Answer:
Even set = {HTT, THT, TTH, TTT}
Step-by-step explanation:
We are given that three coins are tossed; the result is at most one head.
And we have to find the sets of elements that are included in the sample space.
Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.
Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.
So, the sample space so formed is;
S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}
Now, our event is at most one head. So, the sample space for the favorable event is given by;
Even set = {HTT, THT, TTH, TTT}
In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.
Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (x, y, z)→(7, 0, 2) e−xysin π z 4
Answer:
The limit of the function is 0Step-by-step explanation:
Given the limit of the function [tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }[/tex]
First step is to substitute the given values of x, y and z into the function given as shown;
[tex]\lim_{(x,y,z) \to (7,0,2)} e^{-xy}sin\dfrac{\pi z}{4} }\\\\= e^{-(7)(0)}sin\dfrac{\pi (2)}{4} }\\\\\\= e^{-0}sin\dfrac{\pi}{2} }\\\\\\= 1*sin\frac{\pi}{2} \\\\= 1*sin90^0\\\\= 1* 0\\\\= 0[/tex]
The limit therefore exist since the limit of the function at the given point gave us a finite value which is zero.
what is the definition of a sequence
Answer:
the process of combining things in a particular order, or discovering the order in which they are combined: A common sign of dyslexia is that the sequencing of letters when spelling words may be incorrect. biology specialized.
Step-by-step explanation:
Which statements are true about triangle QRS?
Select
three options.
Answer:
The side opposite <Q is RS
The hypothenuse is QR
The side adjacent to <Q is QS
Step-by-step explanation:
Side RS is directly opposite <Q. The first statement provided in the options is correct.
The side that is opposite to <R is QS. The second statement in the options is not correct.
The longer leg of a right triangle is always the hypotenuse. Side QR in ∆QRS is the hypotenuse. The third statement given in the options is correct.
The side adjacent to <R is not SQ. RS is the side adjacent to <R. The fourth statement in the given options is not correct.
Side QS is adjacent to <Q. The fifth option is correct.
Answer:
A, C, E
Step-by-step explanation:
on edge! hope this helps!!~ （‐＾▽＾‐）
cooks are needed to prepare for a large party. Each cook can bake either 5 Large cakes or 14 small cakes per hour . The kitchen is available for 3 hours and 29 large cakes and 260 cakes need to be baked . How many cooks are required to bake the required number of cakes during the time the kitchen is available?
it was all about equating some values
to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.
Let's determine the number of cooks required to bake the required number of cakes during the available time.
We have the following information:
- Each cook can bake either 5 large cakes or 14 small cakes per hour.
- The kitchen is available for 3 hours.
- We need to bake 29 large cakes and 260 cakes in total.
First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:
1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.
Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:
1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.
Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:
Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours
We need to bake 29 large cakes, so:
29 = Number of cooks × 15
Number of cooks = 29 / 15 ≈ 1.93
Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.
Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:
Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours
We need to bake 260 small cakes, so:
260 = Number of cooks × 42
Number of cooks = 260 / 42 ≈ 6.19
Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.
Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.
Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.
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The equation below is written in words. x plus ten equals two. What's the value of x?
Answer:
x+10 =2
x = -8
Step-by-step explanation:
plus means add
x+10 =2
Subtract 10 from each side
x+10-10 =2-10
x = -8
Jamal has two investments, one in Company A, and another in Company B. Jamal purchased 300 shares in Company A at $1.45 per share. Since purchasing the shares, the price per share increased to $1.65 per share, after which Jamal decided to sell, realizing a profit. At the same time, Jamal purchased 200 shares in Company B at $1.20 per share. Since purchasing the shares, the share price fell to $1.10 per share, after which Jamal decided to sell the shares, suffering a loss. Calculate the total profit that Jamal received from his two investments.
Answer:
$20
Step-by-step explanation:
Company A:
Buy 300 shares at $1.45 per share.
Sell 300 shares at $1.65 per share.
Profit: ($1.65 - $1.45) * 300 = $60
Company B:
Buy 200 shares at $1.20 per share.
Sell 200 shares at $1.10 per share.
Loss: ($1.20 - $1.10) * 200 = $20
Net profit:
$40 - $20 = $20
Answer:
Step-by-step explanation:
Profit on Company A =$(1.65−1.45)×300=$60.
Loss on Company B =$(1.20−1.10)×200=$20.
Therefore the total profit Jamal achieved was $60−$20=$40.
Henry is investing at a continuously compounded annual interest rate of 4.5%. How many years will it take for the balance
to triple? Round your answer up to the nearest whole number, and do not include the units in your answer.
Answer:
1 year
Step-by-step explanation:
Hello,
Continuously compounding with an annual interest rate of 4.5% means multiplying the initial investment by (for t tears).
[tex]\displaystyle e^{(1+4.5\%)t}=e^{\left( 1.045\cdot t \right) }[/tex]
So we need to find t so that:
[tex]\displaystyle e^{\left( 1.045\cdot t \right) }=3\\\\1.0.45t=ln(3)\\\\t=\dfrac{ln(3)}{1.045}=1.051304...[/tex]
Rounding to the nearest whole number gives 1 year.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
25
Step-by-step explanation:
Trust me
2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?
Answer:
Percentage of home team supporters =65%
Percentage of visiting team supporters =35%
Step-by-step explanation:
Total attendees=2,000 people
Home team supporters=1,300
Visiting team supporters=700
What percentage of people attending supported the home team?
Percentage of people attending who supported the home team = home team supporters / total attendees × 100
=1,300/2,000 × 100
=0.65 × 100
=65%
Visiting team supporters = visiting team supporters / total attendees
× 100
=700/2000 × 100
=0.35 × 100
=35%
Alternatively,
Visiting team supporters = percentage of total attendees - percentage of home team supporters
=100% - 65%
=35%
a
A solid metal cone of base radius a cm and height 2a cm is melted and solid
spheres of radius are made without wastage. How many such spheres can be
made?
volume of a cone
.
.
.
volume of sphere
.
.
number of spheres that can be made......
.
.
hence a hemisphere can be formed
What is the solution to this equation? 2x + 4 = 16
Answer:
x=6
Step-by-step explanation:
2x+4=16
2x+4-4=16-6
2x=12
x=6
Proof:
2x+4=16
2(6)+4=16
12+4=16
16=16
Hope this helps ;) ❤❤❤
Answer:
find out what x is and it is 6 it is 6 because 2 times 6 is 12 and 12 plus 4 is 16
Step-by-step explanation:
Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.12. See the figure below. There is $28.96 in credit remaining on the card after minutes of calls. How much credit was there after 21 minutes of calls?
Answer:
Credit remaining after 21 minutes = $30.4
Step-by-step explanation:
Credit remaining on a phone card is a linear function of the total calling time.
When graphed, let the linear function representing the line is,
y = mx + b
Where 'm' = slope of the line
b = y-intercept
From the graph,
Slope of the line = -0.12
y = -0.12x + b
If this line passes through a point (33, 28.96),
28.96 = -0.12(33) + b
b = 28.96 + 3.96
b = 32.92
Therefore, the linear function is,
f(x) = -0.12x + 32.92
where x = calling time
Credit left in the card after 21 minutes,
f(21) = -0.12(21) + 32.92
= -2.52 + 32.92
= $30.4
Which property is not used to simplify the following expression 2* (x+5)+7x=(2x+10)+7x
Hence, the commutative property of addition is not used.
What is an expression?
A mathematical expression is in form of variables and constants separated by their arithmetic operation.
As we know that, there are three types of properties they are associative property which is [tex](a+b) + c = a + (b+c)[/tex],
Distributive property which is [tex]a(b+c) = ab + ac[/tex],
Commutative property which is [tex]a + b = b + a[/tex].
Here given that,
[tex]2 (x+5)+7x=(2x+10)+7x[/tex]
[tex](2x+10)+7x=(2x+10)+7x[/tex] ( distributive property of multiplication)
[tex](2x+7x)+10=(2x+7x)+10[/tex] ( it is associative property of addition)
[tex](8x)+10=(8x)+10[/tex] ( it is a commutative property)
Hence, the commutative property of addition is not used.
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Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)
Answer:
Please refer to the attached graph.
Slope = -3.125
Step-by-step explanation:
Given
Time is placed on x axis.
Initially, height of rock climber is 25 feet above sea level.
[tex]t_1 =0\ sec[/tex]
[tex]h_1[/tex] = 25 feet
After 8 seconds, he is at sea level.
[tex]t_2 =8\ sec[/tex]
[tex]h_2[/tex] = 0 feet
To find:
Graph of the given points and Slope of the line depicted.
Solution:
Kindly refer to the attached graph.
Here, we have been given two points to be plotted on the xy coordinate plane.
1st point is (0, 25): Time is 0 and height above sea level is 25 ft
2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)
First of all, mark these points and join them with a straight line.
Please refer to attached graph.
Slope of a line is given as:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]
Using the formula:
[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]
Simplify the expression (6^4)^2
When raising a power inside parentheses to another power, multiply the numbers:
(6^4)^2 = 6^(4x2) = 6^8
Simplified = 6^8
6^8 = 1679616
Answer:
[tex] \boxed{ \purple{ {6}^{8} }}[/tex]Step-by-step explanation:
[tex] \mathsf{ ( { {6}^{4}) }^{2} }[/tex]
It is the example of Power to power law of indices.
Multiply the exponents
⇒[tex] \mathsf{ {6}^{4 \times 2} }[/tex]
Multiply the numbers
⇒[tex] \mathsf{ {6}^{8} }[/tex]
-------------------------------------------------------
[tex] \mathsf{\orange{ \underline{ power \: to \: power \: law \: of \: indices}}}[/tex]
If [tex] \mathsf{ ({x}^{a} )^{b}} [/tex] is an algebraic term then [tex] \mathsf{( {x}^{a} ) ^{b} = {x}^{a \times b} }[/tex]
i.e When an algebraic term in the index form is raised to another index , the base is raised to the power of two indices.
Hope I helped!
Best regards!!
slope of -4/3x with point (7,20) find equation
Answer:
y= -4/3x+10 2/3
Step-by-step explanation:
To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.
I hope my explanation wasn't confusing and that my answer helped.
what is the prime factorization of 55^5 x 65 x 9^15 and why? A. 3^15 * 5^6 *11^5*13 B. 3^30 *5^6 *11^5 *13 C.3^30 * 5^6 *11 * 13 D. 3^30 *5^5*11^5*13
Answer:
B
Step-by-step explanation:
1. Lets focus on 55^5
55^5 = 11^5 * 5^5
2. now on 65
65 = 5 * 13
3. now on 9^15
9^15=(3^2)^15 = 3^30
4. combine all three parts
11^5 * 5^5 * 5 * 13 * 3^30 = 11^5*5^6*13*3^30
so our answer is B
The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Question options :
A. There is sufficient evidence to reject the claim
u < 99.
B. There is sufficient evidence to support the claim
u < 99.
C. There is not sufficient evidence to reject the claim
u < 99.
D. There is not sufficient evidence to support the claim
u< 99.
Answer:
B. There is sufficient evidence to support the claim
u < 99.
Step-by-step explanation:
We construct the n*ll and alternative hypotheses to support our claim
The n*ll hypothesis :H0
The alternative hypothesis : Ha
N*ll hypothesis =H0: u=99
Alternative hypothesis =Ha: u<99
So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99
we can therefore have sufficient evidence to support our claim that u<99
The image of (5,-4) reflected across the y-axis is
A. (-5, 4)
B. (-5, 4)
C. (5, 4)
D. (5, 4)
The image of (3,-2) reflected across the line x - 1 is
A. (-1, -2)
B. (3,0)
C. (0, -2)
D. (-2, -1)
Answer:
Number 1: A
Number 2:D
Step-by-step explanation:
IQ scores have a mean of 100 and a standard deviation of 15. What percentile corresponds to an IQ score of 115? Explain the steps you took to find the percentile.
Answer:
The percentile that corresponds to an IQ score of 115 is 34.13 %
Step-by-step explanation:
Here, we want to find the percentile that corresponds to an IQ score of 115.
To calculate this percentile, we start with making observations. From the question, we are told that the mean score is 100 while the standard deviation is 15.
Now we want to find the percentile for a score if 115. For a score of 115, we can see that the difference between this score and the mean is 15 which is exactly equal to the standard deviation.
What this means is that the score is within +1 SD of the mean.
For a score of within +1 SD of the mean, the percentile is 34.13%
A score at the mean is the 50th percentile, a score which is 1 SD above or below the mean has a percentile value of 34.13%
Please, I will like you to check the attachment to see how percentiles are valued given the number of standard deviations a particular value is from the mean.
Scott start his banking account with 150 and is spending $7 per day on lunch . How would one describe the graph of this model?
Answer:
So this is giving us the slope the slope is y=-7x+150
Step-by-step explanation:
It is giving us the Y intercept which is $150 because thats how much he starts out with
It is giving us the slope -7 dollars because he is spending that everyday
the diameter of Earth's moon is on average 3.8 x 10^8m. Use the formula A=4π² to find the approximate surface area. (Use 3.14 for the value of π)
Answer:
The answer is
[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]
Step-by-step explanation:
Since the Earth's moon is a sphere
Surface area of a sphere from the question is given by
A = 4πr²
where r is the radius
To find the radius using the diameter we use the formula
radius = diameter / 2
[tex]radius \: = \frac{3.8 \times {10}^{8} }{2} [/tex]
[tex]radius = 1.9 \times {10}^{8} \: m[/tex]
π = 3.14
Substitute these values into the above formula
That's
[tex]A = 4 \times 3.14 \times ({1.9 \times {10}^{8} })^{2} [/tex]
We have the final answer as
[tex]A = 4.53 \times {10}^{17} \: {m}^{2} [/tex]
Hope this helps you
Use inductive reasoning to predict the most probable next number in each list.
9, 13, 21, 33, 49, 69, ?
Answer:
93
Step-by-step explanation:
First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.
_____
First differences are ...
13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20
Second differences are ...
8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4
When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.
What is the constant of variation, k, of the line y=kx through (3,18) and (5,30)? 3 6
Answer:
6
Step-by-step explanation:
The constant of variation is the slope
k = (y2-y1)/(x2-x1)
= (30-18)/(5-3)
=12/2
= 6
The value of constant of variation, k, is,
⇒ k = 6
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Here, the constant of variation, k, of the line y = kx through (3,18) and (5,30)
Since, The constant of variation is the slope,
Hence, We get;
k = (y₂ - y₁)/(x₂ - x₁)
= (30 - 18)/(5 - 3)
= 12/2
= 6
Thus, the value of constant of variation, k, is,
⇒ k = 6
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20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are
Answer:
38,760 different ways.Step-by-step explanation:
The question is incomplete. Here is the complete question.
20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?
Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.
20C6 = 20!/(20-6)!6!
20C6 = 20!/14!6!
20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2
20C6 = 20*19*18*1716*15/6*5*4*3*2
20C6 = 27,907,200/720
20C6 = 38,760 different ways.
Hence, the interviewer can create the list in 38,760 different ways.
Sharon tried to solve an equation step by step.
9
9
15
5
=−3(e−2)
=−3e+6
=3e
=e
Step 1
Step 2
Step 3
Find Sharon's mistake.
Choose 1 answer:
Choose 1 answer:
Answer:
step 2
Step-by-step explanation:
9 = -3(e - 2)
9 = -3e + 6
9-6 = -3e
3 = -3e
divide both sides by -3
-1 = e
There are two pitchers of lemonade in the fridge there are 1.5 gallons of lemonade in 1 pitcher and 9 quarts of lemonade in the other pitcher how many cups of lemonade are there in the fridge
Answer:
52 cups
Step-by-step explanation:
1 gallon = 4 quarts
1.5 gallons = 6 quarts
6 + 9 = 13 quarts of lemonade in the fridge.
1 quart = 4 cups
13 quarts = 4 × 13 = 52 cups
52 cups of lemonade are in the fridge.
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
60 cups
Step-by-step explanation:
1 gal = 16 cups
1 quart = 4 cups
16 cups
1.5 gal x ------------- = 24 cups
1 gal.
4 cups
9 quarts x ----------- = 36 cups
1 quart
number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups
Write and equation for each situation and solve. Your car gets 25 miles per gallon in the city if you travel 300 miles how many gallons of gas will you use?
if. 25 miles : 1 gallon
300 miles. : ?
if more less divides
300/25×1
=12 gallons of gas will be used
100 pointer and will mark brainliest thank you. Hi! I ask that you provide a digital scatter plot image of this graph and predict the line of best fit and make sure to sketch it on the graph aswell. Thank you. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61 And then provide the answers to these questions about the scatter plot which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. What does the slope of the line represent within the context of your graph? What does the y-intercept represent Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation. Using the line of best fit that you found, approximate how tall is a person whose arm span is 66 inches According to your line of best fit, what is the arm span of a 74-inch-tall person
I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.
The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.
Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]
The y intercept 3.787 represents the height of that is independent of Arm span.
The height of the person whose arm span is 66 inches is 66.817 inch.
The arm span of a person whose height is 74 inches is 73.52 inch
According to the given data the arm span and heights are given in inches
Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis
The image for the excel work done showing calculations and scatter plot is attached.
Now we can fit the linear tread line and to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]
Slope of line of best fit = 0.955
So we can conclude that height (Y) is related to Arm span according to equation (1)
Equation (1) shows the equation of line of best fit for the given data
The y intercept 3.787 represents the height of that is independent of Arm span.
So the height of the person whose arm span is 66 inches is given following
[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]
Similarly the arm span of a person whose height is 74 inches
[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]
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Question (2)
ASAP Please help.
Construct the "Square root spiral". Take a large sheet of paper and construct the "Square root spiral" in the following fashion.
Start with a point O and draw a line segment [tex]\rm{P_{1} P_{2}}[/tex] perpendicular to [tex]\rm{OP_{1}}[/tex] of unit length. Now draw a line segment [tex]\rm{P_{2} P_{3}}[/tex] perpendicular to [tex]\rm{OP_{2}}[/tex] . Then draw a line segment [tex]\rm{P_{3} P_{4}}[/tex] perpendicular to [tex]\rm{OP_{3}}[/tex]. Continuing in this matter, you get line segment of unit length perpendicular to [tex]\rm{OP_{n-1}}[/tex]. In this manner, you will have created the points [tex]\rm{P_{2}, P_{3},...... P_{n}....}[/tex], and joined them to create a beautiful spiral depicting [tex]\rm{\sqrt{2}, \sqrt{3}, \sqrt{4},...}[/tex]
Answer:
The "square root spiral," donned the "Spiral of Theodorus" was created by Theodorus to visualize a set of 17 isosceles triangles where [tex]n[/tex] is equal to a value between one and seventeen.
The central angle is attached to a central point, and the side opposite of the central angle is always equal to 1.The hypotenuse of the triangle is equivalent to [tex]\sqrt{n+1}[/tex]. The hypotenuse becomes a leg for the next triangle.I have attached an image of the Square Root spiral below.
Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.
Answer: $2750
Step-by-step explanation:
Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.
Given: I= $495
t= 3 years
r= 6% = 0.06
Then, according to the above formula:
[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]
Hence, the principal invested = $2750
