Looks like either [tex]f''(x)=4x^2[/tex] or [tex]f''(x)=\frac4{x^2}[/tex]...
In the first case, integrate both sides twice to get
[tex]f''(x)=4x^2\implies f'(x)=\dfrac43x^3+C_1\implies f(x)=\dfrac13x^4+C_1x+C_2[/tex]
Then the initial conditions give
[tex]f'(1)=2\implies 2=\dfrac43\cdot1^3+C_1\implies C_1=\dfrac23[/tex]
[tex]f(1)=5\implies 5=\dfrac13\cdot1^4+C_1\cdot1+C_2\implies C_2=4[/tex]
so that the particular solution is
[tex]f(x)=\dfrac{x^4}3+\dfrac{2x}3+4[/tex]
If instead [tex]f''(x)=\frac4{x^2}[/tex], we have
[tex]f''(x)=\dfrac4{x^2}\implies f'(x)=-\dfrac4x+C_1\implies f(x)=-4\ln|x|+C_1x+C_2[/tex]
[tex]f'(1)=2\implies 2=-\dfrac41+C_1\implies C_1=6[/tex]
[tex]f(1)=5\implies 5=-4\ln|1|+C_1\cdot1+C_2\implies C_2=-1[/tex]
[tex]\implies f(x)=-4\ln|x|+6x-1[/tex]
Change each of the following points from rectangular coordinates to spherical coordinates and to cylindrical coordinates.
a. (4,2,−4)
b. (0,8,15)
c. (√2,1,1)
d. (−2√3,−2,3)
Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:
[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]
[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]
For angle θ:
If x > 0 and y > 0: [tex]\theta = tan^{-1}\frac{y}{x}[/tex];If x < 0: [tex]\theta = \pi + tan^{-1}\frac{y}{x}[/tex];If x > 0 and y < 0: [tex]\theta = 2\pi + tan^{-1}\frac{y}{x}[/tex];Calculating:
a) (4,2,-4)
[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6
[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]
[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]
For θ, choose 1st option:
[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]
[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]
b) (0,8,15)
[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17
[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]
[tex]\theta = tan^{-1}\frac{y}{x}[/tex]
The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]
c) (√2,1,1)
[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2
[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]
[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]
[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]
d) (−2√3,−2,3)
[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5
[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]
Since x < 0, use 2nd option:
[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]
[tex]\theta = \pi + \frac{\pi}{6}[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:
[tex]r=\sqrt{x^{2}+y^{2}}[/tex]
Angle θ is the same as spherical coordinate;
z = z
Calculating:
a) (4,2,-4)
[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]
[tex]\theta = tan^{-1}\frac{1}{2}[/tex]
z = -4
b) (0, 8, 15)
[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8
[tex]\theta = \frac{\pi}{2}[/tex]
z = 15
c) (√2,1,1)
[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]
[tex]\theta = \frac{\pi}{3}[/tex]
z = 1
d) (−2√3,−2,3)
[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4
[tex]\theta = \frac{7\pi}{6}[/tex]
z = 3
Ashton needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Ashton only has $50 to spend on the car rental, what is the maximum number of miles she can drive?
Answer:
166.9 miles or 166 miles
Step-by-step explanation:
We can form an equation like this:
19.95 + .18x = 50
In this equation, "x" is the number of miles.
=> 19.95 - 19.95 +.18x = 50 -19.95
=> .18x = 30.05
=> .18x/.18 = 30.05/.18
=> x = 166.9
Ashton can drive 166.9 miles.
**Note: We cannot round the answer to 167, as she would not have enough money to drive the extra 0.1 mile.
in golf, a player's score on each hole is always an integer. The more negative the score, the better it is. A golfer's combined score for the 18 holes is -5. The golfer score -2 on each of the several holes. on all the other holes the golfer scored a combined total of +1. On how many holes did the golfer score -2?
Answer:
3
Step-by-step explanation:
3*(-2)=-6
-6+1=-5
So over the course of 15 holes, he had a COMBINED total of +1.
The three remaining holes, he scored -2 on each of them.
The golfer score -2 in the three remaining holes.
What is the unitary method?
The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
It is given that the more negative the score, the better it is. A golfer's combined score for the 18 holes is -5.
The golfer score -2 on each of the several holes.
3*(-2)=-6
Then on all the other holes the golfer scored a combined total of +1.
-6+1 = -5
So, the course of 15 holes, he had a combined the total of +1.
Then the three remaining holes, he scored -2 on each of them.
Hence, the golfer score -2 in the three remaining holes.
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What is the answer to 123*456/789?
answer is 71.08745247
in mix form or in short form it is =
71/23/263
the difference of two complementary angles is 17 degrees. find the measures of the angles
Answer:
The angle measures are 53.5° and 36.5°.
Step-by-step explanation:
We can create a systems of equations, assuming x and y are the angle measures.
Since the two angles are complementary, their angle measures will add up to 90.
x + y = 90
x - y = 17
We can now use the process of elimination, and end up with:
2x = 107
Dividing both sides by two gets us
x = 53.5
Substituting this value into an equation will get us y
53.5 + y = 90
y = 36.5
Hope this helped!
A model for the average price of a pound of white sugar in a certain country from August 1993 to August 2003 is given by the function
S(t) = −0.00003237t5 + 0.0009037t4 − 0.008956t3 + 0.03629t2 − 0.04547t + 0.4778
where t is measured in years since August of 1993. Estimate the times when sugar was cheapest and most expensive during the period 1993-2003. (Round your answers to three decimal places.)
t= __________________________ (cheapest)
t=__________________________ (most expensive)
Answer:
[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar; [tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.
Step-by-step explanation:
Let be [tex]s(t) = -0.00003237\cdot t^{5} + 0.0009037\cdot t^{4}-0.008956\cdot t^{3}+0.03629\cdot t^{2}-0.04547\cdot t + 0.4778[/tex], the times when sugar is the cheapest and the most expensive (absolute minimum and maximum) are determined with the help of first and second derivatives of this function (First and Second Derivative Tests):
First Derivative Test
[tex]s'(t) = -0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547[/tex]
Let equalize the polynomial to zero and solve the resulting expression:
[tex]-0.00016185\cdot t^{4}+0.0036148\cdot t^{3}-0.026868\cdot t^{2}+0.07258\cdot t - 0.04547 = 0[/tex]
[tex]t_{1} \approx 9.511\,s[/tex], [tex]t_{2}\approx 7.431\,s[/tex], [tex]t_{3}\approx 4.511\,s[/tex] and [tex]t_{4}\approx 0.881\,s[/tex]
Second Derivative Test
[tex]s''(t) = -0.0006474\cdot t^{3}+0.0108444\cdot t^{2}-0.053736\cdot t+0.07258[/tex]
This function is now evaluated at each root found in the First Derivative section:
[tex]s''(9.511\,s) = -0.0006474\cdot (9.511\,s)^{3}+0.0108444\cdot (9.511\,s)^{2}-0.053736\cdot (9.511\,s)+0.07258[/tex]
[tex]s''(9.511\,s) = -0.015[/tex] (A maximum)
[tex]s''(7.431\,s) = -0.0006474\cdot (7.431\,s)^{3}+0.0108444\cdot (7.431\,s)^{2}-0.053736\cdot (7.431\,s)+0.07258[/tex]
[tex]s''(7.431\,s) = 6.440\times 10^{-3}[/tex] (A minimum)
[tex]s''(4.511\,s) = -0.0006474\cdot (4.511\,s)^{3}+0.0108444\cdot (4.511\,s)^{2}-0.053736\cdot (4.511\,s)+0.07258[/tex]
[tex]s''(4.511\,s) = -8.577\times 10^{-3}[/tex] (A maximum)
[tex]s''(0.811\,s) = -0.0006474\cdot (0.811\,s)^{3}+0.0108444\cdot (0.811\,s)^{2}-0.053736\cdot (0.811\,s)+0.07258[/tex]
[tex]s''(0.811\,s) = 0.036[/tex] (A minimum)
Each value is evaluated in order to determine when sugar was the cheapest and the most expensive:
Cheapest (Absolute minimum)
[tex]s(0.811\,s) = -0.00003237\cdot (0.811\,s)^{5}+0.0009037\cdot (0.811\,s)^{4}-0.008956\cdot (0.811\,s)^{3}+0.03629\cdot (0.811\,s)^{2}-0.04547\cdot (0.811\,s)+0.4778[/tex]
[tex]s(0.811\,s) = 0.460[/tex]
[tex]s(7.431\,s) = -0.00003237\cdot (7.431\,s)^{5}+0.0009037\cdot (7.431\,s)^{4}-0.008956\cdot (7.431\,s)^{3}+0.03629\cdot (7.431\,s)^{2}-0.04547\cdot (7.431\,s)+0.4778[/tex]
[tex]s(7.431\,s) = 0.491[/tex]
[tex]t = 0.811\,s[/tex] contains the cheapest reference to sugar.
Most expensive (Absolute maximum)
[tex]s(4.511\,s) = -0.00003237\cdot (4.511\,s)^{5}+0.0009037\cdot (4.511\,s)^{4}-0.008956\cdot (4.511\,s)^{3}+0.03629\cdot (4.511\,s)^{2}-0.04547\cdot (4.511\,s)+0.4778[/tex]
[tex]s(4.511\,s) = 0.503[/tex]
[tex]s(9.511\,s) = -0.00003237\cdot (9.511\,s)^{5}+0.0009037\cdot (9.511\,s)^{4}-0.008956\cdot (9.511\,s)^{3}+0.03629\cdot (9.511\,s)^{2}-0.04547\cdot (9.511\,s)+0.4778[/tex]
[tex]s(9.511\,s) = 0.498[/tex]
[tex]t = 4.511\,s[/tex] contains the most expensive reference to sugar.
The required values are,
[tex]t=0.881199[/tex] at the cheapest.
[tex]t=4.51081[/tex] at the most expensive.
Minimum or Maximum:A high point is called a maximum (plural maxima ). A low point is called a minimum (plural minima ).
Given equation is,
[tex]S(t) = -0.00003237t^5 + 0.0009037t^4- 0.008956t^3 + 0.03629t^2-0.04547t + 0.4778[/tex]
Differentiating the given equation we get,
[tex]S'(t)=-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0\\S'(t)=0\\-0.00003237\times 5t^4+0.0009037\times 4t^3-0.008956\times 3t^2+0.03629\times 2t-0.04547+0=0\\t=0.881199\\t=4.51081\\t=7.43087\\t=9.51137\\[/tex]
Now we can directly plug those fours values of t into given function S(t) to find which one gives max or minimum or you can also use the 2nd derivative test. Although that is not compulsory
[tex]t=0.881199,S(t)=0.46031095\\t=4.51081, S(t)=0.50278423\\t=7.43087, S(t)=0.49096762\\t=9.51137, S(t)=0.49832202\\[/tex]
We see that sugar is cheapest at [tex]t=0.881199[/tex] which is approx 1 and corresponds to the year [tex]1993+1=1994[/tex]
Similarly sugar is most expensive at [tex]t=4.51081[/tex] which is approx 5 and corresponds to year [tex]1993+5=1998[/tex]
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help please! I need this ASAP Find the value of x
Answer:
The value of x is 30°
Step-by-step explanation:
We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.
If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.
[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,
[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],
[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]
Solution : x = 30°
Given m -1/2 & the point ( 3, -6), which is the point slope form of the equation?
Answer:
[tex]y+6=-\frac{1}{2} (x-3)[/tex]
Step-by-step explanation:
Since point-slope form is [tex]y-y1=m(x-x1)[/tex], you have to plug in the values given to you to create the equation. The "y1" is the "y" coordinate given to us, while the x1 is the x coordinate given to us. So, you have to plug in the x and y coordinates, 3 and -6, into the equation. Since two negatives cancel out to be a positive, y--6= y+6. The "m" stands for the slope, so -1/2 is inserted into the equation, giving us [tex]y+6=-\frac{1}{2} (x-3)[/tex].
According to the South Dakota Department of Health, the number of hours of TV viewing per week is higher among adult women than adult men. A recent study showed women spent an average of 34 hours per week watching TV, and men, 29 hours per week. Assume that the distribution of hours watched follows the normal distribution for both groups, and that the standard deviation among the women is 4.5 hours and is 5.1 hours for the men.a. What percent of the women watch TV less than 40 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)b. What percent of the men watch TV more than 25 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)c. How many hours of TV do the one percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)
Answer:
a) P(x<40) = 0.90824
Therefore, the percent of the women watch TV less than 40 hours per week is 0.90824 × 100 = 90.8240%
b)P(x>25) = 1 - P(z = -0.78) = 0.7823
Therefore, percent of the men watch TV more than 25 hours per week?is 0.7823 × 100 = 78.230%
c)The number of hours that the one percent of WOMEN who watch the most TV per week watch is for 44.485hours
While, for the MEN, the number of hours that the one percent of men who watch the most TV per week watch is for 40.883 hours
Step-by-step explanation:
To solve this question, we would be using z score formula:
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
a. What percent of the women watch TV less than 40 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
z = (x-μ)/σ,
where x is the raw score = 40 hours
μ is the population mean = 34 hours
σ is the population standard deviation = 4.5
z = (40 - 34)/4.5
z = 1.33333
Approximately to 2 decimal places = z score = 1.33
Using the normal distribution z score table
Probabilty value from Z-Table:
P(z = 1.33) = P(x<40) = 0.90824
Therefore, the percent of the women watch TV less than 40 hours per week is 0.90824 × 100 = 90.8240%
b. What percent of the men watch TV more than 25 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)
z = (x-μ)/σ,
where x is the raw score = 25 hours
μ is the population mean = 29 hours
σ is the population standard deviation = 5.1
z = (25 - 29)/5.1
z = -0.78431
Approximately to 2 decimal places
z score = -0.78
Using the z score normal distribution table:
Probability value from Z-Table:
P(z = -0.78) = P(x<Z) = 0.2177
P(x>25) = 1 - P(z = -0.78) = 0.7823
Therefore, percent of the men watch TV more than 25 hours per week?is 0.7823 × 100 = 78.230%
c. How many hours of TV do the one percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)
First, we find what the z score is.
We were asked in the question to find how many hours 1% of the women watch TV the most.
We have to find the confidence interval
100 - 1% = 99%
The z score for the confidence interval of 99% or 0.99(in decimal form) = 2.33
z score = 2.33
Since we know the z score now, we proceed to find x = raw score.
z = (x-μ)/σ,
where x is the raw score = unknown
μ is the population mean = 34 hours
σ is the population standard deviation = 4.5
2.33= (x - 34)/4.5
Cross Multiply
2.33 × 4.5 = x - 34
10.485 = x - 34
x = 10.485 + 34
x = 44.485 hours.
Therefore, the number of hours that the one percent of women who watch the most TV per week watch is for 44.485hours
In the question, we were also asked to find the comparable value for men.
Hence, for one percent of the men.
We determine what the z score is.
We were asked in the question to find how many hours 1% of the men watch TV the most.
We have to find the confidence interval
100 - 1% = 99%
The z score for the confidence interval of 99% or 0.99(in decimal form) = 2.33
We already have our z score as 2.33
z = (x-μ)/σ,
where x is the raw score = unknown
μ is the population mean = 29 hours
σ is the population standard deviation = 5.1
2.33= (x - 29)/5.1
Cross Multiply
2.33 × 5.1 = x - 29
11.883 = x - 29
x = 11.883 + 29
x = 40.883 hours.
Therefore, the number of hours that the one percent of men who watch the most TV per week watch is for 40.883 hours
Find the Correlation of the following two variables X: 2, 3, 5, 6 Y: 1, 2, 4, 5
Answer:
The correlation of X and Y is 1.006
Step-by-step explanation:
Given
X: 2, 3, 5, 6
Y: 1, 2, 4, 5
n = 4
Required
Determine the correlation of x and y
Start by calculating the mean of x and y
For x
[tex]M_x = \frac{\sum x}{n}[/tex]
[tex]M_x = \frac{2 + 3+5+6}{4}[/tex]
[tex]M_x = \frac{16}{4}[/tex]
[tex]M_x = 4[/tex]
For y
[tex]M_y = \frac{\sum y}{n}[/tex]
[tex]M_y = \frac{1+2+4+5}{4}[/tex]
[tex]M_y = \frac{12}{4}[/tex]
[tex]M_y = 3[/tex]
Next, we determine the standard deviation of both
[tex]S = \sqrt{\frac{\sum (x - Mean)^2}{n - 1}}[/tex]
For x
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{n -1}}[/tex]
[tex]S_x = \sqrt{\frac{(2-4)^2 + (3-4)^2 + (5-4)^2 + (6-4)^2}{4 - 1}}[/tex]
[tex]S_x = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_x = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_x = \sqrt{\frac{10}{3}}[/tex]
[tex]S_x = \sqrt{3.33}[/tex]
[tex]S_x = 1.82[/tex]
For y
[tex]S_y = \sqrt{\frac{\sum (y_i - My)^2}{n - 1}}[/tex]
[tex]S_y = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (4-3)^2 + (5-3)^2}{4 - 1}}[/tex]
[tex]S_y = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_y = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_y = \sqrt{\frac{10}{3}}[/tex]
[tex]S_y = \sqrt{3.33}[/tex]
[tex]S_y = 1.82[/tex]
Find the N pairs as [tex](x-M_x)*(y-M_y)[/tex]
[tex](2 - 4)(1 - 3) = (-2)(-2) = 4[/tex]
[tex](3 - 4)(2 - 3) = (-1)(-1) = 1[/tex]
[tex](5 - 4)(4 - 3) = (1)(1) = 1[/tex]
[tex](6-4)(5-3) = (2)(2) = 4[/tex]
Add up these results;
[tex]N = 4 + 1 + 1 + 4[/tex]
[tex]N = 10[/tex]
Next; Evaluate the following
[tex]\frac{N}{S_x * S_y} * \frac{1}{n-1}[/tex]
[tex]\frac{10}{1.82* 1.82} * \frac{1}{4-1}[/tex]
[tex]\frac{10}{3.3124} * \frac{1}{3}[/tex]
[tex]\frac{10}{9.9372}[/tex]
[tex]1.006[/tex]
Hence, The correlation of X and Y is 1.006
A marathon started at 7:30am. The winner took 3hrs and 47
minutes to complete the race and the last person finished 55
minutes later. At what time did the marathon end?
Answer:
12:12
Step-by-step explanation:
first add 3 hours to 7:30 which makes it 10:30
then add 47 min and it becomes 11:17
add 55 min to that and its 12:12
Do phone surveys provide adequate coverage of households with respect to one particular parameter? The parameter is the proportion of households without children. If telephone surveys provide adequate coverage of households, then p , the proportion of households without children in the set of all future samples reached by phone, must be equal to the proportion of households without children in the population of all households. Suppose that Thomas, a market analyst, contacts a simple random sample of 300 households as part of a national telephone survey. Of the households contacted, 129 households, or 43 %, have no children and 57 % have at least one child. The most recent census indicates that 48 % of all households have no children and 52 % have at least one child.
Complete Question
The complete question is shown on the first uploaded image
Answer:
Based on the result of his test , Thomas should fail to reject null hypothesis at a significance level of 0.01. Thomas sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
Step-by-step explanation:
From the question we see that the p-value is greater than the level of significance (0.01 )so we fail to reject the null hypothesis.
This means that Thomas has sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.
You catch an expected number of 1.51.5 fish per hour. You can catch a fish at any instant of time. Which distribution best characterizes the number of fish you catch in one hour of fishing
Answer:
The distribution is Poisson distribution
Step-by-step explanation:
From the question we are told that
An expected number of fish was caught per hour is 1.5
The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution
This because generally the Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time
The Centers for Disease Control and Prevention (CDC) report that gastroenteritis, or stomach flu, is the most frequently reported type of recreational water illness. Gastroenteritis is a viral or bacterial infection that spreads through contaminated food and water. Suppose that inspectors wish to determine if the proportion of public swimming pools nationwide that fail to meet disinfectant standards is different from 10.7%, which was the proportion of pools that failed the last time a comprehensive study was done, 2008.
A simple random sample of 30 public swimming pools was obtained nationwide. Tests conducted on these pools revealed that 26 of the 30 pools had the required pool disinfectant levels.
Does this sample meet the requirements for conducting a one-sample z ‑test for a proportion?
a. No, the requirements are not met because the population standard deviation is not known.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
c. No, the requirements are not met because the sample is not random, even though the number of successes and the number of failures are both at least 10, ensuring that the distribution is approximately normal.
d. Yes, the requirements are met because the sample size is more than 30, ensuring that the distribution is approximately normal.
e. Yes, the requirements are met because the number of successes and the number of failures of this random sample are both at least 10, ensuring that the distribution is approximately normal.
b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.
Step-by-step explanation:
from the question, the number of successes is equal to 30
and it is more than the number of failures
for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.
if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.
if a lake has high alkalinity, what is closest to the probability that the lake also has a shallow depth?
Answer:
0.22
Step-by-step explanation:
Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The alkalinity of lake is determined by dividing the high shallow depthness by the total of lake alkalinity. The shallow depth is 209 and the total alkalinity of the lake is 966. By dividing the depthness with alkalinity we get 0.22.
209/966 = 0.219
approximately 0.22
Describe in words how you would solve
the linear system y = 3x + 1 and y = - 2x + 3.
Answer:
Below.
Step-by-step explanation:
As both the right sides of the 2 equations are equal to y, by the transitive law of equality 3x + 1 = -2x + 3.
W then solve this equation for x then substitute this value of x in the first equation ( y = 3x + 1) to find the value of y.
PLEASE ANSWER ASAP!!!
Expressions and answer options in picture
If you were asked to subtract in the following pair of expressions, what you use as the least common denominator?
any unrelated answers will be reported
Answer:
C=x (x+3)
Step-by-step explanation:
x cannot divide x+3 definitely so the denominators must be multiplied to get the least common denominator.
how would you write six times the square of a number
Answer:
[tex]\huge \boxed{6x^2 }[/tex]
Step-by-step explanation:
6 times a number squared.
Let the number be [tex]x[/tex].
6 is multiplied to [tex]x[/tex] squared.
[tex]6 \times x^2[/tex]
Please answer this correctly without making mistakes
Step-by-step explanation:
Option A and B are the correct answer because it equal to 688.5 and 688.05
Answer:
it is 1377/2 and 688 1/17 thats the answer
Step-by-step explanation:
Recall the formula V = four-thirds pi r cubed.
Answer:
1308.33
Step-by-step explanation:
In the pic
The angles of a quadrilateral are (3x + 2), (x-3), (2x+1), and 2(2x+5). Find x.
Answer:
3x+2+x-3+2x+1+2(2x+5)=360
10x+10=360
x=35
A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale? a.3.8 grams b.120.01 grams c.800.0 grams d.54 milligrams
Answer:
Step-by-step explanation:
The answer is b
120.01 grams
Find two positive numbers satisfying the given requirements. The sum of the first and twice the second is 400 and the product is a maximum.
Answer:
100 and 200Step-by-step explanation:
Let the first number be 'a' and the second number be 'b'. If the sum of the first and twice the second is 400 then;
a+2b = 400 ....
From the equation above, a = 400 - 2b ... 2
If the product of the numbers is a maximum then;
ab = (400-2b)b
let f(b) be the product of the function.
f(b) = (400-2b)b
f(b) = 400b-2b²
For the product to be at the maximum then f'(b) must be equal to zero i.e f'(b) = 0
f'(b)= 400-4b = 0
400-4b = 0
400 = 4b
b = 400/4
b = 100
Substituting b= 100 into the equation a = 400 - 2b to get a;
a = 400 - 2(100)
a = 400 - 200
a = 200
The two positive integers are 100 and 200.
PLEASE ANSWER ASAP!!
Expression in picture
Multiply the rational expressions below. Write your answer in the lowest terms. Remember to factor if you can!
A. 9/10
B. 10/9
C. 10/7
D. 7/10
any unrelated answers will be reported
Answer:
10/9
Step-by-step explanation:
5x-15 4x+12
--------- * ------------
3x+9 6x-18
Factor
5(x-3) 4( x+3)
----------- * ----------
3(x+3) 6( x-3)
Cancel like terms
5/3 * 4/6
20/18
Divide top and bottom by 2
10/9
Transform the given parametric equations into rectangular form. Then identify the conic. x= -3cos(t) y= 4sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = - 3cos(t) ⇒ x / - 3 = cos(t)
y = 4sin(t) ⇒ y / 4 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / - 3 )² = cos²(t)
+ ( y / 4 )² = sin²(t)
_____________
x² / 9 + y² / 16 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
What is the equation of the line that passes through the point (2, -1) and has a
slope of
3/2
Answer:
The answer is
[tex]y = \frac{3}{2} x - 4[/tex]Step-by-step explanation:
To find the equation of the line using a point and slope we use the formula
y - y1 = m(x - x1)where m is the slope
(x1 ,y1) is the given point
From the question
slope = 3/2
point = ( 2 , - 1)
Substitute these values into the above formula
That's
[tex]y + 1 = \frac{3}{2} (x - 2)[/tex]
[tex]y + 1 = \frac{3}{2} x - 3[/tex]
[tex]y = \frac{3}{2} x - 3 - 1[/tex]
We have the final answer as
[tex]y = \frac{3}{2} x - 4[/tex]
Hope this helps you
Answer:
y= 3/2x -4
Step-by-step explanation:
Since we are given a point and a slope, we can use the point-slope formula.
[tex]y-y_{1} = m(x-x_{1})[/tex]
where m is the slope and (x1, y1) is a point the line passes through.
We know the slope is 3/2 and the point we are given is (2, -1).
[tex]m=\frac{3}{2} \\\\x_{1} = 2\\\\y_{1} = -1[/tex]
Substitute the values into the formula.
[tex]y- -1 = \frac{3}{2} (x-2)[/tex]
[tex]y+1=\frac{3}{2} (x-2)[/tex]
We want to find the equation of line , which is y=mx+b ( m is the slope and b is the y-intercept). Therefore, we must get y by itself on the left side of the equation.
First, distribute the 3/2. Multiply each term inside the parentheses by 3/2.
[tex]y+1= (\frac{3}{2} * x) + (\frac{3}{2} *-2)[/tex]
[tex]y+1= \frac{3}{2}x + (\frac{3}{2} *-2)[/tex]
[tex]y+1=\frac{3}{2} x + -3[/tex]
[tex]y+1=\frac{3}{2} x -3[/tex]
Next, subtract 1 from both sides.
[tex]y+1-1=\frac{3}{2} x + -3 -1[/tex]
[tex]y=\frac{3}{2} x + -3 -1[/tex]
[tex]y=\frac{3}{2} x -4[/tex]
Now the line is in slope intercept form, therefore the equation of the line is y=3/2x -4. The slope of the line is 3/2 and the y-intercept is -4.
what is the distance between the points (4 3) and (1 -1) on the cordinate plane
Answer:
d = 5
Step-by-step explanation:
Distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
d = sqrt[(1-4)^2+(-1-3)^2]
d = 5
Answer:
5
Step-by-step explanation:
distance = square root of (1-4)^2 + (-1-3)^2
=> distance = square root of -3^2 + (-4)^2
=> distance = square root of 9 + 16
=> distance = square root of 25
=> distance = 5
Many countries, especially those in Europe, have significant gold holdings. But many of these countries also have massive debts. The following data show the total value of gold holdings in billions of U.S. dollars and the debt as a percentage of the gross domestic product for nine countries (WordPress and Trading Economics websites, February 24, 2012).
Gold Value ($ billions) Debt (% of GDP)
Country
China 63 17.7
France 146 81.7
Indonesia 203 83.2
Germany 33 69.2
Italy 147 119
Netherlands 36 63.7
Russia 50 9.9
Switzerland 62 55
United States 487 93.2
Using the entire data set, develop the estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings (to 4 decimals (to 4 decimals)
Answer:
X`= -0.60872 Y + 176.4085
or X`= 176.4085-0.60872 Y
Step-by-step explanation:
Country Gold Value Debt (% of GDP)
($ billions) X Y XY X² Y²
China 63 17.7 1115.1 3969 313.29
France 146 81.7 11928.2 21316 6674.89
Indonesia 203 83.2 16889.6 41209 6947.2
Germany 33 69.2 2283.6 1089 4788.64
Italy 147 119 17493 21609 14161
Netherlands 36 63.7 2293.2 1296 4057.69
Russia 50 9.9 495 2500 98.01
Switzerland 62 55 3410 3844 3025
United States 487 93.2 45,388.2 237169 8686.24
∑ 1227 592.6 101245.9 334001 48751.96
The estimated regression equation that can be used to predict the debt of a country given the total value of its gold holdings
X = a1 + bxy Y
wher e
bxy = n ∑XY -∑X∑Y/ n ∑Y²- (∑Y)²
= 9( 101245.9 )- (1227 *592.6)/ 48751.96-(592.6)²
911213.1 - 727120.2/ - 302422.8= - 0.60872
a1= X` -bxy Y`= 136.33- (-0.60872)(65.84)
= 136.33+ 40.07858= 176.4085
Hence X`= -0.60872 Y + 176.4085
or X`= 176.4085-0.60872 Y
7 less than the quotient of a number and 3 is 5. Find the number.
Answer:
The answer is 36
Step-by-step explanation:
Let the number be x
7 less than the quotient of a number and 3 is written as
[tex] \frac{x}{3} - 7[/tex]The result is 5
So we have
[tex] \frac{x}{3} - 7 = 5[/tex]Move - 7 to the right side of the equation
That's
[tex] \frac{x}{3} = 7 + 5[/tex][tex] \frac{x}{3} = 12[/tex]Multiply both sides by 3 to make x stand alone
We have
[tex]3 \times \frac{x}{3} = 12 \times 3[/tex]We have the final answer as
x = 36Hope this helps you
Using a rating scale, Tekinarslan (2008) measured computer anxiety among university students who use the computer very often, often, sometimes, and seldom. Below are the results of the one-way ANOVA. Source of Variation SS df MS F Between groups 1,959.79 3 653.26 21.16* Within groups (error) 3,148.61 102 30.86 Total 5,108.41 105 (a) What are the values for N and k
Answer:
k = 4 ; N = 106
Step-by-step explanation:
Given the result of the one way ANOVA :
- - - - - - - - - - - - - - - SS - - - - df - - MS - - - - - F
Between groups - 1,959.79 - 3 - - 653.26 - 21.16*
Error - - - - - - - - - - 3,148.61 - -102 --30.86
Total - - - - - - - - - - 5,108.41 - 105
To obtain the value of 'k' which is the number of groups observed :
The degree of freedom between groups or degree of freedom of treatment (DFT) is obtained by the formula:
Number of observed groups(k) - 1
DFT = k - 1
From the ANOVA result ; degree of freedom between groups = 3
Hence,
3 = k - 1
k = 3 +1 = 4
Hence, number of observed groups = 4
To obtain N;
N is related to k and the degree of freedom Error (DFE)
DFE = N - k
From the ANOVA result, DFE = 102 and k = 4
102 = N - 4
102 + 4 = N
N = 106
