Identify the radical expression for the perimeter and area of the orange triangle inscribed in the square shown below. Simplify each expression in radical form. No decimals!
Answers
The perimeter and area of the figure are 10+6√5 and 20
What is meant by perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.
There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.
AC=√4²+2²=√20=2√5
AB=√8²+4²=4√5
BC=√8²+6²=√100=10
Perimeter=a+b+c
=AC+AB+BC
=2√5+4√5+10
=10+6√5
Area=20
The perimeter and area of the figure are 10+6√5 and 20
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Related Questions
find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
Answers
The volume of the largest right circular cylinder is [tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
Now, According to the question:
The given sphere is of radius R.
Let h be the height and r be the radius of the cylinder inscribed in the sphere.
We know that:
Volume of cylinder
V = [tex]\pi R^2h[/tex] .....(1)
In right Triangle OBA
[tex]AB^2 + OB^2 = OA^2[/tex]
[tex]R^2 + \frac{h^2}{4} = r^2[/tex]
So, [tex]R^2 = r^2 - \frac{h^2}{4}[/tex]
Putting the value of [tex]R^2[/tex] in equation (1), We get
V = [tex]\pi (r^2 - \frac{h^2}{4} )h[/tex]
V = [tex]\pi (r^2h - \frac{h^3}{4} )[/tex] ....(2)
dV/dh = [tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] .....(3)
For, Stationary point, dV/dh = 0
[tex]\pi (r^2 - \frac{3h^2}{4} )[/tex] = 0
[tex](r^2 - \frac{3h}{4} )[/tex] => [tex]h^2 - \frac{4r^2}{3}[/tex] => [tex]h - \frac{2r}{\sqrt{3} }[/tex]
Now, [tex]\frac{d^2V}{dh^2} = \pi (-\frac{6}{4}h )[/tex]
[tex][\frac{d^2V}{dh^2}]_a_t_h_=_\frac{2r}{\sqrt{3} }[/tex] = x[-3/2 , [tex]2r/\sqrt{3}[/tex]]< 0
Volume is maximum at h = 2r/[tex]\sqrt{3}[/tex]
Maximum volume is :
[tex]= \pi (r^2.\frac{2r}{\sqrt{3} }- \frac{1}{4}.\frac{8r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{2r^3}{\sqrt{3} }-\frac{2r^3}{3\sqrt{3} } )[/tex]
[tex]=\pi (\frac{6r^3-2r^3}{3\sqrt{3} } )[/tex]
[tex]=\frac{4\pi r^3}{3\sqrt{3} }[/tex] cu. unit
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look at attached photo
Answers
The correct answer is A) y = 9000x + 65,000.
Find a linear equation that models the value of the house after x years?The correct answer is A) y = 9000x + 65,000.
This is an equation in slope-intercept form, where "y" is equal to the value of the house after x years, "9000x" is the slope (or rate of change) of the equation, and 65,000 is the y-intercept (or the initial value of the house). The equation can be derived from the given information.The initial value of the house is 65,000, so the y-intercept must be 65,000. To find the slope, we can use the formula "rise/run", or change in y/change in x.The house has increased in value by 54,000 ($119,000 - $65,000) over 6 years (change in x), so the slope must be 9000 (54,000/6).
The equation y = 9000x + 65,000
models the value of the house after x years, where y is the value of the house,
9000x is the slope of the equation,
and 65,000 is the y-intercept.
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A sinusoidal function whose period is π2
, maximum value is 10, and minimum value is −4 has a y-intercept of 10.
What is the equation of the function described?
Responses
f(x)=7cos(4x)+3
f ( x ) = 7 cos ( 4 x ) + 3
f(x)=7sin(4x)+3
f ( x ) = 7 sin ( 4 x ) + 3
f(x)=7cos(4πx)+3
f ( x ) = 7 cos ( 4 π x ) + 3
f(x)=7sin(4πx)+3
Answers
The equation of the function described as; y = 7 sin ( 4x + π/2 ) + 3
The general equation of the sine curve can be written as;
y = a sin ( nx + α ) + b
where : a is the amplitude, n = 2π/period, b = shift in the direction of y
α°= shift in the direction of x
We are Given period = π/2 the maximum value is 10, the minimum value is −4 and y-intercept of 10.
Thus,
a = (maximum - minimum)/2 = (10 - -4)/2
a = 7
n = 2π/period = 2π/(π/2)
n = 4
b = maximum - a = 10 - 7
b= 3
To find α as y-intercept = 10
y = 10 at x = 0
Substitute in the general function;
y = a sin ( nx + α ) + b
10 = 7 sin ( 4*0 + α ) + 3
Thus, we have;
sin α = 1
α = π/2
So, the equation of the function described is;
y = 7 sin ( 4x + π/2 ) + 3
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In AUVW, m/U = (3x - 10)°, m/V = (6x + 5)°, and m/W = (4x - 10)°. What is the value of x?
Answers
Answer:
x = 15
Step-by-step explanation:
You have ∆UVW with angles U=(3x-10)°, V=(6x+5)°, and W=(4x-10)°, and you want to know the value of x.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
U +V +W = 180°
(3x -10)° +(6x +5)° +(4x -10)° = 180°
13x -15 = 180 . . . . . . . divide by °, collect terms
13x = 195 . . . . . . . add 15
x = 15 . . . . . . . divide by 13
The value of x is 15.
Lucy wants to buy a small car. She speaks to her bank and they offer her a loan of £5000 over 5 years at a simple interest rate of 5%. How much simple interest will Lucy have to pay back in total?
Answers
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
What is simple interest?To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest. Most loans with simple interest rates are auto loans and short-term personal loans.
A = $6,250.00
I = A - P = $1,250.00
Formula: A = P(1 + rt)
First, convert R percent to r decimal, which is equal to 5%/100 or 0.05 per year.
Fixing our equation
A = 5000(1 + (0.05 × 5)) = 6250 \sA = $6,250.00
Simple interest at a rate of 5% per year for five years on a principle of $5,000 has resulted in a total accrual of $6,250.00, which includes both the principal and interest.
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A bag contains 3 red, 6 blue, and 7 yellow marbles. What is
the probability of drawing 2 marbles of different colors out of
the bag?
Answers
The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The enrollment at MSU is described by the function
f(x) = 250x + 6000, where x is the number of years since 2010.
I. Find the enrollment in 2016.
II. In what year will the enrollment reach
10,000?
Answers
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function f(x) represents the number of enrollment.
Defined as;
⇒ F(x) = 250x + 6000
Where x represents year since 2010.
(1) Now for finding the enrollment in 2016;
Put x = 2016 - 2010 = 6 in the function
⇒ F(6) = 250x6 + 6000
= 7500
Thus, The required number of enrollment = 7500
(2) Now we have to find the year in which enrollment reach 10,000;
i.e f(x) = 10,000
=> 250x + 6000 = 10000
=> 250x = 4000
=> x = 16
Thus, The required year = 2010 + 16
= 2026 answer.
1) The enrollment in 2016 will be 7500.
2) In 2026 year the enrollment reach 10,000.
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A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?
Answers
The length of the building on the scale drawing is found as 16 centimeters.
Describe the term scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a specific widths is known as a scale factor (bigger or smaller).Scale factor ratios can be written as a colon, 1:2, or as a fraction, 12. A ratio calculates the difference between two values.However, that ratio isn't a scale factor, thus you could not build a ratio for left-handed pupils to all students.For the given data in the question-
Dimensions of the building;
Height of 125 meter length of 80 meters.Dimensions of the drawing of the building;
height is 25 centimetersLet the length be 'x'.Thus, taking ratios of Height to length
125/80 = 25/x
On simplification;
x = 80 x 25 / 125
x = 16
Thus, the length of building on the scale drawing is found as 16 centimeters.
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Is 5x-8+7y=y-6 linear or nonlinear
Answers
Answer:
Step-by-step explanation:
The equation 5x-8+7y=y-6 is linear because it contains only terms with the variables x and y raised to the power of 1. In a linear equation, the highest power of any variable is 1. Nonlinear equations contain exponents that are higher than 1 on one or more variables.
Write a quadratic function in standard form whose graph has a vertex of (2, 6) and passes through the point (4, 10) .
Answers
To write a quadratic function in standard form with a vertex of (2, 6) and that passes through the point (4, 10), we can first use the coordinates of the vertex to determine the values of h and k. We know that h = 2 and k = 6, so we can substitute these values into the formula for the vertex to find the value of a:
k = a(h^2) + bh + c
6 = a(2^2) + b(2) + c
6 = 4a + 2b + c
We can then use the coordinates of the point (4, 10) to find the value of b:
10 = a(4^2) + b(4) + c
10 = 16a + 4b + c
Solving the system of equations formed by these two equations, we find that a = -1, b = 6, and c = 4. Therefore, the quadratic function in standard form whose graph has a vertex of (2, 6) and passes through the point (4, 10) is y = -x^2 + 6x + 4.
In this triangle, what is the value of x?
Enter your answer, rounded to the nearest tenth, in the box.
Answers
Answer:
70
Step-by-step explanation:
Solve. Write answers as an imaginary number
y^2+11=2
Answers
The solution of the equation written as an imaginary number is y = 3i or -3i
How to solve an equation and write the answer as an imaginary number?An imaginary number is a number of the form ai, where a is a real number and i is the square root of -1. Imaginary numbers are often denoted with the letter "i".
Given: y² + 11 = 2
y² + 11 = 2
y² = 2 - 11
y² = -9
y = ±√-9
y = ± 3i
y = 3i or -3i
(Note: √9 = 3 and √-9 = 3i)
Thus, the solution is y = 3i or -3i
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The length of a rectangular poster is 8 more inches than three times its width. The area of the poster is 256 square inches. Solve for the dimensions (length and width) of the poster
The dimensions are
inches ___ by ____ inches.
Answers
When the area of the poster is 256 square inches, the measurements are 32 inch and 8 inch.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
let length be l and width be w.
l=3w+8
l*w=256
(3w+8)*w=256
3w²+8w=256
3w²+32w-24w-256=0
3w(w-8)+32(w-8)=0
(3w+32)(w-8)=0
w=-32/3, 8
w=8 inch
l=3*8+8
l=32 inch
The dimensions for the poster are 32 inch and 8 inch when area of the poster is 256 square inches.
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. Find the solution(s) to the systems of equations algebraically
{(y=x^2-2x+4),(y=3x):} (Use Substitution and factoring)
(multiple choice)
A.(0,0)
B.(4,12)
C.(4,1)
D.(0,4)
E.(1,3)
Answers
The solution to the systems of equations is (4,1). Option C. is the answer
How to find the solution(s) to the systems of equations algebraically?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included
Given the: equations {(y=x²-2x+4), (y=3x):}
y= x²-2x+4 and y = 3x
substitute y = 3x into y= x²-2x+4. That is:
y= x²-2x+4
3x = x²-2x+4
x²-2x -3x+4 = 0
x²-5x+4 = 0
By factoring:
x²-4x -1x+4 = 0
x(x-4) -1(x-4) = 0
(x-4)(x-1) = 0
x-4 = 0 or x-1 = 0
x= 4 or x = 1
Thus, the solution is (4,1)
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what is equivalent to (32−−√5)13
Answers
Answer:
Your answer is 416 + 13 [tex]\sqrt{5}[/tex].
Step-by-step explanation:
Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
Answers
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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Which of the following equations have only one solution? Select all correct answers. x 2 - x - 6 = 0 5 x 2 + 20 x + 20 = 0 9 x 2 - 25 = 0 4 x 2 + 4 x = 0 x 2 + 6 x + 9 = 0
Answers
Answer: wutttttttttt
Step-by-step explanation: i jus need points
In the last 24 days, it rained 18 days. What is the ratio of rainy days to total days written as a percent?
Answers
The ratio of rainy days to total days written as a percent will be 75%.
How to illustrate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Ratio is used to compare two or more numbers. It is also used to indicate how big or small a quantity is when it is compared to another. It should be noted that in a ratio, two quantities are compared using division.
Since in the last 24 days, it rained 18 days.
Number of rainy days = 18.
Number of total days = 24
The ratio of rainy days to total days written as a percent will be:
= Number of rainy days / Total days × 100
= 18/24 × 100
= 3/4 × 100
= 75%
Therefore, the ratio is 3:4 which is 75%.
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Need Awnser asap
Right Awnser gets branliest
Answers
Answer:
x1,y16 is the rate of change
Step-by-step explanatI subtracted 13-32 which gives me 16, then I added 16 to 32 to be sure and it gave me 48 so the change on the Y axis is going up by 16 and x axis is going up by 1
A racetrack charges $85 for each seat in the lower section, $60 for each seat in the upper sections, and $35 for field tickets. There are three times the amount of seats in the upper section as compared to the lower section. The revenue from selling all 22,800 seats is $948,000. How many seats are in the upper section of the racetrack?
Answers
Using a system of equations, the number of seats in the upper section of the racetrack is 3,600.
What is a system of equations?A system of equations, also called simultaneous equations, is two or more equations solved concurrently.
We can use any of the following methods to solve simultaneous equations:
GraphicalSubstitutionEliminationMatrix.In this situation, after forming the equations, we can use substitution and elimination methods to solve them.
Racetrack charge per lower seat = $85
Racetrack charge per upper seat = $60
Racetrack charge per field ticket = $35
Let lower seats = x
Let upper seats = 3x
Let field tickets = y
4x + y = 22,800 ... Equation 1
y = 22,800 - 4x ...Equation 3
85x + 60(3x) + 35y = 948,000
85x + 180x + 35y = 948,000 ... Equation 2
Substitute Equation 3 in Equation 2 to eliminate y:
85x + 180x + 35(22,800 - 4x) = 948,000
85x + 180x + 798,000 - 140x = 948,000
125x = 948,000 - 798,000
125x = 150,000
x = 1,200
Determining the number of seats:
Seats in the Lower section = 1,200
Seats in the Upper section = 3,600 (1,200 x 3)
Field tickets, y = 22,800 - 4x
y = 22,800 - 4(1,200)
= 18,000
Check:
85x + 180x + 35y = 948,000
85(1,200) + 180(1,200) + 35(18,000) = 948,000
102,000 + 216,000 + 630,000 = 948,000
948,000 = 948,000
Thus, based on simultaneous equations, there are 3,600 seats in the upper section of the racetrack.
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After a snowstorm in the town of Golden Glen, the morning temperature was
–
10°F. But by the afternoon, the temperature had risen by 17°F.
Answers
The change in temperature based on the information is 27°F.
How to illustrate the relationship?It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.
Let the change in temperature be represented by x.
Therefore, -10 + x = -17
x = 17 + 10
x = 27
The Temperature is 27°F.
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After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?
How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answers
0.25-3(plus a negative is essentially just minus)
-2.75
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answers
Answer: x = 9/10 - 7/10
Step-by-step explanation:
You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
Answers
20*.6=12
12+20=32
Height (in inches) Mean Minimum Q1 Median Q3 Std Dev 4.21 Maximum 79 68.2 67 , 71 , Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches. Height (in inches) Q3 Mean 68. 2 Std Dev .21 Minimum 62 4 Q1 63 Median 67 Maximum 79 Which conclusion about the distribution is most plausible? (A) 50% of the students are taller than 68.2 inches. (B) 75% of the students are taller than 71 inches. (C) There are more students between 67 inches and 79 inches than are between 62 inches and 67 inches. (D) Less than 25% of the students have heights between 68.2 and 71 inches. (E) The height that occurs most frequently is 67 inches.
Answers
Standard deviation will be √3.3516 .
To calculate the standard deviation for the given data first we have to calculate the total number of students , mid value , fiXi , fiXi².
After that , we have to calculate the Xbar by using
Xbar = ∑fiXi / N
for which we need the value of fi , Xi and N
N = 100
fiXi = 6478
we have calculated the values from the given data ,
Therefore ,
Xbar = 6478 / 100
= 64.78
Var(X) = αx² - ∑fiXi² / N - (Xbar²)
= 419980 / 100 - (64.78)²
= 4199.80 -4196.4484
=3.3516
Thus,
standard deviation ax = √var(X)
= √3.3516
Therefore , the standard deviation will be √3.3516
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One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. (a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.) dy dt = ky 1-y. (b) Solve the differential equation. Assume y(0) = C. y = 1-ce-kt +1 (c) A small town has 1300 inhabitants. At 8 AM, 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Do not round k in your calculation. Round the final answer to one decimal place.) hours after the beginning
Answers
(a) The differential Equation that is satisfied by y is dy/dt = k × y × (1 - y) ,
(b) Solution of the differential equation assuming y(0) = c is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
In the question ,
Part (a)
let the fraction of people who heard the rumor is = y
So , the fraction who have not heard the rumor is = 1 - y .
the rate of rumor spread is ⇒ dy/dt = k×y(1 - y)
dy/y(1-y) = k.dt ...where k is the constant of proportionality .
So , the differential equation is ..
dy/dt = k × y × (1 - y)
Part (b)
So , 1/y(1-y) = 1/y + 1/(1 - y) ....equation(1)
integrating equation(1) , we get
∫dx/(1 + ax) = ㏑(1 + ax)/a ,....where a is the constant
㏑y + ㏑(1-y)/(-1) = kt + d ,.....where d is the constant
By using , ㏑a - ㏑b = ㏑(a/b) and taking exponential . we get ,
y/(1 - y) = c₁[tex]e^{k\times t}[/tex]
for t = 0 and y(0) = c
solving further , we get
c₁ = c/(1 - c)
So , y = (1-y)c₁[tex]e^{k\times t}[/tex]
y(1 + c₁[tex]e^{k\times t}[/tex]) = c₁[tex]e^{k\times t}[/tex]
y = c₁[tex]e^{k\times t}[/tex]/(1 + c₁[tex]e^{k\times t}[/tex])
taking c₁[tex]e^{k\times t}[/tex] common , and substituting the value of c₁ we get ,
the solution as , y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
Therefore , (a) the differential equation is dy/dt = k × y × (1 - y) and
(b) the solution is y = [tex]\frac{1}{(\frac{1-c}{c})e^{-kt} +1 }[/tex] .
The given question is incomplete , the complete question is
One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor.
(a) Write a differential equation that is satisfied by y. (Use k for the constant of proportionality.)
(b) Solve the differential equation. Assume y(0) = C.
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Let the discrete random variable X have the geometric distribution with parameter p. (a) Give a real-life example in which the geometric distribution can be applied. (b) Use the definition of the expected value to show that: E[X] = 1/p. (c) Explain why it makes sense that the expected value of X is inversely proportional to p.
Answers
a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.
b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.
c) E(x) = 1/p
Discrete Random Variable:
A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.
Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...
Geometric Distribution :
The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.
The Geometric Random Variable can be written as X ~ G(p).
The probability mass function is P(X = x) = (1 - p)ˣ⁻¹ p
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Solve the following equation by first writing the equation in the form a x squared = c: t squared minus 49 = 0 a. t = 49 b. t = plus-or-minus 49 c. t = 7 d. t = plus-or-minus 7 Please select the best answer from the choices provided A B C D
Answers
By solving the equation we get ,t = ± 7 using concept of square roots.
How to find the square roots ?
Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.
For example, 2 is the square root of 4, and this is expressed as √4 = 2.
We know that every squared number has two square roots one is positive and another is negative.
In given que,
given condition is t squared minus 49 = 0
Form of equation is ax^ 2 = c.
given condition can also be written as t^2 - 49 = 0
i.e. t^2 = 49
where a = 1
x = t
c = 49
So, the square root are 7 and -7.
So, equation become t = ± 7.
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use the data above to test the claim that marble color preference and club membership are related, as follows: (2 pts) carefully state the hypotheses. Hypothesis is
H0: marble color preference and income class are independent
H1: marble color preference and income class are dependent
Answers
The Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample. Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.
We can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypotheses. However, the hypotheses can also be phrased in a general way that applies to any test.
We are given that to test the claim that marble color preference and club membership are related.
Thus, the Null Hypothesis, H0 is "Marble color preference and income class are independent" and the Alternate Hypothesis, H1 is "Marble color preference and income class are dependent".
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Using the above graphic, it takes about _____ years to transition from using no oil to consuming 100 million barrels per day whereas it takes about______ years to transition from using 100 million to 200 million barrels per day.
A. 60, 10
B. 10, 60
C. 120, 50
D. 50, 120
Answers
It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.
As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.
The right axis indicates the global consumption rate of oil in millions of barrels per day.
To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.
The bottom axis is time in years.
The graph attached at the end of the solution.
Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.
Let the number of years of transition from using 100 million to 200 million barrels per day be b.
From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.
But it takes 50 years to go from 100 million to 200 million.
This is known as exponential growth.
Therefore, the value of a is 120 and the value of b is 50.
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