest = $2,000 x 0.00725 x 1 year
Interest = $14.50
However, statement III is not correct. Since Maria deposited the entire gift of $2,000 into the savings account and did not make any withdrawals during the year, the balance in the account at the end of 2016 would be the sum of the initial deposit and the interest earned, which is $2,000 + $14.50 = $2,014.50. Therefore, the correct option is:
Statement III is incorrect, however Statements I as well as II are true.
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Graph the system of equations.
-x+ 2y = -8
3x-y=-6
If Tan (x) = 1 , find x
Can you help me with this question quickly because I have to do the other questions on other pages?
Answer: Technically its π (pie) 4
Step-by-step explanation:
If tan (x)=1 , then sin x = cos x . We know this is true for x=π4 as a base case. p = nπ , where n is an integer. The first positive value x0 for which tanx=1 is, as stated before, π4 . yw.
True or False. The point (√7, 5) lies on the circle centered at the origin and containing the
point (5,2). Justify your answer.
The point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).
Checking if the point lies on the circle centered at the originThe equation of a cifcle that has its center at the origin is
x² + y² = r²
Where
r = radius
Using the given points, we have
√7² + 5² = r²
Evaluate
32 = r²
For the second point, we have
5² + 2² = r²
Evaluate
29 = r²
The calculated values are not equal
So, the point (√7, 5) does not lie on the circle centered at the origin and containing the point (5,2).
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4. How much of a 560-mg sample of a radioactive substance is left after 102 years if the half-life of the substance is 17 years?
4.67 mg
8.75 mg
64 mg
3,584 mg
Answer:
4.67
Step-by-step explanation:
The hypotheses for this test are Null Hypothesis: p = 0.78, Alternative Hypothesis: p ≠ 0.78. If you randomly sample 23 people and 15 of them believe that global warming is a serious issue, what is your test statistic and p-value?
By answering the presented question, we may conclude that Therefore, null hypothesis the test statistic is -1.942 and the pis 0.050.
What is null hypothesis?A null hypothesis is a sort of statistical hypothesis that asserts that a certain set of observations has no statistical significance. Sample data is used to assess the feasibility of ideas. H0 represents what is sometimes referred to as "zero." The researchers make the premise that there may be a link between the parameters. The null hypothesis, on the other hand, claims that no such association exists. While it may not appear to be relevant, the null hypothesis is a crucial aspect of research.
p = 15/23 = 0.6522
z = (p' - p) / √(p * (1-p) / n)
z = (0.6522 - 0.78) / √(0.78 * (1 - 0.78) / 23) = -1.942
p= 2 * P(Z < -1.942) = 2 * 0.025 = 0.050
Therefore, the test statistic is -1.942 and the 0.050.
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5. A child has eight cans of soft drinks,
consisting of four different brands
with one regular and one diet drink
for each brand. The child arranges four of the cans
in a row in a random manner. Find the probability
that the
(a) arrangement consists of all diet drinks.
(b) first two are diet drinks and the second two are
regular.
The probability of choosing all diet drinks is then: P(all diet drinks) = 24 / 70 ≈ 0.343 or about 34.3%. P(first two are diet drinks and second two are regular) = 288 / 70 ≈ 4.114 or about 4.1%
What is probability?It is expressed as a number between 0 and 1, where 0 represents an impossible event (i.e., it will never happen), and 1 represents a certain event (i.e., it will always happen).
According to question:There are a total of 8 cans of soft drinks, and the child chooses 4 cans to arrange in a row. The total number of ways to choose 4 cans out of 8 is:
C(8,4) = 8! / (4! * 4!) = 70
(a) To find the probability that all four cans are diet drinks, we need to count the number of ways to choose 4 cans that are all diet drinks. Since there is one diet drink for each brand, there are 4 choices for the first can, 3 choices for the second can, 2 choices for the third can, and 1 choice for the fourth can. Therefore, the number of ways to choose 4 cans that are all diet drinks is:
4 * 3 * 2 * 1 = 24
The probability of choosing all diet drinks is then:
P(all diet drinks) = 24 / 70 ≈ 0.343 or about 34.3%
(b) To find the probability that the first two cans are diet drinks and the second two cans are regular drinks, we can count the number of ways to choose 2 diet drinks out of 4 and the number of ways to choose 2 regular drinks out of 4, and then multiply these two numbers together. There are:
C(4,2) = 4! / (2! * 2!) = 6
ways to choose 2 diet drinks out of 4, and also 6 ways to choose 2 regular drinks out of 4. Once we have chosen the 2 diet drinks and 2 regular drinks, there are 4! ways to arrange them in a row. Therefore, the total number of arrangements that have the first two cans as diet drinks and the second two cans as regular drinks is:
6 * 6 * 4! = 288
The probability of this arrangement is then:
P(first two are diet drinks and second two are regular) = 288 / 70 ≈ 4.114 or about 4.1%
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Mila's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
The independent variable, x, represents the number of questions Riley answered correctly, and the dependent variable is the score because the score depends on the number of questions Riley answered correctly. A function relating these variables is R(x) = [3x] So R(23) = [69], meaning 23 correct answers will give a score of 69.
the various kinds of variables.
There are two (2) main categories of variables in an experiment, and these are as follows:
a dependent variable.
the variable that is unrelated.
An independent variable is what?
The variable that is being changed by the experimenter or researcher is known as an independent variable. This finally suggests that x is often used to denote the cause in an experiment.
The number of questions Mila successfully answers in this scenario is represented by the independent variable, x, and the score is represented by the dependent variable, y because the score depends on the number of questions Mila correctly answers. R(x) = [3x] is a function that links these variables. R(23) thus equals [69], indicating 23 correct responses.
Complete Question:
Mila's math teacher said that each question answered correctly on a test would be worth 3 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
The independent variable, x, represents the ______, and the dependent variable is the ______, because the ______ depends on the
A function relating these variables is R(x) = [] So R(23) = [], meaning 23
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The function f(x) = x2 is graphed above. Which of the graphs below represents the function g(x) = (x + 1)2? A parabola declines through (negative 2, 5), (negative 1 point 5, 3), (negative 1, 2), (0, 1) and rises through (1, 2), (1 point 5, 3) and (2, 5) on the x y coordinate plane. W. A parabola declines through (negative 2, 3), (negative 1 point 5, 1), (1, 0), (0, negative 1) and rises through (1, 1), (1 point 5, 1) and (2, 2) on the x y coordinate plane. X. A parabola declines through (negative 3, 4), (negative 2 point 5, 2), (negative 2, 1), (negative 1, 0), (0, 1), (0 point 5, 2) and (1, 4) on the x y coordinate plane. Y. A parabola declines through (negative 1, 4), (negative 0 point 5, 2), (0, 1) and (1, 0) and rises through (2, 1), (2 point 5, 2) and (3, 4) on the x y coordinate plane. Z. A. W B. X C. Y D. Z'
Answer:
374753
Step-by-step explanation:
this is not correct question
A sample of 2,047 American adults was asked how they viewed China, with 29% of respondents calling the country "unfriendly" and 9% of respondents indicating the country was "an enemy." Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."
To construct a confidence interval for the proportion of American adults who viewed China as either "unfriendly" or "an enemy," we can use the following formula:
CI = p ± z*(√(p(1-p)/n))
where:
CI is the confidence interval
p is the sample proportion (0.29 + 0.09 = 0.38)
z is the critical value for the desired confidence level (95% confidence level corresponds to z = 1.96)
n is the sample size (2,047)
Plugging in the values, we get:
CI = 0.38 ± 1.96*(√(0.38*(1-0.38)/2047))
CI = 0.38 ± 0.018
CI = (0.362, 0.398)
Therefore, we can say with 95% confidence that the true proportion of American adults who view China as either "unfriendly" or "an enemy" is between 0.362 and 0.398.
A rectangle is drawn so the width is 14 inches longer than the height .If the rectangle’s diagonal measurement is 34 inches, find the height
Answer:
Let the height be represented as x
width = 14 + x
Length of diagonal = 34 inches.
Taking one diagonal of the rectangle to form a triangle.
using the Pythagoras theorem.
34² = (14 + x)² + x²
1156 = 196 + 28x + x² + x²
2x² + 28x - 960 = 0
divide through by 2
x² + 14x - 480 = 0
x² + 30x - 16x - 480 = 0
x(x + 30) - 16 (x + 30) = 0
(x - 16) = 0 or (x + 30) = 0
x = 16 or x = - 30
since the length can't be negative
therefore 16 inches is correct
What are the answers to these questions?
a) d/dx=?
b) d/dx=?
The indicated derivatives in the question can be found to be :
a. = 3x^2 x e^(x^3)b. = (ln(x)/6) × x^((ln(x)/6) - 1)How to find the derivatives ?To find the derivative of e^(x^3) + log_3(pi) with respect to x, we apply the rules of differentiation to each term:
Using the chain rule, we have:
d/dx (e^(x^3)) = e^(x^3) x (3x^2)
The derivative of log_3(pi) is 0, because log_3(pi) is a constant and the derivative of a constant is 0.
So, the derivative of the entire expression is:
d/dx (e^(x^3) + log_3(pi)) = e^(x^3) x 3x^2 + 0 = 3x^2 x e^(x^3)
To find the derivative of (x^(1/6))^ln(x) with respect to x, we first simplify the expression by using the power rule of logarithms:
(x^(1/6))^ln(x) = x^(ln(x)/6)
Now, we find the derivative of x^(ln(x)/6) using the chain rule:
d/dx (x^(ln(x)/6)) = (ln(x)/6) × x^((ln(x)/6) - 1) × d/dx (x)
The derivative of x is 1, so:
d/dx ((x^(1/6))^ln(x)) = (ln(x)/6) × x^((ln(x)/6) - 1) × 1 = (ln(x)/6) × x^((ln(x)/6) - 1)
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The first graph displays the race times for a group of runners from last year. The
second graph displays the runners' race times from this year.
Which graph has the larger range?
O The first graph has the larger range
The second graph has the larger range
Both graphs have the same range
The range cannot be determined for either graph
To determine which graph has the larger range, we need to understand what is meant by the term “range” in the context of graphs. the answer is: O The first graph has the larger range.
What are the maximum and minimum values in a dataset?In statistics, the range is defined as the difference between the maximum and minimum values in a dataset. It provides a measure of how spread out the data is, and can be used to identify the extent of variability within a dataset.
Looking at the first graph, we can see that the range of race times is from approximately 10 minutes to 25 minutes. Therefore, the range of this dataset is [tex]25 - 10 = 15[/tex] minutes.
Looking at the second graph, we can see that the range of race times is from approximately 8 minutes to 22 minutes. Therefore, the range of this dataset is [tex]22 - 8 = 14[/tex] minutes.
Since the range of the first graph is [tex]15[/tex] minutes and the range of the second graph is [tex]14[/tex] minutes, we can conclude that the first graph has the larger range.
Therefore, the answer is: O. The first graph has the larger range.
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A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. Find P(X=3). Round your answer to three decimal places.
The probability of exactly 3 out of 10 vehicles exceeding the speed limit on US 131 is 0.250.
This problem can be solved using the binomial distribution. We are given that the probability of any given vehicle exceeding the speed limit is p = 0.6, and we are interested in the probability of 3 out of 10 vehicles exceeding the speed limit, i.e., X = 3.
The probability mass function of the binomial distribution is given by:
P(X = k) = (n choose k) ×p^k ×(1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient, which is equal to n!/(k! (n-k)!).
Substituting the given values, we get:
P(X = 3) = (10 choose 3) × 0.6³ ×0.4⁷
P(X = 3) = 0.250
Therefore, the probability of exactly 3 out of 10 vehicles exceeding the speed limit on US 131 is 0.250, rounded to three decimal places.
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(1) Determine the contribution margin per direct-labor hour expended on each product.
(2) Prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year.
The total direct labor hours for each product to get the total direct labor hours required for the projected sales during the coming year.
To determine the contribution margin per direct-labor hour expended on each product, you will need to calculate the contribution margin for each product and divide it by the number of direct labor hours required to produce that product.
Contribution Margin = Sales Revenue - Variable Costs
Once you have calculated the contribution margin for each product, you can divide it by the number of direct labor hours required to produce that product to get the contribution margin per direct-labor hour.
To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, you will need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.
Multiply the number of units by the number of direct labor hours per unit to get the total direct labor hours required for each product.
Contribution Margin = $40 - $20 - $5 - $3 = $12
Direct Labor Hours per unit = 2
Contribution Margin per Direct-Labor Hour = $12 / 2 = $6 MMK YU GHTJUIO7U
Contribution Margin = $60 - $25 - $10 - $5 = $20
Direct Labor Hours per unit = 4
Contribution Margin per Direct-Labor Hour = $20 / 4 = $5
Contribution Margin = $80 - $30 - $15 - $10 = $25
Direct Labor Hours per unit = 5
Contribution Margin per Direct-Labor Hour = $25 / 5 = $5
To prepare a schedule showing the total direct labor hours that will be required to produce the projected sales during the coming year, we need to estimate the number of units that will be sold for each product and the number of direct labor hours required to produce each unit.
Assuming that the projected sales for the coming year are as follows:
Product A: 10,000 units
Product B: 8,000 units
Product C: 5,000 units
And the number of direct labor hours required to produce each unit are as follows:
Product A: 2 hours per unit
Product B: 4 hours per unitF
Product C: 5 hours per unit
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simplify expression
(1+cos a)(1-cos(-a))
Why does -2^2= -4 but (-2)^2= 4?
Answer:
The reason why -2^2=-4 and (-2)^2=4 is due to the rules of mathematical operations and the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
According to the order of operations, when you have an expression with multiple operations, you must perform the operations in a specific order. Exponents come before multiplication and division, and before addition and subtraction.
So, when evaluating -2^2, you first evaluate the exponent, which is 2. However, the negative sign in front of the 2 is not part of the exponent, but rather an arithmetic operation. Therefore, the expression is equivalent to -(2^2), which is equal to -4.
On the other hand, when evaluating (-2)^2, the parentheses indicate that the negative sign is part of the base, so you must first evaluate the base, which is -2, and then apply the exponent of 2. This gives you (-2)^2 = 4.
Step-by-step explanation:
The minus in (-2)^2 is enclosed in parentheses, so it is also squared:
minus × minus = plus
And talking about this one: -2^2, the minus is not included in the parentheses, that's why we only square the number (2 in this case) and keep the minus in front of it
I hope this will help...
please help me with math the following questions are
what is the mean of the data represented by the stem and the leaf plot above
-164.5
-309
-57
-108.75
what is the median of the data represented by the steam and leaf plot
a 164.5
b 57
c 108.75
d 309
For the givn steam and leaf plot, the mean= 11.61 and the median = 7.
What is mean?
In mathematics, the mean is a measure of central tendency of a set of numbers. It is also known as the average.
To find the mean of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.
The stem and leaf plot indicates that we have the following values:
For stem 1: 0, 0, 2, 8
For stem 3: 1, 7, 9
For stem 5: 0, 5, 7, 7, 7
For stem 11: 3, 4, 6
For stem 22: 3
For stem 23: 5
For stem 31: 0, 2, 9
To calculate the mean, we add up all these values and divide by the total number of values.
There are a total of 18 values, so:
(1x4 + 3x3 + 5x5 + 11x3 + 22x1 + 23x1 + 31x3) / 18
= (4 + 9 + 25 + 33 + 22 + 23 + 93) / 18
= 209 / 18
= 11.61 (rounded to two decimal places)
Therefore, the mean of the data represented by the stem and leaf plot is approximately 11.61.
To find the median of the data represented by the stem and leaf plot, we need to first determine the actual values represented by the plot.
The stem and leaf plot indicates that we have the following values:
For stem 1: 0, 0, 2, 8
For stem 3: 1, 7, 9
For stem 5: 0, 5, 7, 7, 7
For stem 11: 3, 4, 6
For stem 22: 3
For stem 23: 5
For stem 31: 0, 2, 9
We can list all the values in order from smallest to largest:
0, 0, 2, 3, 3, 4, 5, 5, 6, 7, 7, 7, 8, 9, 11, 29, 31
There are a total of 17 values. Since there is an odd number of values, the median is the middle value.
The middle value is the ninth value in the ordered list, which is 7.
Therefore, the median of the data represented by the stem and leaf plot is 7.
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Dmitri wants to cover the top and sides of the box shown with glass tiles that are 5 mm square. How many tiles does he need?
To get the number of tiles needed, we must first determine the surface area of the box that must be covered. Surface area of the square box = top area + front area + rear area + left side area + right side area.
Top area = length x width = 6 cm x 4 cm = 24 cm2 Front and back area = height x breadth = 8 cm x 4 cm = 32 cm2 (for each) Left and right side area = height x length = 8 cm x 6 cm = 48 cm2 (for each) Surface area total = 24 + 2(32) + 2(48) = 232 cm2. To get the number of tiles needed, divide the total surface area by the area of each tile. each's area 5 mm × 5 mm = 0.25 cm2 tile Total surface area / Area of each tile = 232 / 0.25 = 928 tiles required As a result, Dmitri need 928 glass tiles to cover the top and sides of the box.
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Four transformations of the function f (x ) = 3x are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
The expressiοn that shοws the result οf that transfοrmatiοn intο the bοx under it are [tex]f(x) - 4 = 3^{x} - 4[/tex]
What is transfοrmatiοn?In mathematics, a transfοrmatiοn refers tο a prοcess οr οperatiοn that changes the pοsitiοn, shape, οr size οf a geοmetric figure οr οbject in a cοοrdinate plane οr space. Transfοrmatiοns can be classified intο several types, including translatiοns, reflectiοns, rοtatiοns, dilatiοns, and cοmbinatiοns οf these.
Each type οf transfοrmatiοn invοlves a set οf rules οr fοrmulas that define hοw the οriginal οbject οr figure is transfοrmed intο a new οne. Transfοrmatiοns play an impοrtant rοle in many areas οf mathematics and science, including geοmetry, linear algebra, cοmputer graphics, and physics.
given functiοn : [tex]f (x ) = 3^{x}[/tex]
fοr transfοrmatiοn, we need tο replace value οf x by the value given in different parts.
part 1 :
-4 f(x) = ?
we have [tex]f (x ) = 3^{x}[/tex]
sο, -4 × f (x ) = -4 × [tex]3^x[/tex]
∴ -4 f(x) = -4 × [tex]3^{x}[/tex]
part 2 :
f(-4x) = ?
we have f (x ) = [tex]3^{x}[/tex]
replacing value οf x by -4x,
∴ f(-4x) = [tex]3^{-4x}[/tex]
part 3
: f(x-4) = ?
we have [tex]f (x ) = 3^{x}[/tex]
sο, replacing value οf x by x-4,
∴[tex]f(x-4) = 3^{x-4}[/tex]
part 4 :
f(x) - 4 = ?
we have [tex]f (x ) =3^{x}[/tex]
sο, [tex]f(x) - 4 = 3^{x} - 4[/tex]
Hence the sοlutiοn are
-4 f(x) = -4 × [tex]3^{x}[/tex]
f(-4x) = [tex]3^{-4x}[/tex]
f(x-4) = [tex]3^{x-4}[/tex]
f(x) - 4 = [tex]3^{x} - 4[/tex]
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Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output ((¬p ∨ ¬r) ∧ ¬q) ∨ (¬p ∧ (q ∨ r)) from input bits p, q, and r.
Step-by-step explanation:
The required combinatorial circuit can be constructed as follows:
Firstly, we need to find the negation of p, q and r which can be achieved using inverters as shown below:
p q r
| | |
| | |
NOT NOT NOT
| | |
| | |
~p ~q ~r
Next, we can use OR gates to form the term (¬p ∨ ¬r) and (q ∨ r) as shown below:
~p ~r q r
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| | | |
OR OR | |
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pORr rORp qORr rORq
Then, we can use AND gates to form the terms (¬p ∨ ¬r) ∧ ¬q and ¬p ∧ (q ∨ r) as shown below:
~p ~r q r
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| | | |
OR OR | |
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pORr rORp qORr rORq
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NOT NOT NOT |
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~q ~pORr ~qORr qORr
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AND OR AND |
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(~pORr ~q) qORr qORr
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OR AND |
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(~pORr ∨ ~q) (~pORr ∧ qORr)
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| | |
| OR |
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((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))
| | |
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| | |
OUTPUT
((~pORr ∨ ~q) ∨ (~pORr ∧ qORr))
Help Please I will give 20points
Answer:
10 acres
Step-by-step explanation:
Land for coconuts =
[tex] \frac{3}{8} = \frac{15}{40} [/tex]
Land for bananas =
[tex] \frac{4}{5} \times \frac{5}{8} = \frac{20}{40} \\ = \frac{4}{8} \\ = \frac{1}{2} [/tex]
Land left for rice =
[tex] \frac{40}{40} - \frac{15}{40} - \frac{20}{40} = \frac{5}{40} \\ = \frac{1}{8} [/tex]
Land for bananas =
[tex] \frac{1}{8} = 2.5 \\ \frac{4}{8} = 2.5 \times 4 \\ = 10[/tex]
You spin the spinner and flip a coin. Find the probability of the compound event.
Answer: 20%
(Please give me brainliest if you can tomorrow, hopefully this helps)
Explanation:
(So if it's even)
There are 5 possible outcomes and 2 evens on the spinner, so 2 favorable outcomes. That gives us a fraction of 2/5.
Flipping a coin, either heads or tails, it'd be 1/2.
Since it's a compound event we would multiply 2/5 and 1/2, getting:
[tex]\frac{2}{5} *\frac{1}{2} = \frac{2}{10}[/tex]
To change that into a percentage, we divide the numerator by the denominator and multiply by 100 which would give us:
.2 * 100 = 20%
9(40÷5+9)+15-9
I need help solving this problem
Answer:
The answer to the problem is 159