The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
What is Dilation:In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.
When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.
Here we have
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.
To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.
The coordinates of A are (-4, 6), multiply each coordinate by 1/8
A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)
The coordinates of B are (-2, 2), multiplying each coordinate by 1/8
B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)
The coordinates of C are (4, -2), multiplying each coordinate by 1/8
C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)
The coordinates of D are (4, 4). Multiplying each coordinate by 1/8
D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)
Therefore,
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
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What is the lcd of 2/5,1/2, and 3/4
The LCD of 2/5, 1/2, and 3/4 is equal to 20.
What is LCD?In Mathematics, LCD is an abbreviation for least common denominator or lowest common denominator and it can be defined as the smallest number that can act as a common denominator for a given set of fractions.
Next, we would determine the factors of the denominators for the given fraction 5, 2, and 4 as follows;
5 = 5 × 1
2 = 2 × 1
4 = 2 × 2 × 1
Therefore, the least common denominator (LCD) would be calculated as follows:
Least common denominator (LCD) = 5 × 2 × 2 × 1
Least common denominator (LCD) = 20.
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the probability of rolling six standard, six-sided dice and getting six distinct numbers is , what is the value of ?
To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we need to calculate the total number of possible outcomes and the number of outcomes that satisfy the given condition.
Total Number of Outcomes:
The total number of possible outcomes when rolling six dice is 6^6, which is 46,656. Each die has six possible outcomes (1, 2, 3, 4, 5, or 6), and there are six dice being rolled.
Number of Outcomes with Six Distinct Numbers:
To get six distinct numbers when rolling six dice, each number must be different from the others. We can choose any six numbers from 1 to 6, and there are 6! (6 factorial) ways to arrange them on the six dice.
This is because there are six choices for the first die, five choices for the second die (since we can't repeat the number on the first die), four choices for the third die, and so on, down to one choice for the sixth die. Therefore, the number of outcomes with six distinct numbers is:6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Probability of Getting Six Distinct Numbers:
To find the probability of rolling six standard, six-sided dice and getting six distinct numbers, we divide the number of outcomes with six distinct numbers by the total number of possible outcomes:
P(six distinct numbers) = number of outcomes with six distinct numbers / total number of outcomes
P(six distinct numbers) = 720 / 46,656
P(six distinct numbers) = 5 / 324
Therefore, the value of the probability is 5/324 or approximately 0.0154.
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Find the lengths of the triangles altitude and base if its area is 384 squared feet
If the area is 384 square feet, then the length of the altitude is 36 feet, and the length of the base is 44 feet.
Let's start by using the formula for the area of a triangle in terms of its base and altitude:
[tex]Area = (1/2) * base * altitude[/tex]
We know that the area of the triangle is 384 square feet:
[tex]384 = (1/2) * base * altitude[/tex]
Next, we're given that the base is 8 feet longer than the altitude:
[tex]base = altitude + 8[/tex]
We can substitute this expression for the base into the area formula:
[tex]384 = (1/2) * (altitude + 8) * altitude[/tex]
Simplifying and multiplying out the right-hand side:
[tex]384 = (1/2) * (altitude^2 + 8altitude)\\768 = altitude^2 + 8altitude[/tex]
Now we have a quadratic equation in terms of the altitude. We can solve for the altitude by first rearranging the equation:
[tex]altitude^2 + 8altitude - 768 = 0[/tex]
Then, we can solve for the altitude using the quadratic formula:
[tex]altitude = (-8 ± sqrt(8^2 - 4(1)(-768))) / (2(1))\\altitude = (-8 ± sqrt(6400)) / 2\\altitude = (-8 ± 80) / 2[/tex]
We get two possible values for the altitude:
altitude = -44 or altitude = 36
Since the altitude of a triangle must be positive, we discard the negative solution and choose altitude = 36 feet.
We can then use the expression for the base in terms of the altitude to find the length of the base:
[tex]base = altitude + 8 = 36 + 8 = 44 feet[/tex]
Therefore, the length of the altitude is 36 feet and the length of the base is 44 feet.
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Correct question:
Find the lengths of the triangles altitude and base if its area is 384 squared feet. If its base is 8 feet longer than its altitude, find the length of the base and the altitude.
If p, q are natural numbers and ε is a positive real number, show that for some natutal number Nn ≥ N and n ∈ N ⇒ |p/n − q/n| < ε.
Conclusion
Therefore, for some natural number N, n ≥ N and n ∈ N implies |(p - q)/n| < ε.
To show that for some natural number N, n ≥ N and n ∈ N implies |p/n - q/n| < ε, we'll use the Archimedean property of real numbers. The Archimedean property states that for any positive real numbers a and b, there exists a natural number n such that n*a > b.
Let's consider the inequality we want to prove: [tex]|p/n - q/n| < ε.[/tex]
Step 1: Rewrite the inequality
First, we can rewrite the inequality as |(p - q)/n| < ε, since we are allowed to combine the fractions.
Step 2: Apply the Archimedean property
By the Archimedean property, we know that for any ε > 0, there exists a natural number N such that N > (p - q)/ε.
Step 3: Rearrange the inequality
We can rearrange the inequality from step 2 to get[tex] N*ε > p - q. [/tex]
Step 4: Divide by N
Now, divide both sides of the inequality by N to get [tex]ε > (p - q)/N.[/tex]
Step 5: Relate this to our original inequality
We want to show that |(p - q)/n| < ε for some n ∈ N, where n ≥ N. Since n ≥ N, and ε > (p - q)/N, we have ε > (p - q)/n for n ∈ N and n ≥ N
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What is the mean of this data set?
A table titled Length of Roses. The first column is labeled length in centimeters. The second column is labeled number of roses. The first row shows 2 roses measuring 22 centimeters in length. The second row shows 4 roses measuring 23 centimeters in length. The third row shows 5 roses measuring 24 centimeters in length. The fourth row shows 3 roses measuring 25 centimeters in length. The fifth row shows 1 rose measuring 26 centimeters in length.
24 cm
twenty-three and twelve-fifteenths
twenty-three and one-half
22 cm
Answer:
Step-by-step explanation:
c
The closest option, 24 cm, is the length of the mode, or the length that appears the most frequently in the data set, but none of the other possibilities fit this value's exact range.
what is mean ?The mean, which is used to indicate the average value of a group of values in statistics, is a measure of central tendency. It is determined by adding up all of the data set's values and dividing the result by the number of values. The mean is frequently chosen as a data set's representative value because it can provide light on the typical value or average performance of a population or sample.
given
The following formula can be used to determine the total number of roses multiplied by each length of roses using the information in the table:
(2 * 22) + (4 * 23) + (5 * 24) + (3 * 25) + (1 * 26) = 222
There are: roses in all.
2 + 4 + 5 + 3 + 1 = 15
As a result, the data set's mean is:
222 / 15 = 14.8
Thus, the data set's roses' average length is 14.8 centimetres.
The closest option, 24 cm, is the length of the mode, or the length that appears the most frequently in the data set, but none of the other possibilities fit this value's exact range.
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Part 2
Tom wanted to go on a 1-mile kayak trip and is wondering how long it will take him to go up and down stream if he is paddling at 4
miles per hour while current is flowing at 3 miles per hour.
Answer:
To calculate the time it will take Tom to complete the 1-mile kayak trip, we need to take into account the speed of the current and the speed at which Tom can paddle relative to the current.
Let's first consider the time it would take for Tom to go upstream against the current. In this case, the speed of the current is subtracted from Tom's paddling speed, so his effective speed is:
Effective speed upstream = 4 miles per hour - 3 miles per hour = 1 mile per hour
To travel 1 mile at 1 mile per hour, Tom would take:
Time upstream = Distance / Effective speed upstream = 1 mile / 1 mile per hour = 1 hour
Now let's consider the time it would take for Tom to go downstream with the current. In this case, the speed of the current is added to Tom's paddling speed, so his effective speed is:
Effective speed downstream = 4 miles per hour + 3 miles per hour = 7 miles per hour
To travel 1 mile at 7 miles per hour, Tom would take:
Time downstream = Distance / Effective speed downstream = 1 mile / 7 miles per hour ≈ 0.14 hours or about 8 minutes
Therefore, the total time it would take Tom to complete the 1-mile kayak trip, including going upstream and downstream, would be:
Total time = Time upstream + Time downstream = 1 hour + 0.14 hours ≈ 1.14 hours or about 68 minutes.
which set of integers is a pythagorean triple? question 1 options: 10, 24, 25 9, 12, 21 8, 15, 23 6, 8, 10
The set of integers is a Pythagorean triple are option (A) 10, 24, 25 and (D) 6, 8, 10
A Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right triangle.
Let's check each set of integers
A. 10^2 + 24^2 = 100 + 576 = 676 = 25^2. Therefore, (10, 24, 25) is a Pythagorean triple.
B. 9^2 + 12^2 = 81 + 144 = 225 = 15^2. Therefore, (9, 12, 15) is a Pythagorean triple. However, the set given is (9, 12, 21), which is not a Pythagorean triple.
C. 8^2 + 15^2 = 64 + 225 = 289 = 17^2. Therefore, (8, 15, 17) is a Pythagorean triple. However, the set given is (8, 15, 23), which is not a Pythagorean triple.
D. 6^2 + 8^2 = 36 + 64 = 100 = 10^2. Therefore, the set of integers (6, 8, 10) is a Pythagorean triple.
Therefore, the correct options are (A) 10, 24, 25 and (D) 6, 8, 10
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The given question is incomplete, the complete question is:
Which set of integers is a Pythagorean triple?
A.
10, 24, 25
B.
9, 12, 21
C.
8, 15, 23
D.
6, 8, 10
each of the letters of the word colorado are written on a piece of paper and then put into a bag. a piece of paper is drawn at random. what is the theoretical probability of not drawing an o?
The theoretical probability of not drawing an "o" is 3/4.
We have,
Each of the letters of the word Colorado are written on a piece of paper and then put into a bag.
Here, The word "Colorado" has 8 letters, including 2 "o"s.
Therefore, the probability of drawing an "o" is,
P = 2/8
P = 1/4
Hence, The probability of not drawing an "o" is the complement of this probability is,
1 - 1/4 = 3/4.
Therefore, the theoretical probability of not drawing an "o" is 3/4.
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What is the greatest common factor of −20x3y − 8xy4 + 4xy3?
4xy2
xy
4xy
4x3y4
Option C, The greatest common factor of −20x³y − 8[tex]xy^4[/tex] + 4xy³ is 4xy by simplifying expressions and solving equations.
To find the greatest common factor (GCF) of the given terms, we need to factor out any common terms that they share.
First, we can factor out 4xy from each term:
−20x³y − 8[tex]xy^4[/tex] + 4xy³ = 4xy(-5x² - 2y³ + y)
Now we need to check if any further common factors can be factored out from the remaining expression (-5x² - 2y³ + y). However, there are no other factors that can be factored out from this expression.
As it enables us to factor out frequent terms and reduce the expression to its most basic form, the GCF is beneficial for simplifying expressions and solving equations.
Therefore, the GCF of the original terms is 4xy, option (c).
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Answer:
4xy
Step-by-step explanation:
I did the test and got it right !
It is the greatest common factor of 20, 8, and 4. And we add the “xy”.
What is the quotient of 3.013 × 10^(8) and 6.55 × 10^(5) expressed in scientific notation?
The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].
What is a quotient?In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).
Generally speaking, any numerical data (number) can be written in scientific notation as shown below:
a × [tex]b^n[/tex]
Where
a represent a real number.b represent an integer.Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:
Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])
Scientific notation = 0.46 × [tex]10^{8-5}[/tex]
Scientific notation = 0.46 × [tex]10^{3}[/tex].
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help i need help with this its very hard
Answer:
3a + 2b
Step-by-step explanation:
Let the unknown side have length X.
X + X + 5a - b + 5a - b = 16a + 2b
2X + 10a - 2b = 16a + 2b
2X = 6a + 4b
X = 3a + 2b
Answer: 3a + 2b
There is an amoeba (a single-celled animal) on a dish.
After one hour, the amoeba divides to form two amoebas.
One hour later, each amoeba divides to form two more.
Every hour, each amoeba divides to form two more.
Write an expression for the number of amoebas after `24` hours.
An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216
How do amoebas develop?Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.
Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.
a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.
b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.
c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.
d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.
Expression = 1 × 2²⁴ = 16,777,216
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If the width and length of a rectangle is 3 by 8 what is the width and length actually if the width is 10. 5
The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.
If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.
The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)
It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.
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If the diameter of a circle is 2.80 inches, what is the radius? Responses a) 5.6 inches b) 4.6 inches c) 1.4 inches d) 1.2 inch
Answer:
The circumference of a circle with radius 2.8 is 17.59(*)
Step-by-step explanation:
Circumference of a cicle in terms of radius:Circumference = 2·π·r = 2·3.14·2.8 = 17.59(*)In terms of diameter:Circumference = π·d = 3.14·5.6 = 17.58(*)In terms of area:Circumference C = √4·π·A = √4·π·24.63 = 17.59(*)(*) 17.59 inches exactly or limited to de precision of this calculator (13 decimal places).Note: for simplicity, the operations above were rounded to 2 decimal places and π was rounded to 3.14.
john paul is 6 years older than angelina. in 9 years the sum of their ages will be 86. how old is john paul now?
If john paul is 6 years older than Angelina and in 9 years the sum of their ages will be 86, then John Paul is 35 years old now.
Let's assume Angelina's current age to be x years old. Then, according to the given information, John Paul's current age would be (x + 6) years old.
In 9 years, the sum of their ages will be 86, which means that (x + 9) + (x + 6 + 9) = 86.
Simplifying the equation, we get 2x + 24 = 86.
Solving for x, we get x = 31.
Therefore, John Paul's current age would be x + 6 = 31 + 6 = 35 years old.
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Dilate point S by a scale factor of 1/2
To dilate a point S by a scale factor of 1/2, we need to multiply the coordinates of the point by the scale factor.So the dilated point S' will have coordinates (2, 3).
What is scale factor?A scale factor is a number that scales or multiplies another quantity by a certain amount, either making it larger or smaller. In geometry, scale factor is used to describe the ratio of the corresponding side lengths of two similar figures.
If the coordinates of point S are (x,y), then the coordinates of the dilated point S' will be:
(x', y') = (1/2 * x, 1/2 * y)
In other words, the x-coordinate of the dilated point is half of the x-coordinate of the original point, and the y-coordinate of the dilated point is half of the y-coordinate of the original point.
For example, if point S has coordinates (4, 6), then the coordinates of the dilated point S' will be:
(x', y') = (1/2 * 4, 1/2 * 6) = (2, 3)
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if you have 20 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
The largest area you can enclose with 20 meters of fencing against a long, straight wall is 50 square meters. Itcan be found using optimization methods.
Step 1: Define the variables
Let x be the length of the fencing parallel to the wall and y be the length of the fencing perpendicular to the wall.
Step 2: Set up the constraint equation
Since you have 20 meters of fencing, the sum of x and 2y (both sides perpendicular to the wall) should equal 20. The constraint equation is:x + 2y = 20
Step 3: Express one variable in terms of the other
Solve the constraint equation for one variable. In this case, solve for x: x = 20 - 2y
Step 4: Write the area function
The area of the rectangle can be expressed as A = xy. Substitute x from the previous step into this equation: A(y) = (20 - 2y)y.
Step 5: Find the critical points
Differentiate the area function with respect to y and set it to zero to find the critical points: dA/dy = 20 - 4y = 0, Solve for y:4y = 20, y = 5
Step 6: Find the corresponding value for x
Plug the value of y back into the equation for x: x = 20 - 2(5), x = 10
Step 7: Check for maximum area
The critical point we found (x=10, y=5) is indeed a maximum since the second derivative of the area function is negative.Step 8: State the largest area
The largest area you can enclose with 20 meters of fencing against a long, straight wall is A = xy = 10 * 5 = 50 square meters.
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Pls help!!!! Urgent!!!! Will give brainliest!!!!
Part A: The system of equations are:
j + g = 23
j = 2g + (- 4)
PART B: The solution of the system is:
Jodi: 14 games
Gerry: 9 games
How to write a system of equations?Part A:
The first equation comes from the fact that they bought a total of 23 games:
j + g = 23 ----- (1)
The second equation comes from the fact that "Jodi buys 4 less than twice the number of games Gerry buys":
j = 2g + (- 4)
j = 2g - 4 ----- (2)
Part B:
We can solve this system of equations by substitution. We can solve the second equation for j, and then substitute that expression for j in the first equation. That is:
j + g = 23
2g-4 + g = 23
3g - 4 = 23
3g = 23 + 4
3g = 27
g = 27/3
g = 9
Put g = 9 in (1):
j + g = 23
j + 9 = 23
j = 23 - 9
j = 14
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if £24=500rubles how many £ are in 648rubles
The answer is 31.10.
Based on the given conditions, formulate: 648 * 24 / 500 Cross out the common factor:dfrac162 * 2412.
I NEED HELP ON THIS ASAP!
Answer:
16 represents the hours available to sew gloves.
2 represents the cost of producing gloves for a small pair.
Step-by-step explanation:
XZ is 12 11/16 units XY is 3 5/8 units find YZ
The required length of YZ is [tex]\frac{145}{16}$[/tex] units.
How to deals with mixed fraction?To find the length of YZ, we can use the fact that the length of XZ is the sum of the lengths of XY and YZ. We are given that XZ is [tex]12 \frac{11}{16}$[/tex]units and XY is [tex]3 \frac{5}{8}$[/tex] units. Let's convert these mixed numbers to improper fractions so that we can add them:
[tex]$XZ = 12 \frac{11}{16} = \frac{12 \times 16 + 11}{16} = \frac{203}{16}$[/tex]
[tex]$XY = 3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{29}{8}$[/tex]
Now we can use the formula:
XZ = XY + YZ
to solve for YZ. Rearranging the equation, we get:
YZ = XZ - XY
Plugging in the values we calculated, we get:
[tex]$YZ = \frac{203}{16} - \frac{29}{8}$[/tex]
To subtract these fractions, we need to find a common denominator. The smallest number that both 16 and 8 divide into evenly is [tex]16 \times 2 = 32$[/tex], so we can rewrite the fractions with a denominator of 32:
[tex]$YZ = \frac{203}{16} \times \frac{2}{2} - \frac{29}{8} \times \frac{4}{4} = \frac{406}{32} - \frac{116}{32}$[/tex]
Now we can subtract:
[tex]$YZ = \frac{406 - 116}{32} = \frac{290}{32}$[/tex]
We can simplify this fraction by dividing both the numerator and denominator by the greatest common factor, which is 2:
[tex]$YZ = \frac{145}{16}$[/tex]
Therefore, the length of YZ is [tex]\frac{145}{16}$[/tex] units.
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Complete question:
XY is a line, Z is a point on this line such that XZ is 12 11/16 units XY is 3 5/8 units find YZ.
PLEASE HELP PLEASE!!!!
Find the area of the regular octagon.
Answer:
48 square centimeters
Step-by-step explanation:
[tex] \frac{1}{2} (4)(8)(3) = 48[/tex]
the average of 8 numbers is 14. the average of 6 of those numbers is 12. what is the average of the other two numbers?
The average of the other two numbers is 16.
This is because the average of 8 numbers is 14, and the average of 6 of those numbers is 12. Therefore, to find the average of the remaining two numbers, you need to find the difference between the average of 8 and the average of 6.
The difference between 14 and 12 is 2. Therefore, if the average of 6 is 12, the average of the remaining two numbers must be 12 + 2 = 16.
To solve this question, you need to use the fact that the average of 8 numbers is 14, and the average of 6 of those numbers is 12. The average of 8 numbers is the sum of all 8 numbers divided by 8. Therefore, if the average of 8 numbers is 14, the sum of all 8 numbers must be 14x8 = 112.
Similarly, the average of 6 numbers is 12, so the sum of those 6 numbers must be 12x6 = 72. The difference between these two sums is 112-72 = 40. This is the sum of the remaining two numbers.
Therefore, if the sum of the remaining two numbers is 40, then the average of the remaining two numbers must be 40/2 = 20.
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3 x 60 = 3 x
tens
Please help me
I think it equals 18 tens
Answer:
3 x 60 x 30 = 5400
Step-by-step explanation:
Shade in the region represented by the inequalities.
The length οf the hypοtenuse AC is 10 units.
What is graph?In mathematics, a graph is a visual representatiοn οf data οr infοrmatiοn that cοnsists οf pοints, called vertices οr nοdes, and lines, called edges οr arcs, that cοnnect them.
Graphs are οften used tο represent relatiοnships between οbjects, events, οr quantities.
They can be used tο mοdel and sοlve prοblems in variοus fields, such as cοmputer science, engineering, ecοnοmics, and sοcial sciences. There are many types οf graphs, including bar graphs, line graphs, scatter plοts, pie charts, and netwοrk graphs, amοng οthers. Each type οf graph is suited fοr visualizing different types οf data οr relatiοnships.
Based οn the given diagram, we can use the Pythagοrean theοrem tο find the length οf the hypοtenuse AC οf the right triangle ABC:
[tex]AC^2 = AB^2 + BC^2[/tex]
Substituting the given side lengths, we get:
[tex]AC^2 = 6^2 + 8^2[/tex]
[tex]AC^2 = 36 + 64[/tex]
[tex]AC^2 = 100[/tex]
Taking the square rοοt οf bοth sides, we get:
AC = 10
Therefοre, the length οf the hypοtenuse AC is 10 units.
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Convert 1.19rads to degree
Answer:
68.2 degrees
Step-by-step explanation:
[tex]1.19\frac{180}{\pi }[/tex]
[tex]68.2[/tex] degrees
A sum of $950 is invested at 17% interest. If A(t) is the amount investment at time t for the case of continuous compounding, w differential equation and an initial condition satisfied by A(t) Select the correct answer. dA O dt17A, AO) 950 dA 0.17A, AO)95 dA dA O 0.17A(0. A- 950 dA O 0.17A, A(O)950 O none of those
ANSWER: dA/dt=0.17A A(0)=950
The correct differential equation and initial condition for the continuous compounding of a sum of 950$ at 17% interest are given by dA/dt = 0.17A and A(0) = 950. This represents the rate of change of the amount A(t) with respect to time and the initial investment value, respectively.
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Doug Bernard specializes in cross-rate arbitrage. He notices the following quotes: Swiss franc/dollar = SFr1.5995/$ Australian dollar/U.S. dollar = A$1.8242/$ Australian dollar/Swiss franc = A$1.1458/SFr Ignoring transaction costs, does Doug Bernard have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how much would he profit if he has $1,000,000 available for this purpose? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Arbitrage profit
, Doug Bernard would profit $4,014.97 from this arbitrage opportunity.
Explanation:
Yes, Doug Bernard has an arbitrage opportunity based on these quotes. To make an arbitrage profit, he can follow these steps:
1. Convert $1,000,000 to Swiss francs using the Swiss franc/dollar rate: $1,000,000 * (SFr1.5995/$) = SFr1,599,500.
2. Convert the Swiss francs to Australian dollars using the Australian dollar/Swiss franc rate: SFr1,599,500 * (A$1.1458/SFr) = A$1,831,604.90.
3. Convert the Australian dollars back to U.S. dollars using the Australian dollar/U.S. dollar rate: A$1,831,604.90 / (A$1.8242/$) = $1,004,014.97.
The arbitrage profit would be the difference between the initial amount and the final amount
: $1,004,014.97 - $1,000,000 = $4,014.97.
Therefore, Doug Bernard would profit $4,014.97 from this arbitrage opportunity
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one ball is drawn at random from a box containing 4 red balls, 7 white balls, and 5 blue balls. determine the probability that the ball drawn is red or white.
Probability of drawing a red or white ball.
One ball is drawn at random from a box containing 4 red balls, 7 white balls, and 5 blue balls.
Determine the probability that the ball drawn is red or white.
The total number of balls in the box is 4+7+5=16 balls. The probability of drawing a red ball is 4/16. The probability of drawing a white ball is 7/16.The probability of drawing either a red or white ball is given by the sum of the individual probabilities. Hence, the probability of drawing a red or white ball is:(4/16) + (7/16) = (11/16)
Therefore, the probability that the ball drawn is red or white is 11/16.
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