Answer:
3 and 4
Step-by-step explanation:
numbers don't repeat in the X side
Q1: Suppose that the height H of a Ferris wheel can be modeled by the function H(t) = -12cos ( πt/45) + 18, where t is the time in seconds. What is the maximum height of a cabin? Use 3. 14 for π.
Q2: The tide at an Eastern seaport is at its maximum at 6:39 a. M. High tide is 9 ft deep. Low tide occurs at 12:30 p. M. With a depth of 3 ft. The water depths can be modeled by a sinusoidal function.
Allow x = 0 represent midnight.
Find the following and make sure to show work for the midline and amplitude:
period=
Amplitude=
Maximum=
Equation of the midline:
minimum=
1. Maximum height of the Function H(t) = -12cos( πt/45 ) + 18 is 30 units.
2. For the given sinusoidal function the values of the following are as follow :
amplitude = 6ft, period = π/3 , Maximum = 9ft,
Equation of the midline y = 6, Minimum = 3 ft.
Function with height 'H' is given by:
H(t) = -12cos( πt/45 ) + 18
Here 't' represents the time in seconds.
As we know that range of cosine trigonometric function is ,
-1 ≤ cosα ≤ 1
This implies cos function lies between -1 and 1.
Replace cos( πt/45 ) by 1 or -1
For cos( πt/45 ) = 1
H(t) = -12(1) + 18
= 6 units
For cos( πt/45 ) = -1
H(t) = -12(-1) + 18
= 30 units
Maximum height is equals to 30 units.
Therefore, function H(t) = -12cos( πt/45 ) + 18 representing maximum height is equal to 30 units.
2. In general sinusoidal function is given by :
y = Asin(Bx + C) + D
A is amplitude
A = High tide - low tide
= 9 - 3 /2
= 3ft
Time = 12:30 p.m. - 6: 39 a.m.
= 6 : 09 minutes
= 6hours(approximately)
period B = 2π /T
= 2π/6
= π/3
Vertical shift = 9 - 3
= 6
Equation of the midline is
y = c
⇒ y = 6
Function is y = 3sin (π/3)x + 6
Maximum sin (π/3)x = 1
y = 9
Minimum sin (π/3)x = -1
⇒ y = 3
Therefore, the values of the following for the given function is :
amplitude = 6ft, period = π/3 , Maximum = 9ft,
Equation of the midline y = 6, Minimum = 3 ft.
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Given
B
(
2
,
2
)
,
C
(
−
5
,
−
2
)
,
D
(
−
2
,
6
)
,
B(2,2),C(−5,−2),D(−2,6), and
E
(
5
,
y
)
.
E(5,y). Find
y
y such that
B
C
‾
∥
D
E
‾
BC
∥
DE
.
Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that B C ‾ ∥ D E ‾ BC ∥ DE .
How to solve the poind?Assume that points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y)
( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 )
∴PA=PB
With the aid of the distance formula
= (x 2 −x 1 )
2 +(y 2 −y 1 )
2
There are
⇒ (x+2) 2 +(y+2) 2
= (x-5) 2 +(y−2)2
(x-2) 2 +(y+6)2
⇒(x+2) 2 +(y+2)
2 =(x+2) 2 +(y+2) 2
⇒ x2−4x+4+y 2
−7y+10= x2 +4x+4+y 2 −7y+14
⇒−4x−4x−10y+7y+14−16=0
⇒−8x−3y+2=0
⇒3x+y−5=0
ΔAD
Eare Similar triangles
∴( CB / DE )=( AB / AD )
B C ‾ ∥ D E ‾ BC ∥ DE .
Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that B C ‾ ∥ D E ‾ BC ∥ DE .
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Find the y-intercept of the line y = 7/9x + 2/3
The y-intercept of the equation of line y = (7/9)x + 2/3 is 2/3.
What is the y-intercept of the given equation of line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of line in the question;
y = 7/9 x + 2/3
Simplify the right hand side
y = (7/9)x + 2/3
Using the slope-intercept form, the y-intercept is 2/3.
Therefore, the y-intercept in point form is (0,2/3).
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Please answer quick! The information is in the picture.
The measure of the side length CL is equal to 9m using trigonometric ratio of cosine 60° for thy right triangle ACL
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Angle m∠BAC = 180° - (m∠C + m∠ABC)
m∠BAC = 180° - (90° + 30°)
m∠BAC = 60°
line AL is an angle bisector so;
m∠CAL = 30° and m∠BAL = 30°
which implies triangle ∆ALB is an isosceles with line LB = AL = 18m
considering the right triangle ∆ACL;
angle m∠L = 180° - (90° + 30°)
m∠L = 60°
cos 60° = CL/18 {adjacent/hypotenuse}
1/2 = CL/18m {cos 60° = 1/2}
CL = 18m/2 {cross multiplication}
CL = 9m
Therefore, the side length CL is equal to 9m using trigonometric ratio of cosine 60° for the right triangle ACL.
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alguien me explica yo no entendi
Note that the median in the data set given above is: 38.5.
What is a median value?The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution in statistics and probability theory. It is sometimes referred to as "the middle" value in data collection.
Not that in the above case, the median is arrived at by finding adding the two central values (37 and 40) and dividing the result by 2. This is because the total number of data in the set is even. Where the total number of values is odd, then the central number, when the avalues are arranged in ascending order is the median.
Thus, median = 37 + 40
= 77/2
Median = 38.5
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5
4 Harriet and Kevin are playing a game. There are a total of 11 rounds in the game and at the end
of each round only one of the players will score some points. In each round the number of points
scored is equal to the number of the round, so 1 point is scored in round 1, 2 points in round 2 and
so on.
Harriet and Kevin have played a total of 8 rounds. Harriet has scored a total of 19 points.
(a) How many points has Kevin scored?
*****
[1]
Answer: 9 points
Step-by-step explanation: 8 rounds=8 points; If Harriet has 19 points and they have played 8 rounds which equal 8 points, 19-8=9 points
a group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream how far did they walk alltogether? thank u for helping !!
Answer:
13.9 miles
Step-by-step explanation:
We know
A group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream. How far did they walk altogether
8 7/10 = 87/10
5 1/5 = 26/5
87/10 + 26/5 = 87/10 + 52/10 = 139/10 = 13.9 miles
So, they walked 13.9 miles.
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
A. Tasha, because she has the lowest ratio since 0.9 > 0.8
B. Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
C. Jana, because she has the lowest ratio since 0.9 > 0.8
D. Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Tasha has the highest batting average because 0.9(27/30) is greater than 0.8( 24/30 ) ( optionD)
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
The batting average for Jana is 12/15 = 0.8
The battling average for Tasha is 9/10 = 0.9
The battling average of Tasha is higher than that of Jana
0.6 can also be in form of 6/10
0.9 can also be in form of 9/10
therefore 8/10 = 24/30 and
9/10 = 27/30
Therefore Tasha has the highest batting average because 27/30 is greater than 24/30
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Answer:
27/30
Step-by-step explanation:
Martin spent $68 on a new drone that he had been saving for. Now, he has $41 left in his savings jar. Click the equation that could be used to find the total of his savings, s, before he bought the drone.
How many dollars did Martin have saved before he bought the drone?
blank/ dollars
109 dollars Martin have saved before he bought the drone .
Using the conditions stated, come up with: x -68 = 41
Put the variables on the equation's left side: x = 41 + 68
Determine the difference or total: x = 109
Savings are the funds that remain after subtracting one's obligations. Cash is stored as a sort of savings.
Savings are unused funds or postponed spending. A deposit account, a pension account, an investment fund, or cash are just a few examples of ways to save money. Reducing expenses, such as recurrent fees, is a part of saving as well. The portion of money left over after paying for current expenses is what is saved. In other words, it refers to money that has been set away for use later on rather than being immediately spent. Saving enhances emotions of security and tranquilly by acting as a financial "backstop" for life's unforeseen events.
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A rectangular lawn is 100m long and 45m wide.
There are 3 circular ponds, with diameters of 20m, 10m and 5 especi Mrs Jones wants to cover the lawn with grass seed.
Each packet of grass seed covers 50m and costs £1. 49
How much will it cost Mrs Jones to cover the lawn with grass seed?
According to the area the amount needed to cover the lawn with grass seed is £121.8075
In math the term called area is defined as the total space occupied by the object.
Here we have know that the Length is 100m and the Breadth is 45m :-
Then the area is calculated as,
=> A = 100 × 45 = 4500m²
Here we have to do the calculation for 3 circular pond, then it can be calculated as,
=> 1st pond = 20/2 = 10m
=> 2nd pond = 10/2 = 5m
=> 3rd pond = 5/2 = 2.5m
Then the Area of 3 circular pond is calculated as,
=> A = (π × 10² + π × 5² + π × 2.5²)
Take the term π as common then we get,
=> A = π × ( 100 + 25 + 6.25)
Apply the value of π = 22/7, then we get,
=> A = 22/7 × (125 + 6.25)
When we simplify this one then we get
=> A = 22/7 × 131.25 = 2887.5/7
Therefore the area of the pond is 412.5m²
Now we need to do the calculation for required area for covering lawn, that can be written as
=> Required area = Area of lawn - Area of 3 circular ponds
Apply the value on it,
=> Required area = 4500 - 412.5 = 4087.5m²
As we know that packet of grass seed covers 50m, then it is simplified as,
=> Required Area = 4087.5/50 = 81.75m²
Now we need to do the calculation for cost of covering lawn is written as
=> Total cost = 81.75 × 1.49 = £121.8075
Therefore the cost of covering lawn with grass seed is £121.8075
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An Olympic-distance triathlon includes a 1. 5 km swim. To determine the swim course of an Olympic-distance triathlon in Shoe Lake, the planners need to first find the distance between points A and B on opposite sides of a lake in order to determine where to place the buoys that will mark the swim course. You have been called in to help with determining the distances. From a point C on the shore, you find that CA = 259 m, CB = 423 m, and angle ACB measures 1320.
A. Determine the distance across the lake
B. Is the lake long enough to simply have an "out-and-back" swim course for this triathlon (that is: swimming from point A to point B and then back to point A)? If not, what additional distance will need to be set off of the straight-line distance between A and B in order to meet the distance requirements for this triathlon?
Answer: A. The distance across the lake is 626.6 m.
B. The lake is not long enough Additional 123.4m distance will need to be set off.
Step-by-step explanation:
An object moves along a straight line with acceleration a(t) = 8 cos t + 2t. If the initial position s(0) = -5 and initial velocity v(0) = -2, find the position function of the object.
A.
-8cos t + t^3/3-2t-3
B.
-8cos t + 3t^3-2t+5
C.
-8cos t + 3t^3 − 2t − 5
D.
-8cos t + t^3/3-2t+3
If the initial position s(0) = -5 and initial velocity v(0) = -2, the position function of the object is -8cost + t^3/3 - 2t + 3. So the option D is correct.
We have to determine the position function of the object.
An object moves along a straight line with acceleration a(t) = 8cost + 2t.
Initial position s(0) = -5
Initial velocity v(0) = -2
Integration of a(t) given us s(t)
[tex]\int a(t)dt = \int (8cost + 2t) dt[/tex]
v(t) = 8sint + 2t^2/2 + C
v(t) = 8sint + t^2 + C
At v(0) = -2
v(0) = 8sin(0) + (0)^2 + C
-2 = 8 × 0 + 0 + C
C = -2
v(t) = 8sint + t^2 - 2
The integration of v(t) gives us s(t)
[tex]\int v(t)dt = \int (8sint + t^2 - 2)dt[/tex]
s(t) = -8cost + t^3/3 - 2t + D
At s(0) = -5
s(0) = -8cos(0) + (0)^3/3 - 2(0) + D
-5 = -8 × 1 + 0 - 0 + D
-5 = -8 + D
Add 8 on both side, we get
D = 3
s(t) = -8cost + t^3/3 - 2t + 3
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a sonar operator on a ship detects a submarine at a distance of 500 meters and an angle of depression of 40 degrees. how deep is the submarine?
To determine the submarine's depth, you would need to use trigonometry. The angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) form a right triangle.
You can use the tangent function (tan) to find the opposite side (depth) of the triangle, given the adjacent side (distance) and the angle.
Depth = distance * tan(angle of depression)
Depth = 500 meters * tan(40 degrees)
You can use a calculator or table to find the value of tan(40 degrees), which is approximately 0.8391.
Depth = 500 meters * 0.8391
Depth = 419.55 meters
So the submarine's depth is 419.55 meters deep.
Right triangles can be used to represent word problems involving angles of elevation and depression. When working right triangles, the trigonometric rates are used to break for the right triangle's sides and angles representing the problem.
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For the angle of depression (40 degrees) and the distance from the ship to the submarine (500 meters) the submarine's depth will be 419.55 meters
Right triangles can be used to express word problems with elevation and depression angles. When working with right triangles, trigonometric rates are employed to break for the sides and angles of the right triangle that represent the problem.
Trigonometry would be required to estimate the depth of the submarine.
Given the neighbouring side (distance) and the angle, you can use the tangent function (tan) to get the opposite side (depth) of the triangle.
Depth = distance multiplied by tan (angle of depression)
500 metre depth * tan (40 degrees)
You may determine the value of tan(40 degrees) using a calculator or a table, which is about 0.8391.
So, the value of the depth = 500 meters * 0.8391
Depth = 419.55 meters
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what is the percent of 50 and 11
Answer:
22%
Step-by-step explanation:
[tex]\frac{11}{50}[/tex] times 100% = 22%
A- write an expression for the number of tiles Bruce used and an expression for the number of tiles Felicia used. Use x to represent the number of tiles in a box.
B- to determine whether the used the same number of tiles, set the two expressions equal to each other and solve for x. Is there a solution for x? Why or why not? If there is a solution, what is it?
C- what conclusion can you draw from this?
D- how could you change the equation from part B so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation?
E- if the equation were 6x + 2 = 5x + 17, would there be one unique solution? What is it, and what would it mean in terms of the situation?
An expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.
Expression
An expression refers to a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
Note: - x represents the number of tiles in a box.
A- For Bruce,
we have,
Expression = 3x + 2x + 2
Expression = 5x + 2.
For Felicia,
we have,
Expression = 5x + 5.
so, the expression for the number of tiles used by Bruce and Felicia are 5x + 2 and 5x + 5 respectively.
B- no, there is no solution for X as the equations are not equal to each other.
5x +2 = 5x + 5 (subtract 5x and 2 on both sides)
0 = 3 No solution
C- We can conclude that someone used more tiles then the other because both equations are not equal.
D- Have 2 or 5 change because they need to be equal to each other. Its fine what you put as long as the equal sign is the same as the other side like 3 = 3 for example or 5 = 5, something like that. Once they have the same end then you can substitute the number to x.
x represents the number of tiles they used.
E- yes.
6x +2 =5x +17
6x - 5x =17 - 2
x =15
unique solution
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Find the value of
x in the equation below.
36=4x
Answer:
4x(÷4)=36(÷4)
x=9
I hope I help you in this ans and tq.
Answer: 9
Step-by-step explanation: Because the problem is 36=4x the X next to the 4 means to multiply BUT since we don't no the answer there are many ways to solve this one way is to find what you can multiply for with or you can divide 36 and 4.
Hope fully that helps!!!
Complete the table for y=1/5x+1 and graph the resulting line
Answer:
yidyf
Step-by-step explanation:
jcyfifjfjhfueujevevve
what is 1/6 less than 2/6?
Answer: 1/6
Step-by-step explanation:
2/6 - 1/6 = 1/6
PLS HELP VERY URGENT AND NEEDED
Answer:
it A ←Have a Nice Day : ) if Incorrect sorry .
The temperature in Chicago, Illinois was -15 F at 6 a.m. By afternoon, the temperature had risen 28 degrees. What was the afternoon temperature (in F)?
Answer:
13F
Step-by-step explanation:
-15+28
I don't know factor out, please slove this questuon.
Answer:
[tex]\displaystyle \frac{1}{10}(x+9)[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{10}x+\frac{9}{10}=\frac{1}{10}(x+9)[/tex] because [tex]\displaystyle \frac{1}{10}(x+9)=\frac{1}{10}(x)+\frac{1}{10}(9)[/tex] by the Distributive Property
PLEASE HELP ITS ARGENT
The amount of glass needed to cover a table measuring 0.8m long and 0.65m wide is (d) 0.52m²
How to determine the amount of the glassfrom the question, we have the following parameters that can be used in our computation:
Length = 0.8 m
Width = 0.65 m
The area of a rectangle can be calculated using tge following equation
Area = Length * Width
substitute the known values in the above equation, so, we have the following representation
Area = 0.8 * 0.65
Evaluate
Area = 0.52
Hence, the amount is 0.52 square meters
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A recipe for Kool-Aid calls for 1/4 cup of sugar for every 3 cups of liquid. How many cups of sugar would be needed for 18 cups of liquid?
Answer:
1.5 cups of sugar
Step-by-step explanation:
Given:
-You need a 1/4 cup of sugar for 3 cups of Kool-Aid
-You need to find the amount of sugar you need for 18 cups of liquid
Solution:
You need to find how many recipes you need
3x = 18
So x = 6
Now you need to multiply 1/4 by 6 to find the amount of sugar
That would be 6/4 which is 1.5
So you need 1.5 cups of sugar for 18 cups of Kool-Aid
A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?
Statement "B. the median is a negative number" will be correct among these options.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Given, that A set of data contains 10 negative numbers and 4 positive numbers.
Since the value of data is not given it can be any positive or negative numbers
mode:
A mode is described as a value in a group of values that occurs most frequently. The value that appears the most frequently is this one.
Range:
When the sample maximum and minimum are subtracted, the range of a set of data in statistics is the difference between the greatest and lowest values.
Median:
The median is the value that's exactly in the middle of a dataset when it is ordered.
Thus, the Median will be negative.
Therefore, Statement "B. the median is a negative number" will be true among these options.
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Complete question:
A set of data contains 10 negative numbers and 4 positive numbers. Which one of these statements must be true?
A. The mean is a negative number.
B. The median is a negative number.
C. The mode is a negative number.
D. The range is a negative number.
What is the domain and range of t(n) = 2x+1
How did you get it?
The domain of the function is all real numbers while the range of the function is also all real numbers.
What is the domain of the function?The domain of the function t(n) = 2x + 1 is all real numbers, since there are no restrictions on the input value of x. The range of the function is also all real numbers, since adding 1 to any real number will also result in a real number. So the domain is (-infinity, infinity) and the range is (-infinity, infinity)
We have to note that in the event that we have a function such as t(n) = 2x+1, x is free to take any of the values on the real number line and this would return a value for t(n).
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x is a whole number if three quarters of x is subtracted from 62. the result is less than 40. find the three lowest values of x
The three lowest values of x are 30, 31 and 32.
How to find the three lowest values of x?Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.
The statement "x is a whole number if three quarters of x is subtracted from 62. the result is less than 40" can be written as:
62 - (3/4)x < 40
- (3/4)x < 40 - 62
-3x/4 < -22
-3x < -22 × 4
-3x < -88
x > -88/-3
x > 29.33
Since x > 29.33 and x is a whole number, the three lowest values of x are 30, 31 and 32.
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let A1, A2, A3, and A4, be events from a common sample space. these events are pairwise mitially exclusive, with the exception tha A1 and A2 occur simultaneously with a probability of 0.1. if events A1, A2, and A3 each occur with probability 0.3, what is the largest possible value for the probability of A4?
how do i go about this
The largest possible value for the probability of A4 is 0.1.
How to determine the largest probability of A4?From the question, we have the following parameters that can be used in our computation:
A1, A2, A3, and A4, be events from a common sample space.
We know that A1 and A2 occur simultaneously with a probability of 0.1, which means that the probability of A1 or A2 occurring is 0.3
We also know that events A1, A2, and A3 each occur with probability 0.3.
So, the probability of A4 occurring is equal to 1 minus the probability of the other three events occurring.
Therefore, the largest possible value for the probability of A4 is:
P(A4) = 1 - (0.3 + 0.3 + 0.3)
P(A4) = 1 - 0.9
P(A4) = 0.1
So, the maximum value that the probability of A4 can take is 0.1.
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Multiply.
[x-(6+4i)][x-(6x4i)]
Note that these expressions contain complex numbers.
Simplify your answer as much as possible
The resultant of the given expression after simplification is (x^2 - 12x - 8xi + 52).
In order to simplify the expression [x-(6+4i)][x-(6x4i)], we must first expand it by using the distributive property.
The first term of the first factor would be x*x = x^2,
The second term would be x*-(6-4i) = -6x - 4xi
The third term would be -(6+4i)x= -6x - 4xi.
The last term would be -(6+4i)*-(6-4i) = 6^2 - (4i)^2 = 36 + 16 = 52
Next, we would combine like terms by adding,
x^2 - 6x - 4xi - 6x - 4xi + 52 = x^2 - 12x - 8xi + 52
This would give us an expression of x^2 - 12x - 8xi + 52. This expression can't be simplified any further as it contains complex numbers.
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Which of the following is a factor of 4x^{2} + 23x + 15
A: (4x + 5)
B: (2x + 3)
C: (4x + 3)
D: (2x + 5)
The factor of the given quadratic equation is (4x + 3). Option C is correct.
What are the factors of a quadratic equation?One way to describe the polynomial as a product of its linear parts is to factor the quadratic equation. We may use this method to locate the roots of quadratic expressions, simplify them, and solve equations.
The formula for a quadratic polynomial usually takes the form ax² + bx + c, where a, b, and c are real values. We can obtain the zeros of the quadratic equation ax² + bx + c = 0 by factoring quadratics.
Given that:
4x² + 23x + 15 = 0
By applying the distributive property, we have:
4x² + 20x + 3x + 15 = 0
Factor out the greatest common factor for each group
(4x² + 3x) + 20x + 15
x(4x + 3) + 5(4x + 3)
Factor the polynomial by factoring out the greatest common factor. 4x + 3, then we have:
(4x + 3) (x + 5)
Therefore, we can conclude that one of the factors of the quadratic expression is (4x + 3).
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problem 5 (30 points, each 10 points). in a chemical plant, 24 holding tanks are used for final product storage. four tanks are selected at random and without replacement. suppose that four of the tanks contain material in which the viscosity exceeds the customer requirements. 1. what is the probability that exactly one tank in the sample contains high-viscosity material? 2. what is the probability that at least one tank in the sample contains high-viscosity material? 3. in addition to the four tanks with high-viscosity levels, four different tanks contain material with high impurities. what is the probability that exactly one tank in the sample contains high-viscosity material and exactly one tank in the sample contains material with high impurities?
1. The probability of selecting exactly one tank with high-viscosity material is 0.
2. The probability of selecting at least one tank with high-viscosity material is 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.
1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.
2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.
3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.
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