Answer:
Obtuse, scalene
Step-by-step explanation:
No same values for sides. So, scalene. Since 7^2 > 6^2 + sqrt5 ^2 , this triangle is obtuse.
what is the (approximate) mass of air in a typical room with dimensions 5.7m×3.9m×3.0m5.7m×3.9m×3.0m ?
The approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m is about 80.14 kg.
How we find the approximate mass?To calculate the approximate mass of air in a typical room with dimensions 5.7m × 3.9m × 3.0m, we need to find the volume of the room first. The volume of the room is given by:
Volume = length x width x height = 5.7m x 3.9m x 3.0m = 66.78 cubic meters
Assuming that the air in the room has a density of approximately 1.2 [tex]kg/m^3[/tex], we can use the formula:
Mass = Density x Volume
where density is in kg/m^3 and volume is in cubic meters.
Substituting the values, we get:
Mass = [tex]1.2 kg/m^3 x 66.78[/tex] cubic meters
Mass ≈ 80.14 kg
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one of two urns is chosen at random with one just as likely to be chosen as the other. then a ball is withdrawn from the chosen urn. urn 1 contains 3 white and 5 red balls, and urn 2 has 1 white and 3 red balls. if a white ball is drawn, what is the probability that it came from urn 1?
The probability that the white ball was drawn from urn 1 given that a white ball was drawn is approximately 0.654. Here we use Bayes' theorem P(A|B) = P(B|A) * P(A) / P(B).
Let A be the event that urn 1 was chosen, and B be the event that a white ball was drawn. We want to find P(A|B), the probability that urn 1 was chosen given that a white ball was drawn. Using Bayes' theorem, we have:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B|A) is the probability of drawing a white ball given that urn 1 was chosen, P(A) is the probability of choosing urn 1, and P(B) is the probability of drawing a white ball (regardless of which urn was chosen).
We can compute these probabilities as follows:
P(B|A) = 3/8 (since urn 1 has 3 white balls out of 8 total balls)
P(A) = 1/2 (since each urn is equally likely to be chosen)
P(B) = P(B|A) * P(A) + P(B|A') * P(A') = (3/8 * 1/2) + (1/4 * 1/2) = 5/16
where A' is the event that urn 2 was chosen.
Plugging these values into Bayes' theorem, we get:
P(A|B) = (3/8 * 1/2) / (5/16) = 0.654
Therefore, the probability that the white ball was drawn from urn 1 given that a white ball was drawn is approximately 0.654.
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What’s the scale factor from ABC to DEF?
The scale factor from ABC to DEF is 2/5
Calculating the scale factor from ABC to DEF?From the question, we have the following parameters that can be used in our computation:
The triangles
From the triangles, we have the following parameters
Side length of ABC = 40
Corresponding side length of DEF = 16
Using the above as a guide, we have the following:
Scale factor of the dilation = Corresponding side length of DEF / Side length of ABC
So, we have
Scale factor of the dilation = 16/40
Evaluate
Scale factor of the dilation = 2/5
Hence, the scale factor of the dilation is 2/5
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find the equations of the tangents to the curve x = 9t2 6, y = 6t3 3 that pass through the point (15, 9). y = (smaller slope) y = (larger slope)
To find the equations of the tangents to the curve x = 9t^2+6, y = 6t^3+3 that pass through the point (15, 9), we first need to find the points where the tangents touch the curve.
We do this by differentiating both x and y with respect to t and finding the value of t when the slope of the tangent line is equal to the slope of the line passing through (15,9).
Differentiating x and y with respect to t, we get dx/dt = 18t and dy/dt = 18t^2. The slope of the tangent line at a point (x,y) on the curve is given by dy/dx = (dy/dt)/(dx/dt) = t/3.
To find the values of t where the tangent line passes through (15,9), we solve the equation (y-9)/(x-15) = t/3 for t. Substituting x = 9t^2+6 and y = 6t^3+3, we get the quadratic equation 2t^2-3t+1 = 0, which factors as (t-1)(2t-1) = 0. Therefore, the two values of t are t = 1/2 and t = 1.
Now, we find the slopes of the tangent lines at t = 1/2 and t = 1 by substituting these values into the expression for dy/dx. We get slopes of -1/6 and 1/3, respectively. Using the point-slope form of the equation of a line, we can write the equations of the tangent lines as y-9 = (-1/6)(x-15) and y-9 = (1/3)(x-15).
Simplifying, we get y = (-1/6)x + 63/2 and y = (1/3)x + 3/2. Therefore, the equations of the tangents to the curve that pass through the point (15,9) are y = (-1/6)x + 63/2 and y = (1/3)x + 3/2.
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A merry-go-round has rotational inertia I as it spins on a frictionless axle with angular speed ω_i . A security guard with mass m stands a distance R from its center, as illustrated. (a) If the security guard walks to a position that is a distance R/3 from the center, what is the resulting angular speed ωf of the guard and merry-go-round? Express your answer in terms of any or all of I, ωi , m, R, and physical or mathematical constants. (b) In the problem above, how much work does the security guard do on the merry-go-round as he walks to the position that is a distance R/3 from the center? Express your answer in terms of any or all of I, wi , m, R, and physical or mathematical constants.
(a) The resulting angular speed ωf of the guard and merry-go-round can be calculated using the principle of conservation of angular momentum.
The new angular speed ωf can be expressed as ωf = ωi/(1 + 4m/9M), where M is the mass of the merry-go-round. Thus, the resulting angular speed is inversely proportional to the sum of the rotational inertia of the system and the square of the distance of the guard from the center.
As the guard moves closer to the center, the rotational inertia of the system decreases, resulting in an increase in angular speed.
(b) To find the work done by the security guard on the merry-go-round, we use the work-energy principle.
The work done is equal to the change in kinetic energy of the system, which is given by (1/2)Iω^2, where I is the rotational inertia and ω is the angular speed. Initially, the kinetic energy of the system is (1/2)Iωi^2. After the guard moves, the new kinetic energy of the system is (1/2)I'ωf^2, where I' is the new rotational inertia of the system and ωf is the new angular speed.
Thus, the work done by the guard is given by W = (1/2)I'ωf^2 - (1/2)Iωi^2.
Substituting the values of I', ωf, and simplifying the expression,
we get W = (2mR^2/9)[(ωi^2/2)(1 - 1/(1 + 4m/9M)^2)].
Therefore, the work done by the security guard is proportional to the square of the initial angular speed of the merry-go-round and inversely proportional to the sum of the rotational inertia of the system and the square of the distance of the guard from the center. As the guard moves closer to the center, the work done by him decreases.
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Find the amount of fencing (ft) needed to enclose a semi-circle having an area of 2.5 km2. Report result to nearest foot.
Answer:
Step-by-step explanation:
2.807 km × 3280.84 ft/km ≈ 9203.2 ft
Rounding this to the nearest foot, we get:
The amount of fencing needed to enclose the semi-circle is approximately 9203 feet.
if n is a positive integer, how many integers from 0 through 2n must you pick in order to be sure of getting at least one that is odd? how many integers must be picked in order to be sure of getting at least one that is even?
To guarantee to select at least one odd integer, pick one from {1,3,5,...,2n-1}. To guarantee at least one even integer, pick two from {0,2,4,...,2n}.
To be sure of getting at least one odd integer, you need to pick just one integer from the set {1,3,5,...,2n-1}. Any integer in this set is odd, so selecting just one integer guarantees that you will get an odd integer.
On the other hand, to be sure of getting at least one even integer, you need to pick two integers from the set {0,2,4,...,2n}. If you pick only one integer from this set, it could be an odd integer, which means you didn't get an even integer. But if you pick two integers, at least one of them must be even. This is because if you pick two odd integers, their sum will be even, and if you pick an even integer and an odd integer, their sum will be odd.
In summary, to be sure of getting at least one odd integer, you need to pick one integer from {1,3,5,...,2n-1}, and to be sure of getting at least one even integer, you need to pick two integers from {0,2,4,...,2n}.
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You are planning to join a gym. Muscles Gym costs $100 to join and $25 each month (
) and Cardio Gym costs nothing to join and $50 each month (
).
Solve this linear system and choose the true statement below. (Look carefully at the order of the numbers in the solution.)
The solution is (200, 4). This means that it will cost me $200 to go to either gym 4 times.
The solution is (4, 200). This means that it will cost me $200 to go to either gym 4 times.
The solution is (200, 4). This means that at 4 months of membership, either gym will cost $200.
The solution is (4, 200). This means that at 4 months of membership, either gym will cost $200.
Answer:
The answer is: (B)
The solution is (4, 200). This means that it will cost me $200 to go to either gym 4 times.
the equations given to you were:
(C = 100 + 25x) and (C = 50x)
well, if you plug in 200 for C and 4 for x you get these equations,
200 = 100 + 25(4), and 200 = 50(x)
I solved both step-by-step below.
1. C = 100 + 25x plug in points
200 = 100 + 25(4) solve the parenthesis's
200 = 100 + 100 combine like terms
200 = 200 both sides are equal
2. C = 50x plug in points
200 = 50(4) solve the parenthesis's
200 = 200 both sides are equal
Suppose college faculty members with the rank of professor at two-year institutions earn an average of $52,500 per year with a standard deviation of $4,000. In an attempt to verify this salary level, a random sample of 60 professors was selected from a personnel database for all two-year institutions in the United States.a What are the mean and standard deviation of the sampling distribution for n = 60?b What’s the shape of the sampling distribution for n = 60?c Calculate the probability the sample mean x-bar is greater than $55,000.d If you drew a random sample with a mean of $55,000, would you consider this sample unusual? What conclusions might you draw?
The sampling distribution for the sample mean can be approximated by a normal distribution with a mean of $52,500 and a standard deviation of $651.89, based on the Central Limit Theorem. The shape of the sampling distribution is approximately normal.
The probability of obtaining a sample mean greater than $55,000 can be calculated using a z-score and the standard normal distribution. The z-score is (55,000 - 52,500) / 651.89 = 3.83. Using a standard normal table or calculator, we find that the probability of obtaining a z-score greater than 3.83 is very low, approximately 0.0001.
If a random sample of size 60 had a mean of $55,000, it would be considered unusual given that it is more than 3 standard deviations above the mean of the sampling distribution. This suggests that the true population mean may be higher than $52,500. However, it is important to note that the sample may not be representative of all two-year institutions in the United States, so further investigation would be needed to draw definitive conclusions.
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help me asap please
Based on the characteristics of the line and parabola, the correct answer is:
A. [tex]\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)[/tex]
Based on the given information, let's analyze the characteristics of the line and parabola to determine the correct representation:
1. Line: In the context of graphing, a line appears as a straight line that can extend in any direction across the coordinate plane. It can have a positive or negative slope, or be horizontal or vertical.
- The line passes through the points [tex](1,1), (2,0), (4,-2), and (8,-6).[/tex]
- It extends along the first and fourth quadrants.
- A closed dot is shown at the point (1,1).
2. Parabola: In the context of graphing, a parabola appears as a curved line. It can open upward or downward and can be concave or convex. The vertex of the parabola represents the lowest or highest point on the curve, and the axis of symmetry is a vertical line that passes through the vertex, dividing the parabola into two symmetric halves.
- The parabola passes through the points [tex](1,3), (-2,6), and (10,-3).[/tex]
- It extends along the first and second quadrants.
- An open dot is shown at the point (1,3).
- The vertex of the parabola lies at (0,2).
Given these characteristics, we can determine the correct representation:
The correct answer is:
A. [tex]\(y = \begin{cases} x^2 + 2, & x \leq 1 \\ -x + 2, & x > 1 \end{cases}\)[/tex]
Explanation: The equation [tex]\(y = x^2 + 2\)[/tex] represents the parabola, and the equation [tex]\(y = -x + 2\)[/tex] represents the line. The closed dot at (1,1) corresponds to the parabola, and the open dot at (1,3) corresponds to the line.
Therefore, the correct answer is A.
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The local tennis club has 250 members. The club plans to survey 50 members about their satisfaction with the tennis club. For which plan would the outcome of the survey be biased?
The outcome of the survey would be biased if the plan for selecting the 50 members to participate in the survey is not representative of the entire membership of 250 people. Several scenarios could introduce bias into the survey:
Convenience Sampling: If the surveyors simply approach the first 50 members they encounter at the club, it would introduce bias because it assumes all members have an equal chance of being selected. However, this method may inadvertently exclude certain groups, such as those who frequently play during specific time slots.
Self-Selection Bias: If the survey is conducted on a voluntary basis, where members can choose whether to participate, it can introduce self-selection bias. Members who have extreme opinions, either highly satisfied or dissatisfied, may be more likely to participate, leading to an inaccurate representation of the overall satisfaction levels.
Demographic Bias: If the surveyors do not consider the demographic diversity within the club while selecting participants, it may result in biased outcomes. For example, if the survey predominantly includes only male or only female members, it may not accurately represent the satisfaction levels of both genders.
To avoid bias, it is crucial to use a random sampling method that ensures each member has an equal chance of being selected for the survey. This way, the selected sample will more accurately reflect the overall satisfaction of the entire membership.
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Which of the x-values are solutions to both of the following inequalities?
30 > x and x > 15
A x=15
B x=22
C=29
Answer:
B, C
Step-by-step explanation:
You want the listed values of x that satisfy both inequalities 30 > x and x > 15.
RangeWhen we have both inequality symbols pointing left, we can write these two inequalities as ...
15 < x < 30
That is, x may be any integer in the range 16 to 29, inclusive. Answer choices in that range are ...
B. x = 22
C. x = 29
The mass of Stewart's favorite frying pan is 0. 52 0. 520, point, 52 kilograms. What is the mass of the frying pan in grams?
The mass of Stewart's favorite frying pan in grams is 520 grams.
To convert the mass of Stewart's favorite frying pan from kilograms to grams, you simply need to multiply the mass in kilograms by 1000, since there are 1000 grams in 1 kilogram. In this case, the mass of the frying pan is 0.52 kilograms. To find the mass in grams, you can perform the following calculation:
0.52 kg × 1000 g/kg = 520 g
So, the mass of Stewart's favorite frying pan in grams is 520 grams.
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Determine the correct nth term formula for the following sequence.
78.65.5,53,40.5
an=90-12.5n
an=78-12.5(n-1)
an=78(12.5)^n-1
an=78-12.5n
The correct explicit formula for the nth term of the arithmetic sequence is given as follows:
[tex]a_n = 78 - 12.5(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
The first term of the sequence in this problem is given as follows:
[tex]a_1 = 78[/tex]
Each term is the previous term subtracted by 12.5, hence the common difference is given as follows:
d = -12.5.
Hence the formula for the nth term is given as follows:
[tex]a_n = 78 - 12.5(n - 1)[/tex]
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mercury melts at 38 degrees fahrenheit below zero. write the temperature as an integer.
The temperature 38 degrees below zero as an integer is -38.
how many ways can the coach select with seven players will be in the batting order on an 11 person team?
There are 330 ways the coach can select a batting order of seven players from an 11 person team.
To determine the number of ways the coach can select a batting order of seven players from an 11 person team, we can use the combination formula, which is given by:
nCr = n! / r!(n-r)!
where n is the total number of players on the team, and r is the number of players in the batting order. In this case, n = 11 and r = 7.
So, the number of ways the coach can select a batting order of seven players from an 11 person team can be calculated as follows:
11C₇ = 11! / (7!(11-7)!)
= (11 x 10 x 9 x 8) / (4 x 3 x 2 x 1)
= 330
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A. Find the perimeter of the figure below.
B. Find the area of the figure below.
Show all work for each step. Work shouk include explanations in words detailing how you simplify radical. Take your time and be thorough. Include units in final answer,
A. The perimeter of the figure is [tex]\(63\sqrt{6}\) cm[/tex].
B. The area of the figure is [tex]\(540 \, \text{cm}^2\)[/tex].
Given the dimensions of the figure below, we can calculate the perimeter and area.
The figure is a right triangle with a height of [tex]\(15\sqrt{6}\) cm[/tex], a base of [tex]\(6\sqrt{24}\) cm[/tex], and a hypotenuse of [tex]\(12\sqrt{54}\) cm[/tex].
To find the perimeter (P), we sum the lengths of all sides:
[tex]\[P = \text{base} + \text{height} + \text{hypotenuse}\][/tex]
Substituting the given values:
[tex]\[P = 6\sqrt{24} + 15\sqrt{6} + 12\sqrt{54}\][/tex]
To simplify the expression, we can evaluate the square roots:
[tex]\[P = 6\sqrt{4 \cdot 6} + 15\sqrt{6} + 12\sqrt{9 \cdot 6}\]\[P = 6 \cdot 2\sqrt{6} + 15\sqrt{6} + 12 \cdot 3\sqrt{6}\]\[P = 12\sqrt{6} + 15\sqrt{6} + 36\sqrt{6}\]\[P = 63\sqrt{6}\][/tex]
The perimeter of the figure is [tex]\(63\sqrt{6}\) cm.[/tex]
To find the area (A) of the right triangle, we can use the formula:
[tex]\[A = \frac{1}{2} \times \text{base} \times \text{height}\][/tex]
Substituting the given values:
[tex]\[A = \frac{1}{2} \times 6\sqrt{24} \times 15\sqrt{6}\][/tex]
Simplifying the expression:
[tex]\[A = 3\sqrt{4 \cdot 6} \times 15\sqrt{6}\]\[A = 3 \cdot 2\sqrt{6} \times 15\sqrt{6}\]\[A = 6\sqrt{6} \times 15\sqrt{6}\]\[A = 90 \times 6\]\[A = 540\][/tex]
The area of the figure is [tex]\(540 \, \text{cm}^2\)[/tex].
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is a footrest or in some vehicles an actual petal which is a footrest for your left foot
A footrest is also called a pedal. It is a device used in various vehicles and machinery to provide a place to rest or support your feet while operating.
Understanding the working principle of footrestIn some vehicles, particularly older models or certain types of cars, there might be a footrest positioned to the left of the driver's foot pedals (accelerator, brake, and clutch). This left footrest is designed to provide additional comfort and support for the left foot when it is not actively engaged in operating the pedals.
The purpose of the left footrest is primarily for ergonomic reasons, allowing the driver to maintain a relaxed and comfortable position during extended drives or when the left foot is not actively required for driving tasks.
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The objective of commercials on TV is to have as many viewers as possible remember the product in a favorable way and eventually buy it. With this in mind, a TV executive wondered if the length of a commercial is related to people’s memory of it. If you were to cast the executive’s thinking into a regression set-up,Select one:a. Memory will be the independent variable and length of commercial will be the dependent variableb. Length of commercial will be the independent variable and memory will be the dependent variable
b. Length of commercial will be the independent variable and memory will be the dependent variable.
The independent variable in a regression analysis is the variable that is hypothesized to influence or explain the dependent variable. In this case, the executive is interested in knowing whether the length of a commercial influences people's memory of the product advertised. Therefore, the length of the commercial is the independent variable and memory is the dependent variable.
The purpose of regression analysis is to estimate the relationship between the independent and dependent variables and to use this relationship to make predictions about the dependent variable. In this case, the regression analysis would allow the TV executive to estimate how much the length of the commercial affects people's memory of the product. The executive could then use this information to make decisions about how long the commercials should be in order to maximize their impact on viewers. For example, if the analysis suggests that longer commercials lead to better memory of the product, the executive might decide to invest in longer commercials to increase the likelihood that viewers will remember the product and eventually buy it.
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what is the probability that in a random sample of adults, more than o not own a credit card?
However, you can plug in the values into the formula in step 4 to find the probability.
To find the probability that in a random sample of adults, more than 0 do not own a credit card, follow these steps:
1. Determine the probability of a single adult not owning a credit card (P(no credit card)).
2. Calculate the complementary probability, which is the probability that an adult does own a credit card (P(credit card) = 1 - P(no credit card)).
3. For a random sample of n adults, determine the probability that all n adults own a credit card. This is given by (P(credit card))^n.
4. Finally, to find the probability that more than 0 adults in the sample do not own a credit card, calculate the complementary probability: 1 - (P(credit card))^n.
Without specific values for the probability of not owning a credit card and the sample size, I cannot provide a numerical answer. However, you can plug in the values into the formula in step 4 to find the probability.
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Find the interval of convergence for the given power series.[infinity]∑n=1(x−4)nn(−5)n
To find the interval of convergence for the power series. In other words, the power series converges for all values of x.
∑n=1∞ (x-4)^n / n*(-5)^n
we can use the ratio test:
lim┬(n→∞)|a_(n+1)/a_n|
=lim┬(n→∞)|(x-4)/(n+1)(-5/n)|
= lim┬(n→∞)|(x-4)(-5)/(n+1)n|
= |-5(x-4)| * lim┬(n→∞)1/(n+1)
= |-5(x-4)| * 0
The series will converge if the limit is less than 1 and diverge if the limit is greater than 1. Therefore, we need to solve the inequality:
|-5(x-4)| * 0 < 1
which simplifies to:
|x-4| > 0
Thus, the interval of convergence is (4 - ∞, 4 + ∞) or (-∞, ∞) in interval notation.
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find an equation of the tangent to the curve at the given point. x = 7 sin(t), y = t2 t, (0, 0)
The equation of the tangent to the curve at the given point. x = 7 sin(t), y = t2 t, (0, 0) is y = 0, To find the equation of the tangent to the curve at the given point (0, 0), we first need to find the derivative of x and y with respect to t, and then find the slope of the tangent at the given point.
Given: x = 7sin(t), y = t^2
Find dx/dt and dy/dt:
dx/dt = 7cos(t)
dy/dt = 2t
Now, find the slope of the tangent at the point (0, 0) by dividing dy/dt by dx/dt:
Slope = (dy/dt) / (dx/dt) = (2t) / (7cos(t))
At t = 0, the slope is:
Slope = (2*0) / (7cos(0)) = 0 / 7 = 0
Now we use the point-slope form of the equation to find the equation of the tangent line:
y - y1 = slope * (x - x1)
Since the point is (0, 0) and the slope is 0, the equation becomes:
y - 0 = 0 * (x - 0)
Simplifying, we get the equation of the tangent line as:
y = 0
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what percent of 240 is 10.8? if necessary, round to four decimal places.
To find the percentage, we can use the formula: (part/whole) x 100%. In this case, the part is 10.8 and the whole is 240. So, substituting these values in the formula, we get (10.8/240) x 100% = 4.5%. Therefore, 10.8 is 4.5% of 240. To round to four decimal places, we can keep the first four digits after the decimal point, which gives us 4.5000%.
To find what percent of 240 is 10.8, follow these steps:
Step 1: Write the problem as a proportion using the given values.
x% = (10.8 / 240)
Step 2: Convert the percentage to a decimal by dividing x by 100.
x/100 = (10.8 / 240)
Step 3: Solve for x by cross-multiplying.
100 * 10.8 = 240 * x
Step 4: Divide both sides by 240 to isolate x.
x = (100 * 10.8) / 240
Step 5: Calculate the value of x.
x = 1080 / 240
Step 6: Simplify the fraction and, if necessary, round to four decimal places.
x = 4.5000
Therefore, 10.8 is approximately 4.5000% of 240.
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find the component form of v given its magnitude and the angle it makes with the positive x-axis. round your answer to four decimals. ‖v‖=8,θ=15°
Therefore, the component form of vector v is (7.7551, 2.0664) (rounded to four decimals).
To find the component form of a vector v given its magnitude and the angle it makes with the positive x-axis, we can use trigonometric functions to determine the x-component (v_x) and y-component (v_y) of the vector. In this case, we are given the magnitude of the vector ‖v‖ = 8 and the angle θ = 15°. The formulas for finding the components are:
v_x = ‖v‖ * cos(θ)
v_y = ‖v‖ * sin(θ)
Plugging in the given values, we have:
v_x = 8 * cos(15°)
v_y = 8 * sin(15°)
By evaluating these trigonometric functions, we can calculate the values:
v_x ≈ 8 * cos(15°) ≈ 7.7551
v_y ≈ 8 * sin(15°) ≈ 2.0664
These values represent the x-component and y-component of the vector v, respectively. So, the component form of vector v is approximately (7.7551, 2.0664) (rounded to four decimals).
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What are three motives of money demand according to Keynes? b. What is equation linking velocity and demand for money according to Keynesian Approach? c. What is the impact on velocity as a result of i. Economy goes in to a recession ii. Credit cards are made illegal iii. Interest rate rises
a) 1.. Transactions motive or Md
2. Speculative motive or Md
3. Precautionary motive or Md
b) Money × Velocity = Price × Transactions or, M × V = P × T.
c) Impact velocity support at the moment of impact.
a) The three motives of money demand according to Keynes are:
1.. Transactions motive or Md
2. Speculative motive or Md
3. Precautionary motive or Md
b) The more money they need for such transactions, the more money they hold. The relation between transactions and money is expressed in equation, called the quantity equation:
Money × Velocity = Price × Transactions or, M × V = P × T.
c) The velocity of money is a measurement of the rate at which money is exchanged in an economy. It is the number of times that money moves from one entity to another. Impact velocity is the velocity of the striker relative to the support at the moment of impact.
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Calculate the area of the figure below.
12 ft.
6 ft.
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=12\\ b=6\\ h=9 \end{cases}\implies A=\cfrac{9(12+6)}{2}\implies A=81~ft^2[/tex]
a consumer affairs investigator records the repair cost for 20 randomly selected refrigerators. a sample mean of $57.22 and standard deviation of $25.76 are subsequently computed. determine the 90% confidence interval for the mean repair cost for the refrigerators. assume the population is approximately normal. step 1 of 2 : find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.
The critical value that should be used in constructing the confidence interval is 1.645.
Given that the sample size is 20, the degree of freedom is 19.
We have to look up the value in a standard normal probability table or a t-distribution table with degrees of freedom n-1 to find the critical value for a 90% confidence interval.
Since the sample size is large (n > 30), we can use the standard normal distribution instead of the t-distribution.
Using a standard normal probability table,
The critical value for a 90% confidence interval is 1.645.
Therefore, the critical value that should be used in constructing the confidence interval is 1.645, rounded to three decimal places.
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помогите, нужно решить систему уравнения
Answer:
x = 5, y = 6
Step-by-step explanation:
x + 5y = 35, поэтому 3x + 15y = 105 (уравнение 1)
Кроме того, 3x + 2y = 27 (уравнение 2)
Мы должны найти y, вычитая второе уравнение из первого
Получаем, 13 y = 78, значит y = 6
А теперь подставьте y в любое уравнение, чтобы найти x = 5
Differential Equation
Consider the system of differential equations
dxdt=?5ydydt=?5x.
Convert this system to a second order differential equation in y by differentiating the second equation with respect to t and substituting for xfrom the first equation.
Solve the equation you obtained for y as a function of t; hence find x as a function of t. If we also require x(0)=4 and y(0)=1, what are x and y?
The general solution of this differential equation is y(t) = c1 cos(5t) + c2 sin(5t), where c1 and c2 are constants determined by the initial conditions.
Differentiating the second equation with respect to t, we get: d^2y/dt^2 = -5 dx/dt, Substituting dx/dt from the first equation, we get: d^2y/dt^2 = -5(-5y) = 25y.
This is a second order differential equation in y. The general solution of this differential equation is y(t) = c1 cos(5t) + c2 sin(5t), where c1 and c2 are constants determined by the initial conditions.
To find x as a function of t, we can substitute y(t) into the first equation and solve for x: dx/dt = -5y = -5(c1 cos(5t) + c2 sin(5t)) , Integrating both sides with respect to t, we get: x(t) = -c1 sin(5t) + c2 cos(5t) + k
where k is a constant of integration. Using the initial conditions x(0) = 4 and y(0) = 1, we can solve for the constants c1, c2, and k: x(0) = -c1 sin(0) + c2 cos(0) + k = c2 + k = 4, y(0) = c1 cos(0) + c2 sin(0) = c1 = 1
Substituting c1 = 1 and c2 + k = 4 into the equation for x, we get:
x(t) = -sin(5t) + 4
So the solution to the system of differential equations with initial conditions x(0) = 4 and y(0) = 1 is x(t) = -sin(5t) + 4 and y(t) = cos(5t).
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Which graph shows the line of best fit for the data ?
A graph that shows the line of best fit for the data include the following: B. graph B.
What are the characteristics of a line of best fit?In Mathematics and Statistics, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:
The line should be very close to the data points as much as possible.The number of data points that are above the line should be equal to the number of data points that are below the line.By critically observing the scatter plots using the aforementioned characteristics, we can reasonably infer and logically deduce that scatter plot B or graph B best models the relationship between the data because the end points would be equally divided on both sides of the line with a positive slope and a y-intercept of 8.
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