Answer:
[tex]\theta = tan^{-1}(\frac{y}{x})[/tex]
Step-by-step explanation:
If we are given components of a vector then we can find the angle between them.
Suppose we are given a vector v
[tex]v = (x, y)[/tex]
Where x is the horizontal component and y is the vertical component.
The angle can be found by using
[tex]tan(\theta)=\frac{y}{x}\\\\\theta = tan^{-1}(\frac{y}{x})[/tex]
The magnitude of the vector v can be found using
[tex]v = \sqrt{x^{2}+y^{2}}[/tex]
Example:
Lets do a quick example:
[tex]v = (2, 4)[/tex]
The angle of the vector is
[tex]tan(\theta)=\frac{4}{2}\\\\\theta = tan^{-1}(\frac{4}{2})\\\\\theta = 63.43^{\circ}[/tex]
The magnitude of the vector is
[tex]v = \sqrt{x^{2}+y^{2}}\\\\v = \sqrt{2^{2}+4^{2}}\\\\v = \sqrt{4+16}\\\\v = \sqrt{20}\\\\v = 4.47[/tex]
Graph the Plane Curve defined by:
x=3cos(t)−t+5, y=sin(t), for t in [0,3π]
Step-by-step explanation:
Use this context for the next 4 questions (Questions 1 - 4): Weight of a rock: In a geology course, students are learning to use a balance scale to accurately weigh rocks. One student plans to weigh a rock 20 times and then calculate the average of the 20 measurements to estimate her rock's true weight. A second student plans to weigh a rock 5 times and calculate the average of the 5 measurements to estimate his rock's true weight. Which student is more likely to come the closest to the true weight of the rock he or she is weighing? (i) The student who weighed the rock 20 times. (ii) The student who weighed the rock 5 times. (iii) Both averages would be equally close to the true weight.
Answer:
The right answer is:
(i) The student who weighed the rock 20 times.
Step-by-step explanation:
Both students are taking a sample from the population. In this case, the population is all the possible weight that can be measured by the scale they are using.
Independently of the sample size, the sampling distribution mean will be centered in the population mean, so they are estimating the true weight of the rock unbiased.
But the spread of the sampling distribution, measaured by the standard deviation, depends on the sample size.
The bigger the sample, the narrower the sampling distribution is expected o be. So it is more likely to be closer to the true mean with a bigger sample.
The right answer is:
(i) The student who weighed the rock 20 times.
I NEED HELP WITH MATH !!!
which type of graph would you use to show the number of water bottles sold at four different stores and water bottles come in packs of 20
Answer:
pictograph
Step-by-step explanation:
i got it right :) so yeah trust me
Math
If A+B+C=pi then prove that cos3A.cos3B+cos3B.cos3C+cos3C.cos3A=1
Step-by-step explanation:
Given:
A+B+C= π
<=> 3A+3B+3C = 3π
<=> cos(3A+3B) = - cos3C
<=> cos3A.cos3B-sin3A.sin3B = - cos3C
<=> cos3A.cos3B = sin3A.sin3B - cos3C (1)
similarly apply for the other two angles, we have:
cos3B.cos3C = sin3B.sin3C - cos3A (2) cos3C.cos3A = sin3C.sin3A - cos3B (3)Grouping three equations, (1) + (2) + (3), we have:
<=> cos3A.cos3B+cos3B.cos3C+cos3C.cos3A = sin3A.sin3B + sin3B.sin3C + sin3C.sin3A - ( cos3A + cos3B + cos3C )
= 1
Hope it can find you well.
Using the sum of angles in a triangle and cosine identities, we proved that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) equals 1.
Given that A + B + C = π, we will use trigonometric identities and properties to prove the required equation.
Recall that A + B + C = π implies that A, B, and C are angles of a triangle.We can use the trigonometric identity for the cosine of a sum of angles. Specifically, for any angle θ, cos(π - θ) = -cos(θ).Consider the expression for the sum of angles, we have cos(3(A+B+C)) = cos(3π). Since cos(3π) = -1, this simplifies to cos(3A + 3B + 3C) = -1.Using the triple angle formula for cosine, we know that cos(3x) = 4cos³(x) - 3cos(x). Applying this to each term, we have:cos(3A) = 4cos³(A) - 3cos(A)cos(3B) = 4cos³(B) - 3cos(B)cos(3C) = 4cos³(C) - 3cos(C)By symmetry and considering the angles sum up to π, we simplify the expression cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) using cos(π - θ) = -cos(θ).Finally, given the periodic and symmetrical nature of the cosine function in this specific triangular setup, it can be shown algebraically or verified computationally (or by specific known identities for triangle angles) that the overall summation leads to the result of 1.Hence, we have proven that cos(3A)cos(3B) + cos(3B)cos(3C) + cos(3C)cos(3A) = 1 for angles A, B, and C summing up to \pi.
Unit 8: Right Triangles & Trigonometry
Homework 2: Special Right Triangles Questions 17-24
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
a) Find the function for the amount to which the investment grows after t years.
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
Answer:
a) [tex]A(t) = 77000(1.01375)^{4t}[/tex]
b)
The amount of money in the account at t = 0 years is $77,000.
The amount of money in the account at t = 3 years is $90,711.
The amount of money in the account at t = 6 years is $106,864.
The amount of money in the account at t = 10 years is $132,961.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
Suppose that $77,000 is invested at 5 1/2% interest, compounded quarterly.
This means that, respectively, [tex]P = 77000, r = 0.055, n = 4[/tex]
a) Find the function for the amount to which the investment grows after t years.
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 77000(1 + \frac{0.055}{4})^{4t}[/tex]
[tex]A(t) = 77000(1.01375)^{4t}[/tex]
b) Find the amount of money in the account at t=0,3, 6, and 10 years.
[tex]A(0) = 77000(1.01375)^{4*0} = 77000[/tex]
The amount of money in the account at t = 0 years is $77,000.
[tex]A(3) = 77000(1.01375)^{4*3} = 90711[/tex]
The amount of money in the account at t = 3 years is $90,711.
[tex]A(6) = 77000(1.01375)^{4*6} = 106864[/tex]
The amount of money in the account at t = 6 years is $106,864.
[tex]A(10) = 77000(1.01375)^{4*10} = 132961[/tex]
The amount of money in the account at t = 10 years is $132,961.
The function for the investment after t years is [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex] To find the amount in the account at different times, trigger this function with the desired time intervals.
Explanation:The subject of the questions is about compound interest which belongs to the finance section of Mathematics.
To solve problems related to compound interest, a simple formula can be used: [tex]A = P(1 + r/n)^{(nt)[/tex] where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal), n is the number of times that interest is compounded per year, and t is time the money is invested for in years.
a) First, identify the variables from the question:[tex]P = $77000, r = 5.5/100 = 0.055[/tex](convert the percentage to a decimal), n = 4 (since interest is compounded quarterly).
We can now plug these values into our formula to determine the function: [tex]A = 77000(1 + 0.055/4)^{(4t).[/tex]
b) To find the amount of money in the account at different time intervals, plug the specified values for t into the function. For t = 0, 3, 6, 10 years, simply replace t in A with each of these time intervals and calculate the resulting A.
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A container contains balls numbered from 1 to 55. A ball is drawn randomly. What is the probability that the first ball is number 9 and the second ball is number 41?
Answer:
1/55 * 1/55 = 1/3025
Step-by-step explanation:
The probability of 2 consecutive events is:
P(A and B) = P(A) * P(B) - where P(something) is the probability of it
so:
P(picking 9) = 1 possibility out of 55 total, so 1/55
P(picking 41) = 1 possibility out of 55 total, so 1/55
Finally:
P(9 and 41) = 1/55 * 1/55 = 1/3025
The probability of drawing a specific number (e.g. 9) from 55 balls is 1/55. After one ball is drawn, the probability of drawing another specific number (e.g. 41) is 1/54. The total probability of these events happening in sequence is (1/55) * (1/54).
Explanation:This problem falls under the category of probability. Probability is a mathematical way of expressing the likelihood of an event happening, using numbers from 0 (impossible) to 1 (certain).
In this case, the total number of balls is 55. Since the ball is drawn randomly, the probability of drawing any specific number (such as 9) on the first draw is 1/55. Similarly, after the first ball is drawn, there are now 54 balls left in the container, but we're again interested in drawing a specific number (41), so the probability for the second draw is also 1/54.
Our task is to find the joint probability of both these events happening - drawing the 9 first and then the 41. To do that, we multiply the probabilities of the individual events, which means the final answer will be (1/55) * (1/54).
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What is the combined weight of all the kittens? Weight of kittens: 1/4 pound: 3 kittens. 3/8 pound: 2 kittens. 1/2 pound: 4 kittens. 5/8 pound: 4 kittens
Answer:
6 pounds
Step-by-step explanation:
1/4 times 3 = 3/4
3/8 times 2: 6/8 = 3/4
1/2 times 4: 4/2 = 2
5/8 times 4: 20/8 = 2 1/2
3/4 + 3/4 = 6/4 = 1 1/2
2 + 2 1/2 + 1 1/2 = 6 pounds
So much dance class is 3 miles away from her home her music class is 12 miles away from her home right now equation that shows the number of times farther so with music class is from her home then the dance class from her home
The music class is 4 times farther from her home than the dance class.
Explanation:To find the number of times farther the music class is from her home than the dance class, we first need to determine the distance of each class from her home. The dance class is 3 miles away, and the music class is 12 miles away. To get the ratio of these distances, we divide the distance to the music class by the distance to the dance class. Therefore, the equation that represents the number of times farther the music class is from her home is:
12 miles / 3 miles = 4
So, the music class is 4 times farther from her home than the dance class.
Let σ be portion of the paraboloid z = x 2 + y 2 − 9 lying on and below the xy-plane. Let σ have downward orientation. Let C be its boundary curve, oriented positively with respect to σ. Let F = x − y, x 2 z, y . (a) Evaluate R C F • T ds as a line integral. (b) Use Stokes’ theorem to evaluate R C F • T ds by evaluating an appropriate surface integral.
Answer:
See explaination
Step-by-step explanation:
Stoke theorem proposes that the surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function round that path.
The Stoke Theorem can be used if you see a two dimensional region bounded by a closed curve, or if you see a single integral ie a line integral.
See attached file for further solution.
Find the measure of the supplement of the angle.Find the supplement of 7°.
Answer:
173
Step-by-step explanation:
Same thing as last time, just instead of 90, it's 180.
Lesson 14
Reflecting points page 134
How do I upload a picture to get help with this?
Answer:
Im pretty sure when your writing a question theres a place where you can upload form computer and add a picture.
Step-by-step explanation:
Hope this helps with future questions!
0.25 + 1 + 4 + 16 + 64 Select the explicit formula for the sequence.
Answer:
Formula could be :: (N)4 with n being the number
Step-by-step explanation:
Answer:
It's B) 0.25 * 4^n-1 and third one is B
Step-by-step explanation:
Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.
Answer:
Length of x ~ 10.5; Option B
Step-by-step explanation:
1. There are three radii present in this problem. Of that the diamter is supposedly 42.2 units. Given that the radii should be ⇒ 42.2 / 2 ⇒ 21.2 units
2. With that being said the 3rd radii contains parts x and 10.6. By radii congruency, the length of all radii should be the same, so this 3rd radii should = 21.2 units as well. If so, by the Partition Postulate 21.2 = x + 10.6
3. Through algebra let us solve for x:
21.2 = x + 10.6,
x = 21.2 - 10.6,
Answer ~ Length of x: 10.5
Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5
Answer:
it is b
Step-by-step explanation:6 square
Answer:
b
Step-by-step explanation:
Find the circumference of a circle with a diameter of 100 feet. Use 3.14 for it (pi).
Answer: 314
Step-by-step explanation:
3.14 * 100= 314
Answer:
314 feet
Step-by-step explanation:
Circumference of a circle is 2pi*r
Radius = 100/2
Circumference = 2*3.14*50 = 314 feet
Finding the Areas of a Rectangular Pyramid's Faces
10 in.
10.4 in.
What are the areas of the faces of the rectangular
pyramid? Select all that apply
12 in 2
24 in 2
30 in.
20.8 in2
60 in.2
61.2 in 2
4 in.
6 in.
Answer: 24 in.2
30 in.2
20.8 in.2
Step-by-step explanation:
2 Points
A baseball league finds that the speeds of pitches are normally distributed,
with a mean of 89 mph and a standard deviation of 2.4 mph. One pitch is
thrown at a speed of 86.2 mph. What is the z-score of this pitch? Round your
answer to two decimal places.
A. -1.17
O O
C. -1.27
O
O D. 1.17
Answer: -1.17
Step-by-step explanation:
I guessed and got it right
Final answer:
The z-score of a baseball pitch thrown at 86.2 mph is -1.17, calculated using the z-score formula with a mean pitch speed of 89 mph and a standard deviation of 2.4 mph. Thus, option A is correct.
Explanation:
The question asks for the z-score of a baseball pitch thrown at a speed of 86.2 mph, given that the mean speed of pitches is 89 mph with a standard deviation of 2.4 mph. To find the z-score, we use the formula:
Z = (X - μ) / σ
Where Z is the z-score, X is the value in question (86.2 mph), μ is the mean (89 mph), and σ is the standard deviation (2.4 mph).
Plugging in the values, we get:
Z = (86.2 - 89) / 2.4
Z = -2.8 / 2.4
Z = -1.17
Thus, the z-score of the pitch thrown at 86.2 mph is -1.17, rounded to two decimal places.
g In American roulette, the wheel has the 38 numbers, 00, 0, 1, 2, ..., 34, 35, and 36, marked on equally spaced slots. If a player bets $1 on a number and wins, then the player keeps the dollar and receives an additional $35. Otherwise, the dollar is lost. Calculate the expected value for the player to play one time. Round to the nearest cent.
The expected value for the player to play one time in American roulette is -$0.05. This suggests that, on average, the player can expect to lose $0.05 every time they play the game.
Explanation:The expected value for the player to play one time in American roulette can be calculated by multiplying the probability of winning by the amount the player wins and subtracting the probability of losing. In this case, the probability of winning is 1/38, since there is one winning number out of the 38 possibilities. The amount the player wins is $35. The probability of losing is 37/38, since there are 37 losing numbers out of the 38 possibilities. Using these values, the expected value can be calculated as follows:
Expected value = (1/38 * $35) - (37/38 * $1) = -$0.0526
Rounded to the nearest cent, the expected value is -$0.05. This means that, on average, the player can expect to lose $0.05 every time they play the game.
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The expected value for a player betting on a single number in American roulette is approximately -$0.03, indicating an average loss of 3 cents per play.
The question asks for the calculation of the expected value for a player betting on a single number in American roulette.
To find the expected value, we consider the winnings and the probability of winning.
In American roulette, there are 38 equally spaced slots with the numbers 00, 0, and 1 through 36, which means the probability of winning for a player when betting on a specific number is 1/38, and the probability of losing is 37/38.
The payoff for a win is $35 plus the return of the original $1 bet, for a total of $36. If the bet is lost, the player loses their $1 bet.
Using these payouts and their associated probabilities, we can calculate the expected value (EV) as follows:
→ EV = (Probability of Winning) × (Winning Amount) + (Probability of Losing) × (Loss Amount)
→ EV = (1/38) × $36 - (37/38) × $1
To calculate the exact value:
→ EV = (1/38) × 36 - (37/38) × 1
→ EV ≈ 0.9474 - 0.9737
→ EV ≈ -$0.0263
When rounding to the nearest cent, the expected value is approximately -$0.03. This means, on average, the player will lose about 3 cents per play.
Jim’s father is older than 40 but younger than 50.If you can divide his age by 2,4,5,8,or 10 ,there will be a remainder of 1. How old is Jim’s father?
Answer:
Step-by-step explanation:
all you have to do is divide each number by 4, 41, 42, 43, 44, 45, 46, 47, 48, 49 ,and 50 until you get a remainder of 1. what I mean is do 2 divided by all the number from 40 50 and do the same with 4,5,8 and 10 until you find one of them that has a remainder of 1. (is a lot of work sorry could't tell you the anwer)
Exhibit 5-11 The random variable x is the number of occurrences of an event over an interval of 10 minutes. It can be assumed the probability of an occurrence is the same in any two time periods of an equal length. It is known that the mean number of occurrences in 10 minutes is 5.3. Refer to Exhibit 5-11. The expected value of the random variable x is
Answer:
The expected value of the random variable x is [tex]E(x) = 5.3[/tex]
Step-by-step explanation:
From the question we are told that
The number of occurance is x
The interval for the x occurance of the event is [tex]t = 10 minutes[/tex]
Generally the expected value is the same as the mean so the expected value the random variable x is
[tex]E(x) = 5.3[/tex]
solve for m m+7=3+m+4 iready
Answer:
m = all real numbers
Step-by-step explanation:
m + 7 = 3 + m + 4m - m = 3 + 4 -70 = 0Using this equation, you end up with 0 = 0. This means that m is all real numbers.
Jennifer starts with a population of 100 amoebas that doubles in size every minute for a number of minutes, m. She writes the expression 100(2m) to find the number of amoeba after m minutes. Nathan starts with a population of 10 amoebas that increases 40% in size every minute for a number of minutes, m. He writes the expression (1+0.4)m to find the number of amoeba after m minutes. Use the drop-down menus to explain what each part of Jennifer's and Nathan's expressions mean.
Answer:
100(2m)
(1+0.4)
Nathan=0.4 is the percent added =the 40 percent added to the 10 amoebas
Jennifer=the first equation is how many total amoebas Jennifer has in total
Hope this helps!Answer:
Hope this helps!
Step-by-step explanation:
A sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10, with 10 corresponding to "completely effective" and 1 corresponding to "completely ineffective". The average rating was 5.6 and the standard deviation was 4.6. Construct a 95% confidence interval for the mean score. 5.2 < μ < 6.0 0 < μ < 5.6 4.6 < μ < 6.6 5.1 < μ < 6.1
Answer:
95% confidence interval for the true mean score is [4.6 , 6.6].
Step-by-step explanation:
We are given that a sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10.
The average rating was 5.6 and the standard deviation was 4.6.
Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average rating = 5.6
s = sample standard deviation = 4.6
n = sample of tobacco smokers = 81
[tex]\mu[/tex] = population mean score
Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.
So, 95% confidence interval for the population mean score, [tex]\mu[/tex] is ;
P(-1.993 < [tex]t_8_0[/tex] < 1.993) = 0.95 {As the critical value of t at 80 degree of
freedom are -1.993 & 1.993 with P = 2.5%}
P(-1.993 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.993) = 0.95
P( [tex]-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.993 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.993 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]5.6-1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] , [tex]5.6+1.993 \times {\frac{4.6}{\sqrt{81} } }[/tex] ]
= [4.6 , 6.6]
Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].
An ice cream machine produced 52 ice creams per minute. After reconditioning, its speed increased to 65 ice creams per minute. By what percent did the speed of the machine increase?
Answer:25 %
Step-by-step explanation:
Given
Earlier machine was producing 52 ice cream per minute and
Now it is Producing 65 ice creams per minute
So percentage increase of the machine [tex]=\frac{\text{final-Initial}}{\text{Initial}}\times 100[/tex]
[tex]=\frac{65-52}{52}\times 100[/tex]
[tex]=\frac{13}{52}\times 100[/tex]
[tex]=\frac{1}{4}\times 100=25\ \%[/tex]
So there is increase of 25 % in speed
265+353=410
124+312=721
410+204=1676
132+230=1021
211+101=?????
Answer:
THIS IS A RIDDLE
Step-by-step explanation:
GO TO THE RIDDLE SECTION
In ΔWXY, w = 880 cm, ∠X=33° and ∠Y=38°. Find the length of y, to the nearest centimeter.
Answer:
[tex]y\approx573cm[/tex]
Step-by-step explanation:
First, take a look to the picture that I attached, however please note the triangle is not drawn to scale, the figure is just to provide visual aid. As you can see the value of [tex]\angle W =109^{\circ}[/tex] this is because of the sum of the interior angles in a triangle is always equal to 180°. So:
[tex]\angle W + \angle X + \angle Y =180\\\\\angle W = 180- \angle X -\angle Y\\\\\angle W =180-38-33\\\\\angle W=109[/tex]
Now, we can use the law of sines, which states:
[tex]\frac{w}{sin(W)} =\frac{x}{sin(X)} =\frac{y}{sin(Y)}[/tex]
Hence:
[tex]\frac{w}{sin(W)} =\frac{y}{sin(Y)}\\\\\frac{880}{sin(109)} =\frac{y}{sin(38)}\\\\Solving\hspace{3}for\hspace{3}y\\\\y=\frac{880*sin(38)}{sin(109)} \\\\y=572.9999518\approx 573 cm[/tex]
Answer:
573 cm
Step-by-step explanation:
Solve the two-step equation and identify the steps.
1.4x + 6.1 = -7.9
1. The first step is to
2. The second step is to
sides.
v on both sides.
von both
The solution is x =
ASAP
Answer:
1. The first step is to subtract 6.1 on both sides.
2. The second step is to divide by 1.4 on both sides.
3. The solution is x = -10
Step-by-step explanation:
I just finished the Egdenuity Assignment
The steps will be
The first step is to subtract 6.1 on both sides.The second step is to divide by 1.4 on both sides.The solution is x = -10How to solve linear equation of one variable?Step-1: we have to balance each side by simplifing the equation
Step-2: add/substract constant term on both side of the equation to separate variable and constant term on both side
Step-3: divide the coefficient of the variable on both side to make the coefficient of the variable 1.
So according to asked question,
1.4x+6.1=-7.9
Step 1: subtract 6.1 on both sides.
1.4x+6.1-6.1=-7.9-6.1
⇒1.4x=-14
Step 2: divide by 1.4 on both of the sides.
1.4x/1.4=-14/1.4
⇒x=-10
Therefore,
The steps will be
The first step is to subtract 6.1 on both of the sides.The second step is to divide by 1.4 on both of the sides.The solution is x = -10.Learn more about linear equation of one variable
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what is the value of x?
Answer:
see below
Step-by-step explanation:
x and 80 are adjacent, supplementary angles
Supplementary angles add to 180
x+80 =180 degrees
Subtract 80 from each side
x+80-80=180-80
x=100