Answer:
The dimensions of the box that minimizes the amount of material of construction is
Square base = (5.98 × 5.98) in²
Height of the box = 2.99 in.
Step-by-step explanation:
Let the length, breadth and height of the box be x, z and y respectively.
Volume of the box = xyz = 107 in³
The box has a square base and an open top.
x = z
V = x²y = 107 in³
The task is to minimize the amount of material used in its construction, that is, minimize the surface area of the box.
Surface area of the box (open at the top) = xz + 2xy + 2yz
But x = z
S = x² + 2xy + 2xy = x² + 4xy
We're to minimize this function subject to the constraint that
x²y = 107
The constraint can be rewritten as
x²y - 107 = constraint
Using Lagrange multiplier, we then write the equation in Lagrange form
Lagrange function = Function - λ(constraint)
where λ = Lagrange factor, which can be a function of x and y
L(x,y,z) = x² + 4xy - λ(x²y - 107)
We then take the partial derivatives of the Lagrange function with respect to x, y and λ. Because these are turning points, at the turning points each of the partial derivatives is equal to 0.
(∂L/∂x) = 2x + 4y - 2λxy = 0
λ = (2x + 4y)/2xy = (1/y) + (2/x)
(∂L/∂y) = 4x - λx² = 0
λ = (4x)/x² = (4/x)
(∂L/∂λ) = x²y - 107 = 0
We can then equate the values of λ from the first 2 partial derivatives and solve for the values of x and y
(1/y) + (2/x) = (4/x)
(1/y) = (2/x)
x = 2y
Hence, at the point where the box has minimal area,
x = 2y
Putting these into the constraint equation or the solution of the third partial derivative,
x²y - 107 = 0
(2y)²y = 107
4y³ = 107
y³ = (107/4) = 26.75
y = ∛(26.75) = 2.99 in.
x = 2y = 2 × 2.99 = 5.98 in.
Hence, the dimensions of the box that minimizes the amount of material of construction is
Square base = (5.98 × 5.98) in²
Height of the box = 2.99 in.
Hope this Helps!!!
To minimize packaging costs for a box with a square base and a fixed volume, we differentiate the surface area function with respect to the side length of the base and find the optimal dimensions, resulting in an approximately 5.15 inches base and a height of approximately 4.03 inches.
To minimize the material used for the open box with a square base and a given volume, we must use calculus to find the dimensions that will give us a box with minimum surface area.
Let the side of the square base be x inches and the height be h inches. Since the volume of the box is fixed at [tex]107 in^3[/tex], we have [tex]V = x^2h[/tex], which implies [tex]h = V / x^2 = 107 / x^2[/tex].
To minimize the surface area, we need to minimize the function [tex]S(x) = x^2 + 4xh[/tex]. Substituting in the equation for h, we get [tex]S(x) = x^2 + 4x(107) / x^2[/tex]. To find the minimum, take the derivative of S with respect to x and set it equal to zero. Solve for x to find the optimal dimension for the base.
After solving, we find that the dimension for the sides of the square base, x, is approximately x = 5.15 in (rounded to two decimal places). The height h would then be [tex]h = 107 / x^2[/tex] ≈ 4.03 in (rounded to two decimal places).
choose the equation with the lowest answer
10 - 0.01
10 × 0.01
10 ÷ 0.01
10 + 0.01
In the figure below, the radius of circle P is 10 units. The arc length of ABC is 16 pi. What is the arc measure of AC, in degrees?
Answer:
25
Step-by-step explanation:
Answer:
72 degrees
Step-by-step explanation:
We need to know the total circumference in order to determine the arc measure for ABC before we figure out AC
Circumference =2πr → =2π(10) → =20π
We know the length of ABC
so we set up a proportion to figure out its arc measure.
arc length/ circumference = arc measure/ degrees in a circle
16π/ 20π = arc measure/ 360 degrees
arc measure= 360 x 16π/ 20π =228 degrees
The arc measure of ABC is 228 degrees
If we combine the major arc ABC, and the minor arc AC we have the entire circle.
288 degrees +m AC= 360
m AC= 72 degrees
The measure of AC is 72 degrees
(i got the explanation off of Klan Academy when i answered the question)
Which statement represents the expression 11 (30 + 7)?
Answer:
330+77= 407
Step-by-step explanation:
*Danganronpa flashbacks*
Circle o is inscribed in triangle rst such that it is tangent at points m,n, and p. if rp is 7, rt is 17 and sm is 5, then what is the length of side st?
Answer:
15
Step-by-step explanation:
Tangents to the circle from the same point are the same length. Then rn = 7, and nt = 10. This means mt = 10, so ...
st = sm +mt = 5 +10
sm = 15
3х2 = 147
Solve by undoing
Answer: +/- 7
Step-by-step explanation:
3x² = 147
To solve for x divide through by three first.
3x² = 147
x² = 49, now we take the square root of both side by trying to apply laws of indices.
√x² = √49
The square root will neutralize the effect of the square because
√a = a¹/² so (x²)¹/², and (x²)¹/² =
x²×¹/² = x, therefore the solution is
x = +/- 7.
Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
(a) Construct and interpret a 90% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
Answer:
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
Step-by-step explanation:
Data provided
[tex]\bar X=9797[/tex] represent the sample mean for the steps
[tex]\mu[/tex] population mean
s=2313 represent the sample standard deviation
n=61 represent the sample size
Solution
The confidence interval for the true population mean is given by :
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
Since we need to find the critical value [tex]t_{\alpha/2}[/tex] we need to calculate first the degrees of freedom, given by:
[tex]df=n-1=61-1=60[/tex]
The Confidence is 0.90 or 90%, the value for the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,60)".And we see that [tex]t_{\alpha/2}=1.67[/tex]
Now we have everything in order to replace into formula (1):
[tex]9797-1.67\frac{2313}{\sqrt{61}}=9302.43[/tex]
[tex]9797+1.67\frac{2313}{\sqrt{61}}=10291.57[/tex]
And we can conclude that at 90% of confidence the true mean for the number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is between 9302.43 and 10291.57
90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps.
To construct a 90% confidence interval for the mean number of steps taken on a typical workday for people working in New York City who wear activity trackers, you can use the following formula:
Confidence Interval = X ± Z * (σ/√n)
Where:
X is the sample mean (9,797 steps).
Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645, but you can use a Z-table or calculator to get the exact value).
σ is the population standard deviation (2,313 steps).
n is the sample size (61).
Now, let's plug in the values and calculate the confidence interval:
Z for a 90% confidence level is approximately 1.645.
Confidence Interval = 9,797 ± 1.645 * (2,313/√61)
Confidence Interval = 9,797 ± 1.645 * (299.98)
Confidence Interval ≈ 9,797 ± 494.06
Now, calculate the lower and upper bounds of the confidence interval
Lower Bound = 9,797 - 494.06 ≈ 9,302.94
Upper Bound = 9,797 + 494.06 ≈ 10,291.06
Interpretation:
We are 90% confident that the true mean number of steps taken on a typical workday for all people working in New York City who wear activity trackers is between approximately 9,302.94 steps and 10,291.06 steps. This means that if we were to take many random samples and calculate a 90% confidence interval for each sample, we would expect about 90% of those intervals to contain the true population mean.
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please help if I get it wrong I cant go back (all I need is an answer)
Answer:
Subtract 9 I agree with the 1st question but can you help me back just comment if you wanna
Graphing Quadratic Equations, if you have a graph, how do you find zeros?
Answer:
look for the x-intercepts
Step-by-step explanation:
A "zero" is a value of x where the function value is zero. On a graph, that point is where the graph meets the x-axis. Every x-intercept is a zero of the function.
__
If there are no x-intercepts, then there are no real zeros. The roots (zeros) will be complex.
The study report gives a scatterplot for a random sample of penguins. The dive duration is measured in minutes and depth (x value) is in meters. The depths are all positive numbers. The dives varied from 40 meters to 300 meters in depth. The report then says, "The regression equation for this bird is y|x = 2.59 + 0.0126x.
(a) What is the y-intercept of the regression line? (Use 2 decimal places)
(b) What is the correct interpretation of the y-intercept?
Answer:
a) y-intercept = 2.59
b) Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.
Step-by-step explanation:
(a) What is the y-intercept of the regression line? (Use 2 decimal places)
The given regression equation is
y = 2.59 + 0.0126x
The standard form of the regression equation is given by
y = a + bx
Where a is the y-intercept of the regression line and b is the slope of the regression line.
Comparing the given equation with the standard form,
y-intercept = 2.59
(b) What is the correct interpretation of the y-intercept?
The y-intercept is the value we get when x = 0
y = 2.59 + 0.0126(0)
y = 2.59 + 0
y = 2.59 minutes
Therefore, we can say that when the penguin is not diving, the mean dive duration is 2.59 minutes.
Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal
Answer:
Indicate whether each of the following statements is true or false (brie y explain your reason). (a) [1pt] Consider a standard LP with four variables and three constraints. Then two basic solutions (0; 0; 0; 4; 0; 12; 18) and (3; 0; 0; 1; 0; 2; 0) are adjacent. (b) [1pt] If a linear program has no optimal solution, then it must have an unbounded feasible region. (c) [1pt] Consider the shadow prices of a standard form of LP. The vector formed by the shadow prices is a feasible solution of the dual problem of this LP. (d) [1pt] A linear program can have exactly 10 feasible solutions. (e) [1pt] Consider a primal problem of maximizing c^Tx and a dual problem of minimizing b^Ty (both subject to some constraints). If for a primal feasible solution x and a dual solution y, we have c^Tx > b^Ty, then y must be dual infeasible. (i.e not a feasible solution for the dual problem). (f) [1pt] In a two player zero sum game, there exists at least one Nash equilibrium.
Step-by-step explanation:
a. true
Because two basic feasible solution stands to be adjacent in case they possess basic variable in common. Two distinct basic solutions with respect to set related with linear constraint under is considered to be adjacent.
b.False.
If a linear problem has no solution it may have null feasible region not important to have unbounded feasible region.
c.True.
If Shadow price is feasible for standard form of LP then it will be feasible solution of dual problem of this LP.
d. False.
As there will be 'n' variables 'm' constraints having nCm feasible solutions.
e.True.
As stated in weak duality theorem
f.True
For every zero-sum 2-player normal-form game, a Nash equilibrium exists. Moreover, a pair of mixed strategies (p,q)(p,q) for the two players is a Nash equilibrium if and only if each strategy is a maximin strategy.
Dylan wanted to find the average number of hours per day that the students in his class practiced their instruments. He chose three students by drawing their names from a hat. What should he do to ensure that he has an accurate average for the class?
A dot plot going from 0 to 4. There is 1 dot above 0, 1 dot above 0.5, and 1 dot above 4.
He should add the three numbers and divide by 3 because that is how one finds an average.
He should poll more students to eliminate the variability caused by a sample size that is too small.
He should take the middle number as his average since he has three observations.
He should just find the average of 0.5 and 4 since 0 does not change anything when adding.
Answer:
D
Step-by-step explanation:
hope I was correct
To get the average he should add the three numbers and divide by 3.
What is average?The mean of a group of numbers is the average of the numbers. It is given by:
Average = (sum of all numbers) / total number of numbers
From the dot plot:
Average = (1 * 0 + 1 * 0.5 + 1 * 4) / 3 = 1.5
To get the average he should add the three numbers and divide by 3.
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The length of a rectangular garden is 7 feet longer than its width. If the garden’s perimeter is 178 feet what is the area of the garden in square feet.
Answer:1968ft^2
Step-by-step explanation:
Perimeter(p)=178feet
P=2L+2w
178=2L+2w
178=2(L+w)
L+w=178 ➗ 2
L+w=89.............(1)
W+7=L
L-w=7...................(11)
L+w=89... ..........(1)
L-w=7...................(11)
Subtract (11) from (1)
2w=89-7
2w=82
w=82 ➗ 2
w=41 width=41feet
Substitute w=41 in (11)
L-w=7
L-41=7
L=7+41
L=48feet
Area= length x width
Area=48 x 41
Area=1968ft^2
The area of the garden is 1968 square feet by setting up and solving equations based on the information about the garden's length, width, and perimeter.
Explanation:The problem is asking for the area of a rectangular garden where the length is 7 feet longer than its width. We also know the perimeter of the garden is 178 feet. Normally in a rectangle, the formula for the perimeter is P = 2(length + width).
Since the length is 7 feet longer, let's denote the width as 'w' and therefore the length as 'w+7'. Substituting in the perimeter formula we get: 178 = 2(w + w + 7).
By simplifying and solving the equation we find that the width, w = 41 feet. Therefore, the length is w+7 = 48 feet.
Lastly, the area of a rectangle is calculated as length * width, so substituting the values we found we get the area = 48 feet * 41 feet = 1968 square feet.
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Smoking levels: According to the Centers for Disease Control and Prevention, the proportion of U.S. adults age 25 or older who smoke is .22. A researcher suspects that the rate is lower among U.S. adults 25 or older who have a bachelor's degree or higher education level. What is the alternative hypothesis in this case? Group of answer choices a.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22. b.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is .22. c.The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is not .22. d.There is a relationship between level of education level and smoking habits.
Answer:
The correct option is (a).
Step-by-step explanation:
According to the Centers for Disease Control and Prevention, 0.22 or 22% of US adults of 25 years or older smoke.
But a researcher suspects that this percentage is lower if the US adults of 25 years or older have a bachelor's degree or higher education level.
So, the researcher needs to test whether the proportion of US adults of 25 years or older who smoke is less in case the adults have bachelor's degree or higher.
To test his suspicion the researcher can use a one-proportion z-test.
The hypothesis of the test can be defined as:
H₀: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is 0.22, i.e. p = 0.22.
Hₐ: The proportion of smokers among US adults of 25 years or older who have a bachelor's degree or higher is less than 0.22, i.e. p < 0.22.
Thus, the correct option is (a).
Final answer:
The alternative hypothesis for the scenario where a researcher suspects a lower smoking rate among U.S. adults with higher education is that the proportion of smokers in this group is less than .22.
Explanation:
The alternative hypothesis in this research scenario is that the proportion of U.S. adults age 25 or older who have a bachelor's degree or higher education level and smoke is lower than .22. The alternative hypothesis translates the researcher's suspicion into a testable statement and is essential for conducting a hypothesis test. The correct alternative hypothesis based on the research question would be: 'The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than .22.'
A survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device.50 (a) According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.51 Conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Answer:
We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Step-by-step explanation:
We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.
We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Let p = proportion of Americans who only use their cell phones to access the internet
SO, Null Hypothesis, [tex]H_0[/tex] : p = 38% {means that the proportion of Americans who only use their cell phones to access the internet is same as that of Chinese proportion of 38%}
Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 38% {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of cell phone owners who browse the internet
exclusively on their phone in a survey of 2,254 adults = 17%
n = sample of adults = 2,254
So, test statistics = [tex]\frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }[/tex]
= -26.542
Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Someone please help.
Answer:
...
Step-by-step explanation:
...
If you drive 27.54 km to school and then 21.86 km to your
friends, how far do you drive?
Answer:
49.4 km
Step-by-step explanation:
you add 27.54 plus 21.86 so 49.4 km total between school and to your friends house
You drive a total distance of 49.4 kilometers when you travel 27.54 kilometers to school and then 21.86 kilometers to your friend's house.
When you drive 27.54 km to school and then 21.86 km to your friend's place, you are covering a total distance of 49.4 kilometers. To calculate this, you simply add the two distances together:
Distance to school: 27.54 km
Distance to friend's place: 21.86 km
Total distance = 27.54 km + 21.86 km = 49.4 km
So, you drive a total of 49.4 kilometers when you travel to both school and your friend's house. This cumulative distance is the sum of the individual distances you cover for each leg of your journey. It's important to keep track of such distances, especially if you want to estimate fuel consumption, plan your commute, or calculate travel time accurately. In this case, you've covered 49.4 kilometers in total, which is the combined distance for your trip.
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Jason has four dollars more than Robert while Nancy has triple Roberts money how much do they each have is some of their money totals to $67
Answer:
r = 12.6, j = 16.6, n = 37.8
Step-by-step explanation:
Set up your system of equations:
j = 4 +r
n = 3r
67 = j + n + r
Plug in the first two to get down to just r so that you can solve:
67 = (4 + r) + 3r + r
67 = 5r + 4
63 = 5r
12.6 = r
Plug in r value into the other two equations above to get j and n:
j = 4 + 12.6 = 16.6
n = 3(12.6) = 37.8
Hope this helps!
Can someone help me?
(-9).(-9).(-9).(-9).(-9)
Answer:
This would be -9 to the 5th power. (-9^5)
Step-by-step explanation:
-9 to the 5th power when put in a calculator equals -59,049.
The exponent is how many times the number is multiplied by itself.
Answer:
-59049
Step-by-step explanation:
(-9).(-9).(-9).(-9).(-9)
=81.(-9).(-9).(-9)
= -729.(-9).(-9)
= 6561.(-9)
= -59049
Tomos is a skier he completed a ski race in 2 min 6 seconds the race was 525 m in length. tomos assumes that his average speed is the same for each race. using this assumption, work out how long tomos should take to complete an 800 m race give your answer in minutes and seconds
By calculating the average speed of Tomos in the 525-meter race, we can estimate that he would take about 3 minutes 12 seconds to complete an 800-meter race if he maintains the same average speed.
Explanation:To solve this problem, we first need to figure out Tomos's average speed in the 525-meter ski race that he completed in 2 minutes and 6 seconds. We convert the time to seconds for ease of calculation. So, 2 minutes 6 seconds equals 126 seconds. Now, we calculate his average speed by dividing the length of the race by the time he took to complete it:
Average speed = Distance / Time
Average speed = 525m / 126s
Average speed = 4.17 m/s
Now to calculate how long Tomos should take to complete an 800 m race, we rearrange the formula to solve for time. Time = Distance / Average Speed:
Time = 800m / 4.17 m/s
Time = 191.84 seconds
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the area of a regular pentagon with a radius of 7 cm is
The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.
Step-by-step explanation:
The given is,
Radius of pentagon - 7 cm
Step:1
Ref the attachment,
The pentagon contain 10 right angled triangle.
Angle of Right angle triangle = [tex]\frac{360}{10}[/tex] = 36°
From the right angle OPQ triangle,
sin ∅ = [tex]\frac{Opp}{Hyp}[/tex]
Where, ∅ = 36°
Radius = Hyp = 7 cm
Trigonometric ratio becomes,
sin 36° = [tex]\frac{b}{7}[/tex]
0.5878 = [tex]\frac{b}{7}[/tex] (∵ sin 36° = 0.5878 )
b = ( 0.5878 × 7 )
b = 4.115 cm
From the right angle OPQ triangle,
cos ∅ = [tex]\frac{Adj}{Hyp}[/tex]
Where, Adj = h
cos 36° = [tex]\frac{h}{7}[/tex]
0.809017 = [tex]\frac{h}{7}[/tex]
h = ( 0.809017 × 7 )
h = 5.663 cm
Step:2
Area of triangle OPR,
[tex]A = \frac{1}{2} (Height )(Base)[/tex]
Where, Height, h = 5.663 cm
Base = b + c = 4.115 + 4.115 = 8.23 cm
Area of OPQ becomes,
A = [tex]\frac{1}{2}[/tex] (8.23)(5.663)
= [tex]\frac{1}{2}[/tex] ( 46.6065)
A = 23.30324 squared centimeters
Step:3
Pentagon contain 5 triangles,
Area of pentagon = 5 × Area of triangle
= 5 × 23.30324
= 116.516 squared centimeters
Area of pentagon = 116.516 squared centimeters
Result:
The area of a regular pentagon is 116.516 squared centimeters, if the pentagon has a radius of 7 cm.
The number of guppies that a fish tank can safely hold depends on its volume.A fish tank should have a volume of 576 cubic inches to safely hold 3 guppies.how many guppies can a fish tank that is 24 inches long, 12 inches wide, and 16 inches highly safely hold?
Answer:
24 guppies
Step-by-step explanation:
Assuming a linear relationship, the volume required per guppy is given by:
[tex]g=\frac{576\ in^3}{3\ guppies}\\ g= 192\ in^3/guppy[/tex]
The volume of the fish tank is given by the product of its length, by its width and its height:
[tex]V = 24*12*16\\V=4,608\ in^3[/tex]
The number of guppies that this tank can safely hold is:
[tex]n=\frac{V}{g}=\frac{4,608}{192} \\n=24\ guppies[/tex]
The tank can safely hold 24 guppies.
Came someone help me please!!
Answer:
D
Step-by-step explanation:
if m increases n increases too and vice versa
please like and Mark as brainliest
A new pair of basketball shoes costs $98.00 at the sporting goods store. If there is a 10% sales tax, what is the actual cost of the shoes?
$
Answer 98x1.10 =107.8
Step-by-step explanation:
Answer:
107.80
Step-by-step explanation:
98*.10+=107.80
I need some help pls
Answer:
160°
Step-by-step explanation:
∠C and ∠D are both inscribed angles of arc AB. Therefore, they are equal.
5w + 20 = 7w − 4
24 = 2w
w = 12
Therefore, ∠C = ∠D = 80°.
Inscribed angles are half the central angle, so mAB = 2 × 80° = 160°.
Hannah is is a keen archer one day she shoots five arrows each arrow scores and eight what is her total score
Answer:
40
Step-by-step explanation:
8*5
which expressions are equivalent to 7•7•7•7•7•7
Answer:7^6
Step-by-step explanation:
Answer:
7^6
Step-by-step explanation:
Let F = sin ( 8 x + 5 z ) i − 8 y e x z k . F=sin(8x+5z)i−8yexzk. Calculate div ( F ) div(F) and curl ( F ) . and curl(F). (Express numbers in exact form. Use symbolic notation and fractions where needed.)
Answer:
Required results are [tex]\nabla .\vec{F}[/tex]=8\cos(8x+5z)-8ye^x[/tex] and [tex]\nabla\times \vec{F}=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Step-by-step explanation:
Given vector function is,
[tex]\vec{F}=\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k}[/tex]
To find [tex]\nabla .\vec{F}[/tex] and [tex]\nabla \times \vec{F}[/tex] .
[tex]\nabla .\vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]=\frac{\partial}{\partial x}(\sin(8x+5z))-\frac{\partial}{\partial z}(8ye^xz)[/tex]
[tex]=8\cos(8x+5z)-8ye^x[/tex]
And,
[tex]\nabla \times \vec{F}[/tex]
[tex]=(\frac{\partial}{\partial x}\uvec{i}+\frac{\partial}{\partial y} \uvec{j}+\frac{\partial}{\partial z} \uvec{k})\times(\sin(8x+5z)\uvec{i}-8ye^xz\uvec{k})[/tex]
[tex]\end{Vmatrix}[/tex]
[tex]=\uvec{i}\Big[\frac{\partial}{\partial y}(-8ye^xz)\Big]-\uvec{j}\Big[\frac{\partial}{\partial x}(-8ye^xz)-\frac{\partial}{\partial z}(\sin(8x+5z))\Big]+\uvec{k}\Big[-\frac{\partial}{\partial y}(-\sin(8x+5z))\Big][/tex]
[tex]=-8e^xz\uvec{i}+(8ye^xz+5\sin(8x+5z))\uvec{j}[/tex]
Hence the result.
Write the polynomial in factored form as a product of linear factors f(r)=r^3-9r^2+17r-9
Answer:
f(r) = (x -1)(x -4+√7)(x -4-√7)
Step-by-step explanation:
The signs of the terms are + - + -. There are 3 changes in sign, so Descartes' rule of signs tells you there are 3 or 1 positive real roots.
The rational roots, if any, will be factors of 9, the constant term. The sum of coefficients is 1 -9 +17 -9 = 0, so you know that r=1 is one solution to f(r) = 0. That means (r -1) is a factor of the function.
Using polynomial long division, synthetic division (2nd attachment), or other means, you can find the remaining quadratic factor to be r^2 -8r +9. The roots of this can be found by various means, including completing the square:
r^2 -8r +9 = (r^2 -8r +16) +9 -16 = (r -4)^2 -7
This is zero when ...
(r -4)^2 = 7
r -4 = ±√7
r = 4±√7
Now, we know the zeros are {1, 4+√7, 4-√7), so we can write the linear factorization as ...
f(r) = (r -1)(r -4 -√7)(r -4 +√7)
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Comment on the graph
I like to find the roots of higher-degree polynomials using a graphing calculator. The red curve is the cubic. Its only rational root is r=1. By dividing the function by the known factor, we have a quadratic. The graphing calculator shows its vertex, so we know immediately what the vertex form of the quadratic factor is. The linear factors are easily found from that, as we show above. (This is the "other means" we used to find the quadratic roots.)
Candy. Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla.
a) If there really were 6 vanilla and 6 peanut butter candies in the box, what is the probability that you would have picked three vanillas in a row?
b) Do you think there really might have been 6 of each? Explain.
c) Would you continue to believe that half are vanilla if the fourth one you try is also vanilla? Explain.
Answer:
a) P=0.091
b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but it is still possible that there are 6 of each taste.
c) The probability of picking 4 vainilla in a row, if there are half of each taste, is P=0.030.
This is a very improbable case, so if this happens we would have reasons to think that there are more than half vainilla candies in the box.
Step-by-step explanation:
We can model this problem with the variable x: number of picked vainilla in a row, following a hypergeometric distribution:
[tex]P(x=k)=\dfrac{\binom{K}{k}\cdot \binom{N-K}{n-k}}{\binom{N}{n}}[/tex]
being:
N is the population size (12 candies),
K is the number of success states in the population (6 vainilla candies),
n is the number of draws (3 in point a, 4 in point c),
k is the number of observed successes (3 in point a, 4 in point c),
a) We can calculate this as:
[tex]P(x=3)=\dfrac{\binom{6}{3}\cdot \binom{12-6}{3-3}}{\binom{12}{3}}=\dfrac{\binom{6}{3}\cdot \binom{6}{0}}{\binom{12}{3}}=\dfrac{20\cdot 1}{220}=0.091[/tex]
b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but is possible.
c) In the case k=4, we have:
[tex]P(x=3)=\dfrac{\binom{6}{4}\cdot \binom{6}{0}}{\binom{12}{4}}=\dfrac{15\cdot 1}{495}=0.030[/tex]
This is a very improbable case, so we would have reasons to think that there are more than half vainilla candies in the box.
Using the hypergeometric distribution, it is found that:
a) 0.0909 = 9.09% probability that you would have picked three vanillas in a row.b) The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.c) The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.The candies are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.Item a:
There is a total of 12 candies, hence [tex]N = 12[/tex].6 of those candies are vanillas, hence [tex]k = 6[/tex].3 candies are chosen, hence [tex]n = 3[/tex].The probability that you would have picked three vanillas in a row is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,12,3,6) = \frac{C_{6,3}C_{6,0}}{C_{12,3}} = 0.0909[/tex]
0.0909 = 9.09% probability that you would have picked three vanillas in a row.
Item b:
The probability is above 5%, hence it is not an unusual event and gives no evidence that there might not have been 6 of each.
Item c:
Now n = 4, and the probability is P(X = 4), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,12,4,6) = \frac{C_{6,4}C_{6,0}}{C_{12,4}} = 0.0303[/tex]
The probability is below 5%, hence it is an unusual event and there is enough evidence to believe that there might not have been 6 of each.
To learn more about the hypergeometric distribution, you can take a look at https://brainly.com/question/4818951
The graph shows sales as a function of time.
Answer:
You can use the graph of a trigonometry function to show sales amounts over a given period of time. Here’s an example: Even though people in many parts of the world play soccer year-round, certain times of the year show an increase in the sales of outdoor soccer shoes.
Step-by-step explanation: