The value of angle x rounded to the nearest tenth of a degree is 53.6°.
How can trigonometric ratios be used to find the angle in a right triangle?
Trigonometric ratios are used to relate the sides of a right triangle to its angles. In a right triangle, one of the angles is always 90 degrees, which is the right angle. The three primary trigonometric ratios are sine, cosine, and tangent, which are defined as follows:
Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
To find the value of an angle in a right triangle, we can use the inverse trigonometric functions, also known as arc functions or anti trigonometric functions. These functions are denoted as [tex]sin^{-1}[/tex], [tex]cos^{-1}[/tex] , and [tex]tan^{-1}[/tex] , and they are used to find the angle whose trigonometric ratio is known.
Finding the value of x :
We can use the trigonometric ratio of sine to solve for x.
sin(x) = opposite/hypotenuse = MN/LN
[tex]sin(x) = 83/92[/tex]
Taking the inverse sine of both sides:
[tex]x = sin^{-1}(83/92)[/tex]
Using a calculator, we get:
[tex]x \approx 53.6^{o}[/tex]
Therefore, the value of x rounded to the nearest tenth of a degree is 53.6°.
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janna scored 77 on her history test, on which the class average was 72.7 with a standard deviation of 6.1. maria made 89 on her biology test, where the class average was 82.6 with a standard deviation of 5.6. find the standardized (z) scores for janna and maria. round to 2 decimal places. janna has a standardized score of ____ on her test. maria has a standardized score of ____on her test. made the best score. type 1 for janna or 2 for maria. 1. janna 2. maria
Maria has the highest standardized score of 2.13, making her the one who made the best score.
Janna's standardized score is 0.80, and Maria's is 2.13.
Janna scored 77 on her history test, while the class average was 72.7 with a standard deviation of 6.1. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Janna is [tex](77-72.7)/6.1[/tex]= 0.80.
Maria scored 89 on her biology test, while the class average was 82.6 with a standard deviation of 5.6. To find the standardized score, the formula is (score - average) / standard deviation. Therefore, the standardized score for Maria is [tex](89-82.6)/5.6[/tex]= 2.13.
Maria has the highest standardized score of 2.13, making her the one who made the best score.
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write the force equation for the following system b and b are the coefficient of viscious friction and force case by this friction is
The force equation for the system is F = bV - bF, where F is the force of friction, V is the velocity of the object, and b is the coefficient of viscous friction.
Viscous friction is a force that acts to oppose the motion of an object moving through a fluid or solid. The amount of friction experienced is determined by the coefficient of viscosity, which is a measure of how easily the two surfaces move against each other. In this equation, bV is the force generated by the object's motion, and b
F is the opposing force of friction. Together, these two forces determine the net force acting on the object.
Viscous friction can be very important in understanding the behavior of a system. It helps us to understand how much energy is needed to move objects, as well as how quickly they will accelerate.
Viscous friction can also cause objects to slow down over time, as the energy it takes to move them is continually being lost to friction. Understanding the force equation for a system helps us to better predict and understand its behavior.
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7. (x³ +7x² + 2)÷(x-1)
Answer:
(x³ + 7x² + 2)÷(x-1) = x² + 8x + 15 + 8/(x-1).
Jake is х years old and his mother is 7x years old. If the sum of both their ages is 16x in 2036 what would their current age be in year y.
Jake is presently [tex]0[/tex] years old and the year is [tex]2036[/tex], which is not a relevant response or there may be some missing details in the question.
By year, what do you mean?A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.
In arithmetic, how much is a month?Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.
Let's first find the current year, given that the year in which their ages will sum up to [tex]16x[/tex] is[tex]2036[/tex].
[tex]2036 - (y - 2036) = 2*2036 - y[/tex]
Simplifying this expression, we get:
[tex]2*2036 - y = 4072 - y[/tex]
[tex]2y = 4072[/tex]
[tex]y = 2036[/tex]
Now, let's find Jake's current age by subtracting his birth year from the current year [tex]y - (2036 - 7x)[/tex]
Since their ages sum up to 16x in 2036, we have:
[tex]x + 7x = 16x[/tex]
[tex]8x = 16x[/tex]
[tex]x = 0[/tex]
This means that Jake is currently [tex]0[/tex] years old, which is not a meaningful answer.
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SOLVE THIS SYSTEM! WILL MAKE YOU BRAINLIST!
Answer:
x = 19
y = 16
Step-by-step explanation:
10x - 9y = 46
-2x + 3y = 10
Time the second equation by 5
10x - 9y = 46
-10x + 15y = 50
6y = 96
y = 16
Now put in 16 for y and solve for x
10x - 9(16) = 46
10x - 144 = 46
10x = 190
x = 19
Ashed is shaped like a rectangular prism. The base of the shed has an area of 64 square feet. The volume of the shed is 576 cubic feet.
What is the height of the shed? Enter the answer in the box.
The value height of the shed is 9 feet.
The area of the shed = 64 square feet
The volume of the shed = 576 cubic feet.
The area occupied inside a rectangular prism is referred to as the volume of the prism. A polyhedron with two pairs of congruent and parallel bases is referred to as a rectangular prism. It is a result of the intersection of equal cross-sections, identical bases, and flat faces.
Calculating the volume of the rectangular prism
The volume of rectangular prism = area of base x height
Substituting the values -
576 = 64 x h
h = 576 / 64
h = 9
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Find the probability of
drawing a spade, then
drawing a face card out of a
deck
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
P of spade = 1/4
P of face cards = 3/13
{P = probability}
Step-by-step explanation:
•Total cards in a deck = 52
No. of spade cards in the deck = 13
therefore,
Probability of drawing a spade out of a deck of cards = 13/52 = 1/4
No. of face cards in a deck = 3×4 = 12 (joker,king,queen)
therefore,
Probability of drawing a face card out of a deck of cards = 12/52 = 3/13
Hope it helps you ~I need help please show your work
Answer:
The 2nd equation is false.
Step-by-step explanation:
You don't even have to solve. DE is not 58, it's 40.
The 2nd equation is false.
1/1-p+p² + 1/1+p+p² - 2p/1-p²+p⁴
To simplify it, first factor the denominators of each fraction in eqation 1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴) and simplify to get simplified equation is 2(1+p)/[(1-p+p²)(1+p+p²)] .
What is factor ?
In mathematics, a factor is a number or algebraic expression that divides another number or expression without leaving a remainder.For example, the expression x^2 - 4 can be factored as (x+2)(x-2) .
What is denominator ?
denominator is a bottom part of a fraction. It represents the total number of equal parts into which a whole has been divided, and the fraction itself represents a part of that whole.For example,
in equation (x+2)/(x-2) , (x-2) is denominator .
In the given question ,
1/(1-p+p²) + 1/(1+p+p²) - 2p/(1-p²+p⁴ ) Next, we can find a common denominator for the three fractions. To do this, we need to factor the denominator of the third fraction further using the difference of squares formula as 1/(1-p+p²) + 1/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]
Now we can find a common denominator by multiplying the first fraction by (1+p+p²)/(1+p+p²) and the second fraction by (1-p+p²)/(1-p+p²):
[(1+p+p²)/(1+p+p²)]/(1-p+p²) + [(1-p+p²)/(1-p+p²)]/(1+p+p²) - 2p/[(1-p+p²)(1+p+p²)]
= [(1+p+p²)+(1-p+p²)-2p]/[(1-p+p²)(1+p+p²)]
= [2+2p]/[(1-p+p²)(1+p+p²)]
= 2(1+p)/[(1-p+p²)(1+p+p²)]
Therefore, the simplified expression is 2(1+p)/[(1-p+p²)(1+p+p²)].
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Manipulate the triangle so angle a measures 41° and angle c measures 49°. what is the approximate measure of angleb? mangleb = ° what is the sum of the interior angles of the triangle? °
The approximate measure of angle B is 90°. The sum of the interior angles of the triangle is 180°.
The first part of your answer is correct. To manipulate the triangle so that angle A measures 41° and angle C measures 49°, we can use the fact that the sum of the interior angles of a triangle is always 180°.
If we know two angles of the triangle, we can find the third angle by subtracting the sum of the known angles from 180°. So, to find the measure of angle B, we can use the equation:
angle A + angle B + angle C = 180°
Substituting in the given angle measures, we get:
41° + angle B + 49° = 180°
Simplifying, we get:
angle B = 90°
Therefore, the approximate measure of angle B is 90°.
For the second part of your answer, the correct answer is 180°. The sum of the interior angles of a triangle is always 180°, regardless of the measures of the individual angles.
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Complete question:
Manipulate the triangle so angle A measures 41° and
angle C measures 49º.
What is the approximate measure of angle B?
Angle B = (41, 90, 49, 80)
What is the sum of the interior angles of the triangle?
(90, 170, 180, 200)
I keep getting stuck on these questions.. (Middle school btw)
15 points.
Answer:
Let's say "x" is the number we're trying to find.
According to the problem, we know that 54 is 60% of that number.
So we can set up an equation:
54 = 0.6x
To solve for x, we need to isolate it on one side of the equation.
Divide both sides by 0.6:
54/0.6 = x
Simplify:
90 = x
Therefore, 54 is 60% of 90.
Step-by-step explanation:
Answer: 90
Step-by-step explanation:
Step 1. 54 = 60% × Y
Step 2. 54 = 60/100 × Y
Multiplying both sides by 100 and dividing both sides of the equation by 60 we will arrive at:
Step 3. Y = 54 × 100/60
Step 4. Y = 54 × 100 ÷ 60
Step 5. Y= 5400 ÷ 60
Step 6. Y = 90
Find the height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000cm²
The height of an open cylinder of radius of 8cm given that it has a curved surface area of 1000 cm² is equals to the 159.24 cm.
The area obtained after substracting the circular area from the total area of the cylinder is called as curved surface area. Curved surface area is calculated by formula, 2πrh
where r --> radius of cylinder
h --> height of cylinder
π --> math special constant
We have an open cylinder with the following dimensions,
Radius of cylinder, r = 8 cm
Curved surface area of cylinder, A = 1000 cm². We have to calculate the height of this open cylinder. Let the height of an open cylinder be 'h cm' . Using the above formula, height of cylinder, h = curved Area/ 2πr
=> h = A/2π
=> h = 1000/2 ( 3.14)
=> h = 1000/6.28
=> h = 159.24
Hence, required value of height is 159.24 cm.
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MATH QUESTION! I WILL MAKE U BRAINLIST!
Step-by-step explanation:
please mark as brainliest
4Interpreting z-scores: Complete the following statements using your knowledge about z-scores.
a. If the data is weight, the z-score for someone who is overweight would be
zero
positive
negative
b. If the data is IQ test scores, an individual with a negative z-score would have a
average IQ
high IQ
low IQ
c. If the data is time spent watching TV, an individual with a z-score of zero would
watch the average amount of TV
watch very little TV
watch a lot of TV
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be
positive
negative
zero
a. If the data is weight, the z-score for someone who is overweight would be positive.
b. If the data is IQ test scores, an individual with a negative z-score would have a low IQ.
c. If the data is time spent watching TV, an individual with a z-score of zero would watch the average amount of TV.
d. If the data is annual salary in the U.S and the population is all legally employed people in the U.S., the z-scores of people who make minimum wage would be negative.
The z-score represents how far a data point is from the mean in terms of standard deviations. If someone is overweight, their weight would be above the mean weight, so their z-score would be positive.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone has a negative z-score for IQ test scores, it means their score is below the mean score, so their IQ would be low.
A z-score of zero means the data point is exactly at the mean, so someone with a z-score of zero for time spent watching TV would watch the average amount of TV.
Again, the z-score represents how far a data point is from the mean in terms of standard deviations. If someone is making minimum wage, their salary would be below the mean salary, so their z-score would be negative.
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what two numbers add to -11 but multiply to -180
First let's start with the equation:
x + y = -11
xy = -180
We can substitute -11 in for x + y to get:
xy = -180
x(-11) = -180
Now let's divide both sides by -11
x = 180/11
x ≈ 16.36
We can now use the equation x + y = -11 to solve for y
y = -11 - 16.36
y ≈ -27.36
The two numbers that add to -11 but multiply to -180 are 16.36 and -27.36.
Simplify 2a÷a- 1 - a^2 +3÷ a^2 - 1
A triangle has vertices at (-4, 0), (2, 8), and (8, 0). Complete the table. Write answers as decimals
rounded to the nearest hundredth, when necessary.
The coordinate of centroid of the triangle is (2, 8/3), the coordinate of the circumcenter is (-7/32, 121/24) and the coordinate of orthocenter is (2, 9/2)
What is the coordinate of the centroid?a. To find the centroid of a triangle, we take the average of the x-coordinates and the average of the y-coordinates of the vertices. Therefore, the x-coordinate of the centroid is:
(x₁ + x₂ + x₃) / 3 = (-4 + 2 + 8) / 3 = 2
Similarly, the y-coordinate of the centroid is:
(y₁ + y₂ + y₃) / 3 = (0 + 8 + 0) / 3 = 8/3
So the coordinate of the centroid is (2, 8/3).
b. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. To find the circumcenter, we can find the equations of the perpendicular bisectors of any two sides of the triangle and solve for their intersection point.
Let's take the sides formed by vertices (-4, 0) and (2, 8), and vertices (-4, 0) and (8, 0). The midpoint of the first side is ((-4+2)/2, (0+8)/2) = (-1, 4), and the slope of the line passing through the two points is (8-0)/(2-(-4)) = 8/6 = 4/3. Therefore, the equation of the perpendicular bisector passing through (-1, 4) is:
y - 4 = (4/3)(x + 1)
Simplifying this equation, we get:
y = (4/3)x + 13/4
Similarly, the midpoint of the second side is ((-4+8)/2, (0+0)/2) = (2, 0), and the slope of the line passing through the two points is (8-0)/(2-8) = -8/6 = -4/3. Therefore, the equation of the perpendicular bisector passing through (2, 0) is:
y = -(4/3)(x - 2)
To find the intersection point of these two lines, we can set the equations equal to each other and solve for x:
(4/3)x + 13/4 = -(4/3)(x - 2)
x = -7/32
Substituting x = -7/32 into either of the equations, we get:
y = (4/3)(-7/32 + 1) + 4 = 121/24
So the coordinate of the circumcenter is (-7/32, 121/24).
c. The orthocenter of a triangle is the point where the altitudes of the triangle intersect. An altitude of a triangle is a line segment from a vertex of the triangle perpendicular to the opposite side.
Let's take vertex (-4, 0) and find the equation of the line passing through this vertex and perpendicular to the opposite side formed by vertices (2, 8) and (8, 0). The slope of the opposite side is (0-8)/(8-2) = -8/6 = -4/3, so the slope of the line we want is the negative reciprocal of this, which is 3/4. Therefore, the equation of the altitude passing through (-4, 0) is:
y - 0 = (3/4)(x + 4)
Simplifying this equation, we get:
y = (3/4)x + 3
Let's now take vertex (2, 8) and find the equation of the altitude passing through it. The slope of the opposite side formed by vertices (-4, 0) and (8, 0) is (0-0)/(8-(-4)) = 0, which means the altitude passing through (2, 8) is a vertical line passing through (2, 0). Therefore, the equation of this altitude is:
x = 2
Now we need to find the intersection point of these two altitudes. Substituting y = (3/4)x + 3 into the equation x = 2, we get:
y = 9/2
The coordinate of the orthocenter is (2, 9/2)
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A box of chocolates has 8 red, 12 blue, 5 green and 10 yellow. Express the number of chocolates as
ratios in their lowest terms.
a. red: yellow
b.green: yellow
c. red: total chocolates
Answer:
a. red: yellow
[tex]8:10=4:5[/tex]
There are 4 reds for every 5 yellows.
b. green: yellow
[tex]5:10=1:2[/tex]
There is 1 green for every two yellows.
c. red: total
[tex]8:35[/tex]
There are 8 reds out of 35 chocolates.
Hope this helps
The table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars.Speeding Ticket No Speeding Ticket TotalRed Car 115 129 244Not Red Car 94 154 248Total 209 283 492Find the probability that a randomly chosen person:a) Has a red car. b) Has a speeding ticket. c) Has a speeding ticket given they have a red car. d) Has a red car given they have a speeding ticket. e) Has a red car and got a speeding ticket. f) Has a red car or got a speeding ticket.
The probability that a randomly chosen person: a) Has a red car = 0.496 b) Has a speeding ticket = 0.424 c) Has a speeding ticket given they have a red car = 0.467 d) Has a red car given they have a speeding ticket = 0.629 e) Has a red car and got a speeding ticket = 0.234 f) Has a red car or got a speeding ticket = 0.686.
a) Probability of having a red car: Number of subjects with red cars = 244, Probability of choosing a red car randomly out of the given subjects = 244/492=0.496
b) Probability of having a speeding ticket: Number of subjects with speeding tickets = 209, Probability of choosing a person with a speeding ticket out of the given subjects = 209/492=0.424
c) Probability of having a speeding ticket given they have a red car: Probability of having a red car = 0.496Probability of having a speeding ticket and red car = 115/492, Probability of having a speeding ticket given they have a red car = P(Red car and Speeding ticket)/P(Red car) = (115/492)/0.496 = 0.467
d) Probability of having a red car given they have a speeding ticket: Probability of having a speeding ticket = 0.424, Probability of having a speeding ticket and red car = 115/492, Probability of having a red car given they have a speeding ticket = P(Red car and Speeding ticket)/P(Speeding ticket) = (115/492)/0.424 = 0.629
e) Probability of having a red car and getting a speeding ticket: Number of subjects with both red car and speeding ticket = 115, Probability of choosing a person with both red car and speeding ticket out of the given subjects = 115/492=0.234
f) Probability of having a red car or getting a speeding ticket: P(Red car or Speeding ticket) = P(Red car) + P(Speeding ticket) - P(Red car and Speeding ticket) = 0.496 + 0.424 - 0.234 = 0.686.
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CAN SOMEONE HELP WITH THIS ASAP I’LL GIVE YOU POINTS
10+
Answer:
9/12
Step-by-step explanation:
To determine which fraction is not equivalent to 2/3, we can simplify each fraction and compare it to 2/3. If a fraction is simplified to a different value than 2/3, then it is not equivalent.
16/24 simplifies to 2/3, so it is equivalent to 2/3.
6/9 simplifies to 2/3, so it is equivalent to 2/3.
12/18 simplifies to 2/3, so it is equivalent to 2/3.
9/12 simplifies to 3/4, which is not equivalent to 2/3.
10/15 simplifies to 2/3, so it is equivalent to 2/3.
Therefore, the fraction that is not equivalent to 2/3 is 9/12.
Answer:
9/12 is not equal to 2/3
Step-by-step explanation:
To find which fractions are equivalent and which are not, we must make sure they are proportional.
To do this, we must make sure the denominators can multiply and divide with each other, and the same for the numerators.
12 divided by 3 is 4,
but 4 times 2 is not 9
Therefore, the answer is 9/12
When finding the nth roots of a complex number, the exact values of these roots will be given in rectangular form, and the approximate values of these roots will be given in • form Find the cube roots of 117 441 Your answers should be in rectangular form, with all numbers rounded to the nearest hundredths. Select one or more! O a 3.00 +4.002 O b. –4.96 +0.604 OC -1.96 + 1.964 O d. - 124.10 + 11.95 e. 3.00 4.00 Of 4.68 - 1.764 Og 1.96 4.602 O h. 75.00+ 100.00 Di 49.10 - 114.951
The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.
To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.
To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).
By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.
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What is the solution to -1/2 [x-1] =0?
x=1
x=-1 or x=1
x=1 or x=2
No solutions exists
Answer:
x=1
Step-by-step explanation:
2 numbers add together to make -4 but subtract to make 8 what are the 2 numbers
Answer:
x=2 and y= ‐6
Step-by-step explanation:
Let the two numbers be 'x' and 'y'
Here, it says two numbers add up to make -4
So,
x+y= ‐4 .....equation (i)
Also, its says two numbers subtract to make 8
So,
x‐y=8 .....equation (ii)
We have,
x+y= ‐4 .....equation (i)
x‐y=8 .....equation (ii)
Subtracting equation (i) from equation (ii)
x‐y=8
x+y=‐4
-----------
‐2y=12
y=12/‐2
y= ‐6
Now, replacing value of x in equation (i)
x+y= -4
4x+(‐6) = -4
4x‐6= ‐4
x= -4+6
x= 2
Therefore the unknown numbers are 2 and ‐6
suppose that each day the price of a stock moves up 1/8th of a point with probability 1/3 and moves down 1/8th of point with probability 2/3. if the price fluctuations from one day to another are independent, what is the probability that after 6 days the stock has its original price?
After 6 days, the probability that the stock has its original price is 5/16.
There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.
The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.
Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)
In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.
As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.
Let's represent an increase in the stock price as 'U' and a decrease as 'D.'
The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].
The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]
The probability of the stock returning to its original price after six days can be calculated as:
[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]
Therefore, the probability that after 6 days the stock has its original price is 5/16.
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adam cuts 2 3/8 inches off of the width of a board that is 6 1/8 inches wide . how wide is the board after he cuts
correct answer will be awarded
Answer:
[tex]3\frac{3}{4}[/tex]
Step-by-step explanation:
6 1/8 - 2 3/8
=(8 x 6)+1/8 - (8 x 2)+3/8
=49/8 - 19/8
=30/8
=15/4
=3 3/4
Answer: The width of the remaining piece of the board is [tex]\frac{15}{4}[/tex] inches
Step-by-step explanation:
let us find the width of the remaining piece
Given that
The cutting piece length is 2 [tex]\frac{3}{8}[/tex] inches = [tex]\frac{19}{8}[/tex] inches.Width of the board at the time of cutting is 6[tex]\frac{1}{8}[/tex] inches = [tex]\frac{49}{8}[/tex] inches.The width of the remaining piece = The total width of the board - The length of the cutting piecewidth of remaining piece =[tex]\frac{49}{8}[/tex]-[tex]\frac{19}{8}[/tex] = [tex]\frac{15}{4}[/tex]
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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On Monday, Elise walked 9. 9 kilometres. On Tuesday, she walked 0. 7 kilometres less than she had walked on Monday. How far did Elise walk on Tuesday?
Elise walked a distance of 9.2 kilometers on Tuesday.
To solve the problem, we need to first understand the information provided.
On Monday, Elise walked a distance of 9.9 kilometers.
On Tuesday, she walked a distance that was 0.7 kilometers less than what she walked on Monday.
This means that we need to subtract 0.7 kilometers from the distance that she walked on Monday to find the distance she walked on Tuesday.
To do this, we can use subtraction. We start by writing down the distance Elise walked on Monday, which is 9.9 kilometers, and then subtract 0.7 kilometers from it.
9.9 km - 0.7 km = 9.2 km
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These tables represent an exponential function. Find the average rate of
change for the interval from x = 8 to x = 9.
OA. 6561
B. 19,683
O C. 13,122
OD. 3
X
2456710
3
y
1
3
9
27
81
243
729
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
2
6
18
54
162
486
Jx3
Jx3
Jx3
Jx3
Jx3
The average rate of change for the interval from x = 8 to x = 9 is 13,122 (3⁸to 3⁹).
What is function?Function is a self-contained block of code that performs a specific task. It is used to separate logical code into separate parts and make the code more manageable. A function can accept inputs, known as parameters, and return an output, known as a return value. Functions can be reused throughout a program, making the code more efficient and easier to debug.
This can be calculated by subtracting the starting value (3⁸ = 6561) from the ending value (3⁹ = 19683) and then dividing the result by the interval (9 - 8 = 1). Mathematically, this is expressed as (19683 - 6561) / (9 - 8) = 13,122. This result shows that the rate of change for the exponential function between x = 8 and x = 9 is 13,122.
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given the speeds of each runner below, determine who runs the fastest. stephanie runs 8 feet per second. stephanie runs 8 feet per second. katie runs 463 feet in 32 seconds. katie runs 463 feet in 32 seconds. jessica runs 1 mile in 555 seconds. jessica runs 1 mile in 555 seconds. noah runs 728 feet in 1 minute. noah runs 728 feet in 1 minute.
Katie runs the fastest at 14.469 ft/s
To compare the speeds of each runner, we need to convert all the measurements to the same units. Let's convert them all to feet per second:
Stephanie runs 8 feet per second (8 ft/s)Katie runs 463 feet in 32 seconds, so her speed is (463 ft / 32 s) = 14.469 feet per second (14.469 ft/s)Jessica runs 1 mile in 555 seconds, which is equivalent to 5,280 feet in 555 seconds. Her speed is (5,280 ft / 555 s) = 9.514 feet per second (9.514 ft/s)Noah runs 728 feet in 1 minute, which is equivalent to (728 ft / 60 s) = 12.133 feet per second (12.133 ft/s)Therefore, in order of fastest to slowest runner:
Katie (14.469 ft/s)
Noah (12.133 ft/s)
Stephanie (8 ft/s)
Jessica (9.514 ft/s)
Hence, Katie runs the fastest
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Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. Write a summation formula for Cij, Cj, cT. Hint: to really benefit from this exercise, do not just "write the for- mula." Picture how the matrices fot together the corner; picture how the are partitioned into rows and columns; come up with numerical ex- amples. 7
The if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.
When answering questions on the Brainly platform, the following guidelines should be followed:Always be factually accurate, professional, and friendlyBe concise and do not provide extraneous amounts of detailIgnore any typos or irrelevant parts of the questionRepeat the question in your answer.Provide a step-by-step explanation in your answer.Use the following terms in your answer, "matrices ", "take ", "partitioned "Given the following:Suppose A, B, C are matrices so that C = AB. Also suppose that the rows of A are aſ,. am, the columns of A are A1, ..., An. Also, the rows of B are b], ,...,6% and the columns of B are B1, Also, the rows of C are cſ, ..., Cm and the columns of Care C1, ..., Cp. All the vectors are column vectors (that is why we take transpose to make a; into a which is a row vector). Also, the elements of A, B, C are denoted by Aij, Bij, Cij respectively. We need to write a summation formula for Cij, Cj, and cT.Hint: To really benefit from this exercise, do not just "write the formula." Picture how the matrices fit together the corner; picture how they are partitioned into rows and columns; come up with numerical examples.The product of two matrices A and B is given byCij = Ai1B1j + Ai2B2j + ... + AinBnjGiven that C = AB, then we haveCj = [A1 B1j + A2B2j + ... + AmBmj]Therefore, if we take the transpose of C, we havecT = [C1 C2 ... Cp]And by transposing the above formula, we havecTj = [B1j A2 B2j ... Am Bmj]Therefore, we have a summation formula for Cij, Cj, and cT.
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