The sample size should be selected as 100 in order to be 99% confident that the sample mean differs from the population mean by ±0.5 km (or within a range of 0.5 km).
To determine the sample size needed to estimate the distance students travel to school with a 99% confidence level and a margin of error of ±0.5 km, we can use the formula for sample size calculation:
n = (Z * σ / E)^2
where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 99% confidence level, which corresponds to Z = 2.576)
σ = population standard deviation
E = margin of error
Plugging in the given values:
n = (2.576 * 2.25 / 0.5)^2
Calculating this equation gives us the required sample size:
n ≈ 99.98
Since we cannot have a fractional sample size, we round up to the nearest whole number.
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What multiplies to -25 and adds to 0?
Answer:
-5 and 5
Step-by-step explanation:
[tex]-5*5=-25\\\\-5+5=0[/tex]
Please help me. I have so much late work I need this asap;
Answer: 7, 6 ,7
Step-by-step explanation:
Within the relevant range, a curvilinear cost function can sometimes be graphed as a:
a) sloping straight line
b) jagged line
c) verticle straight line
d) curved line
e) horizontal straight line
Within the relevant range, a curvilinear cost function can be graphed as a curved line. A curvilinear cost function is a cost function where the total cost changes as a function of the level of activity, but not at a constant rate.
This means that as the level of activity increases, the cost per unit may increase or decrease, resulting in a curved relationship between the level of activity and the total cost. In order to determine the optimal level of activity, a manager can use calculus to find the point where the marginal cost equals the marginal revenue.
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you are a bank officer. Elena comes to you seeking a loan. She tells you that she has sure-fire idea for a business that simply cannot fail. She stays further that the bank will not be risking a penny by granting her the loan. Do Elenas claims encourage you of discourage you from approving the loan.
As a bank officer, Elena's claims would not be enough to encourage me to approve the loan. It's important to look at the details of her business plan, her financial history and her credit score before making a decision. Even if Elena believes that her business idea cannot fail, there is always a risk involved in lending money. It's important to assess the risk and make a decision based on the facts, rather than on promises or guarantees.
Answer:
Step-by-step explanation:
Her claims encourage you.
jaffar bought 5 books. the prices of 4 of the books are $15, $16, $17, and $19. the average he paid for the 5 books is $17. how much did he pay for the fifth book?
Answer:
$18-----------------------
The average price Jaffar paid for the 5 books is $17.
To find the total cost of the 5 books, we multiply the average price by the number of books:
$17 * 5 = $85Now, we'll add up the prices of the first four books:
$15 + $16 + $17 + $19 = $67Finally, we'll subtract the sum of the first four books from the total cost to find the price of the fifth book:
$85 - $67 = $18So, Jaffar paid $18 for the fifth book.
Meghan has a jar containing 15 counters. There are only blue counters, green counters and red counters in the jar.
Hector is going to take at random one of the counters from his bag of 12 counters. He will look at the counter and put the counter back into the bag.
Hector is then going to take at random a second counter from his bag. He will look at the counter and put the counter back into the bag.
Meghan is then going to take at random one of the counters from her jar of counters. She will look at the counter and put the counter back into the jar.
The probability that the 3 counters each have a different colour is 7/24
(c) Work out how many blue counters there are in the jar.
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) = 9sqrt(x)+ 3 cos x
The most general antiderivative of f(x) = 9sqrt(x) + 3cos(x) is:
F(x) = 6x^(3/2) + 3sin(x) + C
To find the most general antiderivative of the function f(x) = 9sqrt(x) + 3cos(x), we can integrate each term separately.
The antiderivative of 9sqrt(x) can be found by using the power rule of integration. We add 1 to the exponent (1/2) and divide by the new exponent:
∫9sqrt(x) dx = 9 * (2/3)x^(3/2) + C = 6x^(3/2) + C
The antiderivative of 3cos(x) can be found using the integral of the cosine function:
∫3cos(x) dx = 3sin(x) + C
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The expression 54a + 42c represents the cost for a adults and c children to attend a play. What is the cost for 2 adults and 3 children to attend?
O A. $102
O B. $300
O C. $234
O D. $480
Answer:
Step-by-step explanation:
which of the following facts should make you the most worried about the reliability of the results of the test in this case? there is no need to worry because all of the expected cell counts are above 5. the sample was only 300 black women and is not representative of all black women. two of the six observed counts are 5 or less. not all of the cells' contributions to the chi-squared statistic are greater than 1. two of the six expected counts are less than 5.
Therefore, the reliability of the results may be questioned due to the small sample size and the fact that the observed and expected counts in some cells are too small.
The fact that two of the six observed counts are 5 or less should make you the most worried about the reliability of the results of the test in this case. This is because when the observed counts in a cell are too small, it is difficult to draw reliable conclusions from them. In such cases, the chi-squared statistic may not accurately reflect the true relationship between the variables being studied. This is because the chi-squared statistic is based on the difference between the observed counts and the expected counts, and if the observed counts are too small, the chi-squared statistic may be biased and not accurately reflect the true relationship between the variables.
Moreover, the fact that two of the six expected counts are less than 5 also raises concerns about the reliability of the results. This is because when the expected counts in a cell are too small, it may indicate that the sample size is too small or that the sample is not representative of the population being studied. In this case, the sample size was only 300 black women, which may not be representative of all black women.
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Work out 3.4 cos 13 degrees rounded to 2 d.p
Answer:
To work out 3.4 cos 13 degrees, you can use a calculator or a table of trigonometric functions that includes cosine values.
Using a calculator, you can simply enter "3.4 * cos(13)" and get the answer. Rounding to 2 decimal places gives:
3.4 * cos(13) ≈ 3.298
Therefore, 3.4 cos 13 degrees, rounded to 2 decimal places, is approximately equal to 3.30.
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Find the value of x in the figure. Figure is not drawn to scale.
Answer:
[tex]x^{0} =105^{0}[/tex]
Step-by-step explanation:
[tex]x^{0} =180-(180-(180-110)-(180-145))[/tex]
[tex]x^{0} =180-(180-70-35)[/tex]
[tex]x^{0} =180-75[/tex]
[tex]x^{0} =105[/tex]
Hope this helps
Answer:
x=105
Step-by-step explanation:
Two methods
Method 1. Solving with Exterior Angles
Method 2. Solving with Interior Angles
Method 1. Solving with Exterior Angles
So that we can keep things organized, let's call the angle in the bottom left of the triangle, Angle 1, the angle in the top of the triangle, Angle 2, and the angle in the bottom right of the triangle, Angle 3.
An Exterior Angle is formed by continuing the line segment of a side, and is the angle that forms a linear pair with the interior angle.
Observe that all of the angles given are Exterior Angles to the Polygon (in this case, a triangle), and only one exterior angle is given for each vertex (we don't want to double-count things).
For any polygon, the sum of its exterior angles is always 360 degrees.
Therefore, we can setup the following equation:
[tex]360^o=m \angle 1_{exterior} + m \angle 2_{exterior} + m \angle 3_{exterior}[/tex]
[tex]360^o=(145^o) + (110^o) + (x^o)[/tex]
Combining like terms on the right hand side...
[tex]360^o=x^o +255^o[/tex]
Isolating x by subtraction 255 degrees from both sides...
[tex](360^o)-255^o=(x^o +255^o)-255^o[/tex]
[tex]105^o=x^o[/tex]
So, x = 105
Method 2. Solving with Interior Angles
An Interior Angle is the angle we usually think of inside of a polygon (in this case, a triangle).
The sum of the Interior angles of any polygon is given by [tex]Interior~Angle~Sum=180^o*(n-2)[/tex], where "n" is the number of sides of the polygon. For triangles, n=3, so
[tex]Interior~Angle~Sum=180^o*((3)-2)[/tex]
[tex]Interior~Angle~Sum=180^o*(1)[/tex]
[tex]Interior~Angle~Sum=180^o[/tex]
In this case, we're given exterior angles for two of the vertices, and we've been asked to find the exterior angle for the third vertex. Each Exterior angle forms a linear pair with the interior angle, and thus is supplementary, meaning a pair of Interior and Exterior angles have measures that add to 180 degrees.
Keeping with our angle numbering described in Method 1, we have the following 3 true equations about each interior/exterior pair, where we can substitute in the known values, and solve for / isolate the unknown angle measure (in the last case, we'll get an expression containing "x" for its measure):
[tex]\begin{array}{ccc}180^o=m \angle 1+m \angle 1_{exterior}&180^o=m \angle 2+m \angle 2_{exterior}&180^o=m \angle 3+m \angle 3_{exterior}\\180^o=m \angle 1+(145^o)&180^o=m \angle 2+(110^o)&180^o=m \angle 3+(x^o)\\180^o-145^o=m \angle 1&180^o-110^o=m \angle 2&180^o-(x^o)=m \angle 3\\35^o=m \angle 1&70^o=m \angle 2&180^o-(x^o)=m \angle 3\end{array}[/tex]
Additionally, since the sum of the interior angles of a triangle is 180 degrees, we also have the following equation...
[tex]m \angle 1 + m \angle 2 + m \angle 3 = 180^o[/tex]
Making substitutions with the quantities found above...
[tex](35^o) + (70^o) + (180^o-x^o) = 180^o[/tex]
Rewriting subtraction as addition of a negative...
[tex]35^o + 70^o + 180^o + (-x^o) = 180^o[/tex]
Adding x degrees to both sides, and subtracting 180 degrees from both sides...
[tex]35^o + 70^o =x^o[/tex]
Combining like terms..
[tex]105^o =x^o[/tex]
So, again, x=105
find the confidence interval. thirty students received scholarship averaging $7,000 with a standard deviation of $500. find the 99% confidence interval.
We can use the formula for the confidence interval for a population mean with a known standard deviation. Plugging in the values, we get the interval (6817.22, 7182.78).
To find the 99% confidence interval for the scholarship averages of thirty students, we need to use the following formula:
CI = X ± zα/2 * (σ/√n)
Where
X = sample mean ($7,000 in this case)
zα/2 = the z-score corresponding to the desired confidence level (99% in this case), which is 2.576
σ = population standard deviation ($500 in this case)
n = sample size (30 in this case)
Substituting these values into the formula, we get:
CI = 7000 ± 2.576 * (500/√30)
Simplifying this expression, we get:
CI = 7000 ± 182.78
Therefore, the 99% confidence interval for the scholarship averages of thirty students is
(7000 - 182.78, 7000 + 182.78)
= (6817.22, 7182.78)
So we can say with 99% confidence that the true population mean scholarship amount lies within this interval.
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A
DX 105°
What is the
measure of angle D?
m/D [?]
Enter the number
of degrees.
Desired graph is attached below.
Steps to draw a desired angle are:
Draw angle ABC of measure 105 degrees.Take a point D in its interior and join BD.Measure angle ABD and angle DBC using a protractor.Add the measures of angle ABD and angle DBC together.Verify that the sum of angle ABD and angle DBC is equal to the measure of angle ABC (which is given as 105 degrees).If the sum of angle ABD and angle DBC is equal to 105 degrees, then the statement is verified.
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Complete question:
Draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.
The points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG. Plot the points then click the "Graph Quadrilateral" button. Then find the area of the rectangle.
If the points D(−3,−4), E(5,0), F(3,4), and G(−5,0) form rectangle DEFG then the area is 40 square units.
The length of the rectangle can be found by finding the distance between D and E (or F and G), which is:
√(5 - (-3))² + (0 - (-4))²] = √8² + 4²
= √80
= 4√5
The width of the rectangle can be found by finding the distance between D and G (or E and F), which is:
√-5 - (-3))² + (0 - (-4))²
= √(-2)²+ 4²
= √20
= 2√5
Therefore, the area of the rectangle is:
length x width = 4√5 x 2√5
= 8 x 5
= 40
Hence, 40 square units is area of the given rectangle DEFG.
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a cube is inscribed in a sphere of radius 6. what is the volume of the cube? exact answer only. no decimal approximations.
The volume of the inscribed cube is equal to twice the cube of the sphere's radius, which is 864 cubic units.
Let the side of the inscribed cube be 's.' The diagonal of the cube is the diameter of the sphere, which is 12 units. Therefore, by using the Pythagorean theorem, we get:
s² + s² + s² = 12²
3s² = 144
s² = 48
The volume of the cube is given by s³, which is 48√3 cubic units.
Now, the volume of the sphere is (4/3)πr³, where r is the radius of the sphere. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the diagonal of the cube, which is s√3. Hence, r = (s√3)/2.
Substituting the value of r in the volume formula, we get:
(4/3)π[(6)(√3)/2]³ = (4/3)π(54√3) = 72π√3 cubic units
Therefore, the volume of the cube is twice the volume of the sphere, which is 864 cubic units.
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I really need help please ️
The solution to all parts is shown below.
1. Using a standard normal distribution table (z-table), the corresponding percentile left of the score for a z-score of 1.93 is approximately 97.65. Therefore, the percentile can be written as an integer of 98.
2. The percentile left of the score corresponding to z-score 1.94 can be found using a standard normal distribution table (z-table).
Looking up the value of 1.94 in the z-table, we find the area under the curve to the left of 1.94 is 0.9732, or 97.32% when rounded to two decimal places.
Therefore, the corresponding percentile left of the score for z-score 1.94 is 97%.
4. Since the normal distribution is symmetrical, we know that the area in the right tail is also 0.0158.
Therefore, the total area of the shaded region is:
= 0.0158 + 0.0158 = 0.0316
7. To determine the percentage of test takers who scored lower than Lorena, we need to find the area to the left of her z-score on the standard normal distribution.
First, we calculate the z-score of Lorena's score:
z = (554 - 495) / 20 = 2.95
Using a standard normal distribution table or calculator, we find that the area to the left of z = 2.95 is approximately 0.9985. This means that approximately 99.85% of test takers scored lower than Lorena.
Therefore, Lorena scored better than about
100% - 99.85% = 0.15% of test takers, which can be rounded to 0.2%.
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Two cats started to run at the same time from the same point in the same direction, but one was running twice as fast as the other. 50 minutes later, the cats were 750 meters apart. Find the speed of each cat.
When entering class, each student is given a card labeled with either A, B. or C. The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}. Which outcomes would be part of the sample space? Select all that apply.
The value of sample space are:
⇒ (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)
We have to given that;
When entering class, each student is given a card labeled with either A, B or C.
And, The sample space showing the possibilities for being given a letter over two days can be represented as {(A,A), (A,B), (A,C), __}.
Hence, the possible outcomes for being given a letter over two days are:
{(A,A), (A,B), (A,C), (B,A), (B,B), (B,C), (C,A), (C,B), (C,C)}
So, the options that would be part of the sample space are:
(B,A), (B,B), (B,C), (C,A), (C,B), (C,C)
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help me variance and standard deviation help me
The variance is 7521.2 and the standard deviation is 86.7.
The variance is 18630.08 and the standard deviation is 136.4.
The variance is 0.0325 and the standard deviation is 0.18.
The variance is 252.8418 and the standard deviation is 15.91.
We have,
1)
Step 1: Find the mean
Mean = (106 + 121 + 152 + 234 + 347) / 5 = 192
Step 2: Find the variance
Variance = [(106-192)^2 + (121-192)^2 + (152-192)^2 + (234-192)^2 + (347-192)^2] / 5
Variance = 37606 / 5 = 7521.2
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(7521.2) = 86.7
2)
Step 1: Find the mean
Mean = (1450 + 1250 + 1776 + 1388 + 1340) / 5 = 1440.8
Step 2: Find the variance
Variance = [(1450-1440.8)^2 + (1250-1440.8)^2 + (1776-1440.8)^2 + (1388-1440.8)^2 + (1340-1440.8)^2] / 5
Variance = 93150.4 / 5 = 18630.08
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(18630.08) = 136.4
3)
Step 1: Find the mean
Mean = (7.7 + 7.4 + 7.3 + 7.9) / 4 = 7.575
Step 2: Find the variance
Variance = [(7.7-7.575)^2 + (7.4-7.575)^2 + (7.3-7.575)^2 + (7.9-7.575)^2] / 4
Variance = 0.0325
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(0.0325) = 0.18
4)
Step 1: Find the mean
Mean = (112 + 100 + 127 + 120 + 134 + 118 + 105 + 110) / 8 = 117.375
Step 2: Find the variance
Variance = [(112-117.375)^2 + (100-117.375)^2 + (127-117.375)^2 + (120-117.375)^2 + (134-117.375)^2 + (118-117.375)^2 + (105-117.375)^2 + (110-117.375)^2] / 8
Variance = 2022.7344 / 8 = 252.8418
Step 3: Find the standard deviation
Standard deviation = sqrt(Variance) = sqrt(252.8418) = 15.91
Therefore,
The variance is 7521.2 and the standard deviation is 86.7.
The variance is 18630.08 and the standard deviation is 136.4.
The variance is 0.0325 and the standard deviation is 0.18.
The variance is 252.8418 and the standard deviation is 15.91.
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a growing farming conglomerate increases its water usage at a rate of 7% every year. if it used 28,390 megaliters of water this year, then how much water will it use 5 years from now?
The farming conglomerate will use approximately 36,912.51 megaliters of water 5 years from now.
To calculate the amount of water the farming conglomerate will use 5 years from now, we can use the given information that its water usage increases at a rate of 7% every year.
Let's denote the current water usage as W₀ and the water usage after 5 years as W₅.
We know that W₅ = W₀ * (1 + r)^n, where r is the growth rate (in decimal form) and n is the number of years.
In this case, W₀ = 28,390 megaliters, r = 7% = 0.07, and n = 5.
Substituting these values into the formula, we have:
W₅ = 28,390 * (1 + 0.07)^5
Calculating this expression, we get:
W₅ ≈ 28,390 * (1.07)^5 ≈ 36,912.51 megaliters
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Find the perimeter of quadrilateral PQRS given that the coordinates of its vertices are
P(1,3),Q(3,1),R(1,−1), and S(−2,−1). You may round your answer to one decimal place.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill PQ=\sqrt{(~~ 3- 1~~)^2 + (~~ 1- 3~~)^2} \\\\\\ ~\hfill PQ=\sqrt{( 2 )^2 + ( -2)^2} \implies \boxed{PQ=\sqrt{ 8}}[/tex]
[tex]Q(\stackrel{x_1}{3}~,~\stackrel{y_1}{1})\qquad R(\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill QR=\sqrt{(~~ 1- 3~~)^2 + (~~ -1- 1 ~~)^2} \\\\\\ ~\hfill QR=\sqrt{( -2)^2 + ( -2)^2} \implies \boxed{QR=\sqrt{ 8}} \\\\\\ R(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill RS=\sqrt{(~~ -2- 1~~)^2 + (~~ -1- (-1)~~)^2} \\\\\\ ~\hfill RS=\sqrt{( -3)^2 + ( 0)^2} \implies RS=\sqrt{ 9}\implies \boxed{RS=3}[/tex]
[tex]S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad P(\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) ~\hfill SP=\sqrt{(~~ 1- (-2)~~)^2 + (~~ 3- (-1)~~)^2} \\\\\\ ~\hfill SP=\sqrt{( 3)^2 + ( 4)^2} \implies SP=\sqrt{ 25}\implies \boxed{SP=5} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{8}+\sqrt{8}+3+5} ~~ \approx ~~ \text{\LARGE 13.7}[/tex]
Find the y-intercept of the line on the graph.
Step-by-step explanation:
'y - intercept' is shorthand for ' y-axis intercept' ....or the value of the graph where it crosses the y - axis
this one is point (0,3) or y-intercept = 3
edwin eats a bowl of granola for breakfast every morning. he wonders how much granola he eats in a year. if edwin eats about one 750-gram bag of granola every month, how many kilograms of granola does he eat in a year?
Edwin eats approximately 9 kilograms of granola in a year.
To calculate how much granola Edwin eats in a year, we need to determine the total amount of granola consumed in a month and then multiply it by the number of months in a year.
Given that Edwin eats about one 750-gram bag of granola every month, we can simply multiply this by the number of months in a year, which is 12.
750 grams * 12 months = 9,000 grams
To convert grams to kilograms, we divide by 1,000 since there are 1,000 grams in a kilogram.
9,000 grams / 1,000 = 9 kilograms
Therefore, Edwin eats approximately 9 kilograms of granola in a year.
It's important to note that this calculation assumes that Edwin's granola consumption remains consistent throughout the year and that he consumes exactly one 750-gram bag each month. Variations in actual consumption may lead to slightly different results.
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Select the expression that shows the distributive property applied to: 13 (2+9)
(A) 13•2+9
(B)13•2+2-9
(C)13(9+2)
(D)13•2+13•9
Answer:
Step-by-step explanation:
to figure out the distributive property of 13(2+9), we multiply the outside number (in this case 13), into the inside numbers (2 and 9). so, 13*2 and 13*9. in this equation the 2 and 9 are separate by a + sign meaning we separate it again by the + sign. (13*2+13*9). making D the correct answer.
how many liters of oil are recquired to supply the electricalenergy needs of an average home for a year?
Approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.
To answer your question, we need to consider a few factors such as the size of the home and the energy consumption of the household. However, on average, a household consumes around 10,000 kilowatt-hours (kWh) of electricity per year. If we convert this into liters of oil, we can use a conversion factor of 0.2778 liters of oil per kWh. Therefore, an average household would require around 2,778 liters of oil per year to supply their electrical energy needs.
It is important to note that this is just an estimate and the actual amount of oil required may vary depending on various factors such as the efficiency of the heating system and the energy usage habits of the household. It is also worth considering alternative energy sources such as solar or wind power, which can reduce the dependence on oil and lower the carbon footprint of the household.
In conclusion, an average household would require approximately 2,778 liters of oil to supply their electrical energy needs for a year. However, it is important to explore alternative energy sources and implement energy-saving measures to reduce the reliance on oil and minimize environmental impact.
The number of liters of oil required to supply the electrical energy needs of an average home for a year depends on the home's energy consumption and the efficiency of the power plant converting the oil into electricity. On average, a US household consumes about 10,649 kilowatt-hours (kWh) of electricity per year.
A typical oil-fired power plant can produce around 1,885 kWh of electricity from one barrel (159 liters) of oil, with an efficiency rate of around 33%. To calculate the number of liters needed for a year, we can use the formula:
(Number of kWh per year) / (kWh per liter of oil) = Liters of oil needed
First, let's find the kWh per liter of oil: 1,885 kWh/barrel * (1 barrel/159 liters) ≈ 11.86 kWh/liter
Now we can calculate the liters of oil needed: 10,649 kWh/year / 11.86 kWh/liter ≈ 897 liters/year
So, approximately 897 liters of oil would be required to supply the electrical energy needs of an average home for a year. Keep in mind that this is a rough estimate, as factors like energy consumption and power plant efficiency can vary.
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35 > 4x, if x = 7 ? What would the equation be then?
35>28
For this problem, just replace x with seven and multiply by four.
35 > 4•7
This should get us to our new equation, 35 > 28
differentiate the function. y = tan[ln(ax + b)]
Answer:
sec² [㏑(ax + b)] X a/(ax +b)
Step-by-step explanation:
chain rule is if y = f(c) and z = f(e), and y = f[f(e)], then:
dy/de = dy/dc X dc/de
This might look complicated. Much easier with example, as in this question.
y = tan [㏑(ax + b)]
y = tan (u),
where u =㏑(v), v = ax + b
so we have y = tan (u), u = ㏑(v), v = ax + b.
dy/du = sec² (u), du/dv = 1/v, dv/dx = a.
dy/dx = dy/du X du/dv X dv/dx
= sec² (u) X (1/v) X a
= sec² [㏑(v)] X (1/(ax + b)) X a
= sec² [㏑(ax + b)] X a/(ax + b)
Help here please i need an answer for this
The measure of angle FCD is given as follows:
m < FCD = 28º.
How to obtain the angle measures?First we consider that the given angles are bisected, meaning that they are divided into two equal parts, hence:
m < E = 2(3x + 1) = 6x + 2.m < F = 2(8x - 10) = 16x - 20.Consecutive angles on a rhombus are supplementary, hence the value of x is obtained as follows:
6x + 2 + 16x - 20 = 180
22x = 198
x = 198/22
x = 9.
Then the measure of angle E is given as follows:
m < E = 6 x 9 + 2
m < E = 56º.
Opposite angles on a rhombus are congruent, hence the measure of angle C is given as follows:
m < C = m < E = 56º.
Considering the bisection, the measure of angle FCD is given as follows:
m < FCD = 0.5 x 56º = 28º.
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A basket of beads contains 8 red beans , 6 yellow beads, and 6 greens . A bead will be drawn from the basket and replaced 150 times. What is the reasonable prediction for the number of times a green bead is drawn
Step-by-step explanation:
green is 6 out of a total of ( 8+6+6 = 20 ) beads
so 6/20 ths of the time it should be a green bead
6/20 * 150 = 45 times should be green
a customer can choose one of two amplifiers, one of four compact disc players, and one of eight speaker models for an entertainment system. determine the number of possible system configurations.
There are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
To determine the number of possible configurations, we multiply the number of choices available for each component of the system. Since the customer can choose one of two amplifiers, one of four CD players, and one of eight speaker models, the total number of possible configurations is given by:
2 (amplifiers) × 4 (CD players) × 8 (speakers) = 64
Therefore, there are 64 possible system configurations that can be made from the given choices of two amplifiers, four CD players, and eight speaker models.
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