Answer:
6 cars
Step-by-step explanation:
Each car wash=15$
Jake raised 90$, so the amount of cars he washed would be 90/15=6
Hope this helps!
Answer:
6
Step-by-step explanation:
this is because
if one car=$15
then how many cars would be=$90.
this will result us in ratio and proportion
if more then less divide ,
and we will get
90\15 × 1= 6
therefore Jake wash 6 cars for $90
let f be a differentiable function defined for all x>=0 such at f(0) = 5 and f(3) = -1.Consider the function g defined by g(x)= 5 st)dt. What is true about the function g? Mark all that apply. The function g has a local minimum at x = 3. The graph of the derivative g' never intersects the x-axis. The graph of g has a horizontal tangent line at x=3. The function g has a local maximum at x = 3.
The correct statements are that the graph of g has a horizontal tangent line at x=3 and the graph of g' never intersects the x-axis.
We know that g(x) = ∫0^x f(t)dt. Therefore, g'(x) = f(x) by the Fundamental Theorem of Calculus. Using this, we can find g'(3) = f(3) = -1.
Since g'(x) = f(x), we can see that g'(x) is negative on the interval [0, 3] because f(3) = -1 and f(x) is a differentiable function. This means that the graph of g is decreasing on [0, 3], so it does not have a local maximum at x=3.
Furthermore, since g'(x) is negative for all x, the graph of g' never intersects the x-axis. Therefore, the statement "The graph of the derivative g' never intersects the x-axis" is true.
Finally, since g'(3) = -1, the graph of g has a horizontal tangent line at x=3. Therefore, the statement "The graph of g has a horizontal tangent line at x=3" is also true.
Overall, we can conclude that the function g has a horizontal tangent line at x=3 and the graph of g' never intersects the x-axis.
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If k kilometres is the same distance as miles. K is given approximately by formula K=8m÷5
Find the number of kilometres in 20 miles
By the formula K = 8m/5, one can calculate the number of kilometers in 20 miles which comes out to be 32 Kilometers.
Kilometers and miles are used to measure length. They are different units and belong to different units of system.
Given in the question,
K is given approximately by the following formula.
K = 8m / 5 -------(i)
where K is the number of kilometers
and m is the number of miles.
According to the question,
we are asked the number of kilometers in 20 miles
put m = 20 in the equation (i)
K = 8 (20) / 5
K = 160 / 5
K = 32 km
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what is the relation between vectors and covectors with
tensors
Answer:
A vector space is always naturally isomorphic to its double dual — the space of all linear functionals on . A tensor is generally defined as a multilinear functional , where is the underlying field. That means it takes vectors and covectors to return a scalar, behaving linearly in each argument.
The relation between vectors, covectors, and tensors is that tensors are generalizations of vectors and covectors, allowing for more complex interactions and transformations.
Vectors and covectors are both specific types of tensors. A vector is a first-order tensor (rank-1), and a covector is its dual, also a rank-1 tensor. Tensors, in general, are multi-dimensional arrays that can represent various mathematical objects, including scalars (rank-0 tensors), vectors, and matrices (rank-2 tensors). They describe the relationships between these objects and how they transform under different coordinate systems. Tensors have a rank, which indicates the number of indices needed to define their components.
Vectors, covectors, and tensors are interconnected, with tensors providing a generalized framework to represent and manipulate various mathematical entities, including vectors and covectors.
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1. Let x ∈ Z. Prove that if 3 | 2x, then 3 | x.2. Let n ∈ Z. Prove that 3 | (2n 2 + 1) if and only if 3 - n.
Answer:
1.Suppose 3 | 2x. Then we can write 2x = 3k for some integer k. Rearranging, we have x = (3/2)k. Since k is an integer, (3/2)k is also an integer, which means that x is divisible by 3. Hence, 3 | x.
First, suppose 3 | (2n^2 + 1). Then we can write 2n^2 + 1 = 3k for some integer k. Rearranging, we have 2n^2 = 3k - 1. Since 3k - 1 is odd, we can write it as 2m + 1 for some integer m. Substituting, we have 2n^2 = 2m + 1, which implies that n^2 = m + (1/2). But since m is an integer, (1/2)m is not an integer, which means that n^2 is not an integer. This is a contradiction, so our assumption that 3 | (2n^2 + 1) must be false.
Now suppose 3 - n. Then we can write n = 3k - 1 for some integer k. Substituting, we have 2n^2 + 1 = 18k^2 - 12k + 3. Factoring out 3, we have 2n^2 + 1 = 3(6k^2 - 4k + 1). But 6k^2 - 4k + 1 is always an integer, so if 3 - n, then 3 | (2n^2 + 1).
give me thanks for more! your welcome!
Step-by-step explanation:
List two multiples of 17
If the differential equationmd2xdt2+3dxdt+7x=0is overdamped, the range of values for m is? ______Your answer will be an interval of numbers given in the form (1,2), [1,2), (-inf,6], etc.
m^2 is always positive or zero, we must have m = 0 for the inequality to hold true. However, since the interval should not include zero (as m=0 results in a trivial equation), the range of values for m is an empty set: ∅.
The range of values for m if the differential equation md2xdt2+3dxdt+7x=0 is overdamped is (-∞, 49/4].
If the given differential equation is overdamped, the discriminant of its characteristic equation must be greater than zero. The characteristic equation is given by:
m^2 * r^2 + 3m * r + 7 = 0
The discriminant, Δ, is calculated as:
Δ = (3m)^2 - 4 * m^2 * 7
To ensure overdamping, we must have Δ > 0:
(3m)^2 - 4 * m^2 * 7 > 0
Simplifying the inequality:
9m^2 - 28m^2 > 0
-19m^2 > 0
Since m^2 is always positive or zero, we must have m = 0 for the inequality to hold true. However, since the interval should not include zero (as m=0 results in a trivial equation), the range of values for m is an empty set: ∅.
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I will mark brainlist for whoever solves this
We have seen that BC = AD and GC = DF_, and can be simplified to AD - DF_ to DC - DF_, and AB to DC which can show that DE = CE.
How do we prove this?ABCD = rectangle
DF_ = GC
AF_ x BG = E
we will prove that DF_= CE.
From rectangle ABCD, we have that AD = BC and AB = DC. case 1
DF_ = DC - CF_ and CE = BC - BE. case 2
C_F = GC, so DF_ = DC - GC and CE = BC - BG. case 3
we know that DF_ = GC,
we go ahead to substituting DF for GC in the mathematical expression for CE: CE = BC - BG = BC - (AF_ + DF_).
AF_ = BG = E and then substitute E for AF_ and BG: CE = BC - (E + DF_).
CE: BC = AD, so CE = AD - (E + DF_) (ABCD is a rectangle)
we also have it that AD and GC = DF_,
simplify AD - DF_ to DC - DF_, and AB to DC.
In conclusion, we have proven that DE = DC - (E + BG) = DC - BC + GC
DE= DC -DF_
DE= CE.
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A report states that 46% of home owners have a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage points with 98% confidence?
The sample size needed to estimate the true proportion of home owners who have vegetable gardens to within 4 percentage points with 98% confidence is 1,529.
To calculate the sample size, we can use the formula:
n = (z² * p * q) / E²
Where:
- n is the sample size
- z is the z-score for the desired level of confidence (98% confidence corresponds to a z-score of 2.33)
- p is the expected proportion of home owners who have vegetable gardens (0.46 based on the report)
- q is 1-p (0.54)
- E is the margin of error (0.04)
Substituting the values:
n = (2.33² x 0.46 x 0.54) / 0.04²
n = 1529.03
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Find the distance between the points (4,9) and (10,9).
Answer:
The distance between (4,9) and (10,9) is 6
Step-by-step explanation:
You need to follow this formula!
√x2 - x1^2 + y2 - y1^2
Your first point (4,9) is point 1
The other (10,9) is labeled as point 2
Take the 10 and subtract it from 4 to find the x coordinate.
10-4 = 6
Then you square it
36
Take the 9 and subtract it from the other 9.
0
So far we have √36
Simplify!
=6
Therefore, the distance between (4,9) and (10,9) is 6
The formula for the distance between point (x_1,y_1) and (x_2,y_2) is,
[tex]\text{d}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Determine the distance between points (4,9) and (10,9) by using distance formula.
[tex]\text{d}=\sqrt{(10-4)^2+(9-9)^2}[/tex]
[tex]=\sqrt{36+0}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]
So distance between the two points is 6.
A random sample of size n = 100 is taken from a population of size N = 2,500 with mean μ = −45 and
variance σ2 = 81.
a-1. Calculate the expected value and the standard deviation of the sample mean. (Negative values should be indicated by a minus sign. Round "standard deviation" to 2 decimal places.)
a-2. Is it necessary to apply the finite population correction factor Yes or No?
b. What is the probability that the sample mean is between −47 and −43? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimalplaces.)
c. What is the probability that the sample mean is greater than −44? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)
Please write full procedure.
a) We can expect the sample mean to be -45 with a standard deviation of 8.1.
b) Since the sample size is less than 5% of the population size, we do not need to apply the finite population correction factor.
c) The probability of getting a sample mean between -47 and -43 is 0.1978,
d) The probability of getting a sample mean greater than -44 is 0.5485.
a) The expected value of the sample mean is equal to the population mean, which is -45. The standard deviation of the sample mean can be calculated using the formula: σ/√n, where σ is the population standard deviation and n is the sample size. Therefore, the standard deviation of the sample mean is 81/√100, which is 8.1.
b) Since the sample size (100) is less than 5% of the population size (2,500), it is not necessary to apply the finite population correction factor.
c) To calculate the probability that the sample mean is between -47 and -43, we first need to standardize the sample mean using the formula: z = (x' - μ) / (σ/√n), where x' is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get z = (-47 + 45) / (8.1) = -0.25 and z = (-43 + 45) / (8.1) = 0.25. Using a standard normal distribution table or calculator, the probability of getting a z-score between -0.25 and 0.25 is 0.1978.
d) To calculate the probability that the sample mean is greater than -44, we need to standardize the sample mean using the formula above and find the area to the right of the z-score using a standard normal distribution table or calculator.
Substituting the given values, we get z = (-44 + 45) / (8.1) = -0.12. The probability of getting a z-score greater than -0.12 is 0.5485.
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Is it a growth or decay?
Domain:
Range:
Y - intercept:
Asymptote:
For the exponential function f(x)= 4ˣ - 7 we have:
a) A growth.
b) All real numbers.
c) (-7, ∞)
d) The y-intercept is -6
e) The asymptote is y = -7
How to identify the characteristics of the exponential function?Here we have the exponential function:
f(x)= 4ˣ - 7
First, notice that the base is 4.
The base being a positive larger than 1 means that we have a growth.
b) Domain.
The domain of any exponential function is the set of all real numbers.
c) Range.
This is a growth, so it eventually tend to positive infinity.
The part 4ˣ tends at zero when x tends to really large negative values, so the y-minimum is -7, like the constant.
Thus the range is (-7, ∞)
d) The y-intercept is what we get when x = 0.
f(0) = 4⁰ - 7 = 1 - 7 = -6
e) The asymptote is the value we found before, y = -7, the function tends to that value but never reaches it.
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a cell phone manufacturer inspects the video display on each color phone to verify that the screen can display all colors with the brilliance their customers have come to expect. each phone is turned on, run through a self-test procedure, and classified as either acceptable or unacceptable based on test performance. based on historical data, the manufacturer produces 0.2 percent defective displays. if they inspect 4000 phones each day for the next 10 days, what are the upper and lower control limits for their control chart if their sample mean mirrors their historical process average?
The upper control limit for the control chart is 12.7433 and the lower control limit is 3.2567.
Assuming that the manufacturer's inspection process is a binomial process, we can use the normal approximation to the binomial distribution to calculate the control limits for their control chart. The mean of the binomial distribution is given by:
μ = np
where n is the sample size (4000 phones per day), and p is the probability of a defective display (0.002). The standard deviation of the binomial distribution is given by:
σ = sqrt(np(1-p))
Using these formulas, we can calculate the mean and standard deviation of the binomial distribution:
μ = 4000 x 0.002 = 8
σ = sqrt(4000 x 0.002 x 0.998) = 1.5811
The upper and lower control limits for the control chart can be calculated using the following formulas:
UCL = μ + 3σ
LCL = μ - 3σ
Substituting the values of μ and σ, we get:
UCL = 8 + 3 x 1.5811 = 12.7433
LCL = 8 - 3 x 1.5811 = 3.2567
Therefore, the upper control limit for the control chart is 12.7433 and the lower control limit is 3.2567. Any sample mean outside this range would be considered statistically significant and would require investigation to identify the cause of the deviation from the historical process average.
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In certain hurricane-prone areas of the United States, concrete columns used in construction must meet specific building codes. The minimum diameter for a cylindrical column is 8 inches. Suppose the mean diameter for all columns is 8.25 inches with standard deviation 0.1 inch. A building inspector randomly selects 35 columns and measures the diameter of each.What is the probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 inches?
The probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 inches is 0.9985.
The minimum diameter for a cylindrical column is 8 inches.
The mean diameter for all columns is 8.25 inches with standard deviation 0.1 inch.
A building inspector randomly selects 35 columns and measures the diameter of each.
We have to determine the probability that the sample mean diameter for the 35 columns will be between 8.2 and 8.4 inches.
P(8.2 < X' < 8.4) = P((8.2 - μ)/(σ/√n) < (X' - μ)/(σ/√n) < (8.4 - μ)/(σ/√n))
P(8.2 < X' < 8.4) = P((8.2 - 8.25) /0.0169 < Z < (8.4 - 8.25) /0.0169)
P(8.2 < X' < 8.4) = P(-2.96 < Z < 8.88)
P(8.2 < X' < 8.4) = P(Z < 8.88) - P(Z < -2. 96)
P(8.2 < X' < 8.4) = 1 - 0.0015
P(8.2 < X' < 8.4) = 0.9985
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A dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once. Find the following probability. (Enter your probability as a fraction.)
The number on the upward face is not 6.
Answer:
11/12
Step-by-step explanation:
There are 12 possibilities, 1 for each number. 1,2,3,4,5,6,7,8,9,10,11,12. The number 6 does not work which is just 1 possibility. 12-1 answer meet the condition, out of the 12 possibilities
Find the geometric mean between 28 and 32. Round to the nearest tenth if necessary.
A.29.9
B.7.7
C.30
D.10.9
The geometric mean between 28 and 32 is equal to 29.9 to the nearest tenth, which makes option A correct.
How to evaluate for the geometric meanIf x, y, z are consecutive terms of a geometric progression, then the expression for the geometric mean is given as: y = √xz
Thus; for the geometric mean between 28 and 32, we evaluate as follows:
geometric mean between 28 and 32 = √(28 × 32)
geometric mean between 28 and 32 = √896
geometric mean between 28 and 32 = 29.9333.
Therefore, the geometric mean between 28 and 32 is equal to 29.9 to the nearest tenth.
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Find the missing side lengtg
Answer:
6.5
Step-by-step explanation:
side a measures 6
side b measuring 2.5
we are trying to find side c
fill the values into the equation
a^2+b^2= c^2
6^2 +2.5^2= c^2
36 +6.25= c^2
42.25= c^2
square root of 42.25 is 6.5, so c=6.5
What is the value of x?
Answer:
x = 25 unitsStep-by-step explanation:
they are two similar triangles, same shape but dimensions in proportion, and we solve, in fact, with a proportion between the corresponding values
24 : 15 = 40 : x
x = 15 × 40 : 24
x = 600 : 24
x = 25
(1 point) Find all the values of x such that the given series would converge.
[infinity]
Σ΄7n (x - 2)ⁿ/n+2
n=1
Answer.
Note: Give your answer in interval notation
To find all the values of x such that the given series converges, we can use the Ratio Test. The series is:
Σ (7n (x - 2)ⁿ) / (n + 2), where n goes from 1 to infinity.
Apply the Ratio Test by taking the absolute value of the ratio of consecutive terms:
|(a_(n+1) / a_n)| = |(7(n+1)(x - 2)^(n+1)/(n+3))/(7n(x - 2)^n/(n+2))|
Simplify the expression:
|((7(n+1)(x - 2))/(n+3))/(7n/(n+2))| = |(n+1)(x - 2)(n+2)/n(n+3)|
Determine the limit as n approaches infinity:
lim (n→∞) |(n+1)(x - 2)(n+2)/n(n+3)|
Since the series converges when the limit is less than 1, we set up the inequality:
|(x - 2)| < 1
Solve for x:
-1 < (x - 2) < 1
1 < x < 3
Therefore, the values of x for which the given series converges are in the interval (1, 3).
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Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is $35. For one performance, 15 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $750. What was the price of each kind of ticket?
The price of the same day ticket is $15 while the price of the advance tickets is $20
What is a simultaneous equation?
We can see that;
The combined cost of one advance ticket and one same-day ticket is $35.For one performance, 15 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was $750.Forming the simultaneous equation we have;
Let the same day ticket be x and the advance ticket be y
x + y = 35
30x + 15y = 750
x = 35 - y
Hence;
30(35 - y) + 15y = 750
1050 - 30y + 15y = 750
1050 - 15y = 750
-15y = 750 - 1050
y = 20
Thus;
x + 20 = 35
x = 35 - 20
x = 15
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A Car Accelerates at 2 m/s^2. Assuming the car starts from rest, how much time does it need to accelerate to a speed of 30 m/s?
A. 15 seconds
B. 2 seconds
C. 30 seconds
D. 60 seconds
Work Shown:
vi = initial velocity = 0 m/svf = final velocity = 30 m/sa = acceleration = 2 m/s per secondt = elapsed time in seconds
t = (vf - vi)/a
t = (30 - 0)/2
t = 30/2
t = 15 seconds
Homes bulit in the suburbs typically have none to three-car garages. Let X be the number of garage stalls per hime found in a sample of 200 homes in a local suburban area. From the data obtained,P(X=0) =0.06, P(X=1) = 0.45 and P(X=2) = 0.32. Find the mean number of garage stalls per home for the sample of home.
a. 1.09
b. 1.15
c. 1.5
d. 1.6
e. 2
The mean number of garage stalls per home in the sample of 200 homes is 1.09.
What is mean?The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.
According to the given information:
To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.
The formula for calculating the expected value of X is:
E(X) = Σ [ x × P(X=x) ]
where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.
Using this formula, we can calculate the expected value of X as follows:
[tex]E(X) = (0 * 0.06) + (1 * 0.45) + (2 * 0.32)[/tex]
[tex]= 0 + 0.45 + 0.64[/tex]
= 1.09
Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.
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The mean number of garage stalls per home in the sample of 200 homes is 1.09.
What is mean?
The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.
According to the given information:
To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.
The formula for calculating the expected value of X is:
E(X) = Σ [ x × P(X=x) ]
where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.
Using this formula, we can calculate the expected value of X as follows:
E(x) = (0.06*0)+(1*0.45)+(2*0.32)
= 1.09
Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.
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a fragrance manufacturer is interested in the relationship between income and demand for its products. consumers are divided into three income categories (low, medium, and high). what is the probability that a randomly selected consumer is middle-income and purchases two or more bottles of perfume annually?
The probability that a randomly selected consumer is middle-income and purchases two or more bottles of perfume annually is 0.06 or 6%.
To find the probability that a randomly selected consumer is middle-income and purchases two or more bottles of perfume annually, we need to know the proportion of middle-income consumers who purchase two or more bottles of perfume annually.
Assuming that we have this information, let's say that the proportion of middle-income consumers who purchase two or more bottles of perfume annually is p. Then, the probability that a randomly selected consumer is middle-income and purchases two or more bottles of perfume annually can be calculated using the following formula
P(middle-income and purchases two or more bottles) = P(middle-income) * P(purchases two or more bottles | middle-income)
Let's say that the proportions of low, medium, and high-income consumers are 0.4, 0.3, and 0.3, respectively. Also, let's assume that the proportion of middle-income consumers who purchase two or more bottles of perfume annually is 0.2.
Then, the probability that a randomly selected consumer is middle-income and purchases two or more bottles of perfume annually is
P(middle-income and purchases two or more bottles) = 0.3 * 0.2 = 0.06
Therefore, the probability is 0.06 or 6%.
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If ∠ M J K and ∠ M J L are a linear pair of angles, then the angles are also supplementary
Answer: They are always suppplementary
Step-by-step explanation:
The volume of a right circular cylinder with radius r and height h is v=πr^2h. Is the volume an increasing or decreasing function of the radius at a fixed height (assume r> 0 and h> 0)? Choose the correct answer below :
A. The volume is a decreasing function because the partial derivative of V with respect to r is given dV/dr=πr^2h
B. The volume is a decreasing function because the partial derivative of V with respect to r is given dV/dh = πr^2
C. The volume is an increasing function because the partial derivative of V with respect to r is given dV/dr=2πrh
D. The volume is an increasing function because the partial derivative of V with respect to r is given dV/dh = πr^2
The volume of a right circular cylinder is an increasing function of the radius at a fixed height. So, the correct answer is option C. The volume is an increasing function because the partial derivative of V with respect to r is given dV/dr=2πrh.
The volume of a right circular cylinder with radius r and height h is given by V=πr^2h. To determine if the volume is an increasing or decreasing function of the radius at a fixed height, we need to find the partial derivative of V with respect to r.
The volume is an increasing function because the partial derivative of V with respect to r is given dV/dr=2πrh.
1. Start with the volume formula: V = πr^2h
2. Differentiate V with respect to r, keeping h constant: dV/dr = 2πrh
3. Since dV/dr is positive (2πrh > 0 for r > 0 and h > 0), the volume is an increasing function of the radius at a fixed height.
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A line passes through the points (–3,3) and (2,0). Write its equation in slope-intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
3 2/3
Step-by-step explanation:
the tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,00 miles and a standard deviation of 2700 miles. what warranty should the company use if they want 96% of the tires to outlast the warranty?
According to the standard deviation, the company should offer a warranty period that covers at least 65,895 miles to ensure that 96% of the tires sold will outlast the warranty.
To do this, we use a z-score table, which gives the probability of getting a z-score less than or equal to a given value. The z-score is a measure of how many standard deviations a data point is from the mean.
To find the z-score for the top 4% of the tires, we first subtract 96% from 100% to get 4%. Then we divide this by 2 to get 2%, as we are interested in the area under the normal distribution curve in the right tail. Using the z-score table, we find that the z-score corresponding to a 2% area under the curve is approximately 2.05.
Next, we use the formula for converting a z-score to a data value:
z = (x - μ) / σ
where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation. Solving for x, we get:
x = z x σ + μ
Plugging in the values, we get:
x = 2.05 x 2700 + 60000
x ≈ 65,895
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(2.1) T/F Two lines can intersect zero times, one time, or infinitely many times.
True. Two lines can intersect zero times if they are parallel, one time if they intersect at a single point, or infinitely many times if they are coincident (i.e., they lie on top of each other).
In geometry, a line is defined as a straight path thas.
If it extends infinitely in both directions. When two lines are in a two-dimensional plane, they can either intersect at a single point, be parallel and never intersect, or be coincident and lie on top of each other.
If two lines have different slopes, they will intersect at a single point. This point of intersection can be found by solving the system of linear equations that represent the two lines.
If two lines have the same slope, they are parallel and will never intersect. This happens when the two lines have the same steepness, but are in different locations.
Finally, if two lines have the same equation (i.e., the same slope and y-intercept), they are coincident and will intersect at every point along the line. In this case, the two lines are essentially the same line and lie on top of each other.
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Select whether the equation has a solution or not.
roots
no roots
The correct statement for the equation is no roots.
What is the solution of the equation?
The solution of the given equation is determined as follows;
√y - √7 = √(y + 7)
√y = √(y + 7) + √7
Simplify by squaring both sides;
(√y)² = (√(y + 7) + √7)²
y = y + 7 + 2√7√(y + 7) + 7
y = y + 14 + 2√7√(y + 7)
0 = 14 + 2√7√(y + 7)
-2√7√(y + 7) = 14
√(y + 7) = 14/-2√7
√(y + 7) = -√7
Square both sides again;
y + 7 = 7
y = 0
So it has zero solution.
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the differential equation y' = sqrt(x y 1)-1 has the solution
The solution of a first order ordinary differential equation, [tex]y' =\sqrt{ x + y + 1} - 1 [/tex], is equals to the y = (x + c)²/4 - x - 1.
Differential equation always relates a function with it's derivative. There are different types of differential equations, like ordinary, partial, etc. An ordinary differential equation of first order and first degree can be written as below, [tex]\frac{dy}{dx}= f( x,y) [/tex], where f(x,y) is function of x and y. We have a differential equation, [tex]y' = \sqrt{x + y + 1} - 1 [/tex]
We have to determine solution of above differential equation. Now, put z = x + y
=> [tex]\frac{dz}{dx} = 1 + \frac{ dy}{dx}[/tex]
=> [tex]\frac{dz}{dx} - 1 = \frac{ dy}{dx}[/tex]
=>[tex] \frac{dz}{dx} - 1 = \sqrt { x + y + 1} - 1[/tex]
=> [tex] \frac{dz}{dx} = \sqrt { x + y + 1} [/tex]
=> [tex] \frac{dz}{dx} = \sqrt { z + 1} [/tex]
=> [tex] \frac{dz}{\sqrt{ z + 1}} = dx[/tex]
Integrating both sides,
=> [tex]\int \frac{dz}{\sqrt{ z + 1}} = \int {1 }dx [/tex]
=> [tex] \frac{{ (z + 1)}^{1 - \frac{1}{2}}}{1 - \frac{1}{2} } = x + c,[/tex], where c is integration constant
=> [tex]2({z + 1})^{ \frac{1}{2}} = x + c [/tex]
=>[tex]2({x + y + 1})^{ \frac{1}{2}}= x + c [/tex]
Squaring both sides
> 4( x + y + 1 ) = ( x + c )²
=> y = (x + c)²/4- x - 1
Hence, required solution is y = (x + c)²/4 - x - 1 .
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Complete question:
The differential equation y' = sqrt(x +y +1) -1 has the solution?
Please answer this question
Required value of b is 4 cm
How to find value of b?
To find the value of b, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, we are given that a = 3 cm and c = 5 cm. So we can use the formula as follows,
c² = a² + b²
Substituting the given values,
[tex]5^2 = 3^2 + b^2[/tex]
[tex]25 = 9 + b^2[/tex]
Subtracting 9 from both sides,
[tex]16 = b^2[/tex]
Taking the square root of both sides,
[tex]b = √16 = 4 \: cm[/tex]
Therefore, the value of b is 4 cm.
This is a triangle related problem.
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Correct question is " see the image and find the value of b where a = 3 cm and c = 5 cm."
