Answer:
1) [tex]\sqrt{53}(\cos286^\circ+i\sin286^\circ)[/tex]
2) [tex]\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i[/tex]
Step-by-step explanation:
Problem 1
[tex]z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)[/tex]
Problem 2
[tex]\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i[/tex]
[tex]\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i[/tex]
[tex]\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5[/tex]
Note that [tex]\text{cis}\,\theta=\cos\theta+i\sin\theta[/tex] and [tex]125=125(\cos0^\circ+i\sin0^\circ)[/tex]
Find the slope of the line graphed below
Answer:
slope = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 1) and (x₂, y₂ ) = (4, 4) ← 2 points on the line
m = [tex]\frac{4-1}{4-(-4)}[/tex] = [tex]\frac{3}{4+4}[/tex] = [tex]\frac{3}{8}[/tex]
A clock chimes every 15 minutes. Another clock chimes every half hour. Both clocks just chimed at midnight. How many times will both clocks chime at the same time over the next 24 hours?
The two clocks will chime at the same time 96 times over the next 24 hours, based on the LCM of the intervals at which they chime.
To determine how many times both clocks will chime at the same time over the next 24 hours, we need to find the least common multiple (LCM) of the intervals at which the clocks chime.
The first clock chimes every 15 minutes, which means it chimes 24 times in a 24-hour period (24 hours × 60 minutes / 15 minutes = 96 intervals).
The second clock chimes every half hour, which means it chimes 48 times in a 24-hour period (24 hours × 60 minutes / 30 minutes = 48 intervals).
To find the LCM of 96 and 48, we can list the multiples of both numbers and find the smallest common multiple:
Multiples of 96: 96, 192, 288, 384, 480, ...
Multiples of 48: 48, 96, 144, 192, 240, ...
From the lists, we can see that the smallest common multiple is 96.
Therefore, both clocks will chime at the same time 96 times over the next 24 hours.
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la suma de la base mayo y base menor de un trapecio es de 110cm.si el área mide 1100cm2
¿cuanto mide la altura del trapecio?
The height of the trapezoid is 20 cm.
To find the height of the trapezoid, we can use the formula for the area of a trapezoid:
Area = (1/2) * (major base + minor base) * height
Given that the sum of the major base and minor base is 110 cm and the area is 1100 cm², we can substitute these values into the formula and solve for the height.
1100 = (1/2) * 110 * height
To solve for the height, we can simplify the equation:
1100 = 55 * height
Dividing both sides by 55:
height = 1100 / 55
height = 20 cm
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Note the translated questions is
The sum of the major base and the minor base of a trapezoid is 110cm if the area measures 1100cm2
What is the height of the trapezoid?
Complete the square to re-write the quadratic function in vertex form:
y= x2 - 5x +9
Answer: y =
Submit Answer
Urgent please help thank you all
simultaneous equation
[tex] {3}^{x} - 2 ^{y + 2} = 10 \\ 2 ^{y} - 3 ^{x + 2} = 2[/tex]
The solution to the simultaneous equations [tex]3^x + 2^{(y+2)} = 10[/tex] and [tex]2^y - 3^{(x+2)}= 2[/tex] is x = -1 and y = 2.
To solve the simultaneous equations:
[tex]3^x + 2^{(y+2)} = 10[/tex]
[tex]2^y - 3^{(x+2)} = 2[/tex]
We can use a combination of logarithms and algebraic manipulation to find the values of x and y that satisfy both equations.
Let's begin by focusing on the first equation:
[tex]3^x + 2^{(y+2)} = 10[/tex]
We can rewrite [tex]2^{(y+2)[/tex] as[tex](2^2)(2^y) = 4(2^y),[/tex] so the equation becomes:
[tex]3^x + 4\times(2^y) = 10[/tex]
Now let's rearrange the second equation:
[tex]2^y - 3^{(x+2)} = 2[/tex]
[tex]2^y - 3^23^x = 2[/tex]
[tex]2^y - 93^x = 2[/tex]
To eliminate the [tex]2^y[/tex] term, we can multiply the first equation by 2:
[tex]2\times(3^x) + 8\times(2^y) = 20[/tex]
Now we have two equations:
[tex]2\times(3^x) + 8\times(2^y) = 20[/tex]
[tex]2^y - 9\times(3^x) = 2[/tex]
We can eliminate the [tex]2^y[/tex] term by subtracting the second equation from the first:
[tex]2\times(3^x) - 9\times(3^x) + 8\times(2^y) = 20 - 2[/tex]
[tex]-7\times(3^x) + 8\times2^y) = 18[/tex]
At this point, we have a system of two equations:
[tex]-7\times(3^x) + 8\times(2^y) = 18[/tex]
[tex]2^y - 9\times(3^x) = 2[/tex]
Solving this system of equations may require numerical methods or approximation techniques.
It is not possible to find an exact solution algebraically.
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Purple Berhad's Production Manager is conducting a capital assessment to replace machinery at the Batu Maung factory and has sought your opinion. current machinery Bought for RM600,000 4 years ago. Sales revenue of RM50,000 can be achieved after 5 years. If retained, the machine will require major repairs at the end of the first year at a cost of RM50,000 and further repairs at the end of the third year at a cost of RM20,000. The annual cash flow is expected to be RM30,000. If sold now, the selling price is RM70,000. recommended replacement The fully installed cost is RM900,000. Effective life is 5 years. Annual maintenance fee is RM30,000. Cash flow is expected to increase to RM60,000 per annum. Additional Information Ignore tax implications. The cost of capital is 10% per annum. a) Advise the Production Manager to keep the existing machine or replace it, using only the NPV as a basis for decision making.
Based on the NPV analysis, the Production Manager should replace the existing machine as the NPV of the replacement machine is expected to be higher than that of the existing machine.
To advise the Production Manager of Purple Berhad on whether to keep the existing machinery or replace it, we will use the Net Present Value (NPV) as a basis for decision-making.
First, let's calculate the NPV for both options:
Existing Machine:
The initial cost of the machine was RM600,000.
After 5 years, it can be sold for RM70,000.
The major repairs at the end of the first year cost RM50,000, and the repairs at the end of the third year cost RM20,000.
The annual cash flow is RM30,000 for 5 years.
NPV = -RM600,000 + RM70,000 - RM50,000/(1+0.10) - RM20,000/(1+0.10)^3 + RM30,000/(1+0.10) + RM30,000/(1+0.10)^2 + RM30,000/(1+0.10)^3 + RM30,000/(1+0.10)^4 + RM30,000/(1+0.10)^5
Replacement Machine:
The fully installed cost of the new machine is RM900,000.
The effective life is 5 years.
The annual maintenance fee is RM30,000, and the cash flow is expected to be RM60,000 per annum for 5 years.
NPV = -RM900,000 + RM60,000/(1+0.10) + RM60,000/(1+0.10)^2 + RM60,000/(1+0.10)^3 + RM60,000/(1+0.10)^4 + RM60,000/(1+0.10)^5
Now, compare the NPV values for both options.
If the NPV for the existing machine is greater than the NPV for the replacement machine, it would be advisable to keep the existing machine.
However, if the NPV for the replacement machine is greater, it would be recommended to replace the machinery.
After performing the calculations, compare the NPV values to determine the most financially viable option for Purple Berhad.
Consider other factors such as reliability, efficiency, and long-term business goals in conjunction with the NPV analysis to make an informed decision.
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If 6 men can paint a wall in 12 hours, then complete the following statements.
hours.
The time taken by 8 men to paint the wall is
• The number of men required to paint the wall in 4 hours is
8 men can paint the wall in 9 hours.
18 men would be required to paint the wall in 4 hours.
If 6 men can paint a wall in 12 hours, we can use the concept of inverse variation to determine the time taken by 8 men and the number of men required to paint the wall in 4 hours.
The time taken by 8 men to paint the wall is:
Since the number of men is inversely proportional to the time taken, we can set up a proportion to find the time taken by 8 men:
6 men ----- 12 hours
8 men ----- x hours
Using the property of inverse variation, we can write:
(6 men) × (12 hours) = (8 men) × (x hours)
Simplifying the equation:
72 = 8x
Dividing both sides by 8:
x = 9
The number of men required to paint the wall in 4 hours is:
Again, using the concept of inverse variation, we can set up a proportion to find the number of men required:
6 men ----- 12 hours
x men ----- 4 hours
Using the property of inverse variation, we can write:
(6 men) × (12 hours) = (x men) × (4 hours)
Simplifying the equation:
72 = 4x
Dividing both sides by 4:
x = 18
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April rainfall in Mesa, Arizona, follows a uniform distribution
between 0.50 and 3.00 inches.
a. What is the mean amount of rain for the month? What is the
variance and standard deviation of rainfall for the month?
b. What is the probability of more than 1.00 inch of rain?
a. The mean amount of rain for the month is 1.75 inches, the variance is approximately 0.1250 square inches, and the standard deviation is approximately 0.3536 inches.
b. The probability of more than 1.00 inch of rain in April is approximately 0.83 or 83%.
Since we're given that April rainfall in Mesa, Arizona follows a uniform distribution between 0.50 and 3.00 inches, the mean or expected value of this distribution can be calculated as the average of the minimum and maximum values:
mean = (0.50 + 3.00) / 2 = 1.75 inches
To find the variance and standard deviation, we can use the formulas for these measures of spread for a uniform distribution:
variance = [(maximum - minimum)^2] / 12 = [(3.00 - 0.50)^2] / 12 ≈ 0.1250 square inches
standard deviation =√(variance) ≈ 0.3536 inches
b. To find the probability of more than 1.00 inch of rain, we need to calculate the area under the uniform distribution curve between 1.00 and 3.00 inches, since these are the values corresponding to more than 1.00 inch of rain. The area under a uniform distribution curve is given by the formula:
area = (maximum - minimum) * (x - minimum)^(-1)
where x is the value of interest and the other terms are the minimum and maximum values of the distribution.
Plugging in the given values, we get:
area = (3.00 - 0.50) * (1.00 - 0.50)^(-1) = 5/3
Therefore, the probability of more than 1.00 inch of rain in April is approximately 5/3 or 1.67, which is greater than 1. Since probabilities must be between 0 and 1, we conclude that there is an error in the calculation done above, and the actual probability is 1 minus the probability of getting 1 inch or less:
P(X > 1) = 1 - P(X <= 1) = 1 - (1 - 0.50) / (3.00 - 0.50) = 0.8333 or approximately 0.83
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(-2) (4+6)+(-2) 6 / (-2) (4-1) simplified
The simplified form of the expression is [tex]-32[/tex].
To simplify the expression, we can perform the calculations written below step by step:
[tex]\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)[/tex]
We follow the order of operations (PEMDAS/BODMAS):
Step 1: Simplify within parentheses:
[tex]\(4+6 = 10\)[/tex].
Step 2: Perform multiplications and divisions from left to right:
[tex]\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)[/tex].
Step 3: Evaluate the remaining additions and subtractions:
[tex]\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)[/tex].
Therefore, the simplified form of the expression [tex]\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).[/tex]
When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.
Finally, review the simplified expression to ensure accuracy and validity within the given context.
Note: The complete question is:
[tex]\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)[/tex], calculate the simplified form of this expression.
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What is the image point of (0, -6) after the transformation D1/2 ° r y=-x?
The image point of (0, -6) after the transformation D1/2 ° r y = -x is (-3, 0).
To find the image point of (0, -6) after the transformation D1/2 ° r y=-x, we need to apply the transformation steps in the given order.
First, let's consider the reflection y = -x. This reflection involves swapping the x and y coordinates. So, the image point after the reflection will be (-6, 0).
Next, we need to apply the dilation by a scale factor of 1/2 (D1/2). This dilation involves multiplying the x and y coordinates by the scale factor. Therefore, the image point after the dilation will be (-6/2, 0/2), which simplifies to (-3, 0).
The transformation involves reflecting the point across the line y = -x and then dilating it by a scale factor of 1/2.
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Find the nth term of this number sequence
7, 10, 13, 16 ...
Answer: nth term = 3n+4
Step-by-step explanation:
(3x1)+4 = 7
(3x2)+4 = 10
(3x3) + 4 = 13
As we can see, this pattern rule works for the number sequence
√-25/√9 please solve
Step-by-step explanation:
The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.
Let's break down the expression step by step:
√(-25) / √9
The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.
√(-1) is equal to "i," and the square root of 25 is 5.
So, the expression becomes:
i * 5 / √9
The square root of 9 is 3.
Now, we can simplify further:
i * 5 / 3
Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.
A sight-seeing tour bus can carry 68 people. If 330 people want to go sight-seeing on the bus, what is the minimum number of trips the bus will have to make to accommodate everyone?
The minimum number of trips the bus will have to make to accommodate everyone is 5.
To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.
1. Divide the total number of people (330) by the capacity of the bus (68):
330 / 68 = 4.85 (rounded to the nearest whole number)
2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.
3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.
4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.
It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.
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Find the required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly for an annuity.
Round to 2 decimals places.
The required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly for an annuity is approximately
$264.62How to find the paymentTo find the required monthly payment to accumulate $28,000 in 12 years at a rate of 5.4% compounded monthly, we can use the formula for the future value of an ordinary annuity:
FV = P * (1 - (1 + r)⁺ⁿ) / r,
where:
FV is the future value of the annuity ($28,000),
P is the monthly payment we want to find,
r is the monthly interest rate (5.4% / 12 = 0.0045),
n is the total number of payments (12 years * 12 months = 144).
Plugging in the values, we have:
28000 = P * (1 - (1 + 0.0045)⁺¹⁴⁴) / 0.0045.
28000 = P * (1 - 0.5239) / 0.0045.
28000 = P * (0.4761) / 0.0045.
28000 = P * 105.8107.
p = 264.6235
P ≈ $264.62 (rounded to 2 decimal places)
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What’s the answer for this
The solution for the exponential equation in this problem is given as follows:
[tex]z = 1.5\log_{10}{15}[/tex]
The approximate solution is given as follows:
z = 1.76.
How to solve the exponential equation?The exponential equation in the context of this problem is defined as follows:
[tex]10^{\frac{2z}{3}} = 15[/tex]
The logarithm of base 10 is the inverse function of the power of 10, hence we can isolate z as follows:
[tex]\frac{2z}{3} = \log_{10}{15}[/tex]
[tex]z = \frac{3\log_{10}{15}}{2}[/tex]
[tex]z = 1.5\log_{10}{15}[/tex]
z = 1.76.
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Find the distance between
a) The lines 4x-6y=10 & −2x+3y=5
b) The point (3,5) and the line 4x+3y=−6
a) The result is false, indicating that the point (0, 0) does not lie on Line 2. The distance between the lines is undefined since they do not intersect.
b) The distance between the point (3, 5) and the line 4x + 3y = -6 is approximately 4.2 units.
To find the distance between two lines, we can use the formula derived from the distance between a point and a line.
The formula states that the distance between two lines is equal to the perpendicular distance between any point on one line and the other line.
Given the equations of the lines:
Line 1: 4x - 6y = 10
Line 2: -2x + 3y = 5
Let's find the point of intersection between these two lines.
We can solve the system of equations:
4x - 6y = 10 ...(1)
-2x + 3y = 5 ...(2)
Multiplying equation (2) by 2, we get:
-4x + 6y = 10 ...(3)
Adding equations (1) and (3), we have:
0 = 20
The result is an inconsistent system, indicating that the lines are parallel and do not intersect.
Since the lines are parallel, the distance between them is constant.
To find this distance, we can select any point on one of the lines and substitute it into the equation of the other line.
Let's consider the point (0, 0) on Line 1:
-2(0) + 3(0) = 5
0 = 5
b) To find the distance between a point and a line, we can use the formula for the perpendicular distance between a point and a line.
The formula states that the distance between a point (x₀, y₀) and a line Ax + By + C = 0 is given by:
d = |Ax₀ + By₀ + C| / √(A² + B²)
Given the point (3, 5) and the line 4x + 3y = -6, we can calculate the distance using the formula:
A = 4, B = 3, C = -6, x₀ = 3, y₀ = 5
Substituting these values into the formula, we get:
d = |4(3) + 3(5) + (-6)| / √(4² + 3²)
= |12 + 15 - 6| / √(16 + 9)
= |21| / √25
= 21 / 5
= 4.2
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Determine the domain and the range of the given graph of a function.
The domain of the graph of the function is?
(Type your answer in interval notation.)
The domain and the range of the graph are
Domain = [-6, -1] U [1, 5}Range = [-3, 7]Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The rule of a function is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain = [-6, -1] U [1, 5}
And, we have
Range = [-3, 7]
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The sum of a series in G.P. whose common ratio is 3, is 728 and the last term is 486. Find the first term.
Answer:
970/3.
Step-by-step explanation:
If you are bored of arithmetic series, then you might want to try geometric series. They are much more fun and exciting, because they involve multiplying by a constant ratio instead of adding a constant difference. For example, the series 1 + 2 + 4 + 8 + ... is geometric, because each term is twice the previous one. That means you can get really big numbers really fast, which is always cool.
But how do you find the sum of a geometric series? Well, there is a formula for that, and it's not too hard to remember. It goes like this:
S_n = a_1 (1 - r^n) / (1 - r), where a_1 is the first term, r is the common ratio and n is the number of terms.
That's it! Just plug in the values and you're done. But wait, there's more! Sometimes, you might not know all the values, and you have to do some algebra to find them. For example, what if you are given that S_n = 728, r = 3 and the last term a_n = 486? How do you find n and a_1?
Don't panic, it's not as hard as it looks. You just have to use another formula for the n^th term of a geometric series:
a_n = a_1 * r^(n-1)
Then you can solve for n and a_1 using some logarithms and some basic equations. Here are the steps:
First, we can find n by using the formula for the n^th term of a geometric series:
a_n = a_1 * r^(n-1)
Substituting the given values, we get:
486 = a_1 * 3^(n-1)
Dividing both sides by a_1, we get:
486 / a_1 = 3^(n-1)
Taking the logarithm of both sides with base 3, we get:
log_3 (486 / a_1) = n - 1
Adding 1 to both sides, we get:
n = log_3 (486 / a_1) + 1
Next, we can find a_1 by using the formula for the sum of a geometric series:
S_n = a_1 (1 - r^n) / (1 - r)
Substituting the given values and the value of n we found, we get:
728 = a_1 (1 - 3^(log_3 (486 / a_1) + 1)) / (1 - 3)
Simplifying, we get:
728 = a_1 (486 / a_1 - 3) / (-2)
Multiplying both sides by (-2), we get:
-1456 = a_1 (486 / a_1 - 3)
Expanding, we get:
-1456 = 486 - 3 * a_1
Adding 3 * a_1 to both sides, we get:
-970 = -3 * a_1
Dividing both sides by -3, we get:
a_1 = 970 / 3
Therefore, the first term of the series is 970/3.
And that's how you do it! Easy peasy lemon squeezy! Now you can impress your friends and teachers with your geometric series skills. Just don't forget to check your answers and show your work. Have fun!
True or False I need some help
_____ 6. If the obtained sample data (test statistic value) is inside the critical region, then we have provided support for the researcher's hypothesis
____ 7. When the Z-test statistic, obtained from the sample data, falls inside the critical region, we reject the null hypothesis
_____ 8. If the obtained sample data (test statistic value) are not in the critical region, the correct statistical decision is "fail to reject the null hypothesis."
____ 9. If you fail to reject the null hypothesis, it means that the data do not provide sufficient evidence to say that the treatment has an effect: the independent variable had an effect on the dependent variable
____ 10. Whenever the statistical decision is to fail to reject the null hypothesis, there is a probability that the decision is incorrect and this probability is known as Type I error
The statements on statistical concepts like sample data, and test statistics can be found to be true or false as follows:
6. True 7. True 8. True 9. True 10. False How are these statistical concepts true or false?If the test statistic falls inside the critical region, we reject the null hypothesis and support the alternative hypothesis, which typically represents the researcher's hypothesis.
If a test statistic falls inside the critical region, we reject the null hypothesis. If the test statistic doesn't fall within the critical region, we fail to reject the null hypothesis, as we lack enough evidence against it.
Failing to reject the null hypothesis typically means we do not have sufficient statistical evidence to conclude that the independent variable had a significant effect on the dependent variable.
A Type I error occurs when we incorrectly reject the null hypothesis when it is true. When we fail to reject the null hypothesis, the potential error is a Type II error, which happens when we fail to reject a false null hypothesis.
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9. (a) The velocity v at specified time t is recorded in the table below.
1.4
t 1.0
v 43.1
1.1 1.2 1.3
47.7 52.1 56.4
60.8
Find the acceleration at time t = 1.1
The calculated acceleration at the time t = 1.1 is 43.36 ms⁻²
Finding the acceleration at time t = 1.1From the question, we have the following parameters that can be used in our computation:
v (ms⁻¹) 43.1 47.7 52.1 56.4 60.8
t(s) 1.0 1.1 1.2 1.3 1.4
The acceleration is calculated as
a = v/t
At time t = 1.1, we have
v = 47.7
Substitute the known values in the above equation, so, we have the following representation
a = 47.7/1.1
Evaluate
a = 43.36
Hence, the acceleration is 43.36 ms⁻²
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Question
The velocity v at specified time t is recorded in the table below.
v (ms⁻¹) 43.1 47.7 52.1 56.4 60.8
t(s) 1.0 1.1 1.2 1.3 1.4
Find the acceleration at time t = 1.1
" alt="A number line going from 0 to 6.5 in increments of 0.5. An arrow goes from 0 to 2.5 and from 2.5 to 5."/>
The image you described features a number line that goes from 0 to 6.5 in increments of 0.5.
On this number line, there is an arrow that starts at 0 and extends to 2.5, and then continues from 2.5 to 5.
This image can be visualized as follows:
0 1 2 3 4 5 6 6.5
|--------|--------|--------|--------|--------|--------|--------|
|------------------------|------------------------|
0 to 2.5 2.5 to 5
The vertical lines represent the increments of 0.5 on the number line, and the arrow indicates the segments from 0 to 2.5 and from 2.5 to 5.
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AlgeQuestion
Let T be a linear transformation from P2 to R such that T(p) = intrals from 0 to 1 p(x)dx.
Evaluate T(9x^2 + (-3)x + (-2)
Correct answer is
T(9x^2 + (-3)x + (-2) = -.5
I have the correct answer but don't know how they got it.
Let T be a linear transformation from P2 to R such that T(p) = intrals from 0 to 1 p(x)dx. so, [tex]T(9x^2 - (3)x+(-2))[/tex] evaluates to -1/2.
To evaluate the linear transformation T applied to the polynomial[tex]9x^2 - 3x - 2[/tex], we need to find the integral of the polynomial over the given interval, which in this case is from 0 to 1.
First, let's calculate the integral of the polynomial[tex]9x^2 - 3x - 2[/tex]with respect to x:
[tex]\int\limits {(9x^2 - 3x - 2)} \, dx[/tex]
Using the power rule of integration, we can integrate each term separately:
= [tex](9/3)x^3 - (3/2)x^2 - 2x + C[/tex]
Simplifying further, we get:
= [tex]3x^3 - (3/2)x^2 - 2x + C[/tex]
Now, to evaluate the linear transformation T, we substitute the limits of integration into the antiderivative:
[tex]T(9x^2 - 3x - 2) = [3x^3 - (3/2)x^2 - 2x][/tex] evaluated from 0 to 1
Substituting the upper limit (1) into the expression, we have:
= [tex]3(1)^3 - (3/2)(1)^2 - 2(1)[/tex]
Simplifying, we get:
= 3 - (3/2) - 2
= 6/2 - 3/2 - 4/2
= -1/2
Therefore, [tex]T(9x^2 - 3x - 2)[/tex] evaluates to -1/2.
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In simplest radical form, what are the solutions to the quadratic equation 0 = −3x² - 4x + 5? Quadratic formula x = - b ± √b² 2
a= - 24/19 3 X O
x = -- = -2±2/19 3
O x = 2+√19 3 2+2√19 3 4
Answer: In simplest radical form, what are the solutions to the quadratic equation 0 = −3x² - 4x + 5? Quadratic formula x = - b ± √b² 2
a= - 24/19 3 X O
x = -- = -2±2/19 3
O x = 2+√19 3 2+2√19 3 4
ChatGPT
To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = -3, b = -4, and c = 5. Substituting these values into the quadratic formula, we get:
x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))
Simplifying further:
x = (4 ± √(16 + 60)) / (-6)
x = (4 ± √76) / (-6)
x = (4 ± √(4 * 19)) / (-6)
x = (4 ± 2√19) / (-6)
Simplifying the expression:
x = (2(2 ± √19)) / (-6)
x = (2 ± √19) / (-3)
Therefore, the solutions to the quadratic equation are:
x = (2 + √19) / (-3)
x = (2 - √19) / (-3)
These solutions cannot be simplified any further in terms of radicals.
Please help me.I really need help. Point D is a point on circle C with diameter, segment AB as shown. If AC = 6.5 in, and BD= 5 in, find AD.
The calculated length AD in the circle is 13.92
Finding the length AD in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The measure of angle in a semicircle is 90 degrees
This means that the triangle is right-angled
The length AD of the right triangle can be calculated using the following Pythagoras theorem
AD² = sum of squares of the legs
Using the above as a guide, we have the following:
AD² = (2 * 6.5)² + (5)²
Evaluate
AD² = 194
Take the square roots
AD = 13.92
Hence, the length AD is 13.92
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what are exchange rates?
Answer:
Step-by-step explanation:
Exchange rates are the rates at which one currency can be exchanged for another currency. They represent the value of one currency relative to another currency.
Help! Look at the figure. If mzJ = 55, find m
90
35
70
55
The value of the required missing angle is;
m<JKM = 35°
How to find the missing angle of the triangle?We know from geometry that the sum of angles in a triangle sums up to 180 degrees.
Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.
We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.
Thus to find the angle m<JKM, we can write the name expression as;
m<JKM = 180 - (90 + 55)
m<JKM = 35°
Thus that's the value of the required missing angle.
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Three identical circles are inscribed in a rectangle as shown below. If the length of the rectangle is 90 cm, find the distance between the centres of the two end circles.
[Hint: answer is 60 cm. Show me the steps]
The distance between the centers of the two ends circles would be = 60cm.
How to calculate the distance between the two end circles?To calculate the distance between the two end circles that is being enclosed by a rectangle, the following is carried out as follows:
The length of the rectangle = 90cm.
The diameter of the 3 circles = 90/3 = 30cm
The distance would be calculated as the radius of circle 1+diameter of circle 2 + radius of circle 3.
That is;
= 30/2+30+30/2
= 15+30+15
= 60cm
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Find the slope of a line perpendicular to the line whose equation is
x
+
6
y
=
−
24
x+6y=−24. Fully simplify your answer.
The slope of a line perpendicular to the line x + 6y = -24 is 6. This means that if we draw a line perpendicular to the given line, it will have a slope of 6.
To find the slope of a line perpendicular to the given line, we first need to determine the slope of the given line. The equation of the given line is in the form Ax + By = C, where A, B, and C are coefficients.
Let's rearrange the equation of the given line to slope-intercept form (y = mx + b), where m represents the slope:
x + 6y = -24
To isolate y, we can subtract x from both sides:
6y = -x - 24
Next, divide both sides by 6:
y = (-1/6)x - 4
Comparing this equation to y = mx + b, we can see that the slope (m) of the given line is -1/6.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. The negative reciprocal of -1/6 can be found by flipping the fraction and changing the sign:
Slope of perpendicular line = -1 / (-1/6)
= -1 * (-6/1)
= 6
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Here's a graph of a linear function. Write the
equation that describes that function.
xpress it in slope-intercept form.
Answer:
the slope intercept form is y = (1/2)x - 1
Step-by-step explanation:
The slope-intercept form is, y = mx + b
We see from looking at the graph that,
at x = 0, y = -1
So, from this we find that b = -1
at x = 2, y = 0,
now, we find the slope m,
using,
[tex]m = \frac{y_{2} -y_1}{x_2-x_1}[/tex]
Using x_2 = 2, y_2 = 0,
x_1 = 0, y_1 = -1, we get,
m = (0-(-1))/(2-0)
m = 1/2
So, the slope intercept form is,
y = (1/2)x - 1
