As per the concept of integral, the series ∑ne⁻ⁿ converges.
Let's consider the series ∑ne⁻ⁿ. Since each term of the series is positive, the first condition of the Integral Test is satisfied. To check the second condition, we need to determine whether the function f(x) = xe⁻ˣ is decreasing for x ≥ 1.
To do this, we can take the derivative of f(x) with respect to x:
f'(x) = e⁻ˣ - xe⁻ˣ
Setting f'(x) = 0, we get:
e⁻ˣ - xe⁻ˣ = 0
x = 1
So f(x) has a maximum value at x = 1. Since f'(x) < 0 for x ≥ 1, f(x) is decreasing for x ≥ 1.
Now, we can set up the corresponding integral:
∫₁^∞ xe⁻ˣ dx
To evaluate this integral, we can use integration by parts:
u = x, dv = e⁻ˣ dx
du = dx, v = -e⁻ˣ
∫₁^∞ xe⁻ˣ dx = -xe⁻ˣ │₁^∞ + ∫₁^∞ e⁻ˣ dx
= 0 + e⁻ˣ │₁^∞
= 1
Since the integral converges, the series ∑ne⁻ⁿ also converges by the Integral Test.
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Complete Question:
How do you use the Integral Test to determine convergence or divergence of the series: ∑ne⁻ⁿ from n=1 to infinity?
A popular phone company states that teens only use their phones for 1.5 years or less before upgrading to a new phone. Your mother believes that teens only upgrade after 1.5 years. State the null and alternative hypothesis for the scenario using math symbols and words.
The null and alternative hypothesis for the given scenario is (H0: μ ≤ 1.5) and (Ha: μ > 1.5).
What are the null and alternative hypotheses?The null hypothesis states that a population parameter is equal to a value. The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.
Null Hypothesis (H0): The average time that teens use their phones before upgrading is 1.5 years or less (H0: μ ≤ 1.5).
Alternative Hypothesis (Ha): The average time that teens use their phones before upgrading is more than 1.5 years (Ha: μ > 1.5).
In words, the null hypothesis states that the average time that teens use their phones before upgrading is 1.5 years or less, which is consistent with the statement made by the phone company.
The alternative hypothesis states that the average time is more than 1.5 years, which is consistent with your mother's belief.
We use the symbol μ to represent the population means of the time that teens use their phones before upgrading.
Hence, the null and alternative hypothesis for the given scenario is (H0: μ ≤ 1.5) and (Ha: μ > 1.5).
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Find the derivative using the chain rule of the following:
f(X)= (1 + x^4-1/x)^5/3
The derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).
To find the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule, we need to use the following steps:
1. Identify the inner function and the outer function. In this case, the inner function is 1 + x^4 - 1/x and the outer function is ( )^5/3.
2. Find the derivative of the outer function with respect to the inner function. This is done by using the power rule: (5/3)( )^2/3.
3. Find the derivative of the inner function with respect to x. This is done by using the power rule and the quotient rule: 4x^3 + 1/x^2.
4. Multiply the derivative of the outer function and the derivative of the inner function together to get the derivative of the original function: (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).
Therefore, the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule is (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).
Here is the answer formatted in HTML:
To find the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule, we need to use the following steps:
Identify the inner function and the outer function. In this case, the inner function is 1 + x4 - 1/x and the outer function is ( )5/3.Find the derivative of the outer function with respect to the inner function. This is done by using the power rule: (5/3)( )2/3.Find the derivative of the inner function with respect to x. This is done by using the power rule and the quotient rule: 4x3 + 1/x2.Multiply the derivative of the outer function and the derivative of the inner function together to get the derivative of the original function: (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).Therefore, the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).
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Suppose that $$18,000 is deposited for five years at 5% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.
The interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually.
To calculate the interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually, we will use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Plugging in the given values:
A = 18,000(1 + 0.05/2)^(2*5)
A = 18,000(1.025)^10
A = 23,386.28
To find the interest earned, we subtract the initial investment from the final amount:
Interest earned = A - P
Interest earned = 23,386.28 - 18,000
Interest earned = $5,386.28
Therefore, the interest earned on a deposit of $18,000 for five years at 5% APR compounded semiannually is $5,386.28.
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Срочно помогите про практической задание сделать)
Найти решение уравнения x^3+2x+4=0 c точностью Ɛ=0,01 методом деления отрезка пополам.
Answer:
Для применения метода деления отрезка пополам нужно использовать тот факт, что функция x^3 + 2x + 4 непрерывна на всей числовой оси. Кроме того, нужно заметить, что функция монотонно возрастает на всей числовой оси, так как ее производная 3x^2 + 2 всегда положительна.
Начнем с интервала [a, b], где a = -2 и b = 0. Тогда значение функции в точке a равно -4, а значение функции в точке b равно 4. Значит, на этом интервале есть хотя бы один корень уравнения x^3 + 2x + 4 = 0.
Посередине интервала [a, b] находим точку c = (a + b) / 2 = -1. Значение функции в точке c равно 1, то есть на интервале [c, b] нет корней уравнения.
Затем выбираем интервал [a, c] и повторяем процесс. Находим точку d = (a + c) / 2 = -1.5. Значение функции в точке d равно -1.375, то есть на интервале [d, c] есть корень уравнения.
Продолжаем делить отрезки пополам и находить корни, пока не достигнем требуемой точности. Например, следующая точка будет e = (d + c) / 2 = -1.25. Значение функции в точке e равно 0.234375, то есть на интервале [e, c] есть корень уравнения.
Таким образом, метод деления отрезка пополам дает корень уравнения x^3 + 2x + 4 = 0 на интервале [-1.25, -1.125], который можно записать в виде x ≈ -1.1875 (с точностью до Ɛ=0,01).
\( \begin{aligned} \frac{\sin x+\tan x \cos x}{\tan x} & =\frac{\sin x+\sin x}{\tan x} \\ & =\frac{2 \sin x}{\tan x}\end{aligned} \)
The simplified expression is \(2 \cos x\).
The question is asking us to simplify the expression \( \frac{\sin x+\tan x \cos x}{\tan x} \) and show the steps to reach the final result.
First, we can use the identity \(\tan x = \frac{\sin x}{\cos x}\) to rewrite the expression:
\( \frac{\sin x+\tan x \cos x}{\tan x} = \frac{\sin x+\frac{\sin x}{\cos x} \cos x}{\frac{\sin x}{\cos x}} \)
Next, we can simplify the numerator by canceling out the \(\cos x\) terms:
\( \frac{\sin x+\frac{\sin x}{\cos x} \cos x}{\frac{\sin x}{\cos x}} = \frac{\sin x+\sin x}{\frac{\sin x}{\cos x}} \)
Now, we can combine the \(\sin x\) terms in the numerator:
\( \frac{\sin x+\sin x}{\frac{\sin x}{\cos x}} = \frac{2 \sin x}{\frac{\sin x}{\cos x}} \)
Finally, we can simplify the expression by canceling out the \(\sin x\) terms:
\( \frac{2 \sin x}{\frac{\sin x}{\cos x}} = \frac{2 \sin x}{\sin x} \cdot \frac{\cos x}{1} = 2 \cos x \)
So the final result is:
\( \frac{\sin x+\tan x \cos x}{\tan x} = 2 \cos x \)
Therefore, the simplified expression is \(2 \cos x\).
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Descriptive statistics and basketball wins: Here are the numbers of wins for the 30 National Basketball Association teams in the 2012–2013 season.
60
44
39
29
23
57
50
43
37
27
49
42
37
29
19
56
51
40
33
26
48
42
31
25
18
53
44
40
29
23
Create a frequency table for the number of wins using the data provided.
What is the Mean, Mode, and Median for the number of wins?
What is the standard deviation and variation?
How many teams had over 41 wins?
What percent of teams scored below 30 wins?
Create a histogram for the number of wins with a normal curve.
Does our data set for age represent a normal curve (somewhat bell-shaped)? If not, is it positively or negatively skewed?
What is the lowest and highest Z-score for wins and make sure to include that in the SPSS data file (2 points)?
What does the Z-score for the number of wins for 37 (2 points)?
The Mean, Mode, and Median for the number of wins are 37.8; 29, 42; 38 respectively. The standard deviation and variation are 11.15 and 124.26 respectively. 9 teams had over 41 wins. 16.67% of teams scored below 30 wins. Our data set for age does not represent a normal curve, it is positively skewed. The lowest and highest Z-score for wins are -1.78 and 1.99 respectively. The Z-score for the number of wins for 37 is -0.07.
To create a frequency table, we need to categorize the number of wins into intervals and count the number of teams in each interval. We can use the following intervals: 15-24, 25-34, 35-44, 45-54, 55-64.
| Interval | Frequency |
|---------|----------|
| 15-24 | 3 |
| 25-34 | 5 |
| 35-44 | 8 |
| 45-54 | 5 |
| 55-64 | 2 |
To calculate the mean, we add up all the values and divide by the number of values:
Mean = (60 + 44 + 39 + 29 + 23 + 57 + 50 + 43 + 37 + 27 + 49 + 42 + 37 + 29 + 19 + 56 + 51 + 40 + 33 + 26 + 48 + 42 + 31 + 25 + 18 + 53 + 44 + 40 + 29 + 23)/30 = 37.8
To find the mode, we look for the value that appears most often. In this case, it is 29 and 42, both appearing twice.
Mode = 29, 42
To find the median, we need to order the values from smallest to largest and find the middle value. If there is an even number of values, we take the average of the two middle values.
Ordered values: 18, 19, 23, 23, 25, 26, 27, 29, 29, 31, 33, 37, 37, 39, 40, 40, 42, 42, 43, 44, 44, 48, 49, 50, 51, 53, 56, 57, 60
Median = (37 + 39)/2 = 38
To calculate the standard deviation, we first find the variance by subtracting the mean from each value, squaring the result, and then taking the average of those squared differences. The standard deviation is the square root of the variance.
Variance = [(60-37.8)^2 + (44-37.8)^2 + ... + (23-37.8)^2]/30 = 124.26
Standard deviation = sqrt(124.26) = 11.15
To find the number of teams with over 41 wins, we can count the values that are greater than 41:
Number of teams with over 41 wins = 9
To find the percent of teams with below 30 wins, we can count the values that are less than 30 and divide by the total number of teams:
Percent of teams with below 30 wins = (5/30)*100 = 16.67%
To create a histogram, we can use the intervals and frequencies from the frequency table and plot them on a graph with the intervals on the x-axis and the frequencies on the y-axis. We can also add a normal curve by calculating the mean and standard deviation and using a normal distribution function.
The data set for the number of wins does not represent a normal curve, as it is slightly positively skewed (there are more values on the lower end of the distribution).
The lowest Z-score is for the value 18, which is (18-37.8)/11.15 = -1.78. The highest Z-score is for the value 60, which is (60-37.8)/11.15 = 1.99.
The Z-score for the value 37 is (37-37.8)/11.15 = -0.07. This means that the value 37 is 0.07 standard deviations below the mean.
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Consider the following matrix.λ003λ+1201λFind the determinant of the matrix. Find the values ofλfor which the determinant is zero. (Enter your answers as a comma-separated list.)λ=
This equation has two solutions: λ = 0 and λ = -1
The determinant of a matrix is given by the formula:
det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 - a22a31)
In the given matrix, the values of a11, a22, and a33 are λ, (λ+1), and λ respectively. The values of a12, a13, a21, a23, a31, and a32 are all 0. Substituting these values into the formula for the determinant gives:
det(A) = λ((λ+1)λ - 0) - 0(0 - 0) + 0(0 - 0) = λ^3 + λ^2
To find the values of λ for which the determinant is zero, we can set the determinant equal to zero and solve for λ:
λ^3 + λ^2 = 0
λ^2(λ + 1) = 0
This equation has two solutions: λ = 0 and λ = -1. Therefore, the values of λ for which the determinant is zero are 0 and -1. The answer can be written as a comma-separated list as follows:
λ = 0, -1
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estion list For the given equation, state the value of the discriminant and the number of real sol 36x^(2)-24x+4=0
The value of the discriminant is 0 and the number of real solutions is 1
For the given equation, 36x^(2)-24x+4=0, we can find the value of the discriminant and the number of real solutions using the quadratic formula.
The quadratic formula is x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation.
The discriminant is the part of the formula under the square root, b^(2)-4ac.
In this equation, a = 36, b = -24, and c = 4. Plugging these values into the discriminant, we get:
Discriminant = (-24)^(2)-4(36)(4) = 576-576 = 0
Since the discriminant is equal to 0, there is only one real solution to this equation.
Therefore, the value of the discriminant is 0 and the number of real solutions is 1.
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Find the surface area of the pyramid. A drawing of a square pyramid. The length of the base is 4. 5 meters. The height of each triangular face is 6 meters. The surface area is square meters
The surface area of the pyramid. A drawing of a square pyramid. The length of the base is 4.5 meters is 74.25 square meters.
To find the area of a pyramid, we need to find the area of the square base and the areas of the four triangular faces, then add them together.
Calculate the area of the base of the square:
The area of the square is the length of one side multiplied by itself, so the area of the base of the square is 4.5 x 4.5 = 20 .25 square meters.
Find the area of each triangle face:
The area of a triangle is the base times the height divided by 2, so the area of each triangle face is 0.5 x 4.5 x 6 = 13.5 square meters.
Add the area of :
The area of the pyramid is the sum of the areas of the square base and the four triangular faces, so the area is 20.25 + 4 x 13.5 = 20.25 + 54 = 74.25 square meters.
The area of the pyramid is therefore 74.25 square meters.
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john's mom lends her R^(840) of 12% per annum how mucch does he owe her mom after 2years?
John owes his mom R1041.6 after 2 years
To find out how much John owes his mom after 2 years, we need to calculate the interest on the loan. The formula for calculating interest is I = Prt, where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.
In this case, the principal is R840, the annual interest rate is 12% (or 0.12), and the time is 2 years. Plugging these values into the formula, we get:
I = (R840)(0.12)(2) = R201.6
So the interest on the loan is R201.6.
To find out the total amount John owes his mom, we need to add the interest to the principal:
Total amount owed = Principal + Interest = R840 + R201.6 = R1041.6
Therefore, John owes his mom R1041.6 after 2 years.
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For h(x)=3x+1, find h(2)
The management of a company analyzes the dependence of sales of the company's main product on investments. Information on investments (X variable, thousand Euro) and the main product's sales for the last 10 years (y variable, thousand Euro) are the following:
Х 17 21 24 27 14 30 33 32 23 28
Y 110 127 140 151 89 187 205 190 136 165
∑Yi2 = 237366 ∑Xi = 249 ∑Yi = 1500 ∑XiYi = 39423 ∑Xi2 = 6557
1) Calculate the correlation coefficient and make conclusions about the closeness of the linear relationship.
2) Find the linear regression from variable Y to the X and forecast the sales volume if the investment volume is planned to be 50 thousand Euro.
1... The coefficient of correlation between X and Y is 0.87, indicating that the linear relationship between the variables is close.
2.... The forecasted sales volume is 410.5 + C thousand Euro.
1) To calculate the correlation coefficient and make conclusions about the closeness of the linear relationship, you can use the formula for the coefficient of correlation (r): r = (∑XiYi - n*Xm*Ym) / √((∑Xi2 - n*Xm2) * (∑Yi2 - n*Ym2)), where n is the number of observations (10 in this case), Xm is the mean of X (24.9 in this case), and Ym is the mean of Y (150 in this case). Calculating, we get: r = (39423 - 10*24.9*150) / √((6557 - 10*24.92) * (237366 - 10*1502)) = 0.87.
2) To find the linear regression from variable Y to the X, you can use the formula for the coefficient of determination (b): b = (∑XiYi - n*Xm*Ym) / (∑Xi2 - n*Xm2). Calculating, we get: b = (39423 - 10*24.9*150) / (6557 - 10*24.92) = 8.21. Therefore, the linear regression equation is Y = 8.21X + C. To forecast the sales volume if the investment volume is planned to be 50 thousand Euro, substitute 50 in the equation and calculate: Y = 8.21*50 + C = 410.5 + C.
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PLS Help me it’s due today
Answer: Using 45π cm^3
a) h = 5 cm
b) approximately $2.83
c) h = 9/5 cm
d) approximately $9.90
Step-by-step explanation:
a) The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex]. Given that the volume is equal to [tex]45\pi cm^{3}[/tex] and radius is [tex]3cm[/tex], we can plug in.
[tex]45\pi = 3^2h\pi \\45\pi = 9h\pi\\\frac{45\pi }{9\pi } = h\\ h = 5[/tex]
b) Since coffee costs $0.02 per cubic centimeter, and there are [tex]45\pi[/tex] cubic centimeters, 0.02 x [tex]45\pi[/tex] = 2.8274338, and rounding gives $2.83
c) Using the same formula from part a, we plug in [tex]5cm[/tex] for r instead of [tex]3cm[/tex].
[tex]45\pi = 5^2h\pi \\45\pi =25h\pi \\\frac{45\pi }{25\pi } = h\\h = \frac{45}{25} = \frac{9}{5}[/tex]
d) Because hot chocolate powder costs $0.07 per cubic centimeter, and there are [tex]45\pi[/tex] cubic centimeters, 0.07 x [tex]45\pi[/tex] = 9.89601685, and rounding makes it $9.90
What is the solution of the system? Solve using matrices.
{ x+2y=9
{x+y=1
Answer:
Step-by-step explanation:
// Solve equation [2] for the variable x
[2] x = y + 1
// Plug this in for variable x in equation [1]
[1] (y +1) - 2y = 9
[1] - y = 8
// Solve equation [1] for the variable y
[1] y = - 8
// By now we know this much :
x = y+1
y = -8
// Use the y value to solve for x
x = (-8)+1 = -7
Solution :
{x,y} = {-7,-8}
Convert the following binary (base -2) value into its decimal (base -10) equivalent: (111)_(2)=(?)_(10)
The decimal (base-10) equivalent of the binary (base-2) value (111)_(2) is (7)_(10).
To convert a binary (base-2) value into its decimal (base-10) equivalent, we need to multiply each digit in the binary value by the corresponding power of 2, and then add the results together.
Here is how to do it step-by-step for the given binary value (111)_(2):
1. Start with the rightmost digit (the least significant bit) and work your way to the left:
(1 * 2^0) + (1 * 2^1) + (1 * 2^2)
2. Simplify the powers of 2:
(1 * 1) + (1 * 2) + (1 * 4)
3. Multiply the digits by the powers of 2:
1 + 2 + 4
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Evaluar expresiones Evalúa a 4 cuando a 7.
The value of the expression a + 4 when a = 7 is 11.
What is Algebra?
Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Function= a+4
Now,
By algebra
If a = 7, then we can substitute this value into the expression a + 4 to get:
=a + 4
= 7 + 4
= 11
Therefore, by algebra the answer will be 11.
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The complete question is;
Evaluate the expression a+4 when a=7?
Test the claim that the proportion of people who own cats is larger than 40% at the 0.025 significance level.
The null and alternative hypothesis would be:
H0:p=0.4H0:p=0.4
H1:p>0.4H1:p>0.4
H0:p=0.4H0:p=0.4
H1:p<0.4H1:p<0.4
H0:μ≥0.4H0:μ≥0.4
H1:μ<0.4H1:μ<0.4
H0:μ≤0.4H0:μ≤0.4
H1:μ>0.4H1:μ>0.4
H0:μ=0.4H0:μ=0.4
H1:μ≠0.4H1:μ≠0.4
H0:p=0.4H0:p=0.4
H1:p≠0.4H1:p≠0.4
The test is:
right-tailed
two-tailed
left-tailed
Based on a sample of 400 people, 43% owned cats
The test statistic is: (to 3 decimals)
The p-value is: (to 4 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
a)H0:p=0.4
H1:p>0.4
b)right-tailed test
c)0.075
d)0.0074
e)reject the null hypothesis
In this problem, we are testing the claim that the proportion of people who own cats is larger than 40% at the 0.025 significance level. The null and alternative hypothesis can be written as:
H0:p=0.4
H1:p>0.4
This is a right-tailed test. Using the sample data, the test statistic is 0.075 and the p-value is 0.0074. Therefore, we reject the null hypothesis and conclude that the proportion of people who own cats is greater than 40% at the 0.025 significance level.
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Suppose you place $2,500 in an account that will pay annual
interest of 6% compounded quarterly. What will be your balance in
your account after 5 years?
After 5 years, the balance of your account with an initial investment of $2,500, 6% annual interest compounded quarterly, will be $3,325.81. This can be calculated using the following formula:
Balance = P(1 + r/n)nt
Where:
P = Principal Amount
r = Annual Interest Rate
n = Number of Compounding Periods
t = Number of Years
Therefore, for your given example, the equation would be:
Balance = 2500(1 + 0.06/4)4 x 5
Balance = 2500(1.015)20
Balance = 2500(1.32581)
Balance = $3,325.81
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PLEASEEE HELP!!!!!!!
Answer:
t=5.2, w=6
Step-by-step explanation:
tan(30)=[tex]\frac{3}{t}[/tex]
[tex]t=\frac{3}{tan(30)} \\t=5.2[/tex]
[tex]sin(30)=\frac{3}{w}\\w=\frac{3}{sin(30)} \\w=6[/tex]
The side w is the hypotenuse and is equal to 6, while f is the adjacent and is equal to 3√3 in radical form and 5.2 expressed as a decimal.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin30° = 1/2 and cos30° = √3/2
sin 30° = 3/w {opposite/hypotenuse}
w = 3/sin 30° {cross multiplication}
w = 3 ÷ 1/2
w = 3 × 2
w = 6
cos 30° = f/6 {adjacent/hypotenuse}
f = 6 × cos 30° {cross multiplication}
f = 6 × √3/2
f = 3√3
Therefore, the side lengths of w and f of the right triangle are 6 and 3√3 respectively using the trigonometric ratio of sine and cosine of angle 30°.
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The mass of a science textbook is 1.15 kilograms. The mass of a history textbook is 950 grams. Rami makes a stack of 4 science textbooks and a stack of 5 history textbooks.
Part A
Write to compare the masses of the stacks of textbooks.
History textbooks O Science textbooks
Part B
By how much mass do the stacks of textbooks differ? Write your answer in kilograms. Explain how you found the difference.
The comparison of textbooks is History textbooks > Science textbooks. The mass of the stacks of textbook differ by 0.15 kilograms.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that,
Mass of science textbook = 1.15 kilograms
Mass of 4 science textbooks = 4 × 1.15 kilograms
= 4.6 kilograms
Mass of a history textbook = 950 grams = 0.95 kilograms
Mass of 5 history textbooks = 5 × 0.95 kilograms
= 4.75 kilograms
Part A :
History textbooks > Science textbooks
Part B :
Mass of History textbooks - Mass of science textbooks = 4.75 - 4.6
= 0.15 kilograms
Hence the history textbooks are 0.15 kilograms more.
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Use a cosine sum or difference identity to find the exact value. Cos (5π/12) = _________
The exact value of cos(5π/12), using the cosine summation identity, is (√6 - √2)/4.
The exact value of cos(5π/12) can be found using the cosine sum identity, which is:
cos(a + b) = cosa · cosb - sina · sin b
In this case, we can rewrite 5π/12 as (π/4) + (π/6) and use the identity:
cos(5π/12) = cos[(π/4) + (π/6)] = cos(π/4) · cos (π/6) - sin(π/4) · sin (π/6)
Using the values of cos(π/4) = √2/2, cos(π/6) = √3/2, sin(π/4) = √2/2, and sin(π/6) = 1/2, we can plug them into the equation:
cos(5π/12) = (√2/2) · (√3/2) - (√2/2) · (1/2) = √6/4 - √2/4 = (√6 - √2)/4
Therefore, the exact value of cos(5π/12) is (√6 - √2)/4.
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21) Following a strenuous basketball workout, Tuan proceeds to 24 Hour
Fitness and does an hour worth of weight-training exercises. It's drawing
close to the end of the day and he is experiencing some tiredness. From
reading this passage, you can conclude that Tuan is experiencing:
Answer: From the passage, we can conclude that Tuan has had a strenuous basketball workout and has also done an hour's worth of weight-training exercises, which suggests that he has had a physically demanding day. Additionally, it is mentioned that he is experiencing some tiredness towards the end of the day, which is not uncommon after such an active day. Therefore, we can conclude that Tuan is experiencing physical fatigue or tiredness due to his physical activity.
Step-by-step explanation:
Find f(g(x))
f(x)=x^2 g(x)=1/x-1 Enter a,b,c,d, or e. a. 1/x^2-1
b. 1/x-1
c. 1/x^2 -2x+1
d. (1/x^2 -1)^2
e. 1/x^2 - 1
The correct answer is c. 1/x^2 - 2/x + 1.
To find f(g(x)), we need to plug in the function g(x) into the function f(x).
f(x) = x^2
g(x) = 1/x-1
So, f(g(x)) = (1/x-1)^2
Using the distributive property, we can expand this expression:
f(g(x)) = (1/x-1)(1/x-1)
f(g(x)) = 1/x^2 - 1/x - 1/x + 1
f(g(x)) = 1/x^2 - 2/x + 1
Therefore, the correct answer is c. 1/x^2 - 2/x + 1.
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Determine if JK←→
and LM←→−
are parallel, perpendicular, or neither!
c. (-10, -7), K(-4, 1), L(-3, 2), M(-4, -2)
JK←→ and LM←→− are neither parallel nor perpendicular.
To determine if JK←→ and LM←→− are parallel, perpendicular, or neither, we need to examine their slopes.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
slope =(y₂ - y₁)/(x₂ - x₁)
The slope of JK←→ passing through J(-10, -7) and K(-4, 1) is:
slope(JK) = (1 - (-7)) / (-4 - (-10)) = 8 / 6
= 4 / 3
The slope of LM←→− passing through L(-3, 2) and M(-4, -2) is:
slope(LM) = (-2 - 2) / (-4 - (-3))
= -4 / (-1)
= 4
If two lines are parallel, their slopes are equal. If two lines are perpendicular, their slopes are negative reciprocals of each other. Otherwise, they are neither parallel nor perpendicular.
Comparing the slopes of JK←→ and LM←→−, we see that they are not equal, so they are not parallel. To determine if they are perpendicular, we need to calculate the negative reciprocal of the slope of JK←→:
slope(JK) = 4 / 3
negative reciprocal of slope(JK) = -3 / 4
If the negative reciprocal of the slope of JK←→ is equal to the slope of LM←→−, then the two lines are perpendicular. Let's check:
slope(LM) = 4
-3 / 4 ≠ 4
Since -3 / 4 is not equal to 4, the lines are neither parallel nor perpendicular.
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10 Calculate the missing terms of each arithmetic sequence given below. Each row represents an arithmetic sequence in which the first and
the last term are given.
First term
-20
54
10
Second term
Third term
Fourth term
19
105
-14
The required,
(a) The missing terms of the first sequence are -7, 6, and 19.
(b) The missing terms of the second sequence are 71, 88, and 105.
(c) The missing terms of the third sequence are 2, -6, and -14.
Arithmetic progression is the series of numbers that have common differences between adjacent values
To find the missing terms of each arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence:
an = a₁ + (n - 1)d
where an is the nth term, a₁ is the first term, n is the number of terms, and d is a common difference.
Sequence 1,
a₁ = -20, an = 19
n = ? (unknown)
d = (an - a1) / (n - 1)
19 = -20 + (n - 1)d
39 = (n - 1)d
d = 39 / (n - 1)
We also know that a₂, a₃, and a₄ are missing, and there are four terms in total. Therefore, n = 4.
d = 39 / (4 - 1) = 13
Using the formula, we can now find the missing terms:
a₂ = a₁ + d = -20 + 13 = -7
a₃ = a₂ + d = -7 + 13 = 6
a₄ = a₃ + d = 6 + 13 = 19
So the missing terms of the first sequence are -7, 6, and 19.
Similarly,
The missing terms of the second sequence are 71, 88, and 105.
The missing terms of the third sequence are 2, -6, and -14.
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A cylinder has a base diameter of 12 foot and a height of 12 foot what is its volume in cubic feet to the nearest 10s place
Answer:
Step-by-step explanation:
A cylinder has a base diameter of 12 foot and a height of 12 foot what is its volume in cubic feet to the nearest 10s place
The volume of a cylinder can be calculated using the formula:
V = πr^2h
where:
V is the volume of the cylinder
π is a mathematical constant, approximately equal to 3.14159
r is the radius of the base of the cylinder
h is the height of the cylinder
We are given the diameter of the base, which is 12 feet. The radius (r) is half of the diameter, so we have:
r = 12/2 = 6 feet
The height (h) is also given as 12 feet.
Substituting the values we have into the formula, we get:
V = π(6)^2(12) ≈ 1357.17
Rounding to the nearest 10's place, the volume is approximately 1360 cubic feet. Therefore, the volume of the cylinder is 1360 cubic feet to the nearest 10's place.
Year 1 Y = 1000+ 0.03 (1000) - 1030.00 Start with the expression for year 1. Recall the identity property of 1 (1000) + 0.03 (1000) = [ ] (1+[ ]) fill in the blanks
The expression by using property is 1000(1+0.03)
What is Number system?A number system is defined as a system of writing to express numbers.
Using the distributive property, we can factor out 1000 from the expression for year 1:
Y = 1000 + 0.03(1000) - 1030.00
= 1000(1 + 0.03) - 1030.00
Using the identity property of 1, we can rewrite (1 + 0.03) as:
(1 + 0.03) = 1.03
Substituting back into the expression for year 1, we get:
Y = 1000(1.03) - 1030.00
Hence, the expression by using property is 1000(1+0.03)
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a bakery is making cakes for a huge weeklong city celebration. the recipe for each cake calls for 96 grams of sugar. each cake serves 12 people and the city plans on serving 1500 slices of cake per day for 7 days. how many total cakes does the bakery need to make?
Find g.
18-√3 in
60°
g
30°
Write your answer in simplest radical form.
The value of g is 9√3 in
What is the radical form?In mathematics, the radical form refers to expressing a mathematical expression or equation using radicals, which are symbolized by the radical sign (√). The radical sign indicates the root of a number, which is a value that when multiplied by itself, produces the original number. The most common type of radical is the square root (√), which represents the positive root of a number.
We have that;
Sin 30 = g/18√3
1/2 = g/18√3
g = 1/2 * 18√3
g = 9√3 in
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Which table(s) represent(s) a function? A. Table 1 only B. Table 2 only C. Tables 1 and 3 only D. Tables 1, 3, and 4 only
The correct answer is option C. Only Table 1 and Table 3 represent a function.
Each input value should be paired with only one output value, as stated in the definition of a function. Therefore, we must verify that each input value is paired with only one output value in order to determine which tables represent a function.
For each input value, Table 1 contains unique output values and unique input values. As a result, a function is represented by Table 1.
For the same input value (input 1), there are two distinct output values in Table 2. As a result, there is no function represented in Table 2.
For each input value, Table 3 contains unique output values and unique input values. As a result, a function is represented by Table 3.
For the same input value (input -2) in Table 4, there are two distinct output values. Subsequently, Table 4 doesn't address a capability.
Consequently, c is the correct response because Tables 1 and 3 only depict functions.
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Complete Question:
Which table(s) represent(s) a function? A. Table 1 only B. Table 2 only C. Tables 1 and 3 only D. Tables 1, 3, and 4 only