Answer:
There are two variables in the description, the estrogen level and the fertility level. Both are continuous variable.
Step-by-step explanation:
We are given the following in the question:
A water sample was taken from various lakes. The data indicate that as the concentration of estrogen in the lake water goes up, the fertility level of fish in the lake goes down.
The estrogen level is measured in parts per trillion (ppt) and the fertility level is recorded as the percent of eggs fertilized.
a) Case in study
The case in study is to find the effect on estrogen level on fertility level in fish.
As the estrogen level increases, the fertility level in fish decreases.
b) Variables in description.
There are two variables.
The estrogen levelFertility leveld) Types of variable
The estrogen level is measured in parts per trillion (ppt) and the fertility level is recorded as the percent of eggs fertilized. thus, both are expressed in numerical values. Thus, they are a quantitative variables.
Also, both the estrogen level and fertility level are measured and not counted. Both can take any value within an interval and can be expressed in decimals. Thus, they bot are continuous variable.
how many ways are there to list the digits {1,2,2,3,4,5,6} so that identical digits are not in consecutive position?
Answer: 2520 ways
Step-by-step explanation:
7!/2!
Answer:
no
Step-by-step explanation:
Question 5 (Fill-In-The-Blank Worth 1 points)
(05.05 MC)
A system of equations is shown below:
6x - 5y = 5 ,
3x + 5y = 4
The x-coordinate of the solution to this system of equations is
Numerical Answers Expected!
Answer:
The x-coordinate of the solution to this system of equations is 1.
Step-by-step explanation:
Given,
[tex]6x - 5y = 5\\\\3x + 5y = 4[/tex]
We have to find out the x-coordinate of the equation.
Solution,
Let [tex]6x-5y=5\ \ \ \ equation\ 1[/tex]
Again let [tex]3x+5y=4\ \ \ \ \ equation \ 2[/tex]
Now using elimination method we will solve the equations.
For this we will add equation 1 and equation 2 and get;
[tex](6x-5y)+(3x+5y)=5+4\\\\6x-5y+3x+5y=9\\\\9x=9[/tex]
Now on dividing both side by '9' we get;
[tex]\frac{9x}{9}=\frac{9}{9}\\\\x=1[/tex]
Hence The x-coordinate of the solution to this system of equations is 1.
1
ur welcome homie
poggers
The exponential probability distribution is a discrete distribution that is often used to describe time between customer arrivals.
Answer:
True
Step-by-step explanation:
The time between customer arrivals is called inter-arrival time. According to Queueing Notation, the inter-arrival time can be model based on difference probability distribution. The probability distribution by which the inter-arrival time can be modeled include:
Exponential Distribution or Markov distributionConstant or DeterministicHyper - exponentialArbitrary or General distributionThere are 5 very different seats in a car. In how many ways can 5 different people be seated in the car for a road trip if only 2 of them know how to drive?
Answer:
48
Step-by-step explanation:
Let A and B be the two people who are able to drive. If A is driving, there are 4! ways to arrange the remaining peoplein the car seats. If B is driving, there are also 4! ways to arrange the remaining people. The number of arrangements 'n' is:
[tex]n=2*4!\\n=2*4*3*2*1\\n=48\ ways[/tex]
They can be arranged in 48 ways.
A student who has created a linear model is disappointed to find that herR2 value is a very low 13%. a) Does this mean that a linear model is not appropriate? Explain. b) Does this model allow the student to make accurate predictions? Explain.
Answer:
a) No it doesn't mean that linear model is inappropriate
b) No. The prediction using this model will not be accurate.
Step-by-step explanation:
a)
For answering this part, firstly consider the concept of [tex]R^{2}[/tex]
The [tex]R^{2}[/tex] also known as coefficient of determination is used to determine the amount of variability in dependent variable is explained by the linear model. Lower [tex]R^{2}[/tex] depicts that less variation of dependent is explained by the independent variable using the linear model. The linearity of model is determined by scatter plot. Thus, if the [tex]R^{2}[/tex] is lower, it doesn't mean that linear model is inappropriate.
b)
The predictions made by the model having lower [tex]R^{2}[/tex] value are erroneous. The model is used for prediction if the linear model explains the larger portion of variability in dependent variation. If the predictions made from the model that have lower [tex]R^{2}[/tex] value then the predicted values will not be close to the actual value and thus residuals will not be minimum as residuals are the difference of actual and predicted values.
1. Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution.
2. What must be true of a linear system for it to have a unique solution?
Select all that apply.
A. The system has no free variables.
B. The system has one more equation than free variable.
C. The system is inconsistent.
D. The system is consistent. Your answer is correct.
E. The system has at least one free variable.
F. The system has exactly one free variable.
Answer:its A
Step-by-step explanation:it was
Not defined?
x-2/5x-10
Answer:
(x-2)/5(x-2)
cancel x-2 from the numerator and the denominator and the answer is 1/5
Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = three-quarters x 2 + 2x − 5
f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1
f(x) = 0x2 − 9x + 7
Answer:
The answer to your question is the second option
Step-by-step explanation:
A Quadratic function is a polynomial of degree two. That means that the higher exponent is 2.
a) This option is incorrect because the highest power is 3 not two.
b) This option is the right answer, the highest power is 2, so, it is a quadratic function.
c) This option is incorrect, the highest power is -2.
d) This option is incorrect, the highest option is 1.
Answer:
Option 2 is the correct answer
Step-by-step explanation:
A quadratic function is a function in which the highest power to which the variable is raised is 2
1) f(x) = −8x3 − 16x2 − 4x
The given function is a cubic function because the highest power
to which the variable,x is raised is 3
2) f(x) = 3x²/4 + 2x - 5
The given function is a quadratic function because the highest power
to which the variable,x is raised is 2
3) f(x) = 4/x² - 2/x + 1
It can be rewritten as
f(x) = 4x^-2 - 2x^-1 + 1
The given function is not a quadratic function because the highest power to which the variable,x is raised is - 2
4) f(x) = 0x2 − 9x + 7
It can be rewritten as
f(x) = - 9x + 7
The given function is not a quadratic function because the highest power to which the variable,x is raised is 1
Find the mean amount hospitals had to pay in wrong-site lawsuits. Round your answer to the nearest whole dollar.
Answer:
dont see much information here but as far as lawsuits go id aim for the highest answer
Step-by-step explanation:
_____________________________________
You are certain to get 3 jacks when selecting 51 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
The question pertains to calculating the probability of drawing exactly 3 jacks from 51 randomly drawn cards from a 52-card deck. While the probability is very high, it's not an absolute certainty. The exact calculations involve complex combinatorial mathematics.
Explanation:The subject of this question pertains to probability in mathematics, specifically to calculate the likelihood of drawing 3 jacks when selecting 51 cards from a shuffled deck of 52 cards.
First off, we need to understand that in a well-shuffled 52-card deck, there are 4 Jacks. Even if you select 51 out of 52 cards, there isn't a guarantee that you will select 3 jacks because the selection is random. The scenario you provided indicates a nearly certain event (since you're pulling nearly all the cards), but it still isn't an absolute certainty.
The exact probability computation for this kind of problem are more complex as they would involve combinatorial calculations. For simplicity, let's consider a similar but simpler scenario. Let's assume you are drawing just 4 cards instead. The probability of getting exactly 3 Jacks would be a combination of the probability of picking a Jack, and the probability of picking a non-Jack card. This would be calculated as (C(4,3) * C(48,1)) / C(52,4), with C representing the combination formula. This gives us how many ways we can draw 3 Jacks and a non-Jack divided by how many ways we can draw any 4 cards.
Learn more about Probability here:https://brainly.com/question/32117953
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Final answer:
The probability of drawing 3 jacks from a standard deck of 52 cards when selecting 51 is 1 (certainty), as it is a guaranteed event given the conditions.
Explanation:
The question asks about the probability of a certain event occurring when dealing with a standard deck of 52 cards. In this case, the event is being certain to get 3 jacks when selecting 51 cards out of 52. Since there are 4 jacks in the deck, and upon drawing 51 cards you're left with only 1 card that is not drawn, it is guaranteed that you'll have the 3 jacks among the drawn cards.
Hence, the probability is 1 (certainty), as there is only one card you're not drawing and 4 chances to have drawn a jack, which means you will always end up with all 3 jacks among the chosen 51 cards.
Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution. What must be true of a linear system for it to have a unique solution? Select all that apply.
If the coefficient matrix has a pivot in each column, it means that it is shaped like this:
[tex]A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right][/tex]
So, the correspondant system
[tex]Ax = b[/tex]
will look like this:
[tex]\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right][/tex]
This turn into the following system of equations:
[tex]\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}[/tex]
The last equation is solvable for [tex]x_4[/tex]: we easily have
[tex]x_4=\dfrac{b_4}{a_{4,4}}[/tex]
Once the value for [tex]x_4[/tex] is known, we can solve the third equation for [tex]x_3[/tex]:
[tex]x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}[/tex]
(recall that [tex]x_4[/tex] is now known)
The pattern should be clear: you can use the last equation to solve for [tex]x_4[/tex]. Once it is known, the third equation involves the only variable [tex]x_3[/tex]. Once
Write as a single integral in the form b f(x) dx. a 1 f(x) dx −3 + 4 f(x) dx 1 − −2 f(x) dx −3
Answer:
\int \limits_{-2}^{4} f(x) \, dx
Step-by-step explanation:
The objective is to write
[tex]\int \limits_{-3}^{1} f(x) \, dx + \int \limits_{1}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx[/tex]
as a single integral in the form
[tex]\int \limits_{a}^{b} f(x)\, dx[/tex].
We consider the segments [tex][-3, 1], [1, 4][/tex] and [tex][-3,-2][/tex]. If we combine the first and the second segment, we obtain
[tex][-3,1] \cup [1,4] = [-3,4][/tex]
Therefore, adding the first two integrals gives
[tex]\int \limits_{-3}^{1} f(x) \, dx + \int \limits_{1}^{4} f(x) \, dx = \int \limits_{-3}^{4} f(x) \, dx[/tex]
Now,we have
[tex]\int \limits_{-3}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx[/tex]
To subtract them, we need to find the difference of the segments [tex][-3,4][/tex] and [tex][-3,-2][/tex].
[tex][-3,4] \; \backslash \; [-3,-2] = [-2,4][/tex]
Therefore,
[tex]\int \limits_{-3}^{4} f(x) \, dx - \int \limits_{-3}^{-2} f(x) \, dx = \int \limits_{-2}^{4} f(x) \, dx[/tex]
Thus, the single integration of all the definite integral is mentioned below:
[tex]\int_{-2}^{4} f(x) dx[/tex]
Given the integral is,
[tex]\int_{-3}^{1} f(x) dx + \int_{1}^{4} f(x) dx - \int_{-3}^{-2} f(x)dx[/tex]
We need to change the whole definite integral into a single integral.
Now, we have the limits of integrations are [ - 3, 1 ], [ 1, 4 ], and [ - 3, -2 ].
Now, the first limit and second limit of integration are in addition, therefore combining forms of the integration are the union of these units.
Thus,
[ - 3, 1 ] U [ 1, 4 ] = [ -3 , 4 ]
Now, the second limit and third limit of integration are in subtraction, therefore combining forms of the integration are the intersection of these units.
Thus,
[ 1, 4 ] intersection [ - 3, -2 ] = [ null set]
Now, the combination of [ -3 , 4 ] and [ -null set] is [ - 2, 4].
Thus, the single integration of all the definite integral is mentioned below:
[tex]\int_{-2}^{4} f(x) dx[/tex]
To know more about the integrals, please refer to the link:
https://brainly.com/question/22008756
The following scores represent the results of a midterm exam in Statistics class. 25 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98 a) Find the lower and upper quartiles for the data. b) Find the interquartile range. c) Construct a boxplot for this data set.
Answer:
a.
lower Quartile= 57.5
Upper Quartile=81
b.
23.5
c.
box-plot is attached in excel file
Step-by-step explanation:
The data is arranged in ascending order so, the lower quartile denoted as Q1 can be calculated as under
Q1=((n+1)/4)th score=(41/4)th score=(10.25)th score
Q1=10th score+0.25(11th-10th)score
Q1=57+0.25(59-57)=57+0.5=57.5
Q1=57.5
The data is arranged in ascending order so, the third quartile denoted as Q3 can be calculated as under
Q3=(3(n+1)/4)th score=(3*41/4)th score=(30.75)th score
Q3=30th score+0.75(31th-30th)score
Q3=81+0.75(81-81)=81+0=81
Q3=81
b)
Interquartile range=IQR=Q3-Q1=81-57.5=23.5
IQR=23.5
c)
The box-plot is made in excel and it shows no outlier. The box-plot shows the 5-number summary(minimum-Q1-median-Q3-maximum) as 25-57.5-72-81-98.
You are designing a rectangular enclosure with 2 rectangular sections separated by parallel walls. The interior wall has a length of 60 feet and the area of the enclosure is 1700 ft2. What amount of fencing is required for this project?
Answer:
236.68 feet needed for fencing
Explanation:
You are designing a rectangular enclosure with 2 rectangular sections separated by parallel walls
Let L be the length and W be the width
Perimeter of rectangle = 3(length )+ 4 (width)
[tex]P=3L+4W[/tex]
Area of the rectangle = length * width
[tex]A=2LW[/tex]
[tex]W= \frac{A}{2L}[/tex]
[tex]W= \frac{1700}{2(60)}=14.17[/tex]
Replace the values in perimeter
[tex]P=3L+4W[/tex]
[tex]P=3(60)+4(14.17)=236.68[/tex]
So 236.68 feet needed for fencing
27. In constructing a confidence interval estimate of the population mean you decide to select 49 random observations to get your point estimate of the mean (sample mean). Your friend is also constructing a similar confidence interval estimate but decides to use a sample size of 36 random observations.
Which of the following is true?
a.) Your confidence interval estimate is narrower
b.) Your friend’s confidence interval estimate has a greater degree of confidence
c.) Your confidence interval estimate is wider
d.) Your confidence interval estimate has a greater degree of confidence
2.) The width of a confidence interval estimate for a proportion will be:
a.) Narrower for 99% confidence level than for a 95% confidence level
b.) Wider for a sample size of 100 than for a sample size of 75
c.) Narrower for 90% confidence level than for a 95% confidence level
d.) Narrower when the sample proportion is .50 than when the sample proportion is 20.
Answer:
1) a.) Your confidence interval estimate is narrower
2) c.) The width of a confidence interval estimate for a proportion will be narrower for 90% confidence level than for a 95% confidence level
Step-by-step explanation:
Confidence Interval can be stated as M±ME where
M is the sample meanME is the margin of errorMargin of Error determines the range of the confidence interval around the mean.
Margin of error (ME) of the mean can be calculated using the formula
ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where
z is the corresponding statistic in the given confidence levels is the standard deviation of the sample(or the population if it is known) N is the sample sizeFrom the formula we can reach the following conclusions:
As N increases, ME decreases.as confidence level increases, corresponding statistic increases, and thus margin of error increases.Since your sample size (49) is bigger than your friend's (36), your confidence interval is narrower, because margin of error is narrower.
Since the confidence level 90% has smaller statistic than the confidence level 95%, its confidence interval is narrower.
That is, we can estimate narrower confidence intervals with less confidence.
Which relationship is a direct variation?
Answer:
A relationship is said to have direct variation when one variable changes and the second variable changes proportionally; the ratio of the second variable to the first variable remains constant. For example, when y varies directly as x, there is a constant, k, that is the ratio of y:x.
Determine which matrices are in reduced echelon form and which others are only in echelon form. a. [Start 3 By 4 Matrix 1st Row 1st Column 1 2nd Column 0 3rd Column 0 4st Column 0 2nd Row 1st Column 0 2nd Column 2 3rd Column 0 4st Column 0 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 4st Column 1 EndMatrix ]1 0 0 0 0 2 0 0 0 0 1 1 b. [Start 3 By 4 Matrix 1st Row 1st Column 1 2nd Column 0 3rd Column 1 4st Column 1 2nd Row 1st Column 0 2nd Column 1 3rd Column 1 4st Column 1 3rd Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 EndMatrix ]1 0 1 1 0 1 1 1 0 0 0 0 c. [Start 4 By 4 Matrix 1st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 2nd Row 1st Column 1 2nd Column 3 3rd Column 0 4st Column 0 3rd Row 1st Column 0 2nd Column 0 3rd Column 1 4st Column 0 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 EndMatrix ]
Answer:
Step-by-step explanation:
Check the attachment for the solution
Answer:
Echelon form.Reduced Echelon form.Neither.Step-by-step explanation:
The objective is to determine which of the following matrices are in reduced echelon form and which others are only in echelon form. The given matrices are
[tex]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0& 2 & 0 & 0 \\ 0& 0 & 1 & 1 \end{bmatrix}[/tex], [tex]\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0& 1& 1 & 1 \\ 0& 0 & 0 & 0 \end{bmatrix}[/tex] and [tex]\begin{bmatrix} 0& 0 & 0 & 0 \\ 1& 3 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0& 0 & 0 & 1 \end{bmatrix}[/tex].
First, recall what is an echelon and reduced echelon form of a matrix.
A matrix is said to be in a Echelon form if
If there is any zero rows, all nonzero rows are placed above them;Each first non-zero entry in a row, which is the leading entry, is placed to the right of the leading entry of the row above it;All elements below the leading entry must be equal to zero in each column.A matrix is said to be in a Reduced Echelon form if
In each non-zero row, the leading entry is 1.In its column, each leading 1 is actually the only non-zero element.A column that contains a leading 1 which is the only non-zero element is called a pivot column.
Now, let's have a look at the first matrix
[tex]\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0& 2 & 0 & 0 \\ 0& 0 & 1 & 1 \end{bmatrix}[/tex]
As we can see, it doesn't have any zero rows. Each leading entry in a row is placed to the right of the leading entry from the row above and all elements below the leading entries in all columns are equal to zero. Therefore, this matrix is in an Echelon form.
In the second row, the leading entry is 2, not 1, so because of the first property of the Reduced Echelon form, it is not in a Reduced Echelon form.
Notice that it can be transformed to the Reduced Echelon form by multiplying the second row by [tex]\frac{1}{2}.[/tex]
The second matrix is
[tex]\begin{bmatrix} 1 & 0 & 1 & 1 \\ 0& 1& 1 & 1 \\ 0& 0 & 0 & 0 \end{bmatrix}[/tex]
There is a zero row, and all non-zero rows are placed above it. Each leading entry in a row, which is the first non-zero entry, is placed to the right of the entry of the row above it and all elements below the leading entry are equal to zero in each column, so it is in the Echelon form.
It is also in the Reduced Echelon form, since all non-zero rows the leading entry is 1 and it is the only non zero element in each column.
The least given matrix is
[tex]\begin{bmatrix} 0& 0 & 0 & 0 \\ 1& 3 & 0 & 0 \\ 0& 0 & 1 & 0 \\ 0& 0 & 0 & 1 \end{bmatrix}[/tex]
This matrix doesn't satisfy the condition that if there is any zero-row, it must be below all other non-zero rows, so it is not in Echelon form.
A matrix that is not in an Echelon form, it is not in an Reduced Echelon form either.
Therefore, this matrix is not in an Reduced Echelon form.
Sketch an approximate solution curve that passes through each of the indicated points.
dy/dx = e^(−0.01) xy²
Answer:
y=-2· e^(0.01)/ x²
Step-by-step explanation:
We calculate the given differential equation, we get
dy/dx = e^(−0.01) xy²
dy/y² = e^(−0.01) x dx
∫ y^(-2) dy= e^(−0.01) ∫ x dx
- y^(-1) = e^(−0.01) x²/2
-1/y= e^(−0.01) x²/2
y=-2/ e^(−0.01) x²
y=-2· e^(0.01)/ x²
We use the site desmos.com, to plot graph for the solution of the the given differential equation. We get a graph.
A general 2x2 diagonal matrix has the form(a00b). Thus the two unknown real numbers a b are needed to specify each 2x2 diagonal matrix. In Exercises 11 16, how many unknown real numbers are needed to specify each of the given matrices
1. An upper triangular 2x2 matrix?
2.) An m × n matrix?
Answer:
1. 3, and 2. m x n
Step-by-step explanation:
1. for an upper triangular 2x2 matrix i.e. (a,0,c,d), three (03) unknown elements a, c, and d are needed to be specified.
2. for m x n matrix, m*n elements are needed to be specified.
Final answer:
To specify an upper triangular 2x2 matrix, 3 unknown real numbers are needed. For an m × n matrix, m × n unknown real numbers are required.
Explanation:
The question asks how many unknown real numbers are needed to specify each of the given matrices: an upper triangular 2x2 matrix, and an m × n matrix.
1. An Upper Triangular 2x2 Matrix
An upper triangular matrix has the form:
(a, b)
(0, c)
Thus, to specify an upper triangular 2x2 matrix, 3 unknown real numbers are needed: a, b, and c.
2. An m × n Matrix
An m × n matrix has m rows and n columns. To specify such a matrix, one needs m × n unknown real numbers, representing each element in the matrix.
Factor the GCF out of the trinomial on the left side of the equation. (2 points: 1 for the GCF, 1 for the trinomial)2x^2 + 6x - 362(x^2 + 3x - 18)
Answer:
2(x+6)(x-3)
Step-by-step explanation:
Factor the GCF out of the trinomial on the left side of the equation.
[tex]2x^2 + 6x - 36 =2(x^2 + 3x - 18)[/tex]
Greatest common factor of 2, 6, 18 is 2
so GCF is 2
divide each term when we take out GCF 2
so [tex]2(x^2 + 3x - 18)[/tex]
now factor the trinomial
product is -18 and sum is +3
6 times -3 is -18 and 6-3=3
[tex]2(x^2+3x-18)\\2(x+6)(x-3)[/tex]
10- [6-2•2 + (8-3)]•2
Answer:
10-[6-4+(5)]×2
10-[2+5]×2
10-(7)×2
10-14= -4
In a sample of 11 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 167 cm. What was the mean height for both groups put together?
Answer:
I'm pretty sure it would be 345, just add the two 178 and 167
Equations - Item 2829
The circumference (C) of a circle is 16 cm. Which formula can you use to find the
diameter (d) if you know that C = 3.14d?
The formula is used to find the diameter of circle is: [tex]d = \frac{C}{3.14}[/tex]
The diameter of circle is 5.1 cm
Solution:
Given that,
Circumference (C) of a circle is 16 cm
The formula for circumference of circle when diameter is given is:
[tex]C = \pi d\\\\\pi \text{ is a constant equal to 3.14}\\\\C = 3.14d[/tex]
Rearrange the formula to get "d"
Divide both sides by 3.14
[tex]d = \frac{C}{3.14}[/tex]
The above formula is used to find the diameter of circle
Given that, circumeference = C = 16 cm
Substituting we get,
[tex]d = \frac{16}{3.14}\\\\d = 5.095 \approx 5.1[/tex]
Thus diameter of circle is 5.1 cm
PLEASE HELP!!!
Carol paid $0.78 per liter for gas while driving across Canada. Find the cost per gallon to the nearest cent.
Please give a step by step
Answer:
2.95 cent
Step-by-step explanation:
1 gallon = 231 cubic inches
1 litre = 1000ml = 61.0237 cubic inches
1 galloon = 231 / 61.0237 = 3.7854118 liters
if Carol paid $0.78 per litre
1 galloon = 0.78 x 3.7854118 = 2.952621204 ≅ 2.95 cent
The data in below relates to characteristics of high-definition televisions A through E. Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.
Screen
Setup Size (in) Type Number of Channels Available
A 47 Projection 300
B 45 Plasma 118
C 60 Plasma 423
D 40 Plasma 269
E 43 Projection 290
Answer:
Step-by-step explanation:
Hello!
You have two variables of interest.
X: Setup size (inches)
Y: Type the number of channels available.
Qualitative variables are those who describe characteristics of the subject of study, for example, the eye color of a person.
Quantitative variables are those that count quantities, for example, the shoe size of a person.
Continuous and discrete variables are quantitative. The difference is that the continuous variables are those who count in a determined range of valours, but between two observed values, there are infinite possible outcomes, for example, the body temperature of a cat. The normal temperature of a cat is around 38ºC, using a normal thermometer you measure the body temperature of two cats and obtain the following values 37.8 and 37.9 if you change the thermometer to one designed to take more precise measurements, it is possible that you obtain more values, for example, 37.81 and 39.94 and with a more precise tool you may become temperatures with more digits, this means that within this two temperatures there are infinite values of temperature, only limited by the equipment available.
A discrete variable is a quantitative variable but between the values, these variables take there are no other possible observations, regardless of the method of equipment used. An example of a discrete variable is the amount of money in a pocket. If you have two bills in one pocket, one is a 10 dollar bill and the other is a 20 dollar bill, there are no possible values in between, you either have ten or twenty, there is not possible, in this example, to count 15 dollars.
Then the variable "Y: Type number of channels available." is quantitative discrete, it counts the number of channels and between each channel there is nothing.
The variable "X: Setup size (inches)", the "inch" is a unit of length, and these variables are usually continuos, but in this example, your variable describes the screen width of the televisions and the type of image definition. Both are characteristics of the TVs so the variable is a qualitative one.
I hope it helps!
Using data from 20 compact cars, a consumer group develops a model that predicts the stopping time for a vehicle by using its weight. You consider using this model to predict the stopping time for your large SUV. Explain why this is not advisable.
No, it is not advisable to predict the stopping time for your large SUV using model trained for compact cars.
Prediction means generating the values of the dependent variable using some specific models in machine learning.
Given that, the model is trained on 20 compact cars and the model is developed such that it predicts the stopping time for a vehicle by using its weight.
Here the dependent variable is stopping time which is required to be predicted. As the model is trained on compact cars that is medium size cars and if we expect the same model to predict stopping time for large SUV, then model is going to predict false stopping time as the weights for large SUV is quiet higher than the compact cars. So, model may consider it as an outlies and will lead to incorrect prediction.
Therefore, it is not advisable to use the same model for predicting the stopping time for your large SUV.
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Final answer:
Using a stopping time model developed from compact car data to predict the stopping time for a large SUV is not advisable due to differences in vehicle dynamics, which may lead to inaccurate results.
Explanation:
When a consumer group develops a model to predict the stopping time of a vehicle based on its weight, the model must be used within the context of the data from which it was derived. Using the model, which was built on data from 20 compact cars, to predict the stopping time of a larger SUV is not advisable due to differences in vehicle dynamics, size, weight distribution, and potentially different braking systems. Models are designed to be predictive within the range of data they are based on, and extrapolating them beyond that range can lead to inaccurate predictions. Specifically, the heavier mass of an SUV compared to compact cars means that it would likely have a longer stopping distance due to greater momentum, and this may not be represented in a model calibrated to lighter vehicles.
Suppose a wheel with radius 16 cm rolls in a straight line over a flat surface rotating a total of 5 radians. How far did the wheel travel?
Answer: 80cm
Step-by-step explanation:
Given:
Radius r = 16cm
Radial distance x = 5 radians
Radian is a measure of angles.
1 radian = 180°/π
To convert radial distance to linear distance
Linear distance = radial distance × radius
d = xr
d = 5 × 16cm
d = 80cm
2-41 The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks. What is the probability the project will be finished in 62 weeks or less? 62-60/4=2/4=0.5=69146 What is the probability the project will be finished in 66 weeks or less? 66-60/4=6/4=1.5 What is the probability the project will take longer than 65 weeks?
The probability that the project will be finished in 62 weeks or less is 0.6915.
The probability that the project will be finished in 66 weeks or less is 0.9332.
The probability that the project will take longer than 65 weeks is 0.1056.
Given that:
The time to complete a construction project is normally distributed.
The mean is :
μ = 60 weeks
The standard deviation is:
σ = 4 weeks
The z-score is:
[tex]z=\frac{x-\mu }{\sigma }[/tex]
When x = 62,
[tex]z=\frac{62-60}{4}[/tex]
[tex]=0.5[/tex]
So, P(x ≤ 62) = P(z ≤ 0.5).
From the standard table, P(z ≤ 0.5) = 0.6915
When x = 66,
[tex]z=\frac{66-60}{4}[/tex]
[tex]=1.5[/tex]
So, P(x ≤ 66) = P(z ≤ 1.5).
From the standard table, P(z ≤ 1.5) = 0.9332
When x = 65,
[tex]z=\frac{65-60}{4}[/tex]
[tex]=1.25[/tex]
So, P(x > 65) = P(z > 1.25).
= 1 - P(z ≤ 1.25).
From the standard table, P(z ≤ 1.25) = 0.8944
So, P(x > 65) = P(z > 1.25)
= 1 - 0.8944
= 0.1056
Hence, the probabilities are 0.6915, 0.9332, and 0.1056 respectively.
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The probability the project will be finished in 62 weeks or less is approximately 69.15%. The probability the project will be finished in 66 weeks or less is approximately 93.32%. The probability the project will take longer than 65 weeks is approximately 10.56%.
Explanation:To find the probability that the project will be finished in 62 weeks or less, we need to calculate the z-score. The z-score formula is (x - μ) / σ where x is the value we are interested in, μ is the mean, and σ is the standard deviation. Plugging in the values, we get (62 - 60) / 4 = 0.5. Using a z-score table, we can look up the probability corresponding to a z-score of 0.5, which is approximately 0.6915 or 69.15%.
Similarly, to find the probability that the project will be finished in 66 weeks or less, we calculate the z-score: (66 - 60) / 4 = 1.5. Looking up a z-score of 1.5 in the table, we find the probability is approximately 0.9332 or 93.32%.
To find the probability that the project will take longer than 65 weeks, we can subtract the probability of it being finished in 65 weeks or less from 1. Using the z-score formula, we get (65 - 60) / 4 = 1.25. The probability of finishing in 65 weeks or less is the area to the left of this z-score, which is approximately 0.8944 or 89.44%. Subtracting from 1, we get the probability of taking longer than 65 weeks is approximately 0.1056 or 10.56%.
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For each part, give a relation that satisfies the condition. a. Reflexive and symmetric but not transitive b. Reflexive and transitive but not symmetric c. Symmetric and transitive but not reflexive
Answer:
For the set X = {a, b, c}, the following three relations satisfy the required conditions in (a), (b) and (c) respectively.
(a) R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)} is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)} is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)} is symmetric and transitive but not reflexive .
Step-by-step explanation:
Before, we go on to check these relations for the desired properties, let us define what it means for a relation to be reflexive, symmetric or transitive.
Given a relation R on a set X,
R is said to be reflexive if for every [tex]a \in X, (a,a) \in R[/tex].
R is said to be symmetric if for every [tex](a, b) \in R, (b, a) \in R[/tex].
R is said to be transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex].
(a) Let R = {(a,a), (b,b), (c, c), (a, b), (b, a), (b, c), (c, b)}.
Reflexive: [tex](a, a), (b, b), (c, c) \in R[/tex]
Therefore, R is reflexive.
Symmetric: [tex](a, b) \in R \implies (b, a) \in R[/tex]
Therefore R is symmetric.
Transitive: [tex](a, b) \in R \ and \ (b, c) \in R[/tex] but but (a,c) is not in R.
Therefore, R is not transitive.
Therefore, R is reflexive and symmetric but not transitive .
(b) R = {(a, a), (b, b), (c, c), (a, b)}
Reflexive: [tex](a, a), (b, b) \ and \ (c, c) \in R[/tex]
Therefore, R is reflexive.
Symmetric: [tex](a, b) \in R \ but \ (b, a) \not \in R[/tex]
Therefore R is not symmetric.
Transitive: [tex](a, a), (a, b) \in R[/tex] and [tex](a, b) \in R[/tex].
Therefore, R is transitive.
Therefore, R is reflexive and transitive but not symmetric .
(c) R = {(a,a), (a, b), (b, a)}
Reflexive: [tex](a, a) \in R[/tex] but (b, b) and (c, c) are not in R
R must contain all ordered pairs of the form (x, x) for all x in R to be considered reflexive.
Therefore, R is not reflexive.
Symmetric: [tex](a, b) \in R[/tex] and [tex](b, a) \in R[/tex]
Therefore R is symmetric.
Transitive: [tex](a, a), (a, b) \in R[/tex] and [tex](a, b) \in R[/tex].
Therefore, R is transitive.
Therefore, R is symmetric and transitive but not reflexive .
Relation from the set of two variables is subset of certain product. The relation for the condition are,
[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]
[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]
[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]
Relation-Relation from the set of two variables is subset of certain product. Relation are of three types-
ReflexiveSymmetricTransitive1) Reflexive and symmetric but not transitive -
Let a data set as,
[tex]X=1,2,3[/tex]
For the data set the relation can be given as,
[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]
[tex]R_1[/tex] is reflexive as it can be represent as [tex]R_1(a,a)[/tex] for,
[tex]a=1,2,3, \;\;\;\;\; [/tex]
[tex]a[/tex] ∈ [tex]X[/tex]
[tex]R_1[/tex] is symmetric as it can be represent as [tex]R_1(a,b)[/tex] for,
[tex]a,b \;\;\;\;(1,2) (2,1)[/tex]
[tex]a,b[/tex] ∈ [tex]X[/tex]
[tex]R_1[/tex] is not transitive as it can be represent as [tex]R_1\neq (a,c)[/tex] .
[tex]a,c\neq \;\;\;\;(1,3) (3,1)[/tex]
2) Reflexive and transitive but not symmetric
Let a data set as,
[tex]X=1,2,3[/tex]
For the data set the relation can be given as,
[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]
[tex]R_2[/tex] is reflexive as it can be represent as [tex]R_2(a,a)[/tex] for,
[tex]a=1,2,3, \;\;\;\;\; [/tex]
[tex]a[/tex] ∈ [tex]X[/tex]
[tex]R_1[/tex] is transitive as it can be represent as [tex]R_1(a,c)[/tex] for,
[tex]a,c \;\;\;\;(1,3) (3,1)[/tex]
[tex]a,c[/tex] ∈ [tex]X[/tex]
[tex]R_1[/tex] is not symmetric as it can be represent as [tex]R_1\neq (a,b)[/tex] .
[tex]a,b\neq \;\;\;\;(1,2) (2,1)[/tex]
3) Symmetric and transitive but not reflexive
Let a data set as,
[tex]X=1,2,3[/tex]
For the data set the relation can be given as,
[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]
[tex]R_1[/tex] is symmetric as it can be represent as [tex]R_3(a,b)[/tex] for,
[tex]a,b=(1,2),(2,1) \;\;\;\;\; [/tex]
[tex]a,b[/tex] ∈ [tex]X[/tex]
[tex]R_3[/tex] is transitive as it can be represent as [tex]R_3(a,c)[/tex] for,
[tex]a,c \;\;\;\;(1,3) (3,1)[/tex]
[tex]a,c[/tex] ∈ [tex]X[/tex]
[tex]R_1[/tex] is not reflexive as it can be represent as [tex]R_3\neq (a,a)[/tex] .
[tex]a,a\neq \;\;\;\;(1,1) [/tex]
Thus the relation for the condition are,
[tex]R_1\;\;\;\;\ (1,1), (1,2),,(2,1), (2,2),(2,3)((3,2),3,3)[/tex]
[tex]R_2\;\;\;\;\ (1,1), (2,2),,(3,3)(1,3)3,1)[/tex]
[tex]R_3\;\;\;\;\ (1,2),,(2,1), ,(2,3)((3,2)[/tex]
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The stop-board of a shot-put circle is a circular arc 1.22 m in length. The radius of the circle is 1.06 m. What is the central angle?
Answer:
Central angle= 1.15 radians
Step-by-step explanation:
[tex]Arc\,\,length=s= 1.22\,m\\Radius=r=1.06\,m\\\\Central\,\, angle=\theta=?\\\\Using\\\\ s=r\theta\\\\\theta=\frac{s}{r}\\\\\theta= \frac{1.22}{1.06}\\\\\theta=1.15 \,rad[/tex]