Find the least common multiple of 15 and 50 .
Answer:
Least common multiple = 150
Step-by-step explanation:
The least common multiple is defined as the smallest multiple that two or more numbers have in common.
We can find the least common multiple by listing the multiples of both numbers:
Multiples of 15:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150
Multiples of 50:
50, 100, 150
Thus, 150 is the least common multiple of 15 and 50.
Answer each of the following questions. Write a sentence stating the
answer where necessary.
One primary drama class and one high school drama class have
earned a field trip to the local theatre to watch a performance today.
1. Mr. Murray's primary drama class is going to the theatre for the
show. They are travelling in three buses. Each bus holds ten
students. How many students are going to the show? Show your
(2mks)
working.
2. The mass of 1 of the buses is 1900
What is the mass
of the bus measured in? kilograms or grams. Explain your answer.
(1mk)
3. There are five rows in the theatre. Mr. Murray wants an equal
number of students to sit in each row. How many students should
sit in each row? Show your working.
(2mks)
4. Mrs. Stewart's high school class is also going to the show. She
has two times as many students as Mr. Murray. How many high
school students are in the theatre for the show? Show your
working.
(2mks)
5. Mrs. Stewart wants her students to sit with an equal number of
students in each of the five rows. How many high school students
should sit in each row? Show your working.
(2mks)
6. The theatre manager needs to make a seating chart to make sure
all the students will have a seat for the performance. Show the total
number of students seated in the theatre and how they will be
seated by drawing a diagram of the theatre. Label the students as
either "M" for Mr. Murray or "S" for Mrs. Stewart.
(3mks)
1. Using multiplication, the number of students from Mr. Murray's primary drama class going to the theatre for the show is 30.
2. The mass of the bus is measured in kilograms because 1,900 cannot represent the mass of a bus that can carry 10 students and the standard unit of mass in the International System (SI) is the kilogram (kg).
3. The number of Mr. Murray's students who should sit in each row, using division operation, is 6.
4. Using multiplication, the number of high school students in the theater for the show is 60, since they are two times as many high students as in Mr. Murray's class.
5. Using division, the number of high school students in each row is 12.
6. The total number of students seated in the theater is 90 with 6 primary school student and 12 high school student sitting (18 students) in each of the 5 rows of the theater.
What are the mathematical operations?The basic mathematical operations are addition, subtraction, multiplication, and division.
1. Mr. Murray's primary drama class:
The number of buses the class is traveling in = 3
The capacity for each bus = 10 stuents
The total number of students going to the show = 30 (3 x 10)
2. Mass of the Buses:
The mass of one bus = 1,900 kg
The masses of the three buses = 5,700 (1,900 x 3)
3. Theater Rows:
The number of rows in the theater = 5
The average number of students that can sit in each row = 6 (30 ÷ 5)
4. Mrs. Stewart's High School Class:
The number of high school students from Mrs. Stewart's class = 60 (30 x 2)
5. The total number of high school students = 60
The number of rows in the theater = 5
The number of high school students in each row = 12 (60 ÷ 5)
6. The Theater Manager:
The total number of primary school students = 30
The total number of high school students = 60
The total number of students attending the show = 90 (30 + 60)
The number of students in each row = 18 (90 ÷ 5) or (12 + 6)
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Please help me with this.
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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Please help! i have no clue what to do. its for Volume! please help me! will mark you brainliest! see attached! thank you
Answer:
The volume of the whole figure is:
8,847 ft^3 + 26,542 ft^3 = 35,389 cubic feet
Step-by-step explanation:
The volume of the rectangle lower part is :
38.4ft*24ft * 28.8ft =26,542.08 cubic foot
to the nearest whole number 26,542 cubic feet
The area of the right side of the triangle face on the top is (Base * height) / 2 :
(19.2ft * (38.4ft /2) / 2 =184.32 square feet
As both side of that triangle on top have the same length of hypothenuse. The area of the whole triangle face:
184.32 *2 = 368.64 square feet
The volume of the triangle top:
368.64 ft^2 * 24ft = 8,847.36 cubic feet .
To the nearest whole number 8847 cubic feet
The volume of the whole figure is:
8,847 ft^3+26,542 ft^3 = 35,389 cubic feet
What is the minimum value of the function f(x)=(2x+6)(x-7)
One way to answer this is to expand the function:
f(x) = (2x+6)(x-7)
= 2x^2 - 14x + 6x - 42
= 2x^2 - 8x - 42
And then use the formula [tex]x=\dfrac{-b}{2a}[/tex] to find the x-value of the vertex and then use that to find the y-value of the vertex, while is the minimum value.
x = -(-8) / 2(2)
= 8/4
= 2
f(2) = 2(2)^2 - 8(2) - 42
= 2(4) - 16 - 42
= 8 - 16 - 42
= - 50
So the minimum value is -50, since (2,-50) is the lowest point on the parabola.
Question 3: Mathematical proficiency and the construction of mathematics ideas. To answer this question, you need to understand paragraphs 2.12 and 2.13 in your study guide: Key to note the following concepts: constructivism and behaviourism. inductive and deductive thinking or reasoning. instrumental and relational understanding conceptual and procedural knowledge; and ● elements of mathematics proficiency. . e . (10 marks) ● 3.1 Create an activity where procedural and conceptual understanding co-exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6) 3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge.
Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
3.1 Activity: Procedural and Conceptual Understanding in Action
Content Area: Fractions
Problem: Comparing Fractions
Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.
Activity Steps:
Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).
Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.
After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:
What does it mean for one fraction to be greater than or less than another?
Can you explain why we need a common denominator when comparing fractions?
How can you visually represent and compare fractions to better understand their relative sizes?
Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.
Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.
Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.
Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.
By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.
3.2 Example: Conceptual Knowledge vs. Procedural Knowledge
Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.
Example: Division of Fractions
Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.
Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.
In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
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What is the equation of the line in slope-intercept form?
-2
=-=x+4
v=-15)+4
5
2
V=--x-4
5
2
V=--x+4
The equation of the line in slope-intercept form is y = 3x + 4.
We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.
The formula for the mixture is provided by:
n C r equals n!/r! (n-r)!
where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.
In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:
36 C 24 = 36! / (24! * 12!)
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In a division the dividend. Quotient and remainder are 1830, 87 and 3 respectively find the divisor?
The divisor in the division problem is 21, given the values of dividend, quotient, and remainder as 1830, 87, and 3 respectively.
To find the divisor in a division problem with the given values of dividend, quotient, and remainder, we can use the formula:
Dividend = Divisor * Quotient + Remainder
Substituting the given values:
1830 = Divisor * 87 + 3
Rearranging the equation:
Divisor * 87 = 1830 - 3
Divisor * 87 = 1827
Divisor = 1827 / 87
Divisor = 21
Therefore, the divisor in the division problem is 21, given the values of dividend, quotient, and remainder as 1830, 87, and 3 respectively.
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If sqrt(4 + x) + (10 − x) = 6 , then find sqrt(4 + x)(10 − x) algebraically.
The algebraic expression for √(4+x)(10-x), which is 121.
To find the value of √(4+x)(10-x) algebraically, we start by simplifying the given equation:
√(4+x) + √(10-x) = 6
To eliminate the square roots, we can square both sides of the equation:
(√(4+x) + √(10-x)[tex])^2 = 6^2[/tex]
Expanding the left side using the binomial formula, we get:
(4+x) + 2√[(4+x)(10-x)] + (10-x) = 36
Simplifying further:
14 + 2√[(4+x)(10-x)] = 36
Subtracting 14 from both sides:
2√[(4+x)(10-x)] = 22
Dividing both sides by 2:
√[(4+x)(10-x)] = 11
Now we can square both sides again to get rid of the square root:
[(4+x)(10-x)] = [tex]11^2[/tex]
Simplifying further:
(4+x)(10-x) = 121
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Suppose you want to measure the height of a tree. Describe the method of indirect measurement being used in each picture.
(1) In diagram 1, the method used is proportional height method.
(2) In diagram 2, the method used is angle of depression method.
(3) In diagram 3, the method used for the indirect measurement is the angle of elevation method.
What is the method of measurement of the heights of the tree?The method of measurement of the height of the tree is determined as follows;
(1) In diagram 1, the method used to estimate the height of the tree is proportional height method.
(2) In diagram 2, the method used for the indirect measurement of the height of the tree is angle of depression method, as indicated in the position of the observer.
(3) In diagram 3, the method used for the indirect measurement of the height of the tree is the angle of elevation method, as indicated in the position of the observer.
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how do i refund and stop my subscription for brainly
To refund and stop your subscription for Brainly.
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24. What is the cost for 5 t-shirts that cost $10 with a sales tax of 6%?
$3
$56
$50
$53
The cost for 5 t-shirts, including Sales tax, is $53.
The cost of 5 t-shirts with a price of $10 each and a sales tax of 6%, we need to multiply the total price of the t-shirts by the sales tax rate and add it to the original price.
The original price of one t-shirt is $10. Therefore, the total price of 5 t-shirts is:
$10 * 5 = $50
To calculate the sales tax, we need to multiply the total price by the sales tax rate of 6%:
$50 * 6% = $50 * 0.06 = $3
Adding the sales tax to the total price:
$50 + $3 = $53
Therefore, the cost for 5 t-shirts, including sales tax, is $53.
The correct answer is: $53.
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What is the multiplicative rate of change for the exponential function f(x)=2(5/2)^-x
The multiplicative rate of change for the exponential function is
5/2How to find the multiplicative inverseThe multiplicative rate of change for an exponential function is determined by the base of the exponent.
In this case, the function is f(x) = 2(5/2)⁻ˣ,
where the base of the exponent is (5/2).
The multiplicative rate of change for an exponential function with a base greater than 1 is greater than 1, indicating exponential growth. Conversely, if the base is between 0 and 1, the multiplicative rate of change is less than 1, representing exponential decay.
In this function, the base (5/2) is greater than 1.
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What is the 45th term of the arithmetic sequence -33, -25, -17,-9....?
Answer:
319
Step-by-step explanation:
You want to know the 45th term of the arithmetic sequence that begins -33, -25, -17, ...
Arithmetic sequenceThe general term of an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
ApplicationFor a1 = -33 and d = (-25 -(-33)) = 8, the n-th term is ...
an = -33 +8(n -1)
Then the 45th term is ...
a45 = -33 +8(45 -1) = -33 +352 = 319
The 45th term of the sequence is 319.
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What is the future value of a $400 per year ordinary annuity for ten years at 10 percent?
Note: provide answer in full dollars/cents form, e.g., $1,234.56
Answer:
sorry
Step-by-step explanation:
A class of students recorded the amount of time spent on homework on Monday night.
The times are recorded below, in hours. Use the data to answer questions 8 – 10.
1 3
4
2 1
2
2 2 3
4
1 1 3
4
1 1
4
3
3 1
4
3 3
4
2 2
8. Make a line plot of the data shown above. Be sure to include a title and correctly
label each value.
A construction of the line plot for the amount of time spent on homework on Monday night is shown in the image attached below.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the amount of time spent on homework on Monday night on a line plot as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 2 because it has the highest frequency of 3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What are parallelograms?
Answer:
a four-sided plane rectilinear figure with opposite sides parallel.
Step-by-step explanation:
Answer:
Parallelograms are a type of quadrilateral, which is a polygon with four sides. A parallelogram is a specific type of quadrilateral that has two pairs of parallel sides. This means that the opposite sides of a parallelogram are parallel and equal in length.
In addition to having parallel sides, parallelograms also have some other notable properties:
Opposite angles are congruent: The opposite angles of a parallelogram are equal in measure. This means that if you label the angles A, B, C, and D, then angle A is congruent to angle C, and angle B is congruent to angle D.
Step-by-step explanation:
calculate the length of b to the nearest centimeter.
Step-by-step explanation:
This is similar to the other problem you posted (problem 16).
Again, use the law of cosines. I won't write it out because I wrote it out for the other problem you asked.
Just plugin in a = 8, b = 20, and gamma = 35 into the law of cosines. Then you get your c value, which in this problem is your b variable.
I got around 14.20814
which of the following statement is not true about sin theta, where theta is 2π/3 radians.
a) it has the same value as sin(8π/3)
b) it has the same value as sin30°
c) it has a positive value
d) it has a negative value
Step-by-step explanation:
2pi/3 is the same thing as 2pi/3 * 180/pi = 120 degrees
From your choices, we know that it is either c or d.
sin(120) is in the 2nd quadrant, so the x is negative and the y is positive. Remember that sin corresponds to the y value, so it is positive. Therefore option (d) is not true.
Quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation. If TY = 2, find RM.
Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.
Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.
A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.
Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.
Therefore, RM = 2.
By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.
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Solve the inequality below. Use the drop-down menus to describe the solution and its graph. 7 13 11 Click the arrows to choose an answer from each menu. The solution to the inequality is Choose.... Choose... A graph of the solution should have Choose.... and be shaded to the
Answer:
[tex]x \leq -4[/tex]
There will be a filled-in hole at -4.
Step-by-step explanation:
We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)
[tex]-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4[/tex]
The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.
For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.
In another example, [tex]x \leq -4[/tex], -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.
A filled-in hole means the number is included in the inequality, while an empty one means it isn't.
In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.
the sector of a circle of radius 5cm subtends an angle of 3π/10 rad at the centre. (all answers to 2 dp)
a) calculate the length of the arc.
b) calculate the area of the sector.
c) calculate the area of the segment in the sector with the angle of 3π/10 rad and a radius of 5cm.
Step-by-step explanation:
3pi / 10 * 180 / pi = 54 degrees.
The circumference of the circle would be 10 pi. Multiply this by 54/360 to get 1.5pi or 3 pi /2
Area of the circle would be 25 pi. Multiply this by 54/360 to get 3.75 pi or 15pi /4
I'm confused on part (c), is it not just the same question as part (b)?
All these answers are assuming that 3pi/10 is the central angle. If it is an inscribed angle, then the central angle would be 6pi/10 or 3pi/5.
Edit: if part (c) is talking about inscribed angle, then the degrees would be 108. Then you just multiply 25pi by 108/360 for your answer
Answer:
Step-by-step explanation:
a.
l=rθ (θ in radians)
l=5×3π/10=3π/2≈3/2×3.14≈3×1.57≈4.71 cm
area of sector=π×5²×3π/10×1/2π=15/4 π=15π/4 cm²
≈15/4 ×3.14
≈15×1.57/4
≈5.8875
≈5.89 cm²
1. Let Z be a standard normal random variable. Use the table, to determine the value of c.. P(0.68 <= Z <= c) = 0.236 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
The cumulative probability 0.68 from the z-score for the cumulative probability 0.236, we find that 'c' is approximately 0.0686.
To determine the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, where Z is a standard normal random variable, we need to use the standard normal distribution table.
The standard normal distribution table provides the cumulative probability for values up to a given z-score. In this case, we are given the cumulative probability of 0.236.
To find the value of 'c', we need to look up the corresponding z-score in the table.
Look up the z-score for the cumulative probability 0.68 in the standard normal distribution table. The closest value in the table is 0.7486.
Subtract the z-score for the cumulative probability 0.68 from the z-score for the cumulative probability 0.236:
c = 0.7486 - 0.68 = 0.0686
In summary, to find the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, we use the standard normal distribution table to find the corresponding z-score. Therefore, the value of 'c' is approximately 0.0686.
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Two men walk at rates of 6 miles per hour and 10 miles per hour respectively simulataneously they started from the same place walking in oppsite directions in how many hours will they be 200 miles apart
Answer:
Hi
Please mark brainliest
Step-by-step explanation:
First man walks in one hour = 6 miles
Second man walks in one hour = 10 miles
Since they are walking in opposite direction so distance between them after 1 hour = 6 + 10 = 16 miles
Since after one hour they are 16 miles apart from each other
Therefore, they will be 200 miles apart from their starting point
= 200 ÷ 16 = 12.5 hours.
Answer:
Answer:I believe the answer is 12.5 hours
Answer:I believe the answer is 12.5 hoursExplanation: one men walked 6 hours
the second men walked 10 hours
6+10=16 so they were 16 miles apart
200÷16=12.5 so the answer would be 12.5 hours
Multiple choice
1. given the figure below what is the correct name for ←2. choose all that apply
Simplify the expression StartFraction a b Superscript 3 Baseline over a Superscript 4 Baseline b EndFraction plus left-parenthesis c Superscript 2 Baseline right-parenthesis Superscript 3 Baseline
The simplification of the expression ab³/a⁴b + (c²)³ is determined as b²/a³ + c⁶.
What is the simplification of the expression?The given expression is simplified as follows;
The given expression is written as;
ab³/a⁴b + (c²)³
To simplify the expression given above, we will divide the fraction with the common factor as follows;
From the numerator; ab³, we will factor out "ab"
From denominator; a⁴b, we will factor out "ab"
The resulting expression becomes;
ab³/a⁴b + (c²)³
= b²/a³ + c⁶
Note: for the power of c, we simplify by multiplying 2 and 3 = 6
Thus, the simplification of the expression ab³/a⁴b + (c²)³ is determined as b²/a³ + c⁶.
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What is the future value of a $400 per year ordinary annuity for ten years at 10 percent? Note: provide answer in full dollars/cents form, e.g., $1,234.56
Answer:
An ordinary annuity has payments made at the end of each period, while an annuity due has payments made at the beginning of each period.
Now, let's calculate the future value of the annuity due, given that the future value of the ordinary annuity is $100,000 and the interest rate is 5 per cent.
Step 1: Determine the future value factor of the ordinary annuity.
Future Value of Ordinary Annuity (FVOA) = $100,000
Interest Rate (r) = 5% = 0.05
Number of Periods (n) = 5 years
Step 2: Use the FVOA formula to find the annuity payment (PMT).
FVOA = PMT * [(1 + r)ⁿ - 1] / r
$100,000 = PMT * [(1 + 0.05)⁵ - 1] / 0.05
PMT = $18,039.37 (approx.)
Step 3: Calculate the future value of the annuity due (FVAD).
FVAD = PMT * [(1 + r)ⁿ - 1] / r * (1 + r)
FVAD = $18,039.37 * [(1 + 0.05)⁵ - 1] / 0.05 * (1 + 0.05)
FVAD = $105,000 (approx.)
Step-by-step explanation:
solve sin∅+ 1 = cos2∅ on the interval 0 ≤ ∅ ≤ 2pie
The solutions to the equation sin(θ) + 1 = cos(2θ) on the interval 0 ≤ θ ≤ 2π are θ = 0, θ = π, θ = 7π/6, and θ = 11π/6.
To solve the equation sin(θ) + 1 = cos(2θ) on the interval 0 ≤ θ ≤ 2π, we can use trigonometric identities and algebraic manipulations to simplify and find the solutions.
Let's start by using the double-angle identity for cosine:
cos(2θ) [tex]= 1 - 2sin^2(\theta)[/tex]
Substituting this into the equation, we have:
[tex]sin(\theta) + 1 = 1 - 2sin^2(\theta)[/tex]
Rearranging the equation, we get:
[tex]2sin^2(\theta) + sin(\theta) = 0[/tex]
Factoring out sin(θ), we have:
sin(θ)(2sin(θ) + 1) = 0
Now we can set each factor equal to zero and solve for θ:
sin(θ) = 0 or 2sin(θ) + 1 = 0
For sin(θ) = 0, the solutions are θ = 0 and θ = π (since sin(θ) = 0 at these values on the interval 0 ≤ θ ≤ 2π).
For 2sin(θ) + 1 = 0, we can solve for sin(θ):
2sin(θ) + 1 = 0
2sin(θ) = -1
sin(θ) = -1/2
The solutions for sin(θ) = -1/2 on the interval 0 ≤ θ ≤ 2π are θ = 7π/6 and θ = 11π/6.
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Minimize a firms total costs, C = 45X^2+90XY=90Y^2 When the firm has to meet a production quota equal to 2X+3Y=60 by
A. Finding the critical values
The solution (X = 8, Y = 16) represents a minimum because the second partial derivatives are both positive.
The quadratic equation's roots 32
+6x+8=0 utilises the quadratic formula to determine. x = is the quadratic formula.
where the quadratic equation's coefficients are a, b, and c. Here, an equals 1, b equals 6, and c equals 8. We obtain the quadratic formula's result by entering these values: x =
x = (-6 ± √(36 - 32)) 2 x = (-6 to 4) 2 x = (-6 to 2) 2 x = (-3 to 1) 1 x = (-2 to 4)
Generally, any quadratic equation of the form may be solved using the quadratic formula to get the roots.
Whereas a, b, and c are real numbers, + bx + c=0. One effective method for tackling a wide range of physics and maths issues is the quadratic formula.
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A gardener has 800 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side:
ft (feet)
longer side:
ft (feet)
greatest possible area:
ft2 (square-feet)
The garden will have the greatest possible area of 80,000 square feet when the shorter side is 400 feet, the longer side is 200 feet, and the garden is bordered by a river on one side.
To find the dimensions that guarantee the garden has the greatest possible area, we can use the concept of optimization.
Let's assume the shorter side of the rectangular garden is x feet.
Since one side of the garden is bordered by a river and doesn't require fencing, we only need to fence three sides of the garden.
The perimeter of the garden is given by the sum of the lengths of the three sides, which is equal to 800 feet.
Thus, we have:
x + 2L = 800
Solving for L (the longer side of the garden) in terms of x:
L = (800 - x)/2
The area of the rectangular garden is given by the product of its length and width, which is:
Area = x [tex]\times[/tex] L
Substituting the expression for L in terms of x:
Area = x [tex]\times[/tex] [(800 - x)/2]
To find the dimensions that guarantee the greatest possible area, we need to find the maximum value of this area.
We can do this by differentiating the area function with respect to x, setting it equal to zero, and solving for x:
d(Area)/dx = (800 - 2x)/2 = 0
800 - 2x = 0
2x = 800
x = 400
So, the shorter side of the garden should be 400 feet.
Substituting this value back into the expression for L:
L = (800 - 400)/2 = 200
Therefore, the longer side of the garden should be 200 feet.
Finally, to find the greatest possible area, we can substitute the values of x and L into the area formula:
Area = 400 [tex]\times[/tex] 200 = 80,000 square feet.
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