The population mean is equal to 80 for the mean of a sampling distribution of sample means with n=49, and the standard deviation is equal to 1/√(n).
What does standard deviation mean?The standard deviation is a statistician's gauge of a group of values' degree of dispersion or variation. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the expected value) of the set.With a sample size of 49, the mean of a sampling distribution of sample means is equal to the population mean of 801.
With a sample size of n=49, the standard deviation of a sampling distribution of sample means is identical.
n=49 is equal to σ/√(n)
= 7/√(49) = 1¹
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Consider the following series. 7n + 18-n n = 1 Determine whether the geometric series is convergent or divergent. Justify your answer. • Converges; the series is a constant multiple of a geometric series. Converges; the limit of the terms, ap, is 0 as n goes to infinity. O Diverges; the limit of the terms, an, is not 0 as n goes to infinity. O Diverges; the series is a constant multiple of the harmonic series. If it is convergent, find the sum. (If the quantity diverges, enter DIVERGES.)
Diverges. Series is not a geometric series as it does not have a common ratio. However, we can rewrite the series as:
7n + 18-n = 7n(1 + 18(-1/n))
As n approaches infinity, the second term inside the parentheses approaches 1, so we can write:
7n(1 + 18(-1/n)) ≈ 7n(1 + 0) = 7n
Thus, we can see that the series is a constant multiple of the series 7n, which is a geometric series with a common ratio of 7. Since the common ratio is greater than 1, the series diverges.
To determine if the series is convergent or divergent, we should find the limit of the terms as n goes to infinity.
The series can be rewritten as: (7n) + (18(-n)n)
As n goes to infinity, the term 7n will also go to infinity. Meanwhile, the term 18(-n)n will approach 0 since any number
raised to a negative power becomes smaller as n increases. However, the 7n term dominates the series, so the limit of
the terms is not 0 as n goes to infinity.
Therefore, the series is divergent. Diverges; the limit of the terms, an, is not 0 as n goes to infinity.
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What’s is the distance between -3.1 and positive 4.1
4 How many terms of the series are needed so that the sum is accurate to within 0.00001. [Give the smallest value of n for which this is true. (2n 1)4 51 X terms 11. 0/1 points | Previous Answers My No How many terms of the series are needed so that the remainder is less than 0.0005? (Give the smallest integer value of n for which this is true.] 6
To find the smallest value of n for which the sum of the series is accurate to within 0.00001, we need to use the formula for the remainder of a convergent series:
R_n = |S - S_n|
where R_n is the remainder, S is the sum of the series, and S_n is the sum of the first n terms.
We want R_n to be less than or equal to 0.00001, so we have:
|R_n| ≤ 0.00001
Substituting the given values, we get:
|(2n+1)^4/5 - 51| ≤ 0.00001
Simplifying and taking the fifth root, we get:
2n+1 ≤ (51.00001)^(1/4)
2n+1 ≤ 3.1673
n ≤ 1.5836
Since n has to be an integer, the smallest value of n that satisfies this inequality is n = 1.
Therefore, we need at least 1 term of the series to get a sum accurate to within 0.00001.
Note: This is a bit of a tricky question because the given series converges very quickly, so only one term is needed to get a sum accurate to within 0.00001.
To determine how many terms of the series are needed so that the sum is accurate to within 0.00001, we can use the remainder estimation theorem.
Given the desired remainder, 0.00001, and the error tolerance, 0.0005, we can find the smallest integer value of n that satisfies these conditions. Since the series is a convergent alternating series, the remainder is less than the absolute value of the (n+1)th term. Therefore, we need to find the smallest integer value of n for which:
|(2n + 1)^(-4)/51| < 0.00001
Solving for n, we can determine the smallest value that meets this criterion. By trial and error or using a calculator, we can find that the smallest integer value of n that satisfies this condition is n = 6.
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What is the product of 50% of 30 and 25% of 40?
Answer:
50% of 30 is 15. 25% of 40 is 10. So, the product of 50% of 30 and 25% of 40 is 150.
Here's the calculation:
```
(50/100) * 30 * (25/100) * 40 = 150
```
Step-by-step explanation:
At a particular restaurant, each slider has 225 calories and each chicken wing has 70 calories. A combination meal with sliders and chicken wings has a total of 10 sliders and chicken wings altogether and contains 1165 calories. Write a system of equations that could be used to determine the number of sliders in the combination meal and the number of chicken wings in the combination meal. Define the variables that you use to write the system. Do not solve the system.
x+y=10
225x+70y=1165 where x is number of slider in the combination
y is the number of chicken wing in the combination.
What is an equation?An equation is a mathematical statement that expresses the equality between two mathematical expressions. It typically consists of mathematical symbols, such as numbers, variables, and mathematical operators, arranged in a specific pattern or format.
What is known as combination?A combination refers to a way of selecting or arranging objects without regard to their order, where the order of selection does not matter. A combination is a selection of objects where the arrangement or order of the objects is considered irrelevant.
Let x=number of slider
y= number of chicken wing
then, x+y= 10 ,
Since each slider has 225 calories and each chicken wing has 70 calories, then
225x+70y= 1165
Hence the system of equations are:
x+y=10
225x+70y=1165
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6.
5.
4.
3. Pat loves the mountains. He's never happier than when he's standing on top of a mountain, gazing out across nature's
The mountains bring Pat
Tiana
My Answer
Tiana wanted to throw her best friend, Maliyah, a surprise birthday party, so she pretended to forget Maliyah's birthday.
Maliyah was so mad! But when she realized Tiana had thrown her a party, Maliyah forgave her and said, "Girl, you really had
me fooled!"
My Answer
James' friends are
Monica was
My Answer
forgetting because
because
When James lost his job, his friends cooked a big dinner and brought it over to his house to try and cheer him up.
My Answer
My Reason
him because
because
My Reason
RRICULUM
When Monica applied to college, she was careful about every detail. She made sure that she had all the forms she n
and double-checked all the information. She made sure to meet every deadline.
My Reason
My Reason
Answer:
the mountains bring Pat joy because it is beautiful
only one I know
Step-by-step explanation:
:)
A key difference between MANOVA and ANOVA is that MANOVA has the ability to handle Select one: O a. multiple comparisons O b. multiple dependent variables о с. multiple error terms O d. multiple independent variables O e. multiple null hypotheses
A key difference between MANOVA and ANOVA is that MANOVA has the ability to handle multiple dependent variables.
The key difference between MANOVA and ANOVA is that MANOVA has the ability to handle multiple dependent variables. ANOVA, on the other hand, only deals with a single dependent variable. MANOVA can also handle multiple independent variables, multiple error terms, and multiple null hypotheses. However, it is important to note that MANOVA is more complex than ANOVA and requires more data to perform accurate analyses.
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.
f(x)= x². What is g(x)?
O A. g(x)=x²
OB. g(x) = (x)²
OC. g(x) = 3x²
OD. g(x) = (x)²
g(x)
-5
-5-
y
f(x) = x²
(3, 1)
5
Since the function f(x) = x², g(x) include the following: D. g(x) = (1/3x)².
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.
What is a dilation?In Mathematics and Geometry, a dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Based on the graph, we can logically deduce that function g(x) can be produced by vertically stretching the parent function by a scale factor of 1/3;
g(x) = 1/3f(x)
g(x) = (1/3x)²
g(x) = (1/9)x²
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Can someone help me answer the second question please. I don't understand
The equation for the total number of coins is given as follows:
x + y = 12.
The equation for the total value of the coins is given as follows:
0.1x + 0.05y = 2.4.
How to define the system of equations?The variables for the system of equations are defined as follows:
Variable x: number of 10 cent coins.Variable y: number of 5 cent coins.They have a total of 12 coins, hence the equation for the total number of coins is given as follows:
x + y = 12.
Considering the value of each coin, 10 cents = 0.1 and 5 cents = 0.05, the equation for the total value of the coins is given as follows:
0.1x + 0.05y = 2.4.
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The equation for the total number of coins is given as follows:
x + y = 12.
The equation for the total value of the coins is given as follows:
0.1x + 0.05y = 2.4.
How to define the system of equations?The variables for the system of equations are defined as follows:
Variable x: number of 10 cent coins.Variable y: number of 5 cent coins.They have a total of 12 coins, hence the equation for the total number of coins is given as follows:
x + y = 12.
Considering the value of each coin, 10 cents = 0.1 and 5 cents = 0.05, the equation for the total value of the coins is given as follows:
0.1x + 0.05y = 2.4.
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5-(6x+9)= 9-(4x-1)
Solve
In each of Problems 7 through 13, determine the Taylor series about the point xo for the given function. Also determine the radius of convergence of the series. 7. sinx, xo =0 8. e^x, Xo = 0 9. x, xo = 1 10. x2, xy =
1) The Taylor series for sin(x) at x=0 is as follows: sin(x) = x - x3/3! + x5/5! - x7/7! +...
This series' radius of convergence is infinite.
What is the Taylor series?2) The Taylor series for ex near x=0 is as follows: ex = 1 + x + x2/2! + x3/3! + x4/4! +...
This series' radius of convergence is infinite.
3) The Taylor series for x near x=1 is as follows: x = 1 + (x-1)
This series has a radius of convergence of one because it converges exclusively for |x-1| 1.
4) The Taylor series for x2 around x=0 is as follows: x2 = 0 + x2
This series' radius of convergence is infinite.
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which is the correct answer?
Answer:
Step-by-step explanation:
Tammy leans across the table to get a saltshaker and her friend is surprised at what she thinks is very rude behavior. Lit's perception of her friend's behavior is based on a. Regulative rules b. Constitutive rules d. Stereotypes e. Personal contracts f. Conflict patterns
Based on constitutive laws, Lit's interpretation of her friend's actions.Therefore, choice b is right.
Tammy should have asked the host to serve her instead of reaching over the table to get the salt shaker since, as per the constitution, you are not allowed to reach across the table and touch objects on it.
Constitutive rules are those that have a creative purpose, making it possible to carry out specific activities or take part in a specific practise. They are typically opposed to regulative rules.
The practises that constitutive norms establish are metaphysically prior to one another.According to John Searle's influential constitutive rules theory, behaviours are only possible when certain conditions are met. This distinguishes regulative rules which aim to control previously existing and established behavior from constitutive norms.
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Simplify: 2 4/5-1 2/5
Answer:
Step-by-step explanation:
24/5-12/5=12/5
To simplify 2 4/5 - 1 2/5, we first need to convert the mixed numbers into improper fractions.
Step 1: Convert the mixed numbers to improper fractions:
2 4/5 = (2 x 5 + 4)/5 = 14/5
1 2/5 = (1 x 5 + 2)/5 = 7/5
Step 2: Subtract the two improper fractions:
14/5 - 7/5 = (14 - 7)/5 = 7/5
Step 3: Convert the resulting fraction back into a mixed number, if necessary:
7/5 can be written as 1 2/5
Therefore, 2 4/5 - 1 2/5 = 1 2/5
let h0, h1, h2,..., hn,....be the sequence defined by hn = (n C 2), (n choose 2). (n>=0). Determine the generating function for the sequence.
To determine the generating function for the sequence h0, h1, h2,..., hn,...., we first need to express the sequence in terms of a polynomial. Using the formula for binomial coefficients, we have:
hn = (n C 2) = n!/(2!(n-2)!) = (1/2)n(n-1)
So, the sequence can be expressed as the polynomial:
h(x) = 0 + (1/2)x(x-1) + (1/2)2(2-1)x(x-1)(x-2) + ... + (1/2)n(n-1)x(x-1)(x-2)...(x-n+1) + ...
Now, we can use the definition of a generating function to write:
H(x) = h0 + h1x + h2x^2 + ... + hnx^n + ...
H(x) = (1/2)0(0-1) + (1/2)1(1-1)x + (1/2)2(2-1)x^2 + ... + (1/2)n(n-1)x^n + ...
H(x) = 0 + 0x + (1/2)x^2 + (1/2)2x^3 + ... + (1/2)n(n-1)x^(n+1) + ...
Hence, the generating function for the sequence h0, h1, h2,..., hn,.... is:
H(x) = (1/2) x^2 (1 + 2x + 3x^2 + ...)
Given the sequence h_n = C(n, 2), where n ≥ 0, we want to find the generating function for this sequence. The generating function, G(x), is defined as the formal power series:
G(x) = h_0 + h_1x + h_2x^2 + h_3x^3 + ...
We know that h_n = C(n, 2) = n(n - 1)/2 for n ≥ 0. So, we can rewrite the generating function as:
G(x) = h_0 + h_1x + h_2x^2 + h_3x^3 + ... = ∑ [n(n - 1)x^n / 2] for n ≥ 0.
By using the binomial theorem, we can express G(x) as:
G(x) = 1/2 * (x * d/dx)^2 (1 - x)^(-1)
Here, (x * d/dx) is the operator that represents the derivative with respect to x multiplied by x. By applying this operator twice to (1 - x)^(-1) and then multiplying the result by 1/2, we obtain the generating function for the sequence.
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Jackie buys some tickets to see the film.
Each ticket costs £4.50
Jackie pays with two £20 notes.
Jackie gets £8.50 change.
(b) How many tickets did Jackie buy?
Answer:7
Step-by-step explanation: as she pays with 2 £20s it'll be 40 so £40 - 8.50 which is £31.50. then 31.50/4.50 which is 7
Which of these strategies would eliminate a variable in the system of
equations?
10x + 4y = -2
5x - 2y = 2
Choose all answers that apply:
B
Multiply the bottom equation by 2, then subtract the bottom
equation from the top equation.
Add the equations.
1
Multiply the top equation by
2'
then add the equations.
Stuck? Review related articles/videos or use a hint.
Report a problem
Answer:
multiply the bottom by 2
Step-by-step explanation:
What is the answer to 71270-32425
Answer: 38845
Step-by-step explanation:
Answer:
38,845
Step-by-step explanation:
Which shapes below are congruent to Z?
N
Select all correct answers.
A
с
D
B
E
Answer:
B and E
Step-by-step explanation:
They both have the same number of untis as Z
There are M green and N red apples in the box. We start removing randomly one apple at a time from the box until we remove all the green apples. What is the probability that there is no apple left in the box after that? What is the probability that there are exactly k apples left after that?
Based on probability, the response to the question is,
[tex]a).\ (\frac{N}{(M+N)} )^M\\\\b).\ C(N+k-1,k)^*((\frac{M}{M+N} )^M)^*((\frac{(N+k-1)}{(M+N)} )^k)[/tex]
What is Probability?Probability measures the likelihood or probability of an event happening. It is a number between 0 and 1, where 0 signifies an unlikely occurrence (one that would never happen) and 1 denotes an expected event (one that would happen frequently). Events between 0 and 1 have probabilities between 0 and 1, and the closer an event's probability approaches 1, the more probable it is to occur.
After removing all of the green apples, there is a chance that there won't be an apple in the box [tex](\frac{N}{(M+N)} )^M[/tex].
This is so that there are always less apples overall and fewer green apples overall after each removal. On the first draw, there is a chance of removing a green apple of M / (M + N).
On the second draw, there is a chance of removing another green apple (M-1) / (M + N - 1) until all M green apples have been taken out. These probabilities can be combined to determine the likelihood that all M green apples are taken out of the box, leaving nothing inside.
The binomial coefficient indicates the likelihood that exactly k apples remain in the box after all the green apples have been removed,
[tex]C(N+k-1, k) * ((\frac{M}{(M+N)} )^M) * ((\frac{(N+k-1)}{(M+N)} )^k)[/tex]
This is due to the fact that C(N+k-1, k) methods for choosing which of the remaining (N+k-1) apples are red, and the likelihood that this
choice will be made is [tex](\frac{(N+k-1)}{(M+N)} )^k*((\frac{M}{(M+N)} )^M)[/tex].
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An LTI filter is described by the difference equation<
y[n]=3x[n]+2x[n-1]+x[n-2]
Obtain an expression for the frequency response of the system.
The frequency response of the LTI system described by the difference equation y[n] = 3x[n] + 2x[n-1] + x[n-2] is given by H( [tex]e^j^\omega[/tex] ) = 3 + 2e^(-jω) +
[tex]e^-^2^j^\omega[/tex] .
1. Convert the difference equation to the frequency domain using the Fourier transform.
2. Replace x[n] with X( [tex]e^j^\omega[/tex]) and y[n] with Y( [tex]e^j^\omega[/tex]).
3. Solve for the transfer function H( [tex]e^j^\omega[/tex]) = Y( [tex]e^j^\omega[/tex]) / X( [tex]e^j^\omega[/tex]).
For the given difference equation:
Y( [tex]e^j^\omega[/tex]) = 3X( [tex]e^j^\omega[/tex]) + 2X( [tex]e^j^\omega[/tex])[tex]e^-^j^\omega[/tex] + X( [tex]e^j^\omega[/tex]) [tex]e^-^2^j^\omega[/tex]
Divide both sides by X( [tex]e^j^\omega[/tex]):
H( [tex]e^j^\omega[/tex]) = Y( [tex]e^j^\omega[/tex]) / X( [tex]e^j^\omega[/tex]) = 3 + 2[tex]e^-^j^\omega[/tex] + [tex]e^-^2^j^\omega[/tex]
This expression represents the frequency response of the given LTI system.
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find the first four terms of the taylor series for the function 3/x about the point α = 2 . (your answers should include the variable x when appropriate.
3/x = ?
The first four terms of the Taylor series for 3/x about the point α = 2 are: 3/2 - (3/4)(x-2) + (3/4)(x-2)² - (9/16)(x-2)³.
To find the Taylor series for a function, we need to calculate its derivatives at the point of expansion and then substitute those values into the general formula for the Taylor series. The general formula for the Taylor series of a function f(x) about a point a is:
f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)²/2! + f'''(a)(x-a)³/3! + ...
Here, we want to find the Taylor series for the function f(x) = 3/x about the point α = 2. First, we will calculate the derivatives of f(x):
f(x) = 3/x
f'(x) = -3/x²
f''(x) = 6/x³
f'''(x) = -18/x⁴
Now we can substitute these derivatives into the general formula for the Taylor series to get:
f(x) = f(2) + f'(2)(x-2)/1! + f''(2)(x-2)²/2! + f'''(2)(x-2)³/3! + ...
We can calculate the first few terms of this series:
f(2) = 3/2
f'(2) = -3/4
f''(2) = 3/4
f'''(2) = -9/16
Substituting these values into the series, we get:
3/x = 3/2 - (3/4)(x-2) + (3/4)(x-2)² - (9/16)(x-2)³ + ...
So the first four terms of the Taylor series for 3/x about the point α = 2 are 3/x = 3/2 - (3/4)(x-2) + (3/4)(x-2)² - (9/16)(x-2)³
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What is the volume of a rectangular prism with a length of 14 yards, a width of 6 yards, and a height of 8 yards?
Answer: 672 Cubic Yards
Step-by-step explanation:
To find the volume of a rectangular prism, you need to multiply its length by its width by its height.
In this case, the length is 14 yards, the width is 6 yards, and the height is 8 yards.
So, the volume of the rectangular prism is:
14 yards × 6 yards × 8 yards = 672 cubic yards
Therefore, the volume of the rectangular prism is 672 cubic yards.
Number of Vertices and Edges What is the number of vertices and edges in the graph K_m,n ?a. mn vertices and m+n edgesb. mn vertices and m-n edgesc. m-n vertices and mn edgesd. m_n vertices and mn edges
The correct option is: a. mn vertices and m+n edges. To determine the number of vertices and edges in the graph K_m,n, you should consider that it is a bipartite graph. A bipartite graph is a graph in which the vertices can be divided into two disjoint sets, and every edge connects a vertex from one set to another.
In the graph K_m,n, there are m vertices in the first set and n vertices in the second set. So, the total number of vertices is m + n.
The graph K_m,n is a complete bipartite graph, meaning that every vertex in one set is connected to every vertex in the other set. Therefore, there are m * n edges in the graph K_m,n.
So, the correct option is: a. mn vertices and m+n edges
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A perfect gas enclosed by an insulated (upright) cylinder and piston is in equilibrium at conditions prv, T,. A weight is placed on the piston. After a number of oscillations, the motion subsides and the gas reaches a new equilibrium at conditions P2, V2, T . Find the temperature ratio T,/T, in terms of the pressure ratio 1 = P2/P,. Show that the change of entropy is given by 1+ (y - 12 Y 2 Also show that, if the initial disturbance is small, that is 1=1+E, € <1, then S2-S R 27 S2 - S = R In *) 0"
The temperature ratio T2/T1 = I^(γ-1), and for small disturbances, the change in entropy ΔS ≈ n * R * 2 * (γ - 1) * ε.
The temperature ratio T2/T1 in terms of the pressure ratio P2/P1 can be found using the adiabatic process equation for an ideal gas. For an adiabatic process, the equation is:
P1 * V1^γ = P2 * V2^γ
Where γ is the heat capacity ratio (Cp/Cv). Since P2/P1 = I, we can rewrite the equation as:
V1^γ = V2^γ * I
From the ideal gas law, we know that P1 * V1 / T1 = P2 * V2 / T2, so:
V1 / T1 = V2 / T2 * I
Now, we can substitute V1^γ from the first equation into the second equation:
T2 / T1 = I^(γ-1)
For the change in entropy, we can use the formula:
ΔS = n * Cv * ln(T2 / T1) + n * R * ln(V2 / V1)
Substituting the temperature ratio and the volume ratio, we get:
ΔS = n * R * [(γ - 1) * ln(I) + ln(I^(γ - 1))]
For small disturbances, where I = 1 + ε and ε << 1, we can use the approximation ln(1 + ε) ≈ ε:
ΔS ≈ n * R * (γ - 1) * ε + n * R * (γ - 1) * ε
ΔS ≈ n * R * 2 * (γ - 1) * ε
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Roll 4 fair six-sided dice. Let X be the value of the lowest die.
Prove that E(X) = (2275/1296)
Hint: For a given k, what is P r(X = k)?
Please show all work
Answer:It is given b the x2 of the anwserr fot the firghjt angle
Step-by-step explanation:
What is the solution to the equation below?
x+1=√19-x
A. x=-3
B. x=3
C. x=10
D. x=-6
Answer:
B. x = 3--------------------
Given equation:
[tex]x+1=\sqrt{19-x}[/tex]
Square both sides, considering 19 - x ≥ 0 ⇒ x ≤ 19:
(x + 1)² = 19 - xSolve the quadratic equation by factoring:
x² + 2x + 1 = 19 - xx² + 3x - 18 = 0x² + 6x - 3x - 18 = 0x(x + 6) - 3(x + 6) = 0(x - 3)(x + 6) = 0x - 3 = 0 and x + 6 = 0x = 3 and x = - 6The matching choice is B.
helpplease 5. KLMN PORS; find x
L 4x + 4 M
K
N
7x-9
R
48
Q
S
60
P
The value of x that satisfies the given conditions is approximately 7.
Given that KLMN is similar to PQRS. This means that the corresponding sides of these two angles are proportional. We can use this property to set up a proportion between the sides of the two angles.
Let LM and RQ be corresponding sides in the two triangles, and let KN and SP be the other corresponding sides. Then we have:
LM/RQ = KN/SP
Substituting the given values, we get:
(4x + 4)/48 = (7x - 9)/60
To solve for x, we cross-multiply, which gives us:
(4x + 4) * 60 = (7x - 9) * 48
Expanding both sides, we get:
336x - 432 = 240x + 240
Simplifying and solving for x, we get:
96x = 672
x = 7
Therefore, the value of x that satisfies the given conditions is approximately 7.
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6. An oil company wants to lay a pipeline from its offshore drilling rig to a storage tank on shore, as illustrated in the accompanying figure. The rig (point R) is 3 miles offshore (point A), and the storage tani (point B) is 8 miles down the shoreline. The cost of laying pipe underwater is $800 per mile and along the shoreline is $400 per mile. Point P is the point on shore where the underwater pipe connects with the shoreline pipe. Where should point P be located so as to minimize the cost of laying pipe? Show the function and domain you need to optimize. Provide a complete answer and state units. R (Oil rig) 3 mi Shoreline B (Storage tank) 8 mi
The units for the cost function C(x,y) are dollars, and the units for x and y are miles.
To minimize the cost of laying the pipeline:
Point P should be located 1.5 miles down the shoreline from the storage tank (point B).
To show this, let x represent the distance from point B to point P along the shoreline, and y represent the distance from point P to the rig (point R) underwater.
Then, the total cost of laying the pipeline can be represented by the function C(x,y) = 800y + 400(8-x).
Since the distance from point A to point R is 3 miles, we know that x + y = 3. Solving for y in terms of x, we get y = 3-x.
Substituting this into the cost function, we get C(x) = 800(3-x) + 400(8-x) = 3200 - 400x.
To minimize this function, we can take the derivative and set it equal to zero:
C'(x) = -400.
Therefore, there is no critical point, but the function is decreasing as x increases.
Since x represents the distance from point B to point P along the shoreline, we want to minimize x while still satisfying the constraint that x + y = 3.
This means that y must be maximized, which occurs when x = 1.5.
Therefore, point P should be located 1.5 miles down the shoreline from the storage tank (point B) and 1.5 miles from the rig (point R) underwater.
The domain of the function we optimized was x in [0,8] (the distance along the shoreline from point B to the right) since we cannot have a negative distance or a distance greater than 8 miles along the shoreline.
The units for the cost function C(x,y) are dollars, and the units for x and y are miles.
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17. sketch each angle. then find its reference angle. show your calculations. a. 13pi/8
The reference angle for 138 is 58.
Let's first sketch the angle and then find its reference angle using the terms you mentioned.
Step 1: Sketch the angle 13π/8
To sketch the angle, first, we need to determine its position on the coordinate plane. Since 13/8 is greater than (or 8/8), it's located in the third quadrant. As a full circle is 2 (or 16/8), we can determine the angle measured counterclockwise from the positive x-axis as:
Angle = 13π/8
Step 2: Find the reference angle
A reference angle is an acute angle formed between the terminal side of the angle and the x-axis. In the third quadrant, the reference angle is calculated as:
Reference Angle = Angle - π
Now we substitute the values:
Reference Angle = 13π/8 - 8π/8 = 5π/8
So, the reference angle for 138 is 58.
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