What must be true of x/y÷3a/b=3a/b? Assume a does not equal 0, b does not equal 0 and y does not equal 0
Answers
For the linear equation (x/y) ÷ (3a/b) = 3a/b to be true, x must equal 9a² × y/b² if a does not equal 0, b does not equal 0 and y does not equal 0.
To determine what must be true of x/y ÷ 3a/b = 3a/b, we can follow the order of operations, which is to perform the division before the multiplication.
First, we can simplify the left side of the equation by dividing x/y by 3a/b, which is equivalent to multiplying x/y by b/3a.
This gives us x / (y × (3a/b)) = 3a/b.
We can simplify further by multiplying both sides of the equation by y*(3a/b), which eliminates the denominators.
This gives us x = 3a × (y/b) × (3a/b).
Simplifying further, we get x = 9a² × y/b².
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Related Questions
the sum of two numbers is 41 . the sum of 3 times the larger and 8 times the smaller is 203 . find the numbers.
Answers
Answer:
The numbers are 16 and 25
if a, b, and c are integers between -10 and 10 inclusive such that a^3 b^3 = c^3, what is the greatest possible value of a b c?
Answers
The greatest possible value of abc, given that a³b³ = c³ and a, b, and c are integers between -10 and 10 inclusive, is 1.
If a, b, and c are integers between -10 and 10 inclusive such that a³b³ = c³, then what is the maximum possible value of abc?We will start with listing the cubes of numbers between -10 and 10. Below is the table of cubes of numbers between -10 and 10 inclusive.
{-1000, -729, -512, -343, -216, -125, -64, -27, -8, -1, 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000}In the table above, the only numbers that occur thrice are 1, -1, and 0.
All the other numbers are either negative or positive and occur once.So, this means that a, b, and c must be either 1, -1, or 0. This is because if a, b, and c are any other numbers, the left side of the equation, a³b³ = c³, is going to be a cube of some number between -10 and 10 inclusive which is not in the table above.
Hence, this would mean that a³b³ ≠ c³. Therefore, a, b, and c must be either 1, -1, or 0.Now, we can determine the largest possible product of abc: abc = (1)(1)(1) = 1 or (1)(1)(0) = 0 or (-1)(-1)(1) = -1. In conclusion, the greatest possible value of abc is 1.
The greatest possible value of abc, given that a³b³ = c³ and a, b, and c are integers between -10 and 10 inclusive, is 1.
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Sarah has been running a dog-walking business since 2010. She walks dogs twice a day, takes them to the park, and returns them to their homes. Each year, she has increased her fee by the same amount. The table shows what Sarah charged each customer for two given years of her business:
Year Annual Dog-walking Fee
2010 $350
2014 $750
A. What is the rate of change and initial value for Sarah's business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Sarah charges each year. (10 points)
Answers
Sarah's company started out with a $350 value and is currently changing at a rate of $100 annually.
The annual fee is expressed as an equation in slope-intercept form:
y = 100x + 350.
Define the term slope-intercept form?y = mx + b, where m is the line's slope and b is its y-intercept, is the formula for a straight line.
Given details:
Since 2010, Sarah has operated a dog-walking service.She has raised her rate the same amount each year.The table displays the prices that Sarah charged each client during the course of her business's first two years:
Year Annual Dog-walking Fee
2010 $350
2014 $750
A.
Sarah has so increased the cost by $400 over the past four years.
For Sarah's company, its rate of change called slope will be,
m = 750 - 350 / 4
m = 100
Therefore, Sarah is raising the cost by $100 yearly.
Due to the payment she received for the first year, the calculated values of a business is $350.
B. Define x as the period of time that has passed since she began her business in 2010.
Consequently, the annual fee equation can be expressed in slope-intercept form as,
y = mx + c
where y stands for the cost she must pay after x years.
Her company's baseline value is therefore $350, and its rate of change is $100 annually.
The annual fee is expressed as an equation in slope-intercept form.: y = 100x + 350.
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Help me with this please
Answers
Answer:
The one you chose
Step-by-step explanation:
Determine which process generates more values that are more than 2 standard deviations from the mean
Answers
The process that generates more values that are more than 2 standard deviations from the mean is called a "fat-tailed" distribution.
In a fat-tailed distribution, the probability of extreme values occurring is higher compared to a normal distribution.
To understand this concept, let's consider two processes: Process A and Process B.
Process A generates a dataset with a normal distribution, while Process B generates a dataset with a fat-tailed distribution.
In a normal distribution, the majority of the data falls close to the mean, with fewer values farther away.
The probability of values more than 2 standard deviations from the mean is relatively low.
On the other hand, in a fat-tailed distribution, there is a higher likelihood of extreme values occurring.
This means that the probability of values more than 2 standard deviations from the mean is higher.
For example, let's say we have two datasets: Dataset A generated by Process A and Dataset B generated by Process B.
We calculate the mean and standard deviation for both datasets.
In Dataset A, if the mean is 50 and the standard deviation is 5, then values more than 2 standard deviations away from the mean would be greater than 60 or less than 40.
In Dataset B, if the mean is 50 and the standard deviation is also 5, then values more than 2 standard deviations away from the mean would have a wider range.
These values could be significantly higher than 60 or lower than 40, depending on the specific distribution of Dataset B.
Therefore, if Process B generates a fat-tailed distribution, it is more likely to produce values that are more than 2 standard deviations from the mean compared to Process A and its normal distribution.
In summary, the process that generates more values that are more than 2 standard deviations from the mean is a fat-tailed distribution, which has a higher likelihood of extreme values occurring.
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Helmets and lunches: The scatterplot shows the relationship between socioeconomic status measured as the percentage of children in neighborhood receiving reduced-fee lunches at school (lunch) and the percentage of bike riders in the neighborhood wearing helmets (helmet). The average percentage of children receiving reduced-fee lunches is 30.8% with standard deviation of 26.7% and the average percentage of bike riders wearing helmets is 38.8% with standard deviation of 16.9%. (a) If the R? for the least-squares regression line for these data is 72%, what is the correlation 60% between lunch and helmet? 1 (b) Calculate the slope and intercept for the least-squares regression line for these data. 40% (c) Interpret the intercept of the least-squares regression line in the context of the application_ 6 (d) Interpret the slope of the least-squares regression 3 20% line in the context of the application: (e) What would the value of the residual be for 2 neighborhood where 40% of the children receive 0% reduced-fee lunches and 40% of the bike riders 0% 20% 40% 60% 80% wear helmets? Interpret the meaning of this Rate of Receiving a Reduced-Fee Lunch residual in the context of the application
Answers
The answers are:
a. The correlation between lunch and helmet is 84.8%.
b. The slope is 0.538 and the intercept is 22.1.
c. It means that even if no children receive reduced-fee lunches, there would still be a baseline percentage of 22.1% of bike riders wearing helmets.
d. It means that for every 1% increase in the percentage of children receiving reduced-fee lunches, there is an expected increase of 0.538% in the percentage of bike riders wearing helmets.
e. The residual is 40 - 41.9 = -1.9%. In this context, the negative residual suggests that the actual percentage of bike riders wearing helmets is slightly lower than the predicted value, given the percentage of children receiving reduced-fee lunches.
(a) The correlation coefficient (r) between lunch and helmet can be calculated using the formula: r = (R^2)^(1/2). Given that R^2 is 72%, we can find r = sqrt(0.72) = 0.848.
(b) The slope (b) and intercept (a) for the least-squares regression line can be calculated using the formulas: b = r * (SDy / SDx) and a = mean_y - b * mean_x. With SDy = 16.9%, SDx = 26.7%, mean_y = 38.8%, and mean_x = 30.8%, we can find b = 0.848 * (16.9 / 26.7) = 0.538 and a = 38.8 - 0.538 * 30.8 = 22.1.
(c) The intercept (a) represents the predicted percentage of bike riders wearing helmets when the percentage of children receiving reduced-fee lunches is 0.
(d) The slope (b) represents the change in the percentage of bike riders wearing helmets for each 1% increase in the percentage of children receiving reduced-fee lunches.
(e) To calculate the residual for a neighborhood where 40% of children receive 0% reduced-fee lunches and 40% of bike riders wear helmets, we can use the formula: residual = observed_y - predicted_y. Given that observed_y is 40% and predicted_y can be calculated as a + b * x, where x is 40%, we have predicted_y = 22.1 + 0.538 * 40 = 41.9%.
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Graph y - 4x + 3 = 0 and {(x , y ): x ≤ 1}. Click on the graph until the correct graph appears.
Answers
True or False?
(9x - 8) - (x + 4) = 8x +12
Answers
Step-by-step explanation:
(9x-8)-(x+4)=8x+12
9x-8-x-4=8x+12
8x-12=8x+12 (no it's not)
So it's false.
Hey guys! I need help with this question urgently, so could you please help me out? Thanks in advance! Merry Christmas!
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the roots of f(x)=-2x^2+8x+13 are __________and __________ the vertex of the parabola is at _________
Answers
Answer:
roots: 2 ± (1/2)√42
-8
axis of symmetry: x = -b/(2a) is x = ---------------- = 2
2(-2)
vertex: (2, f(2) ) = (2, -2(2)^2 + 8(2) + 13 ), or (2, 21)
Step-by-step explanation:
First, let's determine the roots of this quadratic, using the quadratic formula. Here the coefficients are -2, 8, 13.
Thus, the discriminant b^2 - 4ac is 8^2 - 4(-2)(13), or 64 + 104, or 168. Because the discriminant is positive, we know that there are two different real roots.
They are:
-8 ± √168 -8 ± 2√42
x = --------------------- or x = --------------------- = 2 ± (1/2)√42
-4 -4
Express the quotient as a fraction in simplest form. -5-7 divided by 6/7
Answers
Answer:
a) -5/6
Step-by-step explanation:
\( - \frac{5}{7} \div \frac{6}{7} \)
keep, change, flip
\( - \frac{5}{7} \times \frac{7}{6} \)
\( - \frac{35}{42} \)
simplify
35 ÷7=5
42÷7= 6
62. A boat leaves the marina and sails 6 miles north, then 2 miles northeast. How far from the marina is the boat, and in what direction must it sail to head directly back to the marina?
Answers
The marina is 6. 3 miles from the boat
The direction must it sail to head directly back to the marina Is due south
How to determine the distance
From the information given, we have that;
The boat sails 6 miles north
then, the boat sails then 2 miles northeast
Using the Pythagorean theorem which states that the square of the longest leg of a triangle is equal to the sum of the squares of the other two sides of that triangle.
Then, we have to substitute the values, we get;
d² = 6² + 2²
Find the square values, we have;
d² = 36 + 4
d² = 40
Find the square root of both sides
d = 6. 3 miles
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a standing wave is set up in a pool 24 m long which contains six loops. what is the wavelength? a) 24 m b) 48 m c) 8 m d) 4 m
Answers
Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.
Wavelength = Length of Pool / Number of Loops
24 m / 6 loops
= 4 m
Wavelength
= 4 m
Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.
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HELP ME PLEASE!!! HELP ME PLEASE!!!
A Diginacci sequence is created as follows.
• The first two terms are any positive whole numbers.
• Each of the remaining terms is the sum of the digits of the previous
two terms.
For example, starting with 5 and 8 the Diginacci sequence is
5, 8, 13, 12, 7, 10,. . .
The calculations for this example are
5 + 8 = 13, 8 + 1 + 3 = 12, 1+ 3 +1+ 2 = 7, 1 + 2 + 7 = 10.
1. Find, with explanation, two starting terms for a Diginacci sequence
so that its 2021st term is 11.
2. Find, with explanation, a Diginacci sequence that has no term equal
to 11
Answers
1. To find two starting terms for a Diginacci sequence such that the 2021st term is 11, we can work backward from the 2021st term to determine the preceding terms.
Let's denote the first term as a and the second term as b. We need to find the values of a and b that will result in the 2021st term being 11.
Working backward, we know that the 2021st term (which is 11) is the sum of the digits of the previous two terms. Let's denote the (2020)th term as x and the (2019)th term as y. Therefore, we have:
11 = x + y
2. To find a suitable pair of x and y, we can iterate through possible values. Since the first two terms can be any positive whole numbers, we have some flexibility in choosing them.
For example, let's try a = 1 and b = 1:
Term 1: 1
Term 2: 1
Term 3: 2
Term 4: 1
Term 5: 3
Term 6: 4
Term 7: 7
Term 8: 11
The 8th term is 11, which matches our target. Therefore, if we start with a = 1 and b = 1, the 2021st term will indeed be 11.
To find a Diginacci sequence that has no term equal to 11, we need to ensure that none of the subsequent terms sum up to 11.
One way to achieve this is to start with two terms that are relatively large and have no digits summing up to 11. Let's try a = 99 and b = 100:
Term 1: 99
Term 2: 100
Term 3: 19 (9 + 9)
Term 4: 10 (1 + 0)
Term 5: 1
Term 6: 1
Term 7: 2
Term 8: 3
Term 9: 5
Term 10: 8
Term 11: 13
Term 12: 12
Term 13: 7
Term 14: 10
...
By starting with a = 99 and b = 100, the Diginacci sequence continues without reaching the value 11. The terms keep changing without summing up to 11, as seen in the subsequent terms above.
Thus, this particular Diginacci sequence starting with a = 99 and b = 100 does not have any term equal to 11.
Seven more than twice a number is 17
Answers
Answer:
2x + 7 = 17 using algebra equation you can resolve ir
Let a = -4.82 and b = 4.35. All of the following statements are true except
The sum of a and b is negative.
The product of a and - b is positive.
The quotient of a and - b is the same as the quotient of - a and b.
The distance between a and b on the number line is 0.47 units.
Answers
Answer:
the sum of -4.82 and 4.35 = -0.47
so a is correct
the product of -4.82 and 4.35 = -20.967
so b is incorrect
the quotient of -4.82 and -4.35 is 1.10804597701
the quotient of 4.82 and 4.35 is 1.10804597701
so c is correct
if we subtract 4.35 from -4.82 we get -9.17
so d is incorrect
Hope This Helps!!!
Function 1 is defined by the equation y = -2t + 6
Function 2 is defined by line h, shown on the following graph.
Which function has a more negative slope?
Choose 1 answer:
A. Function 1
B. Function 2
C. The functions have the same slope
Answers
Answer:
FUNCTION A
Step-by-step explanation:
It said it was right on khan
Function 1 have more negative slope.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Function 1 is defined by the equation y = -2t + 6
Function 2:
Slope = 4/ 4 = 1
Then, the equation would be
y - 0 = 1( t- 4)
y= t - 4
Hence, Function 1 have more negative slope.
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Find the surface area of the figure. Hint: the surface area from the missing prism inside the prism must be ADDED!
Answers
To find the surface area of the figure, we need to consider the individual surfaces and add them together.
First, let's identify the surfaces of the figure:
The lateral surface area of the larger prism (excluding the base)
The two bases of the larger prism
The lateral surface area of the smaller prism (excluding the base)
The two bases of the smaller prism
The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.
The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.
To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.
Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.
Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.
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Expand LaTeX: (4a - 3b^3)^2.
Answers
(4a-3b^3)^2
(4a-3b^3)(4a-3b^3)
16a-12ab^3-12ab^3+9b^3
16a+9b3
i really dont know this question help please
Answers
Answer:
88
Step-by-step explanation:
x + 49 = 137 (exterior angle of triangle is equal to sum of its opoosite two interior angles)
x = 137-49
so, x = 88
Please can someone help
Answers
Answer:
2406.17 cm³
Step-by-step explanation:
Data obtained from the question include the following:
Height (h) = 24.4 cm
Length of the base (L) = 17.2 cm
Volume (V) =..?
Next, we shall determine the area of the square base of the pyramid.
This can obtained as shown below:
Since the base is a square, we shall use the formula for calculating the area of a square to obtain the area of the square base of the pyramid.
Area of a square is given by :
Area (A) = Length (L) x Length (L)
A = L x L
A = L²
Length of the base (L) = 17.2 cm
Area (A) =...?
A = L²
A = 17.2²
A = 295.84 cm²
Finally, we shall determine the volume of the pyramid as follow:
Height (h) = 24.4 cm
Area (A) = 295.84 cm²
Volume (V) =.?
V = ⅓Ah
V = ⅓ × 295.84 × 24.4
V = 2406.17 cm³
Therefore, the volume of the pyramid is 2406.17 cm³.
What is Desmos in math?
Answers
Answer:
Desmos is a free graphing and teaching tool for math available on the web as well as on iOS and Android. In addition to plotting equations, classroom activities are available to help students learn about a variety of math concepts.
A definition of Desmos has been given below
What is Desmos?
Desmos can be applied in a variety of contexts. Students can avoid spending $100 on a graphing calculator by using it for free. It can be used by teachers to create stunning images for tests and presentations. But Desmos really shines in the classroom exercises. Teachers can use Desmos to assist students in making the connection between mathematical concepts and actual, concrete shapes and images. It's simple to begin an activity with your students: Just instruct the children to enter the website's activity code. Try the student preview of an activity before assigning it. In the teacher moves section at the bottom of each activity, you can find specific ways to guide your children while they work. The teacher dashboard allows for the tracking of progress.
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Answers
To find the z-score for a sales associate who earns $37,500, we can use the formula:
z = (x - μ) / σ
Where:
x is the value we want to convert to a z-score (in this case, $37,500),
μ is the mean of the distribution (in this case, $32,500), and
σ is the standard deviation of the distribution (in this case, $2,500).
Substituting the given values into the formula, we have:
z = (37,500 - 32,500) / 2,500
z = 5,000 / 2,500
z = 2
Therefore, the z-score for a sales associate who earns $37,500 is 2.
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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.
Explanation:The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.
We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:
Z = (Value - Mean) / Standard Deviation
So, the z-score for an associate earning $37,500 would be:
Z = ($37,500 - $32,500) / $2,500
This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.
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you play a game in which you must pick a real number x, between 0 and 924. at the same time, the number y is uniformly and randomly selected in the same range. if x is greater than y, then you have to pay the square of the difference between the two numbers. if y is greater than or equal to x, you pay double the difference.
Answers
Answer: about 2.2 times 8^8
Step-by-step explanation:
Pay the money x=y^2
The radius of a circle is 7 inches. What is the length of a 135º arc?
Answers
Joy went to the community swap meet, where the cost to get in is $2. She plans to buy some candles for $1.60 each. If Joy has $50, how many candles can she buy after she pays to get in? *
Answers
The answer is 30
Step-by-step explanation:
50-2=48 then divide 48 by 1.60 and you get 30!
If A = -1 +5n2 + 9 and B = 3 – n, find an expression that equals 2 A – 3B
in standard form.
Answers
Answer:
10n² + 3n + 7
Step-by-step explanation:
2A - 3B = 2.( -1 + 5n² + 9) - 3.(3 - n)
= -2 + 10n² + 18 - (9 - 3n)
= 10n² + 16 -9 + 3n
= 10n² + 3n +7
if the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score e(x y)?
Answers
The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y).
e(x+y)
e = expected
x = points earned on part 1
y = points earned on part 2
So, the expected recorded score is the total of points earned on both parts: e(x+y).
The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y). This formula is useful for quickly calculating the total score of an assignment, allowing the grade book to be updated quickly and accurately.
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wich is bigger 51.243 or 5.1243
Answers
Answer:
The number 51.243 is bigger than 5.1243.
Step-by-step explanation:
To compare two decimal numbers, we start by looking at the digits to the left of the decimal point. In this case, both numbers have the same digit in the tens place, which is 5. So we need to look at the next digit to the right of the decimal point.In 51.243, the digit to the right of the decimal point is 2, which is larger than the digit to the right of the decimal point in 5.1243, which is 1. Therefore, we can conclude that 51.243 is bigger than 5.1243.
Answer:
51.243
Step-by-step explanation:
because 51 is greater than 5.1
2/5% as a fraction
Pld
Answers
Hey there!
2/5%
= 2/5
= 2 ÷ 5
= 0.40
= 0.40 × 100
= 40%
Therefore, your answer is: 40%
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A jeweler is making pairs of gold earrings. For each earring, the jeweler will
make a circular hoop that measures 25 mm across. The jeweler has 2
meters of gold wire to make earrings from. How many pairs of gold hoops
can the jeweler make?
Answers
7+3#2
Step-by-step explanation:
4(8-4)
16
16-9#7
7+3#2