Find the tangential and normal components of the acceleration vector.
r(t) = 8t i + cos2(t) j + sin2(t) k
Answers
The tangential component of the acceleration vector is (4sin(t)cos(t)^3) / sqrt(64 + 8sin^2(t)cos^2(t)), and the normal component is -2cos^2(t) + 2sin^2(t) j + 2cos^2(t) k - (4sin(t)cos(t)^3 / sqrt(64 + 8sin^2(t)cos^2(t))) v(t).
To find the tangential and normal components of the acceleration vector, we first need to determine the velocity and acceleration vectors.
Given the position vector r(t) = 8t i + cos^2(t) j + sin^2(t) k, we can find the velocity vector v(t) by taking the derivative with respect to time:
v(t) = dr(t)/dt = 8i - 2sin(t)cos(t) j + 2sin(t)cos(t) k.
Next, we differentiate the velocity vector to find the acceleration vector a(t):
a(t) = dv(t)/dt = 0i - 2cos^2(t) + 2sin^2(t) j + 2cos^2(t) k.
Now, we can decompose the acceleration vector into its tangential and normal components.
The tangential component of acceleration, aT, is the component of acceleration in the direction of the velocity vector. It is given by the projection of the acceleration vector onto the velocity vector. We can find it using the formula:
aT = (a · v) / ||v||,
where "·" represents the dot product and "||v||" represents the magnitude of the velocity vector.
The normal component of acceleration, aN, is the component of acceleration perpendicular to the velocity vector. It is given by the substraction of the tangential component from the acceleration vector:
aN = a - aT.
Let's calculate the tangential and normal components of the acceleration vector.
Magnitude of the velocity vector:
||v|| = sqrt((8)^2 + (-2sin(t)cos(t))^2 + (2sin(t)cos(t))^2)
= sqrt(64 + 4sin^2(t)cos^2(t) + 4sin^2(t)cos^2(t))
= sqrt(64 + 8sin^2(t)cos^2(t)).
Dot product of acceleration and velocity vectors:
a · v = (0)(8) + (-2cos^2(t) + 2sin^2(t))(0) + (2cos^2(t))(2sin(t)cos(t))
= 0 + 0 + 4sin(t)cos(t)^3.
Tangential component of acceleration:
aT= (a · v) / ||v||
= (4sin(t)cos(t)^3) / sqrt(64 + 8sin^2(t)cos^2(t)).
Normal component of acceleration:
aN = a - aT
= -2cos^2(t) + 2sin^2(t) j + 2cos^2(t) k - (4sin(t)cos(t)^3 / sqrt(64 + 8sin^2(t)cos^2(t))) v(t).
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Related Questions
Help me with this question on congruent triangles? 20 points
Answers
Answer:
a) 5.7 cm
b) 3.05 cm
Step-by-step explanation:
a)
Since BE is parallel to CD,
Then AB/AC = BE/CD
So Length of CD = 12.3/8.2 x 3.8 = 5.7 cm
b)
AB/AC = AE/AD
So length of AE = 8.2/12/3 x 9.15 = 6.1 cm
ED = AD - AE = 9.15 - 6.1 = 3.05 cm
For rhis problem you will have to simplify correctly .
Answers
Answer:
Step-by-step explanation:
Answer:
The mistake was -9, the answer is 1x -6
Step-by-step explanation:
3 (x - 6) + (4x + 12) - 6x =
3x - 18 + 4x + 12 - 6x = (use distributive property for this step)
3x + 4x - 6x - 18 + 12 = (rearrange so like terms are easy to find)
1x - 6 (use addition and subtraction to get the final answer)
I hope this helps you :)
Waldo Books needs to decide how many copies of a new hardcover release to purchase for its shelves. The store has assumed that demand will be 50, 100, 150, or 200 copies next month, and it needs to decide whether to order 50, 100, 150, or 200 books for this period. Each book costs Waldo $20 and can be sold for $30. Waldo can sell any unsold books back to the supplier for $4.
(a) Which option should Waldo choose if it uses the maximax criterion?
(b) Which option should Waldo choose if it uses the maximin criterion?
(c) Which option should Waldo choose if it uses the equally likely criterion?
(d) Which option should Waldo choose if it uses the criterion of realism with a = 0.7?
(e) Which option should Waldo choose if it uses the minimax regret criterion?
Answers
Answer:
(a) Maximax criterion: Order 200 books.
(b) Maximin criterion: Order 200 books.
(c) Equally likely criterion: Order 200 books.
(d) Criterion of realism with a = 0.7: Calculate the expected payoff based on the chosen value of a and select the corresponding option.
(e) Minimax regret criterion: Order 200 books.
Step-by-step explanation:
The maximax criterion involves selecting the option with the highest possible payoff. We will calculate the maximum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 = $1500
Maximum payoff = $1500Payoff for ordering 100 books:
Revenue = 30 * 100 = $3000
Maximum payoff = $3000Payoff for ordering 150 books:
Revenue = 30 * 150 = $4500
Maximum payoff = $4500Payoff for ordering 200 books:
Revenue = 30 * 200 = $6000
Maximum payoff = $6000Based on the maximax criterion, Waldo should choose the option of ordering 200 books since it has the highest maximum payoff.(b) Maximin Criterion:
The maximin criterion involves selecting the option with the highest minimum payoff. We will calculate the minimum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 - (20 * 50 - 4 * 50) = $900
Minimum payoff = $900Payoff for ordering 100 books:
Revenue = 30 * 100 - (20 * 100 - 4 * 100) = $1800
Minimum payoff = $1800Payoff for ordering 150 books:
Revenue = 30 * 150 - (20 * 150 - 4 * 150) = $2700
Minimum payoff = $2700Payoff for ordering 200 books:
Revenue = 30 * 200 - (20 * 200 - 4 * 200) = $3600
Minimum payoff = $3600Based on the maximin criterion, Waldo should choose the option of ordering 200 books since it has the highest minimum payoff.(c) Equally Likely Criterion:
The equally likely criterion assumes that each demand level is equally likely to occur. We will calculate the expected payoff for each option and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = (30 * 50 + 4 * (50 - 50)) / 4 = $375
Expected payoff = $375Expected payoff for ordering 100 books:
Expected revenue = (30 * 100 + 4 * (50 - 100)) / 4 = $750
Expected payoff = $750Expected payoff for ordering 150 books:
Expected revenue = (30 * 150 + 4 * (50 - 150)) / 4 = $1125
Expected payoff = $1125Expected payoff for ordering 200 books:
Expected revenue = (30 * 200 + 4 * (50 - 200)) / 4 = $1500
Expected payoff = $1500Based on the equally likely criterion, Waldo should choose the option of ordering 200 books since it has the highest expected payoff.(d) Criterion of Realism with a = 0.7:
The criterion of realism involves assigning a weight (0 ≤ a ≤ 1) to the optimistic payoff and the remaining weight (1 - a) to the pessimistic payoff. We will calculate the expected payoff for each option using the given value of a and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = a * (30 * 50) + (1 - a) * (30 * 50 - 20 * 50 + 4 * 50) = $450a
Expected payoff = $450aExpected payoff for ordering 100 books:
Expected revenue = a * (30 * 100) + (1 - a) * (30 * 100 - 20 * 100 + 4 * 100) = $900a
Expected payoff = $900aExpected payoff for ordering 150 books:
Expected revenue = a * (30 * 150) + (1 - a) * (30 * 150 - 20 * 150 + 4 * 150) = $1350a
Expected payoff = $1350aExpected payoff for ordering 200 books:
Expected revenue = a * (30 * 200) + (1 - a) * (30 * 200 - 20 * 200 + 4 * 200) = $1800a
Expected payoff = $1800aTo find the maximum expected payoff, we can compare the values of a * 450, a * 900, a * 1350, and a * 1800 for different values of a. The optimal value of a will determine the corresponding option.(e) Minimax Regret Criterion:
The minimax regret criterion involves calculating the regret for each option and selecting the one with the minimum regret. Regret represents the difference between the maximum possible payoff and the actual payoff.Regret for ordering 50 books:
Regret = 6000 - (30 * 50 - (20 * 50 - 4 * 50)) = $5250
Minimum regret = $5250Regret for ordering 100 books:
Regret = 6000 - (30 * 100 - (20 * 100 - 4 * 100)) = $4200
Minimum regret = $4200Regret for ordering 150 books:
Regret = 6000 - (30 * 150 - (20 * 150 - 4 * 150)) = $3150
Minimum regret = $3150Regret for ordering 200 books:
Regret = 6000 - (30 * 200 - (20 * 200 - 4 * 200)) = $2100
Minimum regret = $2100Based on the minimax regret criterion, Waldo should choose the option of ordering 200 books since it has the minimum regret.
Waldo Books is facing a decision theory problem. By different criteria, the decision to order books can change. By maximax, Waldo should order 200 books, by maximin, 50 books. By equally likely, realism, and minimax regret criteria, computations considering payoffs, optimism levels, and potential regrets are needed.
Explanation:This is a "decision theory problem" in the field of business and economics. Let's calculate the profit from each option. Profit will be $10 for each book sold (revenue of $30 minus cost of $20) and a loss of $16 for each book not sold (cost of $20 minus resell value of $4).
Maximax criterion is when Waldo selects the alternative with the highest possible outcome. In this case, Waldo should order 200 books as he could make the most profit if demand is also at 200. Maximin criterion is when Waldo chooses the option with the best worst-case scenario. Here, Waldo should order 50 books as this would minimize the potential for unsold books. For the equally likely criterion, each level of demand is assumed to be equally probable, so the average profit for each order size should be calculated. The number with the highest average profit should be chosen. In the criterion of realism (also considered a 'compromise' criterion), there's a coefficient of optimism (a value between 0 and 1) that measures the decision-maker's optimism. Here, 'a' is 0.7. The larger the 'a', the more optimistic the decision-maker is. We calculate [a*(max payoff)+(1-a)*(min payoff)] for each alternative and pick the largest. The minimax regret criterion is about minimizing the maximum regret. Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision with the smallest maximum 'regret' is chosen. Learn more about Decision Theory here:
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The weights of tennis balls are normally distributed, with the mean being 5.15 ounces and the standard deviation being 0.10. what percentage of the balls weigh within one standard deviation of the mean?
Answers
The correct option is B.
Thus, 68% percentage of the balls weigh within one standard deviation of the mean.
What is the empirical formula rule?The Empirical Rule indicates that 99.7% of data that are observed to have a normal distribution fall within 3 standard deviations of the mean. According to this formula, 68 percent of the data are within one standard deviation, 95 percent are within two standard deviations, and 99.7 percent are within three standard deviations of the mean.
According to the empirical formula rule:Because approximately 68% of the data falls within a standard deviation of the mean, according to the empirical rule, 68% of the balls' weights fall within that range.
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I understand that the question you are looking for is:
The weights of tennis balls are normally distributed, with the mean being 5.15 ounces and the standard deviation being 0.10. what percentage of the balls weigh within one standard deviation of the mean
A. 50%
B. 68%
C. 95%
D. 99.7%
Find the real square roots of each number. 1/100
Answers
The real square roots of 1/100 are ±1/10. To find them, take the square root of both sides of the equation x^2 = 1/100, simplify, and consider the positive values.
To find the real square roots of 1/100, we need to find the values of x that satisfy the equation x^2 = 1/100.
1. Take the square root of both sides of the equation:
√(x^2) = √(1/100)
2. Simplify:
|x| = 1/10
3. Since the square root of a number is always positive, we can conclude that the real square roots of 1/100 are ±1/10.
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HELP THIS IS DUE TODAY AND I NEED THIS DONE
Answers
Answer:
1240 cm²
Step-by-step explanation:
Surface area of triangular prism:\(\boxed{\text{\bf Surface area of triangular prism = bh + (s_1+s_2+s_3)*l }}\)
\(\boxed{ \text{ \bf Surface area of triangular prism = $ \bf bh + (s_1+s_2+s_3)*l$ }}\)
b = base of the triangle = 16 cm
h = altitude of the triangle = 15 cm
s1 , s2 ,s3 are the edges of the triangle
s1 = 16 cm ; s2 = 17cm ; s3 = 17 cm
l = length of the rectangle = 20 cm
Surface area = 16*15 + (16 + 17 + 17)*20
= 240 + 50*20
= 240 + 1000
= 1240 cm²
which of the following functions is graphed?
A. y= |x - 2| - 3
B. y= |x + 2| - 3
C. y= |x + 2| + 3
D. y= |x - 2| + 3
Answers
Answer:
c
Step-by-step explanation:
darlene uses 4 nails for every 12 inches of wood how many nails will she use in 6 feet of wood
Answers
Answer:
she will use 24 nails
Step-by-step explanation:
Brainliest plz
Answer:24 nails
Step-by-step
How much money will you have in 6 months if you invest $1000 at 3% compounded monthly?
Answers
Step-by-step explanation
Answers
The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 3% per year compounded 12 times per year over 0.5 years is $1,015.09.
Compound InterestGiven Data
Principal = $1000Rate = 3%Time = 6 months = 0.5 yearsFirst, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 1,000.00(1 + 0.03/12)^(12)(0.5)
A = 1,000.00(1 + 0.0025)^(6)
A = $1,015.09
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In a school annual Day 60 students involved is Science Exhibition, 75 involved in Mathematics Exhibition, 20 involved in both Exhibitions, and the rest of 285 students are not involved in any exhibition. Illustrate the above information in a Venn- diagrom. How many students took part in Schools Annual Day? How many of them involved in only one exhibition ?
Answers
Answer:
440 man its so easy just add up all the numbers
Step-by-step explanation:
440
Answer:
1) See the explanation
2) 400 Students
3) 95 Students
Step-by-step explanation:
1) As can be known from the question
Then, draw the venn diagram according to the known conditions.
2) 60 + 75 - 20 = 115 { Draw a venn diagram to calculate }
115 + 285 = 400
3) 60 - 20 + 75 - 20 = 95 ( Draw a venn diagram to calculate }
Choose an expression that is equivalent to negative four raised to the fourth power divided by negative four raised to the second power.
negative four raised to the second power divided by negative four raised to the fourth power
negative four raised to the fifth power divided by negative four
negative four raised to the sixth power divided by negative four raised to the fourth power
negative four divided by negative four raised to the fifth power
Answers
Answer:
C
Step-by-step explanation:
negative four raised to the sixth power divided by negative four raised to the fourth power
because negative four raised to the fourth power divided by negative four raised to the second power = negative four raised to the second power
negative four raised to the sixth power divided by negative four raised to the fourth power also = negative four raised to the second power
The answer is A: negative four raised to the second power divided by negative four raised to the fourth power. This is obtained by applying the rules of exponents, specifically, when dividing with the same base, subtract the exponents.
Explanation:This question pertains to exponents division rules. According to the rule of Power of a Power in exponents, when you divide expressions with the same base, you subtract the exponents. So if you have negative four raised to the fourth power (-4⁴) and you want to divide it by negative four raised to the second power (-4²), you subtract 2 from 4 to get an exponent of 2. This results in a negative four raised to the second power (-4²). So, the correct option from the given choices in your question is A: negative four raised to the second power divided by negative four raised to the fourth power.
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how to find percentage?
Answers
> NEXT E Question 416 Sally and Bobby run every Saturday. The equation d = 5h represents Sally's running rate, where "d" is her distance run in miles and "h" is the number of hours spend running. The graph below represents Bobby's running rate. Bobby's Running у 12 10 8 Distance (mi) 6 1 2 3 4 Time (hr) Choose from the drop-down menu to complete the sentence.
Answers
Answer: Sally
Step-by-step explanation:
True of False: A synonym for pyramidal plan is cubism, which also describes the artistic emphasis on geometric shape.
Answer:
False
Answers
The given statement "A synonym for pyramidal plan is cubism, which also describes the artistic emphasis on geometric shape" is False
A Pyramidal Plan is a specific kind of floor plan with a triangular shape that has a broad base and converges to a point at the top, resembling the shape of a pyramid.
Pyramidal plans can be found in many different types of buildings and structures, including churches, temples, and other religious structures, as well as some secular structures.
Cubism is a style of art that emerged in the early twentieth century and was characterized by a focus on geometric shapes and forms.
The term "cubism" comes from the fact that many of the paintings and sculptures created in this style consisted of complex shapes that were organized into a grid-like pattern that resembled a series of cubes.
However, the given statement is false. Pyramidal Plan is not a synonym for cubism as pyramidal plan has nothing to do with art or geometry.
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BRAINLIST!!
The number of pages read by eight different students during a one hour reading class was used to create the box plot shown above. Which of the sets of numbers below matches the given box plot?
Answers
Answer:
C. Pages Read in an Hour: 10, 14, 16, 16, 18, 19, 21, 25
Step-by-step explanation: Got it on my study island question.
When the scale factor between two circles is “x” the scale factor between the 1_________________________is also “x” and the scale factor of the _________________________is “x2”
Answers
Answer:
When the scale factor between two circles is “x” the scale factor between the radius is also “x” and the scale factor of the area is “x^2"
this is only one possible answer. For example, instead of radius, you could have put diameter or circumference.
Can you check these for my please it would be much appreciated! And yes I will mark brainliest
Answers
ΔDEF ≅ Δ RPQ by ASA rule and line segment RF ≅ line segment HR.
In triangle DEF and triangle PQR,
We can see that:
DF = RQ = 5cm
0∠D = ∠Q = 60°
∠F = ∠R = 80°
So, we get that:
ΔDEF ≅ Δ RPQ ( ASA rule.)
Also, we are given that:
quadrilateral RAUF ≅ Quadrilateral HBQR
This means that:
line segment RF ≅ line segment HR.
Therefore we get that, ΔDEF ≅ Δ RPQ by ASA rule and line segment RF ≅ line segment HR.
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Acme T-Shirt Company charges a $50 set-up fee plus $9 for each shirt printed. Beta T-shirt Company has no set up fee, but charges $14 per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?
Answers
Answer:
Step-by-step explanation:
Acme Company:
Let the number of shirts = x
Cost = 50 + 9x
Beta Company:
Cost = 14x
50 + 9x < 14x
Subtract 9x from both sides
50 < 14x - 9x
50 < 5x
Divide both sides by 5
50/5 < x
10 < x
Minimum number of shirts for which a customer saves money by using Acme = 11 T-shirts
Please solve number 9.
Answers
Answer:
Rs 400
Step-by-step explanation:
MP: market price
CP: cost price
MP = 1.4CP
(MP - 0.15MP) - CP = 76
0.85MP - CP = 76
0.85(1.4CP) - CP = 76
1.19MP - MP = 76
0.19MP = 76
MP = 400
a man and a woman, both with brown eyes (bb), have a child. what is the percentage chance that the child will have blue eyes?
Answers
If a man and a woman, both with brown eyes (Bb), have a child, then the percentage chance that the child will have blue eyes will be 25%.
Cindy's age, x, is 3 times her age 6 years ago.
Answers
The algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
The given statement is Cindy's age, x, is 3 times her age 6 years ago.
We need to represent the given statement as the algebraic expression.
What is an algebraic expression?In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
6 years ago Cindy's age(x) is x-6.
3 times Cindy's age=3(x-6)
Therefore, the algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
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question 2 (10 points)
Answers
The slope of the line between the two points defined in the graph is 1/2.
Slope of the line:
The slope of a line is the change in y coordinate with respect to the change in x coordinate.
m = Δy/Δx
Where the net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx. Where “m” is the slope of a line
Given,
There is a graph presented here.
Through the graph we have identified two points,
They are (3,0) and (-3, -3).
Now we need to find the slope of the line between these points.
Here we consider the values of (x1,y1) as (3,0) and the value of (x2,y2) as (-3,-3).
Through the values we have to identify the slope of the line.
For that, we have to apply the values on the formula,
Then we get,
m = (-3 - 0)/(-3-3)
m = -3/-6
m = 1/2
Therefore, the slope of the line is 1/2.
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6|x - 2| -15= -9|x -2| + 15 PLs help me im a sophomore I'll give anyone a thanks !
Answers
Answer:
6|x - 2| -15= -9|x -2| + 15
x=4,0
a circle with diameter $2$ is translated $5$ units. what is the perimeter of the region swept out by the circle?
Answers
The perimeter of the region swept out by the circle during translation is 2π units.
When a circle is translated, its shape remains the same, but its position in space changes. The perimeter of the region swept out by the circle during translation will be the same as the perimeter of the circle itself.
Given:
Diameter of the circle = 2 units
Translation distance = 5 units
Calculate the radius of the circle.
Radius (r) = Diameter / 2
r = 2 / 2
r = 1 unit
Calculate the perimeter of the circle.
Perimeter of a circle (P) = 2 x π x r
P = 2 x π x 1
P = 2π units
Therefore, the perimeter of the region swept out by the circle during translation is 2π units.
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A region's average movie theater ticket price in 2007 was "$6.08." For 2017, it was estimated to be $7.58. Find the percent of increase in average movie theater ticket price for this 10-year period.
Answers
The percent of increase in average movie theater ticket price for this 10-year period is 24.67% rounded to 2 decimal places
What is percentage increase?
Percentage increase between two numbers can determined as the new number divided the old number minus 1
percentage of increase=(2017 theater ticket price/2007 theater ticket price)-1
2017 theater ticket price=$7.58
2007 theater ticket price=$6.08
percentage of increase=($7.58/$6.08)-1
percentage of increase=24.67%
In other words, over the 10-year period, the theater ticket price has increased by approximately 25%
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For a standard normal distribution, determine the probabilities in parts a through d below
Click here to view page 1 of the standard normal probabilly table.
Click here to view page 2 of the standard normal probabilly table
a. Find P(z ≤ 1.54).
P( z ≤ 1.54) =
(Round to four decimal places as needed.)
Answers
The probability of finding a z-score of 1.54 or lower on the normal distribution is given as follows:
P(z ≤ 1.54) = 0.9382.
How to obtain the probability?The z-score of this problem is given as follows:
z = 1.54.
Each z-score has a p-value, which represents the percentile of the z-score.
Hence the probability of finding a z-score of 1.54 or lower on the normal distribution is the p-value of z = 1.54, which is of 0.9382.
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Please Help I Don't Understand!!!
Answers
Answer:
14.5
Step-by-step explanation:
\( \frac{2}{7} = \frac{5}{m + 3} \)
\(2(m + 3) = 7 \times 5\)
\(2m + 6 = 35\)
\(2m = 35 - 6\)
\(2m = 29\)
\(m = 14.5\)
Answer:
m = 14.5
Step-by-step explanation:
\(\frac{2}{7}\) = \(\frac{5}{m+3}\) ( cross- multiply )
2(m + 3) = 35
2m + 6 = 35 ( subtract 6 from both sides )
2m = 29 ( divide both sides by 2 )
m = 14.5
Need help really bad. I need 2 answers
Answers
Explanation: If we simplify the given expression, we would get -7 3/4x -21, and if you look at the options, the options aren’t fully simplified, but they indicate the operation that should be performed to obtain the right answer. I hope this helps you!
Eggs come in packets of 12 and English muffins come in packets of 10. What is the least number of packages of each that can be bought to be able to make egg sandwiches with no muffins left over?
Answers
Answer:
The LCM of 12 and 10 is 60 so you would need to buy 60 / 12 = 5 packs of eggs and 60 / 10 = 6 packs of muffins.
What is 116.52 plus 8% as tax
Answers
Answer:
125.84
Step-by-step explanation:
116.52(0.08)=9.32
116.52+9.32=125.84
Answer:
The total is $125.84.
Step-by-step explanation:
The total is equal to the original value (100%) + the tax amount (8%) which equals 108%. To multiply it, we move the decimal two to the left to get our figure (1.08) then multiply that times 116.52. So, 116.52x1.08=125.8416; for dollars I rounded to the nearest cent: $125.84.