Answer:
(B)
Step-by-step explanation:
If you count, there'd be 16 blue chairs.
Therefore, B
Answer:
The answer is b
Step-by-step explanation:
When there is only 2 squares it wil be 2(4) (for 2 squares) and then 2(2) for the single square lw
So adding in another square will make it 2(6)+2(2)
=16 chairs
Noreen can walk 1/3 of a mile in 12 minutes what is her average speed in miles per hour. (this is multiple choice)
A. 36 miles per hour
B. 12 miles per hour
C. 1/4 a mile per hour
D. 1 2/3 miles and hour
ANSWER FAST PLEEEEASE
A-1hour in 36
B-16 min 12
Please do these questions for me separately(in the picture)
Based on the cost of each of the snacks in a s'more, the number that the summer camp counselor can make is E.10.
The total change in temperature on the surface of Mercury is C. 1,168°F.
What is the total s'mores that can be made?First, find out the cost of one s'more:
= (2 x 0.50) + 0.75 + (2 x 1.25)
= 1 + 0.75 + 2.50
= $4.25
The total s'mores that can be made is:
= 45 / 4.25
= 10 complete s'mores
What is the change in temperature?= 869 - (-299)
= 869 + 299
= 1,168°F
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the alkalinity level of water specimens collected from a river has a mean of 80 milligrams per liter and a standard deviation of 4.2 milligrams per liter. assume that the distribution of alkalinity levels is normal and find the probability that a water specimen collected from the river has an alkalinity level
less than 85 milligrams per liter.
To find the probability that a water specimen has an alkalinity level of fewer than 85 milligrams per liter, we can use the standard normal distribution and convert the value of 85 milligrams per liter to a standard score (z-score). The z-score can be calculated using the formula:
z = (x - mean) / standard deviation
Where x is the value of interest (85 milligrams per liter), mean is the mean of the distribution (80 milligrams per liter), and the standard deviation is the standard deviation of the distribution (4.2 milligrams per liter).
Plugging in the values, we get:
z = (85 - 80) / 4.2 = 1.19
Next, we can use a standard normal table or calculator to find the probability of getting a value less than the z-score of 1.19. This probability is approximately 0.8707, so there is about an 87.07% chance that a water specimen collected from the river has an alkalinity level of fewer than 85 milligrams per liter.
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Match each system of equations to the inverse of its coefficient matrix, A-1, and the matrix of its solution, X.
The system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X is shown in the figure.
Given that the system of equations are shown in given figure.
The first system of equations are
\(\begin{aligned}4x+2y-z&=150\\x+y-z&=-100\\-3x-y+z&=600\\\end\)
By writing in matrix AX=b, we get
Coefficient matrix \(A=\left[\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right]\) and \(B=\left[\begin{array}{l}150&-100&600\end{array}\right]\)
Firstly, we will find the A⁻¹ by finding the determinant and adjoint of A and divide the adjoint with determinant, we get
\(\begin{aligned}|A|&=\left|\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right|\\ &=4(1-1)-2(1-3)-1(-1+3)\\&=4(0)-2(-2)-1(2)\\ &=2\neq 0\end\)
\(\begin{aligned}Adj A&=\left[\begin{array}{lll}0&2&2\\-1&1&-2\\-2&3&2\end{array}\right]^T\\&=\left[\begin{array}{lll}0&-1&-2\\2&1&3\\2&-2&2\end{array}\right]\end\)
\(\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0&-0.5&-0.5\\1&0.5&1.5\\1&-1&1\end{array}\right]\end\)
For a solution Consider [A B] and apply row operations, we get
\(\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{lll1}4&2&-1&150\\1&1&-1&-100\\-3&-1&1&600\end{array}\right]\\ R_{2}&\rightarrow 4R_{2}-R_{1},R_{3}\rightarrow 4R_{3}+3R_{1}\\ &\sim \left[\begin{array}{lll1}4&2&-1&150\\0&2&-3&-550\\0&2&1&2850\end{array}\right]\\ R_{3}&\rightarrow R_{3}-R_{2}\\ &\sim \left[\begin{array}{llll}4&2&-1&150\\0&2&-3&-550\\0&0&4&3400\end{array}\right]\end\)
Thus, \(x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}-250\\1000\\850\end{array}\right]\)
The second system of equations are
\(\begin{aligned}x+y-z&=220\\5x-5y-z&=-640\\-x+y+z&=200\\\end\)
Similarly, we will find for second system of equations
\(\begin{aligned}|A|&=\left|\begin{array}{lll}1&1&-1\\5&-5&-1\\-1&1&1\end{array}\right|\\ &=1(-5+1)-1(5-1)-1(5-5)\\&=1(-4)-1(4)-1(0)\\ &=-8\neq 0\end\)
\(\begin{aligned}Adj A&=\left[\begin{array}{lll}-4&-4&0\\-2&0&-2\\-6&-4&-10\end{array}\right]^T\\&=\left[\begin{array}{lll}-4&-2&-6\\-4&0&-4\\0&-2&-10\end{array}\right]\end\)
\(\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.5&0.25&0.75\\0.5&0&0.5\\0&0.25&1.25\end{array}\right]\end\)
\(\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}1&1&-1&220\\5&-5&-1&-640\\-1&1&1&200\end{array}\right]\\ R_{2}&\rightarrow R_{2}-5R_{1},R_{3}\rightarrow R_{3}+R_{1}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&2&0&420\end{array}\right]\\ R_{3}&\rightarrow 5R_{3}+R_{2}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&0&4&360\end{array}\right]\end\)
Thus, \(x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}100\\210\\90\end{array}\right]\)
The third system of equations are
\(\begin{aligned}2x+2y-z&=290\\x+y-3z&=500\\x-y+2z&=600\\\end\)
Similarly, we will find for third system of equations
\(\begin{aligned}|A|&=\left|\begin{array}{lll}2&2&-1\\1&1&-3\\1&-1&2\end{array}\right|\\ &=2(2-3)-2(2+3)-1(-1-1)\\&=2(-1)-2(5)-1(-2)\\ &=-10\neq 0\end\)
\(\begin{aligned}Adj A&=\left[\begin{array}{lll}-1&-5&-2\\-3&5&4\\-5&5&0\end{array}\right]^T\\&=\left[\begin{array}{lll}-1&-3&-5\\-5&5&5\\-2&4&0\end{array}\right]\end\)
\(\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.1&0.3&0.5\\0.5&-0.5&-0.5\\0.2&-0.4&0\end{array}\right]\end\)
get
\(\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}2&2&-1&290\\1&1&-3&500\\1&-1&2&600\end{array}\right]\\ R_{2}&\rightarrow 2R_{2}-R_{1},R_{3}\rightarrow 2R_{3}-R_{1}\\ &\sim \left[\begin{array}{llll}2&2&-1&290\\&0&-5&710\\0&-4&5&910\end{array}\right]\end\)
Thus, \(x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}479\\-405\\-142\end{array}\right]\)
Hence, each system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X.
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one kind of scale for weighing trucks can measure their weight as they drive across a plate. however, it is not known whether this method is equivalent to the traditional method of static weighing. find a 95 % confidence interval of the weight differences. interpret this interval in context.
The interval provides a range within which we estimate the population mean weight difference to lie with a 95% level of confidence.
To find a 95% confidence interval of the weight differences between the two methods of weighing trucks, you would typically need data from both methods of weighing. The data would consist of paired observations, where each truck's weight is measured using both the dynamic (driving across a plate) and static (traditional) methods.
Assuming you have the necessary data, you can follow these steps to calculate the confidence interval:
1. Calculate the difference in weights between the two methods for each paired observation.
2. Calculate the mean of the weight differences.
3. Calculate the standard deviation of the weight differences.
4. Determine the sample size, denoted by 'n'.
5. Use the t-distribution with (n-1) degrees of freedom to find the critical value, denoted by 't', for a 95% confidence level.
6. Calculate the margin of error by multiplying the critical value 't' with the standard deviation of the weight differences divided by the square root of 'n'.
7. Construct the confidence interval by subtracting the margin of error from the mean of the weight differences to obtain the lower bound and adding the margin of error to the mean to obtain the upper bound.
Once you have the confidence interval, you can interpret it in the context of the problem. For example, you can say, "Based on our sample data, we are 95% confident that the true difference in weights between the dynamic and static weighing methods for trucks falls between [lower bound] and [upper bound] yards." The interval provides a range within which we estimate the population mean weight difference to lie with a 95% level of confidence.
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on Saturday 90 people visited a museum tickets to the museum cost 12$ for each adult and $7 for each child the museum collected 950 in ticket sales that day how many adults visited the museum?
Let's call:
a: number of adults
c: number of children
90 people visited a museum, then:
a + c = 90
Tickets to the museum cost $12 for each adult and $7 for each child and the museum collected $950, then:
12a + 7c = 950
Isolating c in the first equation:
c = 90 - a
Replacing it into the second equation:
12a + 7(90 - a) = 950
12a + 7(90) - 7a = 950
5a + 630 = 950
5a = 950 - 630
a = 320/5
a = 64
64 adults visited the museum
Help please !!!!!!!!
Answer:
ITS B
Step-by-step explanation:
I GOT IT ALL RIGHT
Hello there, pls I need help with this topic and if someone could explain it to me I would be so thankful
Answer:
25.612
Step-by-step explanation:
by using Pythagorean theorem
\( \sqrt{ {10}^{2} + {8}^{2} } = 12.806\)
ad=dc
12.806 x 2 =25.612
Solve by completing the square.
u²+26u - 49 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
U =
Submit
or u =
As integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth is \(u=-13+\sqrt{218}, u=-13-\sqrt{218}\)
What is fractions?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
\(u^2+26 u-49=0\)
Solve with the quadratic formula
\(u_{1,2}=\frac{-26 \pm \sqrt{26^2-4 \cdot 1 \cdot(-49)}}{2 \cdot 1}\)
\(\sqrt{26^2-4 \cdot 1 \cdot(-49)}=2 \sqrt{218}\)
\(u_{1,2}=\frac{-26 \pm 2 \sqrt{218}}{2 \cdot 1}\)
Separate the solutions
\($$u_1=\frac{-26+2 \sqrt{218}}{2 \cdot 1}, u_2=\frac{-26-2 \sqrt{218}}{2 \cdot 1}$$\)
\(u=\frac{-26+2 \sqrt{218}}{2 \cdot 1}: \quad-13+\sqrt{218}\)
The solutions to the quadratic equation are:
\($$u=-13+\sqrt{218}, u=-13-\sqrt{218}$$\)
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3/10+21/100 as a fraction
Answer:
51/100Step-by-step explanation:
3/10 + 21/100=> 30/100 + 21/100=> 51/100Conclusion:
Therefore, 3/10 + 21/100 equals 51/100 as a fraction.
Hoped this helped.
\(BrainiacUser1357\)
0.51000 which as smaller is 0.51
Step-by-step explanation:
simplify 21/ 100 then add 3/10 + 21/100 then simplify 3/10 then you would do 3×10+21/100 which equals 51/100
Which type of triangle can be constructed with a 50° angle between two 8-inch sides? A. Equilateral B. Isosceles C. Scalene D. Obtuse.
The correct option is (C) Isosceles. An Isosceles triangle can be constructed with a 50° angle between two 8-inch sides.
This is because isosceles triangle having two sides that are equal in length, and have 50° angle, which is acute angle, that is less than 90°. This state that the remaining angle in the triangle must also be acute triangle, as the sum of all angles in a triangle must equal 180°.
This means that the remaining angle must be 80° (i.e. 180 - 50 = 80). An isosceles triangle is triangle consisting of two sides of equal length and two angles of equal measure. The two equal sides that make up the isosceles triangle are referred to as the base and the remaining side is height or altitude.
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f(x)=2x^4-8x^2+6
2 Differentiate 2 F(x) = 2x² - 8x² +6
To differentiate \(2F(x) = 2x^2 - 8x^2 + 6\), we need to find the derivative of each term separately. The derivative of \(2x^2\) is 4x, and the derivative of \(-8x^2\) is -16x.
To differentiate \(2F(x) = 2x^2 - 8x^2 + 6\), we can differentiate each term separately. The derivative of \(2x^2\) is found using the power rule, which states that the derivative of \(x^n\) is \(nx^{(n-1)}\). Applying this rule, the derivative of \(2x^2\) is 4x.
Similarly, the derivative of \(-8x^2\) is found using the power rule as well. The derivative of \(-8x^2\) is -16x.
Lastly, the derivative of the constant term 6 is zero since the derivative of a constant is always zero.
Combining the derivatives of each term, we have 4x - 16x + 0. Simplifying this expression gives us -12x.
Therefore, the derivative of \(2F(x) = 2x^2 - 8x^2 + 6\) is -12x.
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For the following set of data, find the percentage of data within 2 population standard deviations of the mean, to the nearest percent
chart is in the photo
Percentage of data within 2 population standard deviations of the mean is 68%.
To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.
The mean can be found by summing all the values and dividing by the total number of values:
Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68
To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.
Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98
Standard Deviation = sqrt(139.98) = 11.83
Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.
Range = 2*11.83 = 23.66
The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:
Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34
Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:
Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).
Therefore, approximately 68% of the data falls within two population standard deviations of the mean.
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find me the radius with the arc length and angle already being provided
Answer: 8.63844
Step-by-step explanation:
A study of 702 high school graduates found that 58 of them will study mathematics at university. Use the survey results to estimate, with 90% confidence, the proportion of high school graduates that will study mathematics at university. Report the lower bound of the interval only, giving your answer as a percentage to two decimal places.
With 90% confidence, we estimate that the proportion of high school graduates studying mathematics at university is at least 6.07%
The proportion of graduates studying mathematics can be calculated by dividing the number of graduates who will study mathematics (58) by the total number of surveyed graduates (702).
Proportion = Number of graduates studying mathematics / Total number of surveyed graduates
Proportion = 58 / 702
Now, to construct a confidence interval, we need to consider the sample size, the proportion of graduates studying mathematics, and the desired level of confidence. Since the question specifies a 90% confidence level, we will use the z-value associated with this level, which is approximately 1.645.
The formula for the confidence interval is:
Confidence Interval = Sample Proportion ± (z-value) * Standard Error
The standard error is calculated as the square root of (p * (1 - p) / n), where p is the proportion of graduates studying mathematics and n is the sample size.
In this case:
Sample Proportion = 0.0826
Sample Size = 702
z-value (for 90% confidence) ≈ 1.645
Standard Error = √(0.0826 * (1 - 0.0826) / 702)
Standard Error ≈ 0.0133 (rounded to four decimal places)
Substituting these values into the confidence interval formula, we get:
Confidence Interval = 0.0826 ± (1.645 * 0.0133)
Now, calculating the confidence interval:
Confidence Interval = 0.0826 ± 0.0219
To obtain the lower bound of the confidence interval, we subtract the margin of error from the sample proportion:
Lower Bound = 0.0826 - 0.0219
Lower Bound ≈ 0.0607
To express the lower bound as a percentage, we multiply it by 100:
Lower Bound as a Percentage ≈ 6.07%
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Select the three equations that are correct.
A
56 ÷ 7 = 8
B
8 × 4 = 34
C
64 ÷ 9 = 7
D
42 ÷ 7 = 6
E
6 × 9 = 54
Answer:
A
C
D
Step-by-step explanation: Every other answer is wrong
Answer:
A, C,
Step-by-step explanation:
An art teacher buys 9 bags of cotton balls. There are 68 cotton balls in each bag.
Which expression is best to estimate the number of cotton balls the teacher
buys?
Answer:
9(68)
Step-by-step explanation:
9(68) = 612 cotton balls.
The vertices of a feasible region are (0, 0), (0, 2), (5, 2), and (4, 0). For which objective function is the maximum cost C fond at the vertex (4, 0)?
1. C = -2x + 3y
2. C = 5x + 3y
3. C = 2x + 7y
4. C = 4x - 3y
For C = 5x + 3y the cost found at the vertex (4,0) is maximum,
The correct option (2), C = 5x + 3y
In the question it is given that
The vertices of a feasible region are (0, 0), (0, 2), (5, 2), and (4, 0).
To find the maximum C for the vertex (4,0).
We substitute the x = 4 and y = 0 in every option,
On substituting the value of x and y in option 1 we get
C = -2x + 3y
C = -2(4) + 3(0)
C = -8 + 0
C = -8 …(i)
Substituting in option 2 we get,
C = 5 x + 3y
C = 5(4) + 3(0)
C = 20 ….(ii)
Substituting in option 3 we get,
C = 2x + 7y
C = 2(4) + 7(0)
C = 8 +0
C = 8 …(iii)
Substituting in option 4 we get,
C = 4x - 3y
C = 4(4) - 3(0)
C = 16 - 0
C = 16 …(iv)
As we can see that from equation (i) , (ii) , (iii) and (iv) , the maximum value is given by the function C = 5x + 3y, that option2.
Therefore, for C = 5x + 3y the cost found at the vertex (4,0) is maximum,
The correct option (2) C = 5x + 3y
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Distance of (-4,-7) and (14,-7)
Answer:
18 units
Step-by-step explanation:
since the y- coordinates are equal then the 2 points lie on a horizontal line and the distance (d) between them is the absolute value of the x- coordinates, that is
d = | - 4 - 14 | = | - 18 | = 18
or
d = | 14 - (- 4) | = | 14 + 4 | = 18 = 18
ind the first partial derivatives of the function. w = ln(x 8y 9z) ∂w ∂x = ∂w ∂y = ∂w ∂z =
The first partial derivatives are:
∂w/∂x = 8/x∂w/∂y = 9/y∂w/∂z = 1/zTo find the first partial derivatives of the function w = ln(x^8y^9z), we differentiate with respect to each variable separately while treating the other variables as constants.
∂w/∂x:
When differentiating with respect to x, we treat y and z as constants:
∂w/∂x = (∂/∂x) ln(x^8y^9z)
To differentiate ln(u), where u is a function of x, we apply the chain rule:
∂w/∂x = (1/u) * du/dx
In this case, u = x^8y^9z, so:
∂w/∂x = (1/(x^8y^9z)) * (∂/∂x) (x^8y^9z)
Differentiating x^8y^9z with respect to x gives us:
∂w/∂x = (1/(x^8y^9z)) * (8x^7y^9z)
Simplifying:
∂w/∂x = 8x^7y^9z / (x^8y^9z)
∂w/∂x = 8/x
Similarly, we can find the other partial derivatives:
∂w/∂y:
Treating x and z as constants, differentiate x^8y^9z with respect to y:
∂w/∂y = (1/(x^8y^9z)) * (∂/∂y) (x^8y^9z)
∂w/∂y = (1/(x^8y^9z)) * (9x^8y^8z)
∂w/∂y = 9x^8y^8z / (x^8y^9z)
∂w/∂y = 9/y
∂w/∂z:
Treating x and y as constants, differentiate x^8y^9z with respect to z:
∂w/∂z = (1/(x^8y^9z)) * (∂/∂z) (x^8y^9z)
∂w/∂z = (1/(x^8y^9z)) * (x^8y^9)
∂w/∂z = 1/z
Therefore, the first partial derivatives are:
∂w/∂x = 8/x
∂w/∂y = 9/y
∂w/∂z = 1/z
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Which relation is a function?
A coordinate grid containing a V shaped graph with arrows on the ends of the V and the point of the V is located at the origin. The V shape opens upwards.
A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.
Coordinate grid with graph of a vertical line at x equals 3.
Answer:
C) A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.
Step-by-step explanation:
not sure tho lol
V + Iwh
I = 32, w = 14, and h = 7
V = ___
Options:
A: 53
B: 3,136
C: 448
Please show your work
Equation V + Iwh , I = 32, w = 14, and h = 7, V = -3,136. The correct answer is B.
To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:
1. V + Iwh = V + (32)(14)(7)
2. V + 3,136 = V + 3,136
3. Subtract 3,136 from both sides of the equation: V = -3,136
The correct answer is option B: 3,136. Here is the solution in HTML format:
To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:
V + Iwh = V + (32)(14)(7)
V + 3,136 = V + 3,136
Subtract 3,136 from both sides of the equation: V = -3,136
The correct answer is option B: 3,136.
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simplify -4 1/2 + 3 1/4
Answer:
-5/4 or -1.25 or -1 1/4
Step-by-step explanation:
Alex wants to pay off his credit card balance before he gets married. He decides to take the $2,300 out of his savings and apply it to his credit card debt of $5,390. The credit card has an APR of 16. 5%. What will Alex's minimum monthly credit card payment be in order to pay off his debt in 14 months? a. $109. 40 b. $190. 83 c. $244. 15 d. $572. 32.
Answer:
$244.51
Step-by-step explanation:
Credit card payment =$5390
After paying $2300 from savings account,
Remaining payment left = 5390-2300 = $3090
APR = 16.5% or 0.165
Time (t) = 14 months = 14/12 years
Using credit card payment calculator,
Monthly payment = $244.15
Hence, minimum monthly payment to be made to pay off the whole debt in 14 months = $244.15
Are the following functions analytic? Use (1) or (7). 2. f(z)=iz
z
ˉ
3. f(z)=e
−2x
(cos2y−isin2y) 4. f(z)=e
x
(cosy−isiny) 5. f(z)=Re(z
2
)−iIm(z
2
) 6. f(z)=1/(z−z
5
) 7. f(z)=i/z
8
8. f(z)=Arg2πz 9. f(z)=3π
2
/(z
3
+4π
2
z) 10. f(z)=ln∣z∣+iArgz 11. f(z)=cosxcoshy−isinxsinhy
The following functions are analytic:
1. f(z) = iz
2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)
4. f(z) = \(e^x(cosy - isiny)\)
5. f(z) = \(Re(z^2) - iIm(z^2)\)
8. f(z) = \(i/z^8\)
11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)
Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.
f(z) = iz: This function is linear and can be expressed as a power series, therefore it is analytic.f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y)\): This function can also be expressed as a power series expansion and has derivatives of all orders, making it an analytic function. f(z) = \(e^x(cosy - isiny)\): Similarly, this function can be written as a power series expansion and has derivatives of all orders, making it analytic. f(z) = \(Re(z^2) - iIm(z^2)\): Although this function involves the real and imaginary parts of \(z^2\), both of these components can be expressed as power series expansions, implying that f(z) itself can be written as a power series and is thus analytic.f(z) = \(i/z^8\): This function can be rewritten as i*\((1/z^8)\) , where \(1/z^8\) can be expressed as a power series expansion. Since the multiplication of a constant (i) and an analytic function (\(1/z^8\)) results in an analytic function, f(z) is analytic. f(z) = cos(x)cos(hy) - isin(x)sin(hy): This function consists of the multiplication and addition of trigonometric functions, which are themselves analytic. Therefore, f(z) is an analytic function.Learn more about Analytic functions
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Parrel lines and angles how do I do this one
Answer:
Step-by-step explanation:
if two lines are parallel and a transversal cuts it,then corresponding angles are equal.
?=130°(corresponding angles)
If a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee. The average of three real numbers is greater than or equal to at least one of the numbers. cubicroot 2 is irrational. You can use the following fact in your proof: If n is an integer and n^3 is even, then n is even. There is no smallest integer.
To prove that if a person buys at least 400 cups of coffee in a year, then there is at least one day in which the person has bought at least two cups of coffee, we can use the Pigeonhole Principle.
There are 365 days in a year, and if a person buys at least 400 cups of coffee, there are more cups of coffee than days. By the Pigeonhole Principle, there must be at least one day where the person buys at least two cups of coffee.
The average of three real numbers is greater than or equal to at least one of the numbers. This is true because the average of the three numbers is the sum of the numbers divided by three. If all the numbers are equal, then the average is equal to each number. If at least one number is greater than the other two, the average will be greater than or equal to the smallest number.
To show that the cube root of 2 is irrational, we can use proof by contradiction. Assume that the cube root of 2 is rational, meaning it can be expressed as a fraction a/b where a and b are integers with no common factors. Then (a/b)^3 = 2. This implies a^3 = 2b^3. Since a^3 is even (because it is equal to 2 times an integer), we know that a must be even based on the given fact. Let a = 2c, then (2c)^3 = 2b^3. This simplifies to 8c^3 = 2b^3, or b^3 = 4c^3. Now, b^3 is also even, meaning b is even. However, this contradicts our assumption that a and b have no common factors, as both are divisible by 2. Thus, our assumption that the cube root of 2 is rational must be false, and the cube root of 2 is indeed irrational.
Regarding the statement "there is no smallest integer," we can prove this by considering any integer n. Since integers include negative numbers, we can find a smaller integer by subtracting 1 from n, resulting in n - 1. This process can be repeated indefinitely, showing that there is no smallest integer.
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Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.Which of the following is the most appropriate conclusion?There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.Find the p-value for the hypothesis test. A random sample of size 50 is taken. The sample has a mean of 420 and a standard deviation of 81.H0: µ = 400Ha: µ > 400The p-value for the hypothesis test is
We accert H1 alternative that is result is population mean greater than 400.
There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
We have given: μ = 14, x bar = 16, n = 40, s = 6, α = 5%, = 0.05
To test μ0 : μ = 14 Vs H1: μ > 14
Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081
So, P value = 0.021
Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
P value for the hypothesis test
n = 50, x bar = 420, sx = 81, μ = 400,
To test: H0: μ 400 Vs H1: μ > 400
It is right tail test
Test statistics = (X bar - μx)√n / sx = (420 - 400) √50 / 81 =
z = 1.7459
P value = 0.04093
Declsion: We reject H0 is p value < α
Here α = 0.05
Hence P value < α
Conclusion: We accert H1 alternative that is result is population mean greater than 400.
Hence, we accert H1 alternative that is result is population mean greater than 400.
There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
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What is the IQR for the following set of data
17, 11, 12, 18, 12, 16, 15, 14, 13
Answer:
First, we have to set it from least to greatest 11, 12, 12, 13, 14, 15, 16, 17, 18
The interqurtile range is q3 - q1
Q3 is 16.5 and the q1 is 12
16.5 - 12 = 4.5
Step-by-step explanation:
Answer is 4.5
Interquartile range (IQR) :
The interquartile range shows the range in values of the central 50% of the data. To find the interquartile range, subtract the value of the lower quartile ( or 25%) from the value of the upper quartile ( or 75%).
=> IQR = Q3 – Q1
Here,
First Arrange the data in ascending order.
11, 12, 12, 13, 14, 15, 16, 17, 18
Median = 14.
Q1 = 12 and Q3 = 16.5
IQR = Q3 - Q1 => 16.5 - 12 = 4.5
Answer is 4.5
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Van a poner balfosas en una calle que mide 3 hm y 9 dam de largo. Ya han embaldosado 125 m de calle ¿A cuantos metros les falta poner baldosas
Answer:
Faltan 265 metros por embaldosar.
Step-by-step explanation:
Un decámetro equivale a 10 metros, mientras que un hectómetro equivale a 100 metros. A continuación, calculamos la longitud equivalente de calle en metros:
\(x = 3\,hm \times \left(\frac{100\,m}{1\,hm} \right)+9\,dam\times \left(\frac{10\,m}{1\,dam} \right)\)
\(x = 390\,m\)
La longitud pendiente por poner baldosas es la longitud total menos la longitud ya embaldosada, es decir:
\(y = 390\,m-125\,m\)
\(y = 265\,m\)
Faltan 265 metros por embaldosar.