As asked in the question the value of xz and y will be even ,
xz is even and y is also even
given
X = factor of Y
Y = factor of Z
Therefore,
z= mnz = mnx , xz = even
because
either z even, so the answer is directly yes or x is even (or both) but if x is even and as then z= mnz = mnx must be even too (one of the multiples of z is even, so z is even too).
(2) y= even
because
as z=ny then as one of the multiples of z even then only z will be even
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part. Thus, we can say, integers are numbers that can be positive, negative or zero, but cannot be a fraction. We can perform all the arithmetic operations, like addition, subtraction, multiplication and division, on integers.
The examples of integers are, 1, 2, 5,8, -9, -12, etc. The symbol of integers is “Z“.
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Here is an incomplete calculation of 534 divided by 6
The missing number for A is
The missing number for B is
The missing number for C is
Answer:
Step-by-step explanation:
a 23
b 43
c 56
A researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Which of the following tests is most appropriate?
analysis of variance
Since , a researcher is attempting to determine which ethnic group is more likely to go to the movies at a movie theatre. The dependent variable is metric. Therefore, the Multiple Regression method will be more appropriate analysis of variance.
Multiple regression analysis is a statistical technique that analyzes the relationship between two or more variables and uses that information to estimate the value of the dependent variable. The goal of multiple regression is to develop a model that describes the dependent variable y with multiple independent variables. Linear regression has only one independent and dependent variable. But for multiple regression, there are many independent variables that help explain or predict the dependent variable y better.
The multiple regression equation is given by
y = a + b 1×1+ b2×2+……+ bk xk
where x1, x2, ….xk are the k independent variables and y is the dependent variable
Advantages of multiple stepwise regression:
Only independent variables with non-zero regression coefficients are included in the regression equation. Several standard estimation errors and R-squared trends are displayed. Stepwise multiple regression is efficient for finding regression equations with only significant regression coefficients. The steps to create the regression equation are straightforward.Learn more about Multiple regression:
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Write [tex]\frac{x^{2} - 5 }{x} + \frac{x + 8}{x-1}[/tex] as a single fraction.
The given expression can be simplified as (x³ + 3x + 5)/(x² - x).
How to add two fractions?If the fractions have the same denominators then their numerators are added keeping the denominators as the same.
For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.
The given expression is as below,
(x² - 5)/x + (x + 8)/(x - 1)
It can be simplified as follows,
(x² - 5)/x + (x + 8)/(x - 1)
= ((x² - 5)(x - 1) + x(x + 8))/(x(x - 1))
= ((x³ - x² - 5x + 5) + x² + 8x)/(x² - x)
= (x³ + 3x + 5)/(x² - x)
Hence, the given expression can be written in the form of single fraction as (x³ + 3x + 5)/(x² - x).
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Ella has 23 red blocks and 41 green blocks. She will use all of the blocks to build 8 equal towers.
Answer:
8
Step-by-step explanation:
23:41
41+23=64
64/8=8
3
Select all the correct answers.
Which expressions are equal to ¹.2*?
O 12³
0 2³.33
0 26.33
O 125
It seems that there is perhaps some missing info here. Could you double check your question to validate the information being asked? Tysm!
A single toss of a fair coin results in either 0 or 1 head, each with probability 1/2. Define H= number of
heads obtained on a single toss. The mean of His My = 0.5 and the standard deviation of His oH = 0.5.
Suppose you toss a fair coin four times. Define T= total number of heads obtained. Find the mean and standard deviation of T.
Answer:
µT = 2 (The mean of T is 2)
σT = 1 (The standard deviation of T is 1)
Step-by-step explanation:
This involves the transformation and combination of random variables. We know that the coin flips are independent as the knowledge of one coin flip will not affect the next or another coin flip.
The question has a transformation of H by essentially multiplying it by 4 that, then turns it into T. Knowing that we can multiply the mean of 0.5 by 4 with rules of a linear transformation when multiplying each observation by a positive constant. With that, we get the mean of T to equal 2.
Since we know it is independent, we can solve for standard deviation. To do so, we have to add 0.5 squared 4 times and square root it. That will look like this: Squareroot(0.5^2+0.5^2+0.5^2+0.5^2). That will give you 1 as the standard deviation for T.
obtain the three best subsets according to the c p criterion, whicbi:of these subset models appears to have the smallest bias?
I may utilize the Cp Criterion, AICp, and SBCp to aid in choosing the optimal model. All of them impose sanctions for introducing predictions.
What is subset regression model?
Best subsets regression is a model-building regression analysis that is exploratory. It compares every model that might be built using a specified set of predictors.
There are Cp Criterion, AICp and SBCp that I can use to help select the best model. They all place penalties for adding predictors.
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pls help me i really need help
Answer:
4 mph
1.5 mph
5 mph
Fastest: Kaliel, slowest: steve
Step-by-step explanation:
The unit for Melissia can be found by finding the slope of the line. The slope is shown to be 4 miles per hour. That is the unit rate, 4 miles per hour.
The unit rate for steve is also shown in the equation y = 1.5x. This equation is the filled in form of y = mx + b where m is equivalent to the slope. Therefore 1.5 is the slope meaning the unit rate is 1.5 miles per hour.
The unit rate for Kaliel is found using the information that he walks 10 miles in two hours. To find how much he goes in 1 hour divide by two getting you 5 miles per hour.
The fastest unit rate is Kalie with 5 miles per hour, and the slowest steve with 1.5 miles per hour.
If the probability that the Islanders will beat the Rangers in a game is 4/7, what is the probability that the Islanders will win exactly two out of four games in a series against the Rangers? Round your answer to the nearest thousandth.
The probability that the islanders will win exactly two games is 0.359.
How to find probability using binomial distribution?The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+ ⁿCₙa₀bⁿ.
In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.
Given that,
The probability of winning is 4/7.
Then the probability to lose is 1 - 4/7 = 3/7.
If islanders win exactly two games out of four, it implies that they will lose 2 as well.
Now, the probability of winning exactly two games can be found using binomial distribution as given below,
⁴C₂(4/7)²(3/7)²
= 6 × 16/49 × 9/49
= 864/2401
= 0.359
Hence, the probability of winning exactly two games is 0.359.
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last qustion i need so i need a right answer
The exponential equation of the logarithmic equation ㏑ (x² - 5 · x + 17) = 3 · x + 2 is x² - 5 · x + 17 = e³ˣ ⁺ ².
What is the exponential form of a logarithmic equation?
In this question we find that a logarithmic equation, in which we must eliminate the log operator must be eliminated by relationship between logarithmic and exponential equations, whose relationship is shown below:
Logarithm of an exponential equation
㏒ aˣ = x
Exponential up to an logarithmic equation
[tex]a^{\log x}[/tex] = x
Now, we proceed to eliminate the log operator by algebra properties and relationship between logarithmic and exponential equations:
㏑ (x² - 5 · x + 17) = 3 · x + 2
By using an "exp" operators, we get the following expression:
x² - 5 · x + 17 = e³ˣ ⁺ ²
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What is the difference between survey and experiment?
The main difference between experiment and survey is that experiment is laboratory research and survey is field research. Experiments are used to prove theories or hypotheses. Surveys are used to understand the notions of a group of people.
if 40% of population is 4500 what is the total population?
Answer:
11250
Step-by-step explanation:
Question 1
Conor is going to the movie theater. A ticket to a movie costs t dollars, and there
is a 15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost.
Please help !!!!
The expressions of the total cost are 1.15t and t * (1 + 0.15)
How to determine the expression of the total cost?From the question, we have the following parameters that can be used in our computation:
Cost of a ticket = t dollars
Amusement tax on each ticket = 15%
The above parameters mean that the total cost of a ticket can be calculated using the following equation
The total cost of a ticket = Cost of a ticket * (1 + Amusement tax on each ticket)
Substitute the known values in the above equation, so, we have the following representation
The total cost of a ticket = t * (1 + 15%)
Evaluate the percentage
The total cost of a ticket = t * (1 + 0.15)
So, we have
The total cost of a ticket = t * (1.15)
Evaluate the product
The total cost of a ticket = 1.15t
Hence, the expression is 1.15t
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a repeated-measures anova with 5 subjects has df within-treatment equal to 12. what is the value for dferror for this analysis?
the value for dferror for this analysis is 8.
What is error?
Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.
df-error = (df-within treatment) - (df-subjects)
df-subjects = n - 1 = 5 - 1 = 4 {n is the no of subjects}
df-within treatment = 12
df-error = 12 - 4 = 8
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ASAP PLEASE! A rectangular swimming pool is 8 ft deep. One side of the pool is 2.5 times longer than the other. The amount of water needed to fill the swimming pool is 2000 cubic feet. Find the dimensions of the pool.
The smaller dimension of the pool is {} ft and the larger dimension of the pool is {} ft.
The dimensions of the rectangular swimming pool are 25ft long 10ft wide and 8 feet deep.
What is a cuboid?A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges. It is one of the most commonly seen shapes around us which has three dimensions: length, width, and height. Sometimes the cuboid shape is confused with a cube since it shares some properties of a cube, however, they are different from each other.
Volume of a cuboid = Length(L) x Width(W) x Depth(d)
but L = 2.5w
2.5w x w x 8 = 2000
20W^2 = 2000
W^2 = 2000/20
W^2 = 100
W = [tex]\sqrt{100}[/tex]
W = 10fft
L = 2.5W, but W = 10ft
L = 2.5 x 10
L = 25ft
In conclusion the length, width and depth are 25ft, 10ft, and 8ft respectively.
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an urban economist wishes to estimate the proportion of americans who own their homes. what size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if (a) he uses a 2010 estimate of 0.669 obtained from the u.s. census bureau
The sample size for the given problem is 1499.
What is sample size?
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
Given:
An urban economist wishes to estimate the proportion of Americans who own their homes.
p cap = 0.669
1 - p cap = 0.331
margin of error = E = 0.02
[tex]Z_a_l_p_h_a_/_2[/tex]= 1.645
Sample size = n
[tex]n = (Z_a_l_p_h_a_/_2/E)^2*Pcap*(1 - Pcap)\\= (\frac{1.645}{0.02})^2*0.669*0.331\\ = 1499[/tex]
Hence, the sample size for the given problem is 1499.
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Mitch can make 7 bracelet every 30 minute. At thi rate, how many bracelet can he make in 3. 5 hour?
Answer:
49 bracelets
Step-by-step explanation:
Let the number of bracelets that can be made be x.
First, let us convert 3.5 hours into minutes.
3.5 * 60 = 210 minutes
Accordingly,
Time (min) Number of bracelets
30 ⇒ 7
210 ⇒ x
Now, we can make an expression like this using cross multiplication.
30x = 7 × 210
30x = 1470
Divide both sides by 30.
x = 49
Line d pae through point (3, 5) and (10, 1). Line a pae through point (5, 8) and (2, 13). Are line d and line are parallel or perpendicular
lines a and d are neither parallel nor perpendicular.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
The given points of line d is (3,5) and (10,1)
and line an of line a is (5, 8) and (2, 13).
The slope of line d is m 1 = [tex]\frac{1-5}{10-3}[/tex]
m1 = -4/ 7
The slope of line d is m2 = [tex]\frac{13-8}{2-5}[/tex]
m2 = -5/3
if the slope of two lines is equal that is m1 = m2 , then the lines are parallel and the relation m1*m2=−1, then the lines are perpendicular to each other.
Here both condition fails.
Hence, lines a and d are neither parallel nor perpendicular.
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Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpoint
Answer: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpoint
Step-by-step explanation: Identify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointvvIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpointIdentify the concluion of the tatement. If AB i a egment, then it ha two endpoint. O The egment ha two endpoint. O If AB i a egment. O
AB i a egment. O Then, the egment ha two endpoint
a scatterplot shows: a. the average value of groups of data. b. scores on one variable plotted against scores on a second variable. c. the frequency with which values appear in the data d. the proportion of data falling into different categories.
Scores on one variable plotted against scores on a second variable.
The correct answer is (b)
Now, According to the question:
Let's know:
A scatterplot shows:
A scatterplot shows the relationship between two quantitative variables measured for the same individuals. The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis. Each individual in the data appears as a point on the graph.
Hence, The correct answer is (b) i.e.,
Scores on one variable plotted against scores on a second variable.
Given,
In the question:
A scatterplot shows:
a. the average value of groups of data.
b. scores on one variable plotted against scores on a second variable.
c. the frequency with which values appear in the data
d. the proportion of data falling into different categories.
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For what value of x is line m parallel to n?
Answer: X is equal to 21
Step-by-step explanation:
Answer:
25 degrees
Step-by-step explanation:
5x - 10 = 115
5x = 115 + 10
5x = 125
5/5 x = 125/5
x = 25
Put the steps in order that are used to solve the following systems of equations by substitution.
-7x - 2y
2y
= x= 2 (-4) +11 → x = 3
x
-
=
= - 13
11
= x - 2y = 11 → x = 2y + 11
=y=-4
= -7 (2y + 11) - 2y = -13
= (3,-4)
= -16y = 64
= -16y - 77 = -13
= -14y-77-2y = -13
Answer:
yes I will get suspicious and then
Step-by-step explanation:
he was in a meeting
Let n be the number of trials and p be the probability of success in the binomial distribution. Under which conditions do the Binomial and Poisson distributions give approximate results? n → [infinity], p → 0 n → [infinity], p → 1 n → 0, p → 0 n → 0, p → 1
Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
One of the common discrete distribution which is used in Statistics is the Binomial distribution. The Binomial distribution often deals with two types of situations, first, the occurring of an event and second, the non-occurring of an event termed respectively as success and failure. The Binomial distribution can be typically characterized by the two parameters namely “n” and “p” where “n” represents the number of trials and “p” represents the fixed probability of occurring of the desired event.
Further, the Binomial distribution can be visualized as an approach to determine the probability of observing a specified number of successes in a specified number of trials. The typical examples of Binomial distribution in our day-to-day life may include the survival of number of cancer patients, from the treatment offered, over a specified period of time;
Winning the number of seats against the number of candidates filed by a certain political party for an election;
Number of people benefiting from a certain house scheme when applied;
Number of covid patients discharged within three days from the hospital after their admission to a hospital for the treatment.
There is another discrete distribution which is equally popular as the Binomial distribution is the Poisson distribution. While the Binomial distribution deals with the number of trials and the probability of a success, Poisson distribution deals with the average number of successes per day or the number of successes observed per unit of time.
Unlike, in the case of a Binomial distribution, for a Poisson distribution, the knowledge of number of trials to get the observed number of successes is not required. The Poisson distribution has only one parameter namely “m” the mean number of successes per given unit of time.
The Poisson distribution is often taken as a limiting case of Binomial distribution, under the following conditions.
The number of trails is indefinitely large i.e., n → ∞
The probability of success, “p” is very small i.e., p → 0
np is finite i.e., np = m where p = m/n and q = 1 – m/n and m > 0.
However, it is not defined if “n” is large means how large and “p” is closed to zero means how small? It is left to the readers to assume how large n should be and how small p should be? As mentioned earlier, the Poisson distribution is often described as a limiting case of Binomial distribution.
Based on the results of the study , published by me clearly proves that even when 10 ≤ n ≤50 and p ≤ 0.2, the Poisson distribution can be a good approximation to Binomial distribution.
Hence the answer is Under the Binomial and Poisson distributions gives approximate result is p → 0 n → ∞.
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in the photo below please!!!!
Answer:
[tex]\cos(\theta) + \sin(\theta)[/tex]
Step-by-step explanation:
Use the sine angle sum identity.
[tex]\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)[/tex]
[tex]\sin(45\textdegree + \theta)=\sin(45\textdegree)\cos(\theta)+\cos(45\textdegree)\sin(\theta)[/tex]
Now, simplify [tex]\sin(45\textdegree)[/tex] and [tex]\cos(45\textdegree)[/tex] to [tex]\dfrac{\sqrt2}{2}[/tex]:
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot \cos(\theta)+\dfrac{\sqrt2}{2} \cdot \sin(\theta)[/tex]
Then, factor out [tex]\dfrac{\sqrt2}{2}[/tex] from each term.
[tex]\sin(45\textdegree + \theta)=\dfrac{\sqrt2}{2} \cdot ( \cos(\theta)+\sin(\theta))[/tex]
Finally, identify what is in the parentheses corresponding to the blank space in the question.
[tex]\cos(\theta) + \sin(\theta)[/tex]
For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.
The equation of circle for both the parts will be as,
(a) (x-3)² +(y-2)²= 4
(b) x²+y² = 1
What is circle?
A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.
Main Body:
(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.
Circle centered at (h, k) with radius r:
(x -h)² +(y -k)² = r²
The given circle is ...
(x -2)² +(y -2)² =2²
(x -2)² +(y -2)² = 4
__
(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:
x²+y² = 1
Hence the equation of circle is such.
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Let F be the radial force field F(x, y) = xi + yj. Find the work done by this force along the following two curves, both which go from (0, 0) to (4, 16). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!) A. If C_1 is the curve: x = t, y = t^2, 0 lessthanorequalto t lessthanorequalto 4, then integral_C_1 F middot dr = B. If C_2 is the curve: x = 4t^2, y = 16t^2, 0 lessthanorequalto t lessthanorequalto 1, then integral_C_2 F middot dr =
To know the answer check the given file.
Two occupations predicted to greatly increase in number of jobs are pharmacy technicians and network systems and data communication analysts. The number of pharmacy technician jobs predicted for
2003 through 2014 can be approximated by 7.3x-y=-256. The number of network and data analyst jobs for the same years can be approximated by 12.1x-y=-234. For both equations, x is the
number of years since 2003 and y is the number of jobs in thousands.
The year in which the number of both jobs pharmacy technicians and network systems and data communication analysts is equal is 2008.
Explain the term two variable linear equation?The linear equation in 2 variables is any equation that can be written as ax + by + c = 0, in which a, b, and c are all real values while a and b are not equal to zero.Considering the set of equations
7.3x - y = -256
12.1x - y = -234
where x represents the period of time since 2003.
y represents the quantity of jobs in thousands.
We have the answer after solving the system:
(x, y) ==> (4.5, 292)
Find the year where the total number of both jobs is equal.
At the solution point, the graphs of the two lines will collide.
The year in which the number from both jobs is equal will be 4.5 years after 2003, since x is the number of years after 2003.
So, here we are:
Year where the sum of the two jobs is equal:
2003 + 4.5 = 2007.5
= 2008 year
As a result, there will be an equal number of both jobs in 2008.
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Select the correct answer. The average rate of change of f(x) is given by the formula . Over what interval does this formula give the average rate of change for f(x)? A. [4, 7] B. [-7, 3] C. [3, 7] D. [3, 4]
Answer:
34
Step-by-step explanation:
hope u new it have fun hsm s
Water leaks from a crack in a vase at a rate of 0.5 cubic inches per minute. How long does it take for 20% of the water to leak from a full vase? I either got 10 minutes or 2.5...
The amount of time it would take for 20% of the water to leak from a full vase is equal to 24.128 minutes.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
V represents the volume of a cone.h represents the height.r represents the radius.From the diagram of the cone (see attachment), we have the following parameters:
Diameter of cone = 4.8 in.
Height of cone = 10 in.
Radius of cone = diameter/2 = 4.8/2 = 2.4 in.
Substituting the given parameters into the formula, we have;
Volume of cone, V = 1/3 × 3.142(2.4² × 10)
Volume of cone, V = 60.32 in³.
For the volume of water that has leaked, we have:
Volume of water leaked = 20/100 × 60.31
Volume of water leaked = 12.062 in³.
For the required amount of time, we have:
Time = Volume/Rate
Time = 12.064/0.5
Time = 24.128 minutes.
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A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own. If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25. (a) Find the probability that a savings account customer selected at random will have more than two credit cards. (b) Find the expected value of the number of credit cards a randomly selected customer owns. (c) Find the standard deviation of the number of credit cards a randomly selected customer owns.
a)The probability that a customer selected will have more than two credit cards is 0.11 ,b)expected value is 1.34 and c)standard deviation is 0.96.
Given, probability distribution table
X p(X)
0 0.18
1 0.44
2 0.27
3 0.08
4 0.03
where,X= number of credit cards people own
probability that a savings account customer selected at random will have more than two credit cards, p(X>2)=p(3)+P(4)=0.08+0.03=0.11Expected value of the number of credit cards a randomly selected customer owns Expected value or mean,[tex]\mu=\sum\limits^4_{n=0} X*P(X)=0*P(0)+1*P(1)+2*P(2)+3*P(3)+4*P(4)\\\\\mu=0+1(0.44)+2(0.27)+3(0.08)+4(0.03)\\\\\mu=0+0.44+0.54+0.24+0.12\\\\\mu=1.34[/tex]Standard deviation of number of credit cards. Standard deviation,[tex]\sigma=\sqrt{\sum(X-\mu)^2P(X)}\\\\=\sqrt{(-1.34)^2(0.18)+(0.34)^2(0.44)+(0.66)^2(0.27)+(1.66)^2(0.08)+(2.66)^2(0.03)}\\\\=\sqrt{(1.7956)(0.18)+(0.1156)(0.44)+(0.4356)(0.27)+(2.7556)(0.08)+(7.0756)(0.03)}\\\\=\sqrt{0.323208+0.050864+0.117612+0.220448+0.212268}\\\\=\sqrt{0.9244}\\\\=0.96[/tex]Thus, the probability that a customer selected will have more than two credit cards is 0.11 ,expected value is 1.34 and standard deviation is 0.96.
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Your question is incomplete, Here is the complete question.
A bank vice president feels that each savings account customer has, on average, three credit cards. He collected data over a period of time and found the probability distribution given in the following table. The random variable X, represents the number of credit cards people own.
X p(X)
0 0.18
1 0.44
2 0.27
3 0.08
4 0.03
If necessary, use a leading zero and round to 2 decimal places, e.g, 0.25.
(a) Find the probability that a savings account customer selected at random will have more than two credit cards ?
(b) Find the expected value of the number of credit cards a randomly selected customer owns ?
(c) Find the standard deviation of the number of credit cards a randomly selected customer owns ?