The value of the expression is 2
What are index forms?Index forms are described as those forms that are used to represent numbers that are too large or small in more convenient forms.
They are also described as numbers that are raised to a variable or an exponents.
Other names for index forms are scientific notations and standard forms.
One of the rules of index forms is that the exponents are added when the have the same and are being multiplied.
From the information given, we have that;
(2^-1/2) / (2^1/2)
subtract the exponents
2^-1/2-1/2
subtract the values
2^ -1
Then, we have;
2
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The seventh- and eighth-grade classes surveyed 180 of their classmates to help decide which of three options is best to raise money for school activities. Some results of the survey are given here:
66 participants preferred having a car wash.
50 participants preferred having a bake sale.
64 participants preferred having a talent show.
98 participants were seventh graders.
16 seventh-grade participants preferred having a talent show.
15 eighth-grade participants preferred having a bake sale.
a. Complete the two-way frequency table that summarizes the data on grade level and options to raise money.
Car Wash Bake Sale Talent Show Total
Seventh Graders
Eighth Graders
Total
b. Calculate the row relative frequencies. Round to the nearest thousandth.
Car Wash Bake Sale Talent Show
Seventh Graders
Eighth Graders
Question 2
c. Is there evidence of an association between grade level and preferred option to raise money?
Explain your answer
c. Yes, there is evidence of an association between grade level and preferred option to raise money.
How is the association between grade level and the preferred option to raise money determined?a. The completed two-way frequency table summarizing the data on grade level and options to raise money is as follows:
Car Wash | Bake Sale | Talent Show | Total
Seventh Graders[tex]| 66 | 15 | 16 | 98[/tex]
Eighth Graders [tex]| - | 50 | - | 50[/tex]
Total [tex]| 66 | 65 | 16 | 148[/tex]
Note: The "-" indicates that no data is available for those specific combinations.
b. To calculate the row relative frequencies, we divide each cell value by the corresponding row total and round to the nearest thousandth:
Car Wash | Bake Sale | Talent Show
Seventh Graders [tex]| 0.673 | 0.153 | 0.163[/tex]
Eighth Graders [tex]| - | 1.000 | -[/tex]
Total [tex]| 0.446 | 0.439 | 0.115[/tex]
c. To determine if there is evidence of an association between grade level and preferred option to raise money, we can observe the row relative frequencies. If the relative frequencies differ substantially between the rows, it suggests an association. In this case, since the row relative frequencies for each option vary between the seventh and eighth graders, there is evidence of an association between grade level and the preferred option to raise money.
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Consider the function f(x) = 7(x-2)^{2/3}. For this function there are two important intervals: (-[infinity], A) and (A, [infinity]) where A is a critical number.
A is
The critical number A is 2
To find the critical number A for the function f(x) = 7(x-2)^(2/3):
We need to first find the derivative of the function and then set it equal to zero or identify where it is undefined.
Step 1: Find the derivative of f(x).
f'(x) = d/dx[7(x-2)^(2/3)]
Using the chain rule, we get:
f'(x) = (2/3) * 7(x-2)^(-1/3) * (1)
= (14/3)(x-2)^(-1/3)
Step 2: Set the derivative equal to zero or identify where it is undefined.
The derivative will never be zero since (14/3) is a constant and (x-2)^(-1/3) will never equal zero.
However, the derivative is undefined when the exponent -1/3 leads to a division by zero in the denominator.
This occurs when (x-2) = 0.
Solving for x, we get:
x-2 = 0
x = 2
Therefore, the critical number A is 2. The two important intervals for the function f(x) = 7(x-2)^(2/3) are (-∞, 2) and (2, ∞).
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What is the probability of rolling an even number and then an odd number when rollling two number cubes what is the number of desired outcomes
The probability of rolling an even number and then an odd number is 1/4.
Calculating the probability valuesThe probability of rolling an even number on a fair number cube is 1/2, since there are three even numbers (2, 4, 6) and six possible outcomes (1, 2, 3, 4, 5, 6).
Similarly, the probability of rolling an odd number is also 1/2.
To find the probability of rolling an even number and then an odd number, we need to multiply the probabilities of each event. So:
P(even and odd) = P(even) × P(odd)
P(even and odd) = (1/2) × (1/2)
P(even and odd) = 1/4
So the probability of rolling an even number and then an odd number is 1/4.
The number of desired outcomes for rolling an even number and then an odd number is 9
Since there are three even numbers and three odd numbers, and therefore 3 × 3 = 9 possible outcomes.
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If you spin a spinner 75 times, how many multiples of 2?
If you spin a spinner 75 times, the number of multiples of 2 could be either 7 or 38.
Assuming the spinner has an equal chance of landing on any number from 1 to 6, we can find the probability of landing on a multiple of 2 (2, 4, or 6) by dividing the number of multiples of 2 by the total number of possible outcomes:
Number of multiples of 2 = 3
Total number of possible outcomes = 6
So the probability of landing on a multiple of 2 is:
P(multiple of 2) = 3/6 = 1/2
This means that out of 75 spins, we can expect to land on a multiple of 2 about half the time. To find the exact number, we multiply the probability by the number of spins:
Number of multiples of 2 = P(multiple of 2) x Number of spins
Number of multiples of 2 = (1/2) x 75 = 37.5
Since we can't have a fraction of a spin, we need to round to the nearest whole number. In this case, we can round up or down depending on how we interpret the question. I
f we want to know how many times we can expect to land on a multiple of 2 on average, we should round down to 37.
If we want to know the closest integer to the expected value, we should round up to 38.
So depending on the context of the question, the answer could be either 37 or 38.
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Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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Please Help I cant figure this out
The value of angle Y in the pentagon is 139°.
How to find the value of angle Y in the pentagon?
The sum of the interior angles of a polygon can be found using the formula:
sum of interior angles = (n - 2) * 180
where n is the number of sides of the polygon
A polygon with 5 sides is called pentagon. Thus, n = 5.
sum of interior angles = (5 - 2)*180 = 540°
Thus,
∠U + ∠W + ∠X + ∠Y + ∠Z = 540°
90 + 108 + 121 + ∠Y + 82 = 540
401 + ∠Y = 540
∠Y = 540 - 401
∠Y = 139°
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Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of n experts (i. E. A slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some c t i in [0, 1]. You want to minimize the regret R, defined as:
To minimize your losses while gambling at a casino and playing slot machines, you need to minimize your regret R in the experts problem. R is defined as the difference between your total cost and the best expert's cost.
To minimize R, follow these steps:
1. Begin by assigning equal weight to each expert (slot machine).
2. After each day t, observe the cost c_ti for each expert i.
3. Update the weights by multiplying them by (1 - c_ti), making sure they remain non-negative.
4. Normalize the weights so they sum up to 1.
5. On day t+1, choose the expert with the highest weight to take advice from.
By following this adaptive strategy, you will minimize your regret R, allowing you to reduce your losses while gambling at the slot machines.
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later, the teaching assistant in charless economics course gives him some advice. the teaching assistant says, based on past experience, working on 25 problems raises a students exam score by about the same amount as reading the textbook for 1 hour. for simplicity, assume students always cover the same number of pages during each hour they spend reading. given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems and how many should he have spent reading? 1 hour working on problems, 3 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
From the margin gain formula, the number of hours he should have spent working on problems are equal to 2 hours and number of hours he should have spent reading are equal to other 2 hours. So, option (c) is correct one.
The meaning of ''margin'' is either the ''edge'' or the last unit and it is calculated by the incremental adjustment to the outcome, due to a unit change in the control variable. Marginal gain = Ratio of change in the outcome variable to the change in the control variable.
We have, total number of practice questions raises a students exam score
= 25
Along with practice questions the same amount as reading the textbook for 1 hour. In this problem, the outcome variable is the number of practice problems solved and the control variable is the number of hours Eric spent working on the practice problems. The above figure 1 table shows the total number of problems solved and time. First we determine the marginal gain of each hour Eric spent working on the practice questions. See the table present in above figures 2. Now, he has only 4 hours of study time for the best exam score as possible. We have to determine number of hours he should have spent reading and working on problems. It is assumed that students always cover the same number of pages during each hour they read the textbook so the advice provide by their teaching assistant that they can establish the relationship between time spent on reading the textbook and doing practice problems. The relation is below, 1 hour of reading the textbook = 15 practice problems solved. So, we can compare the the effectiveness of Eric's time spent on either working on practice problems or reading the textbook by using the table above figure 3. The decision rule for the optimal allocation of Eric's 4 hours of work is, If he can solve more than 15 practice problems in any of the 4 hours, then he should spend that particular hour working on the practice problems instead of reading the textbook. If not, then Eric should spend that hour to read the textbook instead.
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Complete question:
The table present in above figure 1 complete the question.
Eric is a hard-working college freshman. One Sunday, he decides to work nonstop until he has answered 100 practice problems for his math course. He starts work at 8:00 AM and uses a table to keep track of his progress throughout the day. He notices that as he gets tired, it takes him longer to solve each problem. later, the teaching assistant in charless economics course gives him some advice. the teaching assistant says, based on past experience, working on 25 problems raises a students exam score by about the same amount as reading the textbook for 1 hour. for simplicity, assume students always cover the same number of pages during each hour they spend reading. given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems and how many should he have spent reading?
a) 1 hour working on problems, 3 hours reading
b) 2 hours working on problems, 2 hours reading
c) 3 hours working on problems, 1 hour reading
d) 4 hours working on problems, 0 hours reading
Geometry
three squares with areas of 64, 225, and 289 square units are arranged so that when their vertices coincide a triangle is formed. find the area of that triangle.
please explain how you solved this along with the answer.
Answer:
The area of the largest square is 289 square units, because it is the sum of areas of the two smaller squares, 64 square units and 225 square units.
Step-by-step explanation: JUST PASSED IT ON STUDY ISLAND 100% CORRECT ANSWER
A bag contains 3 gold marbles, 6 silver marbles, and 28 black marbles. A. Two marbles are to be randomly selected from the bag. Let X be the number of gold marbles selected and Y be the number of silver marbles selected. Find the joint probability distribution. B. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
A. The joint probability distribution is:
- P(X=2, Y=0) = 6/1332
- P(X=1, Y=1) = 36/1332
- P(X=0, Y=2) = 30/1332
B. The expected value of playing this game is approximately $0.19 each time you play.
A. To find the joint probability distribution, we need to determine the probabilities of all possible outcomes for X and Y when selecting two marbles from the bag.
There are a total of 37 marbles in the bag (3 gold, 6 silver, and 28 black).
1. Probability of selecting 2 gold marbles (X=2, Y=0):
(3/37) * (2/36) = 6/1332
2. Probability of selecting 1 gold and 1 silver marble (X=1, Y=1):
(3/37) * (6/36) + (6/37) * (3/36) = 36/1332
3. Probability of selecting 2 silver marbles (X=0, Y=2):
(6/37) * (5/36) = 30/1332
So, the joint probability distribution is:
- P(X=2, Y=0) = 6/1332
- P(X=1, Y=1) = 36/1332
- P(X=0, Y=2) = 30/1332
B. To find the expected value of playing the game, we need to calculate the probability of selecting each type of marble and multiply it by its corresponding value.
1. Probability of selecting a gold marble: 3/37
Winning amount: $3
2. Probability of selecting a silver marble: 6/37
Winning amount: $2
3. Probability of selecting a black marble: 28/37
Losing amount: -$1
Expected value = (3/37 * $3) + (6/37 * $2) + (28/37 * -$1)
= 9/37 + 12/37 - 28/37
= -7/37
So, the expected value of playing this game is -$7/37, which means you can expect to lose approximately $0.19 each time you play.
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Can you help me with number 19?
The possible values of the arc AE are 175 and 185 degrees
Calculating the possible values of the arc AEFrom the question, we have the following parameters that can be used in our computation:
The circle R
Where the measures of the arcs are
AB = 60
BC = 25
CD = 70
DE = 20
Add the measures of the above arcs
So, we have
AE = 60 + 25 + 70 + 20
Evaluate
AE = 175
Another possible value is
AE = 360 - minor AE
AE = 360 - 175
Evaluate
AE = 185
Hence, the possible values of the arc AE are 175 and 185 degrees
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Simplify the expression five to the third power +3(5-3)
Answer:
Step-by-step explanation:
The expression +3(5-3) can be simplified using the order of operations (PEMDAS) as follows: first, we need to perform the exponentiation operation, which gives us 125.
Then, we need to perform the operation inside the parentheses, which gives us 6. Finally, we multiply 3 by 6, giving us 18. Therefore, the simplified expression is 125 + 18 = 143.
To further explain this solution, we use the order of operations, which is a set of rules that dictate the order in which operations must be performed when evaluating an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, which represents the order of operations from left to right.
In this expression, we first need to evaluate the exponentiation operation, which is 5 to the third power. This gives us 125. Next, we need to perform the operation inside the parentheses, which is 5-3. This gives us 2. We then multiply 3 by 2, which gives us 6. Finally, we add 125 and 6, giving us 131.
It is important to follow the order of operations when simplifying an expression to ensure that we obtain the correct result. By using PEMDAS, we can systematically simplify an expression step-by-step, avoiding any potential errors and obtaining a clear and concise solution.
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Olivia and her friends went to a movie at 1:50 P.M. The movie ended at 4:10 P.M. How long was the movie?
Answer: The movie was 2 hours and 20 minutes long.
Step-by-step explanation:
basic adding + subtracting
Amelia is making bags of snack mix for a class party. The snack mix includes dried fruit, cashews, and peanuts. Amelia buys 2 more pounds of peanuts than she does cashews and 1 pound of dried fruit. If her total bill is $41. 11, complete the table to show how many pounds of each ingredient Amelia buys
The table attached represents the pounds of each ingredient Amelia buys.
What is the number of pounds?Let's denote the number of pounds of cashews that Amelia buys by "c", and the number of pounds of peanuts that she buys by "p".
According to the problem, Amelia buys 2 more pounds of peanuts than cashews. So, we have:
p = c + 2
Also, she buys 1 pound of dried fruit, which we can simply denote as "1".
The total bill for the snack mix is $41.11, so we can write:
0.5c + 0.75p + 1.5(1) = 41.11
where;
0.5 represents the cost per pound of cashews, 0.75 represents the cost per pound of peanuts, and 1.5 represents the cost per pound of dried fruit.Simplifying the equation, we get:
0.5c + 0.75(c + 2) + 1.5 = 41.11
0.5c + 0.75c + 1.5 + 1.5 = 41.11
1.25c = 38.11
c = 30.488
Since we know that p = c + 2, we have:
p = 30.488 + 2 = 32.488
Now we can complete the table to show how many pounds of each ingredient Amelia buys:
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Can someone explain ._.
The mark-up value percentage is 25 %
Given data ,
The markup amount is the selling price minus the cost price, so:
Markup = $8630 - $6900 = $1730
The markup percentage is the markup amount divided by the cost price, expressed as a percentage:
Markup percentage = (Markup / Cost price) x 100%
Markup percentage = ($1730 / $6900) x 100%
Markup percentage = 0.25 x 100%
Markup percentage = 25%
Hence , the markup percentage is 25%
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Question is attached.
Please show workings
When solved, the value of either a or b would be 0 such that we have a = 0 or b = 0. They could also both be zero.
How to solve the equation ?If the product of two numbers is zero, it necessitates that one or both of the values in question contain a value of zero. Similarly, when calculating the cross product of two given vectors and its resulting answer is equivalent to zero, then such vectors exist parallel with one another.
Alternatively, there is the possibility that only one vector holds a value of zero themselves:
( a × b ) = 0
This equation is true if either a = 0 or b = 0, or both a and b are zero.
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brandy has a rectangular wooden deck that measures 7 feet by 12 feet she builds an addition to the deck that is 4 feet longer. what is the perimeter of the deck now
Answer:
new perimeter of Brandy deck is 46 feet .
Step-by-step explanation:
The new perimeter of Brandy deck is 46 feet.
Perimeter of a rectangleThe entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.
How can we find new perimeter of a deck?Using the given information,
Width = 7 Feet
Length = 12 feet
Perimeter = 2 (Width + Length)
[tex]= 2(7+12)[/tex]
[tex]=2(19)[/tex]
[tex]=38[/tex]
Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet
Hence, the new perimeter of a deck is 46 feet.
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The spies of Syracuse report that enemies are marching towards the city. Archimedes needs to build death rays and claws to defend the city with. He'll need at least 10 machines but the city only gave him 3000 lbs of gold to build the machines with. A claw costs 200 lbs of gold to build while a death ray is worth 350 lbs of gold. Write a system of inequalities to find a possible number of claws and death rays that Archimedes can build. â
Possible number of death rays (D) and claws (C) that Archimedes can build are given by the following system of inequalities: 350D + 200C ≤ 3000. D, C ≥ 0
The first inequality represents the fact that the total amount of gold used to build the machines cannot exceed the 3000 lbs of gold given by the city. The second inequality ensures that the number of death rays and claws cannot be negative.
To explain this system, let us assume that Archimedes builds x death rays and y claws. The amount of gold required to build x death rays and y claws is given by 350x + 200y. The first inequality ensures that this value cannot exceed 3000 lbs of gold. The second inequality ensures that the number of death rays and claws cannot be negative.
Therefore, the solution to this system of inequalities gives us all the possible combinations of death rays and claws that Archimedes can build with the given amount of gold.
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And number d -
is q(x) the equation of a line?
Justify your answer.
Answer: for d the answer is yes
Step-by-step explanation:
a line is in the form of y=mx+c or y=mx+b, as p(x)=3x+5 then the equation passes by being compatible with the general equation of a line
Step-by-step explanation:
1d.
yes.
f(x) = 2x + 3
g(x) = x + 2
p(x) = f(x) + g(x) = (2x + 3) + (x + 2) = 3x + 5
p(x) is still a linear function (highest exponent of x is 1). therefore it is a line.
A young doctor is working at night in an emergency room. Emergencies come in at times of a Poisson process with rate 0. 5 per hour. The doctor can only get to sleep when it has been 36 minutes (6 hours) since the last emergency. For example, if there is an emergency at 1:00 and a second one at 1:17 then she will not be able to get to sleep until at least 1:53, and it will be even later if there is another emergency before that time.
(a) Compute the long-run fraction of time she spends sleeping, by formulating a renewal reward process in which the reward in the ith interval is the amount of time she gets to sleep in that interval.
(b) The doctor alternates between sleeping for an amount of time si and being awake for an amount of time u. Use the result from (a) to compute Eui
The probability of getting to sleep in an interval is 0.0903.
The expected time the doctor spends awake in each interval is 1.8648 hours.
(a) To compute the long-run fraction of time the doctor spends sleeping, we can formulate a renewal reward process. In this process, each interval represents the time between consecutive emergencies.
Let T be the inter-arrival time between emergencies, which follows an exponential distribution with a rate of λ = 0.5 per hour. The average inter-arrival time is given by E(T) = 1/λ = 1/0.5 = 2 hours.
In each interval, the doctor can only get to sleep if it has been 36 minutes (6 hours) since the last emergency. Otherwise, she remains awake.
Let R be the reward obtained in each interval, which is the amount of time the doctor gets to sleep. If the doctor gets to sleep in an interval, the reward is (T - 0.6) since she has already waited for 0.6 hours (36 minutes). Otherwise, the reward is zero.
The long-run fraction of time spent sleeping, denoted by ρ, can be calculated as the expected reward per unit time:
ρ = E(R)/E(T)
To compute E(R), we need to consider the conditional probability that the doctor gets to sleep in an interval.
Given an interval length T, the probability that T > 0.1 (36 minutes) is given by P(T > 0.1) = 1 - P(T ≤ 0.1). This probability is equal to the cumulative distribution function (CDF) of the exponential distribution with rate λ evaluated at 0.1.
P(T > 0.1) = 1 - F(0.1) = 1 - (1 - exp(-λ * 0.1))
Substituting the value of λ = 0.5, we get:
P(T > 0.1) = 1 - (1 - exp(-0.5 * 0.1)) ≈ 0.0903
Therefore, the probability of getting to sleep in an interval is approximately 0.0903.
E(R) = (T - 0.6) * P(T > 0.1) + 0 * (1 - P(T > 0.1))
= (T - 0.6) * 0.0903
Substituting the average inter-arrival time E(T) = 2 hours:
E(R) = (2 - 0.6) * 0.0903 ≈ 0.1352 hours
Finally, we can compute ρ:
ρ = E(R)/E(T) = 0.1352/2 ≈ 0.0676
Therefore, the long-run fraction of time the doctor spends sleeping is approximately 0.0676.
(b) To compute E(ui), the expected time the doctor spends awake in each interval, we can use the fact that the total time spent in each interval is T, and the time spent sleeping is (T - R), where R is the reward obtained in each interval.
E(ui) = E(T - R)
= E(T) - E(R)
= 2 - 0.1352
≈ 1.8648 hours
Therefore, the expected time the doctor spends awake in each interval is approximately 1.8648 hours.
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Declan says, "To write an equivalent
fraction name for 5. I can write 5 as the
denominator and 1 as the numerator. "
Do you agree with Declan? Explain.
Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
Declan's statement is mathematically correct, but it is not a useful way to write an equivalent fraction for 5 in most contexts.
In general, to write an equivalent fraction, we need to multiply or divide both the numerator and the denominator by the same nonzero number. This preserves the value of the fraction, but changes its form.
For example, to write an equivalent fraction for 5, we can multiply both the numerator and denominator by any nonzero number. Let's say we multiply both by 2:
5/1 = (5x2)/(1x2) = 10/2
So 10/2 is an equivalent fraction for 5.
However, if we follow Declan's approach and write 5 as the denominator and 1 as the numerator, we get:
5/1 = 1/5
This is indeed an equivalent fraction for 5, but it is not a particularly useful or common way to write an equivalent fraction. In general, we prefer to write equivalent fractions with a denominator that has some mathematical or practical significance, such as a power of 10 or a factor of the original denominator.
So while Declan's statement is technically correct, it is not a very helpful way to write an equivalent fraction for 5.
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Calculate the area.....................................
A museum charges 12. 50 admission Each special  sip it cost extra 2. 00 Write an expression that represents the cost in dollars of admission to the museum including admittance to n special exhibits.
The expression that represents the cost, in dollars, of admission to the museum including admittance to n special exhibits can be written as 12.50 + 2n
Here, 12.50 is the base admission cost without any special exhibit, and 2n represents the cost of n special exhibits, where each exhibit costs an extra $2.00.
By multiplying the number of special exhibits, n, by $2.00, we get the total cost of special exhibits, which we can then add to the base admission cost to get the total cost of admission to the museum including admittance to n special exhibits.
For example, if someone wants to visit the museum and see 3 special exhibits, the cost of admission would be:
12.50 + 2(3) = 12.50 + 6 = $18.50
Therefore, the expression 12.50 + 2n represents the total cost of admission to the museum including admittance to n special exhibits.
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Complete question is:
A museum charges $12.50 for admission. Each special exhibit costs an extra $2.00. Part A Write an expression that represents the cost, in dollars, of admission to the museum including admittance to n special exhibits
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.\
The statement that is true is: "The range of the function is all real numbers less than or equal to 9
What is the function about?This quadratic function is indicated by a downward-opening parabola due to the negative coefficient of the squared term.
Found at coordinates (-2, 9), the vertex will be the highest point on this curved graph
Located on the x-axis at points (-5, 0) and (1, 0), each one serves as an intersection. Because of these intersections the following statement can be confidently said: "The range of the function consists of all actual numbers that are lesser or equal to 9."
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Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance. P r compounded t $ % Daily
The account balance after 2 years is approximately $107.15.
What is the formula calculating account balance A, given the principal P, interest rate r, number of compounding periods per year n, time t in years, and A is account balance when interest is compounded daily?The compound interest formula is given by:
A = P * [tex](1 + r/n)^(^n^*^t^)[/tex]
Where:
P = Principal
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Time in years
A = Final account balance
In this problem, we are given:
P = $100
r = 3.5% per year = 0.035 per year
n = 365 (since interest is compounded daily)
t = 2 years
Substituting these values in the formula, we get:
A = [tex]100 * (1 + 0.035/365)^(^3^6^5^*^2^)[/tex]
A ≈ $107.15
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If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 4
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 4
Evaluate
y < 1
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
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SOMEONE HELP PLS!! giving brainliest to anyone!!
Answer:
252
Step-by-step explanation:
So their are 38 more numbers to get to 41 and the numbers are adding by 6, so mulitply 6 by 38 and you get 228 and add 228 to the biggest number of 24 and your final answer becomes 252.
Mia crosses a river when she drives from her house to the beach. The function d(t)=40|t-1. 25| shows Mia's distance from the river, d, in miles after t hours. The domain of the function is 0
The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.
The given function is:
d(t) = 40|t-1.25|
Here, t represents the time elapsed in hours and d represents the distance from the river in miles.
To find Mia's distance from the river, we need to plug in values of t into the function.
For example, if t=2, then:
d(2) = 40|2-1.25|
d(2) = 40|0.75|
d(2) = 30
So Mia's distance from the river after 2 hours of driving is 30 miles.
Similarly, we can find Mia's distance from the river at other points in time.
To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.
Graph of the function d(t) = 40|t-1.25|
The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.
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Consider the following. sin u = 3/5 π/2 (a) Determine the quadrant in which u/2 lies. O Quadrant 1 O Quadrant II O Quadrant III O Quadrant IV (b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2 sin(u/2) cos(u/2) = tan(u/2) =
(a) The quadrant in which u/2 lies is either Quadrant I or Quadrant II.
(b) The exact values of sin(u/2), cos(u/2), and tan(u/2) are:
sin(u/2) = √10/5
cos(u/2) = 3√10/10
tan(u/2) = 2/3
(a) To determine the quadrant in which u/2 lies, we need to look at the value of sin u. Since sin u is positive (3/5 is positive and π/2 is in Quadrant I), we know that u is in either Quadrant I or Quadrant II.
To find u/2, we divide u by 2, which means u/2 will be in either Quadrant I or Quadrant II as well. Therefore, the answer is either Quadrant I or Quadrant II.
(b) We can use the half-angle formulas to find the values of sin(u/2), cos(u/2), and tan(u/2):
sin(u/2) = ±√[(1 - cos u)/2]
cos(u/2) = ±√[(1 + cos u)/2]
tan(u/2) = sin(u/2)/cos(u/2)
Since sin u = 3/5, we can find cos u using the identity sin^2 u + cos^2 u = 1:
cos u = ±√[(1 - sin^2 u)] = ±√[(1 - 9/25)] = ±4/5
Since u/2 is in either Quadrant I or Quadrant II, we know that sin(u/2) and cos(u/2) are positive. Therefore, we can choose the positive square roots for sin(u/2) and cos(u/2):
sin(u/2) = √[(1 - cos u)/2] = √[(1 - 4/5)/2] = √[1/10] = √10/10 = √10/5
cos(u/2) = √[(1 + cos u)/2] = √[(1 + 4/5)/2] = √[9/10] = 3/√10 = 3√10/10
Finally, we can use these values to find tan(u/2):
tan(u/2) = sin(u/2)/cos(u/2) = (√10/5)/(3√10/10) = 2/3
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A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 3 cm and segment BE = 3. 5 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. Quadrilateral BCDE inscribed within circle A a 3. 91 cm b 4. 24 cm c 4. 61 cm d 4. 95 cm
Using the Pythagorean theorem, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
To determine the smallest diameter of the pipe that will fit the fiber optic line in rectangular casing BCDE, we need to find the diagonal AC of the rectangle. Since the rectangle is inscribed within circle A, the diameter of the circle will be equal to the diagonal of the rectangle.
Using the Pythagorean theorem, we can find the length of AC:
AC^2 = DE^2 + BE^2
AC^2 = (3 cm)^2 + (3.5 cm)^2
AC^2 = 9 + 12.25
AC^2 = 21.25
AC = √21.25 ≈ 4.61 cm
Therefore, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
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