The bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe
To solve this problem, we can use trigonometry. Let's assume that the bus is at point A on the street, and the top of the l'Arc de Triomphe is at point B. The height of the arc is 162 feet.
We want to find the distance AB, which is the horizontal distance from the bus to the base of the arc. We know that the angle of elevation from the bus to the top of the arc is 34 degrees. Let's call the height of the bus H, and the distance AB D.
From the perspective of the bus, we can see that the height of the arc and the height of the bus together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = (162 + H)/D
We can solve this equation for D:
D = (162 + H)/tan(34)
We need to find H to solve for D. To do this, we can use similar triangles. The triangle formed by the bus, the base of the arc, and the top of the arc is similar to the triangle formed by the bus, the ground, and the point directly beneath the top of the arc. Let's call the distance from the base of the arc to the point directly beneath the top of the arc x.
From the perspective of the bus, we can see that the height of the arc and the distance from the base of the arc to the point directly beneath the top of the arc together form a right triangle with angle of elevation 34 degrees. Therefore, we have:
tan(34) = 162/x
Solving for x, we get:
x = 162/tan(34)
Now, the height of the bus is simply H = x*tan(34). Substituting this into the equation for D, we get:
D = (162 + x*tan(34))/tan(34)
Substituting the value of x, we get:
D = (162 + (162/tan(34))*tan(34))/tan(34) = 373.8 feet (rounded to the nearest tenth)
Therefore, the bus is approximately 373.8 feet away from the base of the l'Arc de Triomphe.
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the width of this rectangle is 1/3 of the length. Find the width of the rectangle
Answer:
length = 42 in , width = 14 in
Step-by-step explanation:
given the width is [tex]\frac{1}{3}[/tex] of the length , then
y - 4 = [tex]\frac{1}{3}[/tex] (2y + 6) ← multiply both sides by 3 to clear the fraction
3y - 12 = 2y + 6 ( subtract 2y from both sides )
y - 12 = 6 ( add 12 to both sides )
y = 18
then
length = 2y + 6 = 2(18) + 6 = 36 + 6 = 42 in
width = y - 4 = 18 - 4 = 14 in
pls help me with both of them
The year that saw 164 billion dollars being spent on advertising, given the function for the advertising would be c. 1994
The dimensions of the rectangle, given the area of the rectangle would be:
Length : 12. 8 meters Width : 6.9 meters How to find the year ?The function is given by y = 0.93x² + 2.2x + 130, where y is the amount of money spent (in billions of dollars) and x is the number of years since 1990. We need to find the value of x when y = 164.
164 = 0.93x² + 2.2x + 130
0.93x² + 2.2x + 130 - 164 = 0
0.93x² + 2.2x - 34 = 0
x = 2.5
Now, we'll find the year by adding the value of x to 1990:
Year = 1990 + 2.5 = 1992.5
= 1994 which is the closest year in options
How to find the dimensions of the rectangle ?The area of the rectangle is given by:
Area = width × length
91 = (x + 2)(2x + 3)
91 = 2x² + 3x + 4x + 6
91 = 2x² + 7x + 6
2x² + 7x - 85 = 0
When solved differently:
x = 4.9
x = -3.5
Using the positive values:
Width = x + 2 ≈ 4.9 + 2 = 6.9 meters
Length = 2x + 3 ≈ 2(4.9) + 3 ≈ 9.8 + 3 = 12.8 meters
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how do i solve these ? ( step by step )
Therefore , the solution of the given problem of equation comes out to be the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.
How do equations work?In intricate algorithms, variable words are frequently used to demonstrate consistency between two incompatible assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in c + 7 rather than a singular formula that divides 12 into two components and can be applied to data obtained from y + 9.
Here,
We must isolate y on the left side of the equation in order to convert the provided equations to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
=> y = -x - 4:
=> x + y = -4
=> y = -x - 4
As a result, the equation has a slope of -1 and a y-intercept of -4, and is written as y = -x - 4.
=> y = 1/2x - 1:
=> y - 1/2x = -1
=> y - 1/2x + 1 = 0
The words with y and the constant term must be combined in order to represent this equation in slope-intercept form:
=> y + 1 = 1/2x
By taking away 1 from both edges, we obtain:
=> y = 1/2x - 1
As a result, the equation has a slope of 1/2 and a y-intercept of -1, and is written as y = 1/2x - 1.
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a line segment has endpoints (0, 5) and (6, 5). after the line segment is reflected across the x-axis, how long will it be?
The length of the reflected line segment is approximately 11.66 units.
The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.
Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.
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a triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers. is it a right triangle?
Answer:
Step-by-step explanation:
no because 6 , 7 and 10 doesn't add up to 180 so it is not
A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.
To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:
a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.
In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.
The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.
The sum of 36 kilometers and 49 kilometers is 85 kilometers.
The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.
Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.
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5 cards are drawn randomly from a regular deck of cards. how many ways can you draw 5 cards and get 4 hearts and 1 spade?
Answer:
There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52. After the first heart is drawn, there are 12 hearts left in the deck out of a total of 51 cards, so the probability of drawing another heart is 12/51. This process continues until we have drawn 4 hearts and 1 spade. Therefore, the total number of ways to draw 5 cards with 4 hearts and 1 spade is:
(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 5!
The factor of 5! accounts for the fact that the 5 cards can be drawn in any order. Simplifying the expression above, we get:
(13/52) x (12/51) x (11/50) x (10/49) x (13/48) x 120 = 0.000495 or approximately 1 in 2,020 ways.
Therefore, there are approximately 2020 ways to draw 5 cards from a regular deck of cards and get 4 hearts and 1 spade.
There are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.
There are 13 hearts in a deck of cards, so the probability of drawing a heart on the first draw is 13/52 or 1/4. The probability of drawing another heart on the second draw, given that one heart has already been drawn, is 12/51. The same goes for the third and fourth draws. The probability of drawing a spade on the fifth draw is 13/50.
To calculate the number of ways to draw 4 hearts and 1 spade, we need to multiply the number of ways to choose 4 hearts from 13 (13 choose 4 or 715) by the number of ways to choose 1 spade from 13 (13 choose 1 or 13) and then multiply that by the number of ways to arrange those 5 cards (5!). So, the total number of ways is:
715 * 13 * 5! = 54,145,200
Therefore, there are 54,145,200 ways to draw 5 cards and get 4 hearts and 1 spade from a regular deck of cards.
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Tell whether the angles are adjacent or vertical. Then find the measure of each angle.
The measure of the angles are 27 and 63 degrees. The angles are adjacent.
How to find adjacent angles?The two angles are said to be adjacent angles when they share the common vertex and side. In other words, adjacent angles have common side and vertex but do not overlap.
Therefore, the angles are adjacent angles.
The sum of the angles is 90 degrees. This means the angle is a right angle.
Therefore,
3x + 7x = 90
10x = 90
x = 90 / 10
x = 9
Therefore, the angles are as follows:
3(9) = 27 degrees
7(9) = 63 degrees
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which numbers will round to 19 when they are rounded to the nearest whole number? select each correct answer. responses 19.46 19.46 18.48 18.48 19.91 19.91 18.82 18.82 19.33 19.33 1, fully attempted. 2, fully attempted. 3, fully attempted. 4, fully attempted. 5, fully attempted. 6, fully attempted. 7, unattempted. 8, unattempted.
The numbers that will round to 19 when rounded to the nearest whole number are 19.46 and 19.91.
To round a number to the nearest whole number, we look at the decimal part of the number. If it is less than 0.5, we round down to the nearest integer. If it is greater than or equal to 0.5, we round up to the nearest integer.
For the given set of numbers, we can round them to the nearest whole number and check which ones round to 19:
19.46 rounds up to 19
18.48 rounds down to 18
19.91 rounds up to 20
18.82 rounds up to 19
19.33 rounds up to 19
Therefore, the numbers that round to 19 when rounded to the nearest whole number are 19.46 and 19.33.
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Emily and john will be hiking for 42 hours. Hikers should drink at 2. 7 cups of water for every 2 hours of hiking. How many cups of water should emily and john drink?
From the given information provided, emily and john should drink 56.7 cups of water for 42 hours hiking.
If hikers should drink 2.7 cups of water for every 2 hours of hiking, then we can use a proportion to find how much water Emily and John should drink over their 42-hour hike:
2.7 cups / 2 hours = x cups / 42 hours
To solve for x, we can cross-multiply:
2.7 cups × 42 hours = 2 hours × x cups
113.4 cups = 2x
Finally, we can divide both sides of the equation by 2 to solve for x:
x = 56.7 cups
Therefore, Emily and John should drink a total of 56.7 cups of water during their 42-hour hike.
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a ferris wheel has five cars, each containing four seats in a row. there are 20 people ready for a ride. in how many ways can the ride begin? what if a certain two people want to sit in different cars?\
There are 5 possible ways for the ride to begin.
The ferris wheel has 5 cars with 4 seats in each car, making a total of 20 seats. If there are 20 people ready for the ride, then each car can have 4 people. Therefore, there are 5 possible ways for the ride to begin.
If two certain people want to sit in different cars, then there are 4^2 (4x4) combinations of cars for these two people. This gives us 16 possible ways for the ride to begin.
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in two successive years, the population of a town is increased by 12% and 25%. what percent of the population is increased after two years?
In two successive years, the population of the town increased by 12% and 25%. So the percentage of the population increased after two years is 40%
The population growth rate of the town can be calculated as follows:
The population of the town increased by 12% in the first year.
Hence, the population of the town after one year becomes 1.12x where x is the initial population of the town. In the second year, the population of the town increased by 25%.
Therefore, the population of the town after two years becomes
1.25(1.12x) = 1.4x.
Now, the percentage increase in the population of the town after two years can be calculated as follows:
Total percentage increase = ((New population - Old population) / Old population) x 100%
Total percentage increase = ((1.4x - x) / x) x 100%Total percentage increase = (0.4x / x) x 100%
Total percentage increase = 40 %
Therefore, the percentage increase in the population of the town after two years is 40%.
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Find the volume of a right circular cone that has a height of 20 ft and a base with a radius of 18 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
The answer should be 20,365.714 but I am not sure
Step-by-step explanation:
pLeAsE hElP
I need help solving this: 1+1
Answer:2
Step-by-step explanation:
1+1=2
point N is the incenter of ∆ABC, NK=9x-1, and NL=5x+3. find NM
NM = 8,we need to use the fact that N is the incenter of triangle ABC. This means that the angle bisectors of ∠ABC, ∠ACB, and ∠BAC intersect at point N.
We can use the fact that the incenter of a triangle is the intersection of its angle bisectors, and that the incenter is equidistant from the sides of the triangle. This means that if NM is the distance from N to side BC, then NK and NL must be equal to NM as well.
We can set up an equation to solve for NM using the given information:
NK = NM = 9x - 1
NL = NM = 5x + 3
Since NK = NL, we can set the two expressions equal to each other:
9x - 1 = 5x + 3
Solving for x, we get:
4x = 4
x = 1
Now we can substitute x = 1 into either of the expressions for NK or NL to get the value of NM:
NM = NK = 9x - 1 = 9(1) - 1 = 8
NM=8
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Brainlist answer
I will make you brainlist but show all steps and the answer needs to be correct!
Answer:
[tex]11xy - 9x + 2y[/tex]
Step-by-step explanation:
[tex]6xy - 9x + 5xy + 2y[/tex]
Add the xy terms together:
[tex]11xy - 9x + 2y[/tex]
Latasha looked at 3 websites every 15 hours. At that rate, how long, in hours, will it take to look at 5 websites
Since Latasha looked at 3 websites every 15 hours, at that rate, it will take Latasha 25 hours to look at 5 websites.
What is the unit rate?The unit rate shows the ratio between two values.
The unit rate is the quotient of two numbers, computed using the division and multiplication operations.
The number of websites Latasha looked in 15 hours = 3
The time it will take Latasha to look at 5 websites = 25 (15/3 x 5)
Thus, based on the rate, we can conclude that Latasha uses 5 hours to look at one website.
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discuss in this part. example 8.1 we use the method of steepest descent to find the minimizer of f(xi,x2,xs)
Here, we will use the method of steepest descent to find the minimiser of the function f(x1, x2, x3). The steepest descent method is an iterative optimization algorithm used to find the local minimum of a function.
Step 1: Initialize the starting point (x1, x2, x3) and set the initial values.
Step 2: Compute the gradient of the function f(x1, x2, x3) with respect to each variable (x1, x2, x3). The gradient is a vector that points in the direction of the steepest increase of the function.
Step 3: Calculate the step size, which determines how far along the descent direction we move. This can be done using various techniques, such as line search or a constant step size.
Step 4: Update the current point by moving in the direction of the negative gradient (steepest descent direction) with the computed step size. The new point will be (x1_new, x2_new, x3_new).
Step 5: Check the convergence criteria. If the change in the function value or the variables is below a certain threshold, stop the iteration process. Otherwise, return to Step 2 with the updated point.
By following these steps, the method of steepest descent will help us find the minimizer of the function f(x1, x2, x3).
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An app store opened in 2018, and consumers downloaded one million apps. The owner of the app store predicts that the number of app downloads (in millions) will increase at a rate of about 30% per year.
Write an exponential growth function f(x) that gives the number of app downloads (in millions) in year x
As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.
What is expοnential functiοn ?A mathematical functiοn with the fοllοwing fοrmula is an expοnential functiοn: f(x) = [tex]a^x[/tex] where x is the expοnent and an is a cοnstant knοwn as the base. Expοnential functiοns have a distinctive structure where the value οf the functiοn rapidly rises (οr falls) as the expοnent x value rises. The rate οf increase οr decline is determined by the expοnential functiοn's base. If a > 1, the functiοn will quickly increase as x rises, and if 0 a 1, the functiοn will quickly decrease as x rises.
We can use the fοrmula: tο create an expοnential grοwth functiοn f(x) that prοvides the number οf app dοwnlοads (in milliοns) in year x.
[tex]f(x) = f(0) * (1 + r)^x[/tex]
where x is the number οf years since the app stοre first launched, r is the grοwth rate, and f(0) is the οriginal number οf dοwnlοads.
In this instance, there were 1 milliοn initial dοwnlοads, and the grοwth rate was 30%, οr 0.30. Thus, the fοllοwing is the expοnential grοwth equatiοn fοr the milliοns οf app dοwnlοads in year x:
[tex]f(x) = 1 * (1 + 0.30)^x[/tex]
[tex]f(x) = 1.3^x[/tex]
Therefοre, fοr instance, entering x=3 intο the functiοn will return the amοunt οf app dοwnlοads (in milliοns) fοr the third year.
[tex]f(3) = 1.3^3[/tex]
[tex]f(3) = 2.197[/tex]
As a result, the app stοre's οwner prοjects that in its third year οf οperatiοn, there will be rοughly 2.197 milliοn app dοwnlοads.
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There are 59 students going on a field trip if costs 2$ no taxes how much money does it cost for all the students to go to the field trip
Answer:
$118
Step-by-step explanation:
If there are 59 students going on the field trip, and the cost is $2 per student, then the total cost for all the students to go on the field trip would be:
Total cost = Number of students × Cost per student
Total cost = 59 × $2
Total cost = $118
It would cost $118 in total for all 59 students to go on the field trip, assuming there are no taxes or additional fees involved.
x=10
x-7y=-18 what is the answer
Answer: y=4
Step-by-step explanation:
you would plug in 10 wherever x would be so your new equation would be 10-7y=-18.
subtract 10 from both sides.
-7y=-28
then divide by -7
y=4
a waste management company is designing a rectangular construction dumpster that will be twice as long as it is wide and must hold 20 yd^3 of debris. find the dimensions of the dumpster that will minimize its surface area.
The width of the dumpster that minimizes its surface area is approximately 1.71 yards, and the length is approximately 3.42 yards.
The length of the rectangular dumpster is equal to two times its width, or 2x, if x is its width. The dumpster's height is not specified, however it is not necessary for this issue.
We need to determine the dumpster's size to reduce the amount of surface area it has. The following sources provide the rectangular dumpster's surface area:
A = lw + lh + lw
where w stands for width, l for length, and h for height.
Given that the container must hold [tex]20 yd3[/tex] of waste, we can use the formula for the volume of a rectangular solid to create the following sentence:
[tex]V = lwh = (2x) (x)\\h = 2x^2 h = 20\\h = 10/x^2[/tex]
Inputting this expression for h into the surface area A formula yields the following results:
[tex]A = 2lw + 2lh + 2wh = 2(x)(2x) + 2(x)(10/x) + 2(2x)(10/x) = 4(x)(2x) + 40(x)[/tex]
We can take the derivative of A with respect to x, set it equal to zero, and solve for x to determine the dimensions that minimise A:
[tex]dA/dx = 8x - 40/x^2 = 0\\8x = 40/x^2\\x^3 = 5\\x = (5)^(1/3)\\[/tex]
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which of the following is true about a sample proportion? a. since sample proportion is a mean, one can find the z-value and an acceptance interval. b. it is impossible to find an acceptance interval of a sample proportion. c. it is not possible to standardize a sample proportion, meaning, the z-value cannot be calculated. d. none of the above.
Since sample proportion is a mean, one can find the z-value and an acceptance interval is true statement about sample proportion. (A)
The sample proportion is the ratio of the number of items in the sample having a given attribute (the numerator) to the total number of items in the sample (the denominator).
By taking a sample of data and calculating the sample proportion, one can use the z-score to find the acceptance interval and estimate the true population proportion.
For example, if the sample size is 100, and the number of items with a given attribute is 35, then the sample proportion would be 35/100 = 0.35. Using the z-score, one can then calculate the acceptance interval, which is the range of values in which the true population proportion is likely to fall.
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If the diameter in the semicircle is 10.5 what is the perimeter
Answer:
Perimeter of semi-circle = 16.5 cm.
Step-by-step explanation:
Given that,
Diameter of the semi-circle, [tex]\text{d} = 10.5 \ \text{cm}[/tex]
So, Radius of the semi-circle, [tex]\text{r} = 10.5\div2 \ \text{cm}[/tex]
We know that,
Perimeter of a Circle [tex]= 2\pi r[/tex]
So, Perimeter of a semi-circle [tex]= \dfrac{1}{2} \times 2\pi r[/tex]
[tex]= \pi r[/tex]
[tex]= \dfrac{22}{7} \times 10.5\div2[/tex]
[tex]= 16.5 \ \text{cm}[/tex]
Hence, Perimeter of the semi-circle with diameter 10.5 cm is 16.5 cm.
Find the amount accumulated after
investing a principal P for t years at an
interest rate compounded k times per year.
k = 365
P = $3,350 r = 6.2% t = 8
Hint: A = P (1+)kt
A = $[?]
Hence, after investing $3,350 for 8 years at a 6.2% interest rate, compounded 365 times a year, the total amount is roughly $4,865.25.
what is amount ?In mathematics, the term "amount" typically refers to a number or a thing's numerical value. It can stand in for anything that can be counted or measured, such as the amount of money in a checking account, the time needed to finish a task, or the concentration of a specific item in a solution. Several branches of mathematics, such as arithmetic, algebra, and calculus, all depend on the idea of amount.
given
With a principal of P and an interest rate of r compounded k times annually, the amount amassed after t years is calculated as follows:
[tex]A = P(1 + r/k)^(kt) (kt)[/tex]
Putting in the specified values
P = $3,350
r = 6.2%
t = 8
k = 365
[tex]A = $3,350(1 + 0.062/365)^(365*8)[/tex]
A ≈ $4,865.25 (rounded to the nearest cent) (rounded to the nearest cent)
Hence, after investing $3,350 for 8 years at a 6.2% interest rate, compounded 365 times a year, the total amount is roughly $4,865.25.
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What is the image point of ( 1 , 8 ) after a translation left 2 units and down 1 unit?
Answer: It should be -1,7
Step-by-step explanation: x=1-2=-1
y=8-1=7
Answer:
(-1, 7)
Step-by-step explanation:
A left translation is a negative number affecting the x-coordinate.
1 - 2 = -1
A down translation is a negative number affecting the y-coordinate.
8 - 1 = 7
(1, 8) --------> (-1, 7)
Triangle ABC will be dilated with a scale factor of 2, centered at the origin. What will be the resulting coordinate of B'?
(look at pic below for graph)
answer options:
A) (4,6)
B) (4,12)
C) (-4,-12)
D) (2,12)
pls answer asap
Triangle ABC will be dilated with a scale factor of 2, centered at the origin. What will be the resulting coordinate of B' will be (4,12).
What is a triangle?A polygon with three sides and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with points A, B, and C. In Euclidean mathematics, any three points that are not collinear produce a distinct triangle and a distinct plane.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more integers, or coordinates. The order of the coordinates is important, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". In elementary mathematics, the coordinates are assumed to be real numbers. Analytic geometry is based on the use of a coordinate system, which enables issues with geometry to be converted into problems with numbers and vice versa.
Triangle ABC will be dilated with a scale factor of 2, centered at the origin.
Coordinates of B are (2,6).
When the triangle is dilated, we multiply the coordinates by 2.
hence, B'(4,12)
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Which system of inequalities has the solution shown in the graph?
if tan 0=11/9, find sec 0
Answer:
[tex]\frac{\sqrt{202} }{9}[/tex] OR ≈ 1.57919
Step-by-step explanation:
tanθ = opp/adj
opp/adj = 11/9
hyp = [tex]\sqrt{202}[/tex]
secθ = 1/cosθ
cosθ = [tex]\frac{9}{\sqrt{202} }[/tex]
1/cosθ = [tex]\frac{1}{\frac{9}{\sqrt{202} } }[/tex]
= [tex]\frac{\sqrt{202} }{9}[/tex] or ≈ 1.57919
Please use the information below for an arithmetic sequence to do the following:
a. sub 1 equals 3 d equals 4
A) List the first 6 terms of the sequence
B) Write the terms of this sequence as a series.
C) Provide a graph of the aritmetic sequence.
D) List the first 6 partial sums of the series.
SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!
Answer:
See below, please.
Step-by-step explanation:
A) The first term of the sequence is given as sub 1 = 3 and the common difference is given as d = 4. Therefore, the first 6 terms of the sequence are
sub 1 = 3
sub 2 = sub 1 + d = 3 + 4 = 7
sub 3 = sub 2 + d = 7 + 4 = 11
sub 4 = sub 3 + d = 11 + 4 = 15
sub 5 = sub 4 + d = 15 + 4 = 19
sub 6 = sub 5 + d = 19 + 4 = 23
B) The terms of this sequence can be written as a series as
3 + 7 + 11 + 15 + 19 + 23 + ...
C) The graph of the arithmetic sequence is a straight line with a positive slope, as each term of the sequence is obtained by adding a constant (d = 4) to the previous term.
D) The first 6 partial sums of the series can be calculated as
S1 = 3
S2 = 3 + 7 = 10
S3 = 3 + 7 + 11 = 21
S4 = 3 + 7 + 11 + 15 = 36
S5 = 3 + 7 + 11 + 15 + 19 = 55
S6 = 3 + 7 + 11 + 15 + 19 + 23 = 78
Therefore, the first 6 terms of the sequence are 3, 7, 11, 15, 19, and 23. The terms of the sequence can be written as a series as 3 + 7 + 11 + 15 + 19 + 23 + ..., and the graph of the sequence is a straight line with a positive slope. The first 6 partial sums of the series are 3, 10, 21, 36, 55, and 78.
a bag contains red balls, green balls, and yellow balls. if balls are drawn one at a time without replacement, the probability that the first yellow ball is drawn on the eighth draw is , what is the value of ?
The probability of drawing the first yellow ball on the eighth draw is 1/2772.
The probability of drawing a yellow ball on the eighth draw is the probability of drawing 7 non-yellow balls followed by a yellow ball.
The probability of drawing a non-yellow ball on the first draw is 7/12 since there are 7 non-yellow balls out of a total of 12 balls in the bag. After the first non-yellow ball is drawn, there will be 6 non-yellow balls left out of a total of 11 balls. So the probability of drawing a non-yellow ball on the second draw is 6/11. Continuing in this manner, the probability of drawing 7 non-yellow balls in a row is
(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6)
Now, there are 5 yellow balls left out of a total of 5 + 7 + 3 = 15 balls. So the probability of drawing a yellow ball on the eighth draw is 5/15.
Therefore, the probability of drawing the first yellow ball on the eighth draw is
(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6) × (5/15)
Simplifying this expression, we get
(7 × 6 × 5 × 4 × 3 × 2 × 1 × 5) / (12 × 11 × 10 × 9 × 8 × 7 × 6 × 15)
which simplifies to:
1/2772
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The given question is incomplete, the complete question is:
A bag contains 3 red balls, 4 green balls, and 5 yellow balls. If balls are drawn one at a time without replacement, what is the probability that the first yellow ball is drawn on the eighth draw?