Answer:
The answer is "[tex]\bold{\frac{32}{3}}\\[/tex]"
Step-by-step explanation:
The rectangle should also be symmetrical to it because of the symmetry to the y-axis The pole of the y-axis. Its lower two vertices are (-x,0). it means that
and (-x,0), and (x,0). Therefore the base measurement of the rectangle is 2x. The top vertices on the parabola are as follows:
The calculation of the height of the rectangle also is clearly 16-x^2, (-x,16,-x^2) and (x,16,-x^2).
The area of the rectangle:
[tex]A(x)=(2x)(16-x^2)\\\\A(x)=32x-2x^3[/tex]
The local extremes of this function are where the first derivative is 0:
[tex]A'(x)=32-6x^2\\\\32-6x^2=0\\\\x= \pm\sqrt{\frac{32}{6}}\\\\x= \pm\frac{4\sqrt{3}}{3}\\\\[/tex]
Simply ignore the negative root because we need a positive length calculation
It wants a maximum, this we want to see if the second derivative's profit at the end is negative.
[tex]A''\frac{4\sqrt{3}}{3} = -12\frac{4\sqrt{3}}{3}<0\\\\2.\frac{4\sqrt{3}}{3}= \frac{8\sqrt{3}}{3}\\\\\vertical \ dimension\\\\16-(\frac{4\sqrt{3}}{3})^2= \frac{32}{3}[/tex]
Let's list the elements of these sets and write whether thoy are empty
(null), singleton, finite or Infinito sots.
a) A = {prime number between 6 and 7)
b) B = {multiples of 2 less than 20}
Answer:
a. They are empty set.
b. they are finite set.
Solution,
a. A={ prime number between 6 and 7}
There are not any number between 6 and 7.
So there will be no Elements.
A={ }
It is empty set.
Empty set are those set which doesn't contain any Element.
b.B={multiples of 2 less than 20}
B={2,4,6,8,10,12,14,16,18}
It is a finite set.
Finite set are those set which we can count easily.
Hope this helps...
Good luck on your assignment...
For a specific location in a particularly rainy city, the time a new thunderstorm begins to produce rain (first drop time) is uniformly distributed throughout the day and independent of this first drop time for the surrounding days. Given that it will rain at some point both of the next two days, what is the probability that the first drop of rain will be felt between 8: 40 AM and 2: 35 PM on both days? a) 0.2479 Web) 0.0608 om c) 0.2465 d) 0.9385 e) 0.0615 f) None of the above.
Answer:
b) 0.0608
Step-by-step explanation:
As it is mentioned that the next two days i.e 24 hours, the probability of the rain is uniformly distributed
Therefore the rain probability is
[tex]= \frac{T}{24}[/tex]
where,
T = Length of the time interval
Plus, as we know that rain is independent
So let us assume the rain between the 8: 40 AM and 2: 35 PM on single day is P1 and the time interval is 5 hours 55 minutes
i.e
= 5.91666 hours long.
So, P1 should be
[tex]= \frac{5.91666}{24}[/tex]
= 0.2465
Now we assume the probability of rain on day 2 is P2
So it would be same i.e 0.2465
Since these events are independent
So, the total probability is
[tex]= 0.2465 \times 0.2465[/tex]
= 0.0608
Hence, the b option is correct
The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a point estimate Kilowatt usage when the Temperature is 90 degrees outside?
The question is incomplete. The complete question is as follows.
The city of Oakdale wishes to see if there is a linear relantionship between the temperature and the amount of electricity used (in kilowatts). Using the estimated regression equation found by using Temperature as the predictor variable, find a pont estimate Kilowatt usage when the Temperature is 90 degrees outside?
Temperature(x) Kilowatts(y)
73 680
78 760
85 910
98 1510
93 1170
83 888
92 923
81 837
76 600
105 1800
Answer: The point estimate is 1132.5 Kilowatts
Step-by-step explanation: Regression analysis is used to find an equation that fits the data. Once this equation is found, it's used to make predictions. One of the regressions is linear regression.
To find the linear regression model:
1) Create a table with the following: ∑y; ∑x; ∑xy; ∑x²; ∑y²;
2) Use these equations to find coefficients a and b:
a = (∑y)(∑x²) - (∑x)(∑yx) / n(∑x²) - (∑x)²
b = n(∑xy) - (∑x)(∑y) / n(∑x²) - (∑x)²
3) Substitute the coefficients into the equation of form: y = a + bx
For the table above, the linear regression equation is:
y = - 2004 + 34.85x
When Temperature is 90, i.e. x = 90:
y = - 2004 + 34.85*90
y = 1132.5
The estimate Kilowatt is 1132.5.
what is between 1/3 and 7/8 answer
Answer:
The number which is exactly in between 1/3 and 7/8 will be their average. The average = (1/3 + 7/8) / 2 = (8/24 + 21/24) / 2 = (29/24) / 2 = 29/48.
Please answer this correctly
Answer:
0| 2
1| 2
2| 0 0 3 9
3| 2 4 4 4 8 8
4| 2 2 4 5 5 6 7
Step-by-step explanation:
Same as the other similar questions
hope this helps!
The populations and areas of four states are shown.Which statement regarding these four states is true?
in a classroom 5/8 of the students are wearing blue shirts and 1/4 for wearing white shirts there are 24 students in the classroom how many are wearing shirts other than blue shirts and
Answer:
3
Step-by-step explanation:
Those wearing a shirt of another color are ...
1 - 5/8 -1/4 = 8/8 -5/8 -2/8 = 1/8
of the total number of students in the classroom
(1/8)×(24 students) = 3 students . . . . wearing another color
_____
Alternate solution
With the given information, you know ...
(5/8)(24) = 15 . . . students wear blue
(1/4)(24) = 6 . . . . students wear white
24 -15 -6 = 3 . . . students wear another color
Heidi looks at the donkeys and
tourists. She counts 50 heads
and 114 legs.
How many donkeys are there?
o
ANSWER:
O The retired question
Answer:
7 donkeys
Step-by-step explanation:
Given
A system consisting of donkeys and tourists
Heads = 50
Legs = 114
Required
Calculate number of donkeys.
Represent donkeys with D and tourists with T.
By means of identification; donkeys and tourists (human) both have 1 head.
This implies that
Number of Heads = D + T
50 = D + T ----- Equation 1
While each donkey have 4 legs, each tourists have 2 legs.
This implies that
Number of legs = 4D + 2T
114 = 4D + 2T ---- Multiply both sides by ½
114 * ½ = (4D + 2T) * ½
57 = 4D * ½ + 2T * ½
57 = 2D + T ----- Equation 2
Subtract equation 1 from 2
57 = 2D + T
- (50 = D + T)
---------------------
57 - 50 = 2D - D + T - T
7 = D
Recall that D represents the number of donkeys.
So, D = 7 implies that
The total number of donkeys are 7
Rectangle is 5ft in length and 3 ft in height. What is the area of the rectangle
Answer: 15
Step-by-step explanation:
to find the area multiply the length by height
in this case it’s 5ft and 3ft
5 • 3 = 15
A=15
Can someone please help me?
Answer:
''0 is neither a rational number nor an irrational number.''
Step-by-step explanation:
Zero is a rational number. Zero can be written as a fraction, where p/q = 0, where p = 0 and q is any non-zero integer. Hence, 0 is a rational number.
Change 3.2t into kilograms please help me
Let's think:
1 ton ------------ 1000 kilograms
3.2 tons ----------- x kilograms
Multiply in cross
1 . x = 1000 . 3.2
x = 3200
So 3.2t = 3200 kilograms
Answer:
It is 2902.99 to be exact
Step-by-step explanation:
s the last book a person in City Upper A read a discrete random variable, continuous random variable, or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable.
Answer:
Not a random variable
Step-by-step explanation:
The last book a person read in City A is not a random variable because it is not a number as there is no numerical description for the outcome of this experiment.
Thus, the last book read by someone in City A is not a random variable.
Answer:
not random
Step-by-step explanation:
Could you please help me with this problem.
Answer:
x=6√2please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
Please answer this correctly
Answer:
Pillows:
Blankets:
Pet Beds:
Step-by-step explanation:
18 + 45 + 27 = 90 (there are 90 students)
18 out of 90 = 20%
45 out of 90 = 50%
27 out of 90 = 30%
Hope this helps!
A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them. If four of the homes are new and six have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new
Answer:
0.48% probability that all four are new
Step-by-step explanation:
The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Total of 10 homes, so N = 10.
We want 4 new, so x = 4.
In total, there are 4 new, so k = 4.
Sample of four homes, so n = 4.
Then
[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]
0.48% probability that all four are new
The calculated probability is "0.0048".
Probability calculation:From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.
Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.
X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.
[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]
[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]
[tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]
Using the excel function:
[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex] for calculating the [tex]P_{X} (4)[/tex]:
[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]
[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]
Find out more information about the probability here:
brainly.com/question/2321387
Give the equation of the line parallel to a line through (-3, 4) and (-5, -6) that passes through the origin. y = 5x
Answer:
y = 5x
Step-by-step explanation:
First, find the slope of the first equation by doing rise/run
This gets you -10/-2 or 5
A parallel line will have the same slope. Since it goes through the origin, the y-intercept and b value will be zero
The equation will be y = 5x
Solve the equation.
5x + 8 - 3x = -10
x = -1
x=1
x=9
Answer:
x=-9solution,
[tex]5x + 8 - 3x = - 10 \\ or \: 5x - 3x + 8 = -10 \\ or \: 2x + 8 = -10 \\ or \: 2x = -10 - 8 \\ or \: 2x = -18\\ or \: x = \frac{-18}{2 } \\ x = -9[/tex]
hope this helps..
Good luck on your assignment
Answer:
x = -9
Step-by-step explanation:
5x + 8 - 3x = -10
Rearrange.
5x - 3x + 8 = -10
Subtract like terms.
2x + 8 = -10
Subtract 8 on both sides.
2x = -10 - 8
2x = -18
Divide 2 into both sides.
x = -18/2
x = -9
For each ordered pair, determine whether it is a solution to x=-3.
Answer: no, no, no, yes
Step-by-step explanation:
x=-3 is a vertical line. It goes straight up and down at x=-3. In order for the points to be on this line, the x-axis has to be -3. Looking at all the choices, all points are not a solution with the exception of (-3,0) which is right on the line.
Answer:
no no no yes
Step-by-step explanation:
i think
A game require rolling a six sided die numbered fro 1 to 6. What is the probability of rolling a 1 or a 2?
Answer:
1/3
Step-by-step explanation:
hello,
probability of 1 = 1/6
probability of 2 = 1/6
probability of 1 or 2 = 1/6+1/6 as probability of 1 and 2 = 0
so the answer is 2/6=1/3
we nendndhdhebdbdbdd
Step-by-step explanation:
Joe mama
If the volume of a cube is
64 cubic feet, what is the
surface area of the cube in
square feet?
Answer:
96 ft^2
Step-by-step explanation:
volume=l^3
l=4
4x4x4=64
Surface area (4x4)=16
16x6=96
Answer:
SA =96 ft^2
Step-by-step explanation:
The volume of a cube is given by
V = s^3
64 = s^3
Take the cube root of each side
64 ^ 1/3 = s^3 ^ 1/3
4 =s
The side length si 4
The surface area of a cube is
SA = 6 s^2
SA = 6 * 4^2
SA = 6 * 16
SA =96 ft^2
You have been assigned to determine whether more people prefer Coke or Pepsi. Assume that roughly half the population prefers Coke and half prefers Pepsi. How large a sample do you need to take to ensure that you can estimate, with 95% confidence, the proportion of people preferring Coke within 3% of the actual value? [Hint: proportion est. = 0.5] Round your answer to whole number
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
For this case we have the following info given:
[tex] ME=0.03[/tex] the margin of error desired
[tex]Conf= 0.95[/tex] the level of confidence given
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
the critical value for 95% of confidence is [tex] z=1.96[/tex]
We can use as estimator for the population of interest [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
A restaurant sees about 600 orders on Tuesday. This is down from last Tuesday by about 0.85%. How many did they see last Tuesday
Answer:
Number of orders seen on last Tuesday = 605
Step-by-step explanation:
Number of orders seen on Tuesday = 600
It is given that it is 0.85% less than last Tuesday.
Let number of sales on last Tuesday = [tex]x[/tex]
As per question statement:
Number of order on last Tuesday - 0.85% of Number of order on last Tuesday = 600
OR
i.e. if we subtract 0.85% of x from x, it must be equal to 600.
[tex]x-\dfrac{0.85}{100}x =600\\\Rightarrow x-\dfrac{0.85}{100}x =600\\\Rightarrow \dfrac{100-0.85}{100}x =600\\\Rightarrow \dfrac{99.15}{100} \times x =600\\\Rightarrow x =\dfrac{600\times 100}{99.15}\\\Rightarrow x =\dfrac{60000}{99.15}\\\Rightarrow x \approx 605[/tex]
So, there were about 605 order seen last Tuesday.
To solve the system given below using substitution, it is best to start by
solving the second equation for y.
5x + 2y = 33
6y + x = 3
true or false
Answer:
False, it is easier to isolate x.
Step-by-step explanation:
6y+x=3
x=3-6y
Choose the ratio that you would use to convert 1.5 feet to miles. Remember
that there are 5,280 feet in one mile.
Answer: B, 1 mile / 5280 ft.
Step-by-step explanation: If you need to convert feet to miles the unit multiplier (ratio) that you use should have miles on top and feet on the bottom so that the feet cancel when you multiply, leaving miles as the unit. B is the only answer that has miles on top and feet on the bottom as well as the correct amounts (1 mile and 5280 ft).
an oil company conducts a geological study that indicates that an exploratory oil well should have a 20% chance of striking oil. assuming independence, what is that probability that the third strike comes on the seventh well drilled
Answer:
4.92% probability that the third strike comes on the seventh well drilled
Step-by-step explanation:
For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% chance of striking oil.
This means that [tex]p = 0.2[/tex]
What is that probability that the third strike comes on the seventh well drilled
2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]
Strike during the 7th drill, with 0.2 probability. So
[tex]P = 0.2P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]
Then
[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]
4.92% probability that the third strike comes on the seventh well drilled
The computer hardware company requires all of its chips purchased from its supplier of computer chips to meet specifications of 1.2 cm with the margins of error of plus and minus 0.1 cm. Based on the computer chip supplied last month, the mean length of a computer chip was 0.9 cm. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications
Answer:
Step-by-step explanation:
The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm
This means that the required length of computer chips is between 1.1cm - 1.3cm
Where 1.1cm = [1.2 - 0.1]
1.3cm = [1.2 + 0.1]
Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.
The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:
- The length of the chips.
The length of the chips his production team produces should be tailored to meet the length specification of his client.
What is the slope of the line represented by the equation y = 4/5x - 3?
in
Answer:
[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]
Step-by-step explanation:
when the equation is like y = ax + b
the slope is a
in this case we have
[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]
so the slope is
[tex]\dfrac{4}{5}[/tex]
Heights of Women. Heights of adult women are distributed normally with a mean of 162 centimeters and a standard deviation of 8 centimeters. Use the Table B.3 Areas under the Normal Curve (page 519 of the textbook) to find the indicated quantities: a) The percentage of heights less than 150 centimeters b) The percentage of heights between 160 centimeters and 180 centimeters
Answer:
a) 6.68% of heights less than 150 centimeters
b) 58.65% of heights between 160 centimeters and 180 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 162, \sigma = 8[/tex]
a) The percentage of heights less than 150 centimeters
We have to find the pvalue of Z when X = 150. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{150 - 162}{8}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% of heights less than 150 centimeters
b) The percentage of heights between 160 centimeters and 180 centimeters
We have to find the pvalue of Z when X = 180 subtracted by the pvalue of Z when X = 160.
X = 180
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 162}{8}[/tex]
[tex]Z = 2.25[/tex]
[tex]Z = 2.25[/tex] has a pvalue of 0.9878
X = 160
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{160 - 162}{8}[/tex]
[tex]Z = -0.25[/tex]
[tex]Z = -0.25[/tex] has a pvalue of 0.4013
0.9878 - 0.4013 = 0.5865
58.65% of heights between 160 centimeters and 180 centimeters
Please answer this correctly
Answer:
20-39 ⇒ 5
40-59 ⇒ 3
60-79 ⇒ 5
80-99 ⇒ 10
Answer:
20-39: 5
40-59: 3
60-79: 5
80-99: 10
Step-by-step explanation:
If you just added up, you can find all the values.