To build a series for the given function f(x) = (e^(2x) - 1 - 2x)/2x^2, we can start by finding the MacLaurin series for e^(2x) and then manipulate it to obtain the desired series.
The MacLaurin series for e^(2x) is given by:
e^(2x) = Σ (2x)^n / n! for n = 0 to ∞
Expanding the series, we get:
e^(2x) = 1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...
Now, we can substitute this back into the original function:
f(x) = (e^(2x) - 1 - 2x)/2x^2 = (1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ... - 1 - 2x) / 2x^2
Simplifying, we have:
f(x) = (2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...) / 2x^2
Now, we can divide by 2x^2 to obtain the series for f(x):
f(x) = 1/2! + 2x/3! + 2^3x^2/4! + 2^4x^3/5! + ...
Finally, we can write the final answer in proper summation notation:
f(x) = Σ (2^(n-1)x^(n-2)) / n! for n = 2 to ∞
To begin, we can write f(x) as:
f(x) = (1/2x^2)[e^(2x) - 1 - 2x]
Next, we will use the Maclaurin series for e^x, which is:
e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...
Substituting 2x for x, we have:
e^(2x) = 1 + 2x + (4x^2)/2! + (8x^3)/3! + ...
Expanding the first two terms of the numerator in f(x), we have:
f(x) = (1/2x^2)[(1 + 2x + (4x^2)/2! + (8x^3)/3! + ...) - 1 - 2x]
Simplifying, we get:
f(x) = (1/2x^2)[2x + (4x^2)/2! + (8x^3)/3! + ...]
Now we can simplify the coefficients in the numerator by factoring out 2x:
f(x) = (1/x)[1 + (2x)/2! + (4x^2)/3! + ...]
Finally, we can write the series in summation notation:
f(x) = Σ[(2n)!/(2^n*n!)]x^n, n=1 to infinity.
To learn more about function visit;
brainly.com/question/12431044
#SPJ11
7 2 14 3 8 11 5 each time a card is picked it is replaced estimate the expected number of even numbers picked in 35 picks
We can estimate that the expected number of even numbers picked in 35 picks is 15.
To estimate the expected number of even numbers picked in 35 picks, we need to first understand the probability of picking an even number in one pick. Out of the seven given numbers, there are three even numbers (2, 14, 8) and four odd numbers (7, 3, 11, 5). Therefore, the probability of picking an even number in one pick is 3/7.
To find the expected number of even numbers picked in 35 picks, we can multiply the probability of picking an even number in one pick (3/7) by the number of picks (35).
Expected number of even numbers picked = (3/7) x 35 = 15
Therefore, we can estimate that the expected number of even numbers picked in 35 picks is 15. This means that if we were to repeat the process of picking a card and replacing it 35 times, we would expect to pick 15 even numbers on average.
It is important to note that this is an estimate and the actual number of even numbers picked may vary. However, this estimation gives us a good idea of what to expect on average.
To know more about expected, visit:
https://brainly.com/question/30456668#
#SPJ11
Brian deposited $9,083 into a savings account for which interest is compounded quarterly at a rate of 2.90%. How much interest will he earn after 6 years? Round answer to the hundredths place. If answer does not have a hundredths place then include zeros so it does. Do not include units in the answer. Be sure to attach your work for credit.
Using the compound interest formula, the interest Brian will earn after 6 years is: $2,347.22.
How to Calculate Compound Interest?We can use the formula for compound interest to calculate the interest earned by Brian:
A = P (1 + r/n)^(nt)
where:
A = the amount after t years
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time in years
In this case, P = $9,083, r = 2.90% or 0.029, n = 4 (since interest is compounded quarterly), and t = 6.
So,
A = 9083(1 + 0.029/4)^(4*6)
= $11,430.22
The interest earned will be the difference between the amount after 6 years and the initial investment:
Interest = A - P = $11,430.22 - $9,083 = $2,347.22
Therefore, Brian will earn $2,347.22 in interest after 6 years.
Learn more about compound interest on:
https://brainly.com/question/24274034
#SPJ1
Casey recently purchased a sedan and a pickup truck at about the same time for a new business. The value of the sedan S, in dollars, as a function of the number of years t after the purchase can be represented by the equation S(t)=24,400(0. 82)^t. The equation P(t)=35,900(0. 71)^t/2 represents the value of the pickup truck P, in dollars, t years after the purchase. Analyze the functions S(t) and P(t) to interpret the parameters of each function, including the coefficient and the base. Then use the interpretations to make a comparison on how the value of the sedan and the value of the pickup truck change over time
Answer: Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.
Step-by-step explanation:
The functions S(t) and P(t) represent the value of the sedan and pickup truck, respectively, as a function of time t in years since the purchase. Let's analyze each function:
For S(t)=24,400(0.82)^t, the coefficient 24,400 represents the initial value or starting point of the function. This means that the value of the sedan at the time of purchase was $24,400.
The base 0.82 represents the rate of depreciation or decrease in value of the sedan over time. Specifically, the sedan's value decreases by 18% per year (100% - 82%).
For P(t)=35,900(0.71)^t/2, the coefficient 35,900 represents the initial value or starting point of the function.
This means that the value of the pickup truck at the time of purchase was $35,900. The base 0.71 represents the rate of depreciation or decrease in value of the pickup truck over time.
Specifically, the pickup truck's value decreases by approximately 29% every two years, since the exponent is divided by 2.
Comparing the two functions, we can see that the initial value of the pickup truck was higher than the initial value of the sedan.
However, the rate of depreciation of the pickup truck is greater than that of the sedan. This means that the pickup truck will lose its value at a faster rate than the sedan.
For example, after 5 years, we can evaluate each function to see the values of the sedan and pickup truck at that time:
S(5) = 24,400(0.82)^5 ≈ $10,373.67
P(5) = 35,900(0.71)^(5/2) ≈ $15,864.48
We can see that after 5 years, the pickup truck is still worth more than the sedan, but its value has decreased by a greater percentage. Specifically, the pickup truck has lost about 56% of its value compared to the initial value, while the sedan has lost about 58% of its value.
To know more about initial value refer here
https://brainly.com/question/29081397#
#SPJ11
22. Look at the given triangles.
4x + 2
7x+7
X+3
2x-5
x+7
5x-4
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
c. Find the perimeter for each triangle when x = 3
Two triangles have perimeters that can be expressed as 12x + 12 and 8x - 2, with a difference of 4x + 14, and have perimeters of 47 and 28 when x = 3.
a. The perimeter of each triangle can be found by adding up the lengths of all three sides:
Triangle 1: (4x+2) + (7x+7) + (x+3) = 12x + 12
Triangle 2: (2x-5) + (x+7) + (5x-4) = 8x - 2
b. To find the difference in perimeter between the larger triangle and the smaller triangle, we can subtract the smaller perimeter from the larger perimeter:
(12x + 12) - (8x - 2) = 4x + 14
c. To find the perimeter for each triangle when x = 3, we can substitute x = 3 into the expressions found in part (a):
Triangle 1: (4(3)+2) + (7(3)+7) + (3+3) = 47
Triangle 2: (2(3)-5) + (3+7) + (5(3)-4) = 28
Therefore, the perimeter of Triangle 1 is 47 units and the perimeter of Triangle 2 is 28 units when x = 3.
Learn more about perimeter click;
brainly.com/question/6465134
#SPJ1
BRANLIEST!!
Three coins are tossed. Let the event H = all Heads and the event K = at least one Heads.
1. 7/8 P(K) =
2. 1/7 The probability that the outcome is all heads if at least one coin shows a head
3. 1/8 P(H∩K) =
The probability that the outcome is all heads if at least one coin shows a head is 8/49.
How to find the probability?To solve these problems, we'll use the basic principles of probability.
The probability of an event K (at least one head) can be calculated by subtracting the probability of the complement of K (no heads) from 1.
Since the coins can either show all heads or not, the complement of K is the event of no heads, which is denoted as T (tails for all coins). Therefore, we have:
P(K) = 1 - P(T)
Each coin toss is independent, and the probability of getting tails on a single toss is 1/2. Since there are three coins tossed independently, we multiply the probabilities together:
P(T) = ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) * ([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{8}[/tex]
Substituting this into the equation for P(K):
P(K) = 1 - P(T) = 1 - [tex]\frac{1}{8}[/tex] = [tex]\frac{7}{8}[/tex]
So, the probability of event K (at least one head) is [tex]\frac{7}{8}[/tex].
The probability that the outcome is all heads if at least one coin shows a head can be calculated using conditional probability. We want to find P(H | K), which represents the probability of event H (all heads) given event K (at least one head).
The formula for conditional probability is:
P(H | K) = [tex]\frac{P(H \∩ K) }{ P(K)}[/tex]
To find P(H∩K), we need to determine the probability of the intersection of events H and K (i.e., the probability of getting all heads and at least one head).
Since H is a subset of K (if all coins show heads, then at least one head is shown), we have:
P(H∩K) = P(H)
Therefore, P(H∩K) is the same as P(H). According to the problem, P(H) = [tex]\frac{1}{7}[/tex].
Now, substituting P(H∩K) = P(H) and P(K) = [tex]\frac{7}{8}[/tex] into the conditional probability formula:
P(H | K) = [tex]\frac{P(H\∩K) }{ P(K)}[/tex] = ([tex]\frac{1}{7}[/tex]) / ([tex]\frac{7}{8}[/tex]) = ([tex]\frac{1}{7}[/tex]) * ([tex]\frac{8}{7}[/tex]) = [tex]\frac{8}{49}[/tex]
So, the probability that the outcome is all heads if at least one coin shows a head is [tex]\frac{8}{49}[/tex].
To summarize:
P(K) = [tex]\frac{7}{8}[/tex]
P(H | K) = [tex]\frac{8}{49}[/tex]
P(H∩K) = [tex]\frac{1}{7}[/tex]
Learn more about probability.
brainly.com/question/30034780
#SPJ11
the temperature is -7. Since midnight the temperature tripled and then rose 5 degrees. What was the temperature at midnight?
Taking the data into consideration, we can calculate and conclude that the temperature at midnight was -4, through the use of an equation.
How to find the temperatureAccording to the prompt, the temperature is now -7. We also know that, since midnight, the temperature tripled and then rose 5 degrees.If we let x be the temperature at midnight, then we can set up the following equation:
3x + 5 = -7
Subtracting 5 from both sides, we get:
3x = -12
Dividing by 3, we get:
x = -4
Therefore, the temperature at midnight was -4 degrees. With that in mind, we conclude we have correctly answered this question.
Learn more about equations here:
https://brainly.com/question/2972832
#SPJ1
A new laptop is on sale for $550 dollars. To pay for it you place it on your credit card which charges 12% percent interest each month. Complete the table to determine the total cost of the laptop each month if you make no payments
To determine the total cost of the laptop each month if you make no payments, we need to calculate the balance on the credit card after each month, including the simple interest charged.
Starting balance = $550
Month Balance Interest Total Cost
0 $550 $0 $550
1 $616 $66 $616 + $66 = $682
2 $689.92 $73.92 $689.92 + $73.92 = $763.84
3 $770.15 $80.23 $770.15 + $80.23 = $850.38
4 $857.09 $86.94 $857.09 + $86.94 = $944.03
5 $951.19 $94.10 $951.19 + $94.10 = $1045.29
To calculate the balance for each month, we multiply the previous balance by 1.12, which represents the 12% interest charged. For example, for month 1, the balance is $550 * 1.12 = $616.
To calculate the interest charged each month, we subtract the previous balance from the new balance. For example, for month 1, the interest charged is $616 - $550 = $66.
To calculate the total cost each month, we add the new balance to the interest charged.
For example, for month 1, the total cost is $616 + $66 = $682.
Note that if you make no payments on the credit card, the balance will continue to grow each month due to the interest charged.
It is always advisable to make at least the minimum payment each month to avoid high interest charges and potential late fees.
To learn more about simple intrest go to:
https://brainly.com/question/25845758?referrer=searchResults
#SPJ11
A cistern is to be built of cement. The walls and bottom will be 1 foot thick. The outer height will be 20 feet. The inner diameter will be 10 feet. To the nearest cubic foot, how much cement will be needed for the job? Use 3. 14 for π
847 cubic feet of cement will be needed for the job.
To find the amount of cement needed for the cistern, we need to calculate the difference in volume between the outer and inner cylinders.
First, let's find the volume of the outer cylinder:
Outer radius (R) = (Inner diameter + 2 * Wall thickness) / 2 = (10 + 2 * 1) / 2 = 6 feet
Outer height (H) = 20 feet
Outer cylinder volume (V1) = π * R^2 * H = 3.14 * 6^2 * 20 = 3.14 * 36 * 20 ≈ 2260.96 cubic feet
Next, let's find the volume of the inner cylinder:
Inner radius (r) = Inner diameter / 2 = 10 / 2 = 5 feet
Inner height (h) = Outer height - 2 * Wall thickness = 20 - 2 * 1 = 18 feet
Inner cylinder volume (V2) = π * r^2 * h = 3.14 * 5^2 * 18 = 3.14 * 25 * 18 ≈ 1413.72 cubic feet
Finally, subtract the inner cylinder volume from the outer cylinder volume to find the amount of cement needed:
Cement volume = V1 - V2 ≈ 2260.96 - 1413.72 ≈ 847.24 cubic feet
To the nearest cubic foot, approximately 847 cubic feet of cement will be needed for the job.
To learn more about volume, refer below:
https://brainly.com/question/1578538
#SPJ11
Match the term to its description.
Match Term Definition
Elliptical galaxy A) Has a large flattened core
Galaxy B) Forms a perfect sphere or an ellipse and is flattened to some degree
Lens galaxy C) Has a central core from which curved arms spiral outward
Spiral galaxy D) Is a collection of several billion stars and interstellar matter isolated in space
The type of galaxy matched to its description.
Elliptical galaxy: B) Forms a perfect sphere or an ellipse and is flattened to some degree
Galaxy: D) Is a collection of several billion stars and interstellar matter isolated in space
Lens galaxy: A) Has a large flattened core
Spiral galaxy: C) Has a central core from which curved arms spiral outward
Elliptical galaxy: An elliptical galaxy is a type of galaxy that typically forms a perfect sphere or an ellipse shape. It is characterized by its smooth and featureless appearance, lacking the distinct spiral arms seen in spiral galaxies. Elliptical galaxies often have a flattened shape due to their rotation and gravitational interactions with other galaxies.
Galaxy: A galaxy refers to a vast collection of stars, interstellar gas, dust, and dark matter, all held together by gravity. Galaxies come in various shapes and sizes, and they can contain billions or even trillions of stars. They are the building blocks of the universe and are distributed throughout the cosmos.
Lens galaxy: A lens galaxy is a type of galaxy that has a large flattened core. It gets its name from the gravitational lensing effect it produces. Gravitational lensing occurs when the gravitational field of the lens galaxy bends and distorts the light from objects behind it, creating a lens-like effect.
Spiral galaxy: A spiral galaxy is a type of galaxy that has a central core or bulge from which curved arms spiral outward. These arms are made up of stars, gas, and dust, and they give spiral galaxies their distinct appearance. Spiral galaxies often have a flattened disk shape with a central bulge and extended arms that can stretch out across the disk.
Learn more about the galaxy:
https://brainly.com/question/17117676
#SPJ11
Alguien q pueda explicar esto
To add fractions with unlike denominators, we need to find the least common multiple of the denominators. In this case, the least common multiple of 3 and 4 is 12. So, we must find equivalents of each fraction with a denominator of 12.
How to add the fractions?To add fractions with unlike denominators, we need to find the least common multiple of the denominators. In this case, the least common multiple of 3 and 4 is 12. So, we must find equivalents of each fraction with a denominator of 12.
Multiplying the numerator and denominator of 2/3 by 4, we get 8/12. On the other hand, multiplying the numerator and denominator of 1/4 by 3, we get 3/12.
Therefore, we can rewrite the sum as:
8/12 + 3/12
And adding the numerators, we get:
11/12
So, 2/3 + 1/4 = 11/12.
The final answer is a proper fraction, which means that the numerator is less than the denominator, and can be further simplified if necessary.
Learn more about fractions at: https://brainly.com/question/10354322
#SPJ1
50 POINTS ASAP Use the image to determine the type of transformation shown.
image of polygon ABCD and a second polygon A prime B prime C prime D prime above it
180° clockwise rotation
Horizontal translation
Reflection across the x-axis
Vertical translation
Since polygon A prime B prime C prime D prime above is above the image of polygon ABCD, the type of transformation shown is: D. vertical translation.
What is a transformation?In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a function or object is transformed, all of its points would also be transformed.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.Read more on function and translation here: brainly.com/question/31559256
#SPJ1
Answer:
Vertical translation
Step-by-step explanation:
I am in the middle of taking the quiz and belive this is the correct answer!
Please help it would be amazing if you knew this
The solution of the composite function, (f + g)(x) is 8x + 7
How to solve function?A function relates input and output. In other words, a function is a special relationship among the inputs (independent variable) and their outputs (dependent variable).
A composite function is a function that depends on another function.
Therefore, let's solve the composite function
f(x) = x + 3
g(x) = 7x + 4
Hence,
(f + g)(x) can be solved as follows:
(f + g)(x) = f(x) + g(x)
(f + g)(x) = x + 3 + 7x + 4
combine like terms
(f + g)(x) = x + 7x + 3 + 4
(f + g)(x) = 8x + 7
learn more on function here: brainly.com/question/29153126
#SPJ1
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 19. 1 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 18. 1, 21. 1, 22. 1, 23. 1, 21. 1, 27. 1, and 27. 1 pounds. If α = 0. 200, what is the critical value? The population standard deviation is unknown
Since the population standard deviation is unknown, we use a t-distribution to find the critical value. The degrees of freedom for the t-distribution is n-1, where n is the sample size. In this case, n = 7, so the degrees of freedom is 7-1 = 6. The critical value for a t-distribution with 6 degrees of freedom and a significance level of α = 0.200 (two-tailed) can be found using a t-table or calculator. The critical value is approximately ±1.94.
A line is described by the equation y=3/5x+4/7 in slope intercept form identify the slope and y-intercept to the line
The slope of the line is 3/5 and the y-intercept is 4/7.
What is the slope and y-intercept of the line given by the equation y = 3/5x + 4/7 in slope-intercept form?The equation of the line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
In this form, the slope of the line tells us how steeply the line is rising or falling, while the y-intercept tells us where the line crosses the y-axis.
In the given equation y = 3/5x + 4/7, we can see that the coefficient of x, 3/5, is the slope of the line. This means that for every 1 unit increase in x, the line will increase by 3/5 units in y.
A positive slope means that the line is rising from left to right, while a negative slope means that the line is falling.
We can also see that the constant term, 4/7, is the y-intercept of the line. This tells us that the line crosses the y-axis at the point (0, 4/7). In other words, when x is 0, y is equal to 4/7.
So, to summarize, the slope of the line y = 3/5x + 4/7 is 3/5, which means the line rises 3 units for every 5 units it moves to the right.
The y-intercept is 4/7, which tells us the line crosses the y-axis at the point (0, 4/7).
Learn more about slope intercept form
brainly.com/question/29146348
#SPJ11
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an Interval, enter your answer using interval notation. If the Interval of convergence is a finite set, enter your answer using set notation.)
Sum = (n!(x+5)^n) / 1 . 3 . 5 ...... (2n-1)
To find the interval of convergence of the power series, we can use the ratio test:
lim (n->inf) |((n+1)!(x+5)^(n+1)) / (1.3.5....(2n+1))| / |(n!(x+5)^n) / (1.3.5....(2n-1))|
= lim (n->inf) |(x+5)(2n+1)| / (2n+2) = |x+5| lim (n->inf) (2n+1)/(2n+2) = |x+5|
So the series converges if |x+5| < 1, and diverges if |x+5| > 1. Thus the interval of convergence is (-6, -4).
To check for convergence at the endpoints, we can use the limit comparison test with the divergent series:
1/1.3 + 1/1.3.5 + 1/1.3.5.7 + ... = sum (2n-1) terms = inf
At x = -6, we have:
sum (n=0 to inf) (n!(-1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = inf
Since the series diverges at x = -6, the interval of convergence is (-6, -4] using set notation.
At x = -4, we have:
sum (n=0 to inf) (n!(1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = 1 - 1/3 + 1/15 - 1/105 + ...
This is an alternating series that satisfies the conditions of the alternating series test, so it converges. Thus the interval of convergence is (-6, -4] using set notation, or [-6, -4) using interval notation.
To find the interval of convergence of the power series, we'll use the Ratio Test, which states that if the limit L = lim(n→∞) |aₙ₊₁/aₙ| < 1, then the series converges. Here, the series is given by:
Σ(n!(x+5)^n) / 1 . 3 . 5 ... (2n-1)
Let's find the limit L:
L = lim(n→∞) |(aₙ₊₁/aₙ)|
= lim(n→∞) |((n+1)!(x+5)^(n+1))/(1 . 3 . 5 ... (2(n+1)-1)) * (1 . 3 . 5 ... (2n-1))/(n!(x+5)^n)|
Now, simplify the expression:
L = lim(n→∞) |(n+1)(x+5)/((2n+1))|
For the series to converge, we need L < 1:
|(n+1)(x+5)/((2n+1))| < 1
As n approaches infinity, the above inequality reduces to:
|x+5| < 1
Now, to find the interval of convergence, we need to solve for x:
-1 < x + 5 < 1
-6 < x < -4
The interval of convergence is given by the interval notation (-6, -4). To check the endpoints, we need to substitute x = -6 and x = -4 back into the original series and use other convergence tests such as the Alternating Series Test or the Integral Test. However, the power series will diverge at the endpoints, as the terms do not approach 0. Therefore, the interval of convergence remains (-6, -4).
Learn more about interval of convergence here: brainly.com/question/14394994
#SPJ11
How do I solve this?
Step-by-step explanation:
you can solve cos(u) by
cos(u) = adjecent / hypotenes...general formula of cos
cos(u) = √44 / 12
cos(u) = 2√11 / 12 ..... √44 = √4×11 = 2√11
cos(u) = √11 / 6
u = cos^-1 ( √11 / 6 ) ..... divided both aide by cos ( multiple by cos invers )
u = 56.442 .... so we get it's angle
Answer:
[tex]cos(U)=\frac{\sqrt{11} }{6}[/tex]
Step-by-step explanation:
In a right triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, we have:
cos(U) = adjacent/hypotenuse = TU/SU
We are given that TU = sqrt(44) and SU = 12, so:
cos(U) = sqrt(44)/12
To simplify this expression, we can first factor 44 into 4 * 11, since 4 is a perfect square and a factor of 44:
cos(U) = sqrt(4 * 11) / 12
cos(U) = (sqrt (4) * sqrt (11)) / 12
cos (U) = (2 * sqrt (11)) / 12
Simplifying the fraction by dividing both the numerator and denominator by 2, we get:
cos(U) = sqrt(11)/6
Therefore, the exact value of cos(U) in simplest radical form is sqrt(11)/6
Furthermore, if you want another way to write the answer, dividing by 6 is the same as multiplying by 1/6 so you can do cos (U) = 1/6 * sqrt (11)
Although the other individual was correct that you use inverse trig (cos ^ -1) to find the measure of U, getting an exact answer requires us to leave it in simplest radical form since the number is so large and at best will yield an approximation if you don't keep it in simplest radical form.
How much simple interest is earned on $1,272 deposited in a bank for 20 years at 3% annual interest rate?
The simple interest earned on $1,272 deposited in a bank for 20 years at 3% annual interest rate is $764.40.
To calculate the simple interest earned on a principal amount deposited in a bank, we use the formula:
Simple Interest = (Principal) x (Rate) x (Time)
where the rate is the annual interest rate, and the time is the number of years the money is deposited.
In this case, the principal is $1,272, the rate is 3%, and the time is 20 years.
Plugging in these values into the formula, we get:
Simple Interest = (1272) x (0.03) x (20)
Simple Interest = $764.40
Therefore, the simple interest earned on $1,272 deposited in a bank for 20 years at 3% annual interest rate is $764.40.
To learn more about interest, click here:
https://brainly.com/question/13324776
#SPJ11
at the end of practice, there are 240 ounces of sports drink left in the cooler. every player had some sports drink from the cooler. based on the equation y = 648 - 24x, how many players were at practice?
10
15
17
21
Answer: 17 or C
Step-by-step explanation:
24 times 17 is 408 and 648 - 408 is 240 ounces
The water hose fills A bucket at 1/3 per minute how many minutes does it take to fill a 2 gallon bucket
It will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
To determine the time required to fill a 2-gallon bucket using a water hose that fills at a rate of 1/3 gallon per minute, you can use a simple calculation.
First, identify the fill rate of the hose, which is 1/3 gallon per minute. Now, consider the bucket's capacity, which is 2 gallons. To find out how many minutes it takes to fill the bucket, divide the total capacity of the bucket by the fill rate:
Time (minutes) = Bucket capacity (gallons) / Fill rate (gallons per minute)
In this case:
Time (minutes) = 2 gallons / (1/3 gallons per minute)
To solve this, you can multiply the numerator and denominator by the reciprocal of the fill rate:
Time (minutes) = 2 gallons * (3 minutes per gallon)
Time (minutes) = 6 minutes
So, it will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
To know more about fill rate, refer to the link below:
https://brainly.com/question/14821930#
#SPJ11
What is the maximum volume of a square pyramid that can fit into a cube with a side length of 30cm ?
A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 30 cm x 30 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 30 cm ).
The volume of the pyramid:
V = 1/3 · 30² · 30 = 1/3 · 900 · 30 = 9,000 cm³
Answer:The maximum volume of the pyramid is 9,000 cm³.
The difference of two rational numbers is 17/28,if the small rational number is -9/14 find the other
Step-by-step explanation:
Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:
x - (-9/14) = 17/28
Simplifying the left-hand side:
x + 9/14 = 17/28
Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:
28(x + 9/14) = 28(17/28)
Simplifying:
4(2x + 9) = 17
Expanding:
8x + 36 = 17
Subtracting 36 from both sides:
8x = -19
Dividing by 8:
x = -19/8
Therefore, the other rational number is -19/8.
Bharat sent a chain letter to his friends, asking them to forward the letter to more friends. The relationship between the elapsed time ttt, in days, since Bharat sent the letter, and the number of people, P(t)P(t)P, left parenthesis, t, right parenthesis, who receive the email is modeled by the following function: P(t)=2401⋅(87)t1. 75
The exponential term (87^t)^(1.75) increases, leading to an exponential growth in the number of people who receive the email.
The relationship between the elapsed time t, in days, since Bharat sent the letter and the number of people P(t) who receive the email is modeled by the following function:
P(t) = 2401 * (87^t)^(1.75)
In this function, t represents the number of days that have passed since Bharat sent the letter, and P(t) represents the number of people who receive the email at that time.
The function is an exponential growth model where the base is 87, and the exponent is t raised to the power of 1.75. The constant 2401 is a scaling factor that determines the initial number of people who receive the email at t=0.
As time passes, the exponential term (87^t)^(1.75) increases, leading to an exponential growth in the number of people who receive the email.
To know more about exponential , refer here :
https://brainly.com/question/12490064#
#SPJ11
which number is equal to 7 hundred thousands 4 thousands 3 tens and 6 ones?
The number that is equal to the place values, 7 hundred thousands 4 thousands 3 tens and 6 ones, is 704,036
Place value: Determining the number that is equal to the place valuesFrom the question, we are to determine the number that is equal to the given place values
From the given information, the given place value is
7 hundred thousands 4 thousands 3 tens and 6 ones
Now, we will write each of the values in figures
7 hundred thousands = 700,000
4 thousands = 4,000
3 tens = 30
6 ones = 6
To determine the number that is equal to the place values, we will sum all the digits
700,000 + 4,000 + 30 + 6
704,036
Hence,
The number that is equal to the place value is 704,036
Learn more on Place value here: https://brainly.com/question/17180368
#SPJ1
Please help asap! thank you!
solve the system of equations:
6x / 5 + y / 15 = 2.3
x / 10 - 2y / 3 = 1.2
(the slashes represent fractions.)
The solution of the given system of equations is x = 3.2 and y = 1.5.
To solve this system of equations, we can use the method of elimination, where we eliminate one of the variables by adding or subtracting the equations.
First, let's eliminate y by multiplying the first equation by 2 and the second equation by 15:
12x/5 + 2y/15 = 4.6 (multiply the first equation by 2)
3x/2 - 10y = 18 (multiply the second equation by 15)
Now we can eliminate y by multiplying the first equation by 5 and adding it to the second equation:
12x + y/5 = 23 (multiply the first equation by 5 and simplify)
12x - y = 54 (subtract the second equation from the previous equation)
Adding the two equations, we get:
24x = 77
Therefore, x = 77/24.
Substituting x = 77/24 into the first equation, we get:
6(77/24)/5 + y/15 = 2.3
Simplifying this equation, we get:
y = 1.5
To know more about system of equations, refer here:
https://brainly.com/question/21620502#
#SPJ11
Determine the equation of the circle graphed below.
The equation of the circle graphed is given as follows:
(x + 1)² + (y + 3)² = 36.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle.
The coordinates of the center of the circle are given as follows:
(-1, -3).
The radius of the circle is given as follows:
r = 6 units.
Then the equation of the circle is given as follows:
(x + 1)² + (y + 3)² = 36.
More can be learned about the equation of a circle at https://brainly.com/question/1506955
#SPJ1
There are 43 children at a school. they want to make teams with 8 children on each team for kickball. one of the children goes home. how many complete teams can they make? explain.
Answer:
They can make 5 complete teams of 8 children even after one child goes home.
Step-by-step explanation:
If there are 43 children and they want to make teams of 8, we can find out how many complete teams they can make by dividing the total number of children by the number of children per team:
43 ÷ 8 = 5 remainder 3This means that they can make 5 complete teams of 8 children, with 3 children left over.
However, since one child goes home, there are only 42 children left. We can repeat the division:
42 ÷ 8 = 5 remainder 2This means that they can make 5 complete teams of 8 children, with 2 children left over. Therefore, they can make 5 complete teams of 8 children even after one child goes home.
(- 3 / (2/5)), - 1/2 please someone slove this answer
Answer:
The answer is -8
Step-by-step explanation:
Here's a key
()= Do first
/ = Divide
If something is outside the () and there is no symbol then multiply.
What is the perimeter of the triangle below
Answer:
16.7 units
Step-by-step explanation:
its a 45°-45°-90° right triangle, so n1=4.9
r=4.9[tex]\sqrt{2}[/tex] =6.9
perimeter = 4.9+4.9+6.9=16.7 units
We collected data from 9th and 10th. 9th grade students were 45% of the responses and 10th grade were the
rest. Of the 9th graders 31% said they did like the school lunches and 42% of the 10th graders said they did like
the school lunches. Find the probability that if we chose a student at random that they would not like the school
lunches.
Answer is 64.05% probability that if we chose a student at random
To find the probability that a randomly chosen student would not like the school lunches, we need to find the complement of the probability that they do like the school lunches.
The proportion of 9th graders in the sample is 45%, so the proportion of 10th graders is 100% - 45% = 55%.
Of the 9th graders, 31% said they liked the school lunches, so the proportion that did not like them is 100% - 31% = 69%.
Of the 10th graders, 42% said they liked the school lunches, so the proportion that did not like them is 100% - 42% = 58%.
So, the probability that a randomly chosen student would not like the school lunches is:
(0.45 * 0.69) + (0.55 * 0.58) = 0.6405 or 64.05% (rounded to two decimal places).
Therefore, there is a 64.05% probability that if we chose a student at random, they would not like the school lunches.
To know more about probability:
https://brainly.com/question/251701
#SPJ11
Can someone answer this, please?
[tex]\sf y =\dfrac{2}{5}x-4[/tex]
Step-by-step explanation:
Slope intercept form:To find the equation of the required line, first we need to find the slope of the given line in the graph.
Choose two points from the graph.
(0 ,4) x₁ = 0 & y₁ = 4
(2,-1) x₂ = 2 & y₂ = -1
[tex]\sf \boxed{\sf \bf Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-1-4}{2-0}\\\\=\dfrac{-5}{2}[/tex]
[tex]\sf m_1=\dfrac{-5}{2}[/tex]
[tex]\sf \text{Slope of the perpendicular line m = $\dfrac{-1}{m_1}$}[/tex]
[tex]\sf = -1 \div \dfrac{-5}{2}\\\\=-1 * \dfrac{-2}{5}\\\\=\dfrac{2}{5}[/tex]
[tex]\boxed{\sf slope \ intercept \ form \ : \ y = mx + b}[/tex]
Here, m is slope and b is y-intercept.
Substitute the m value in the above equation,
[tex]\sf y =\dfrac{2}{5}x + b[/tex]
The line is passing through (5 , -2),
[tex]\sf -2 = \dfrac{2}{5}*5+b[/tex]
-2 = 2 + b
-2 - 2 = b
b = -4
Slope-intercept form:
[tex]\sf y = \dfrac{2}{5}x-4[/tex]