Answer:
\(v=u+at\)
\(v= 5+(10)\times2\\v=25\)
is the integer k divisible by 4 ? (1) 8k is divisible by 16. (2) 9k is divisible by 12.
Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
To determine if the integer k is divisible by 4, let's analyze the given statements:
Statement (1): 8k is divisible by 16.
This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.
8k = 16
k = 2
b)
This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.
9k = 12
k = 12/9
k = 4/3
So , it is not an integer
In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.
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in the simple linear regression equation , the term b0 represents: a. estimated or predicted response b. estimated intercept c. estimated slope d. explanatory variable
In the simple linear regression equation , the term b0 represents b) Estimated intercept
Define estimated intercept.The expected mean value of Y when all X=0 is the intercept, also referred to as the constant. Create a regression equation with X as the only predictor to begin. The expected mean value of Y at that value is the intercept in the event that X occasionally equals 0. When x is 0, the projected value for y—the intercept of the regression line—is simply 0. A line's slope and intercept can be expressed in terms of the equation y = slope x x + intercept. The Value of Interception The point where the function crosses the y-axis is known as the intercept and is frequently denoted as a constant. In some analyses, removing the intercept and reducing the regression line to Y = bX + error causes the regression model to only become significant.
Given,
In the simple linear regression equation , the term b0 represents:
b) Estimated intercept
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please help i need an answer ASAP
Answer:
I'm not sure, but yeah.
Step-by-step explanation:
I pretty sure it's X=5 :)
Answer:
x=5
Step-by-step explanation:
This is because if you half 4 it equals 2 positive and negative
So does 16 in half is 4 positive and negative
the answers 4 and two are whole numbers not decimals so to find your answer , the question is asking which answer is not a whole number when you half it
25=5
16=4
4=2
0=0
1=1
all positive and negative whole numbers
HOWEVER LETS HALF 5
5=2.23
5 does not become a whole number it is a decimal so that is your answer
PLS HELP ME PLEASE!!! how would I graph this. A freight company charges $25 plus $4.50 per pound to ship an item that weighs n pounds. The total shipping charges are given by the equation C = 4.5n+ 25. Identify the slope and y-intercept, and use them to graph the equation for n between 0 and 50 pounds.
The slope and y-intercept are 4.5 and 25 respectively.
A graph of the equation for the total shipping charges is shown below.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this freight company, the total shipping charges are given by;
C = 4.5n + 25
By comparison, we have the following:
Slope, m = 4.5.
y-intercept = 25.
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3/4 x 200 in decimal
According to the authors of a certain book, in a global village of 200 people, 28 suffer frommalnutrition. How many people of the world's 6.9 billion people (2010 population) sufferfrom malnutrition?The number of people of the world's population that suffer from malnutrition is billion.(Type an integer or decimal rounded to the nearest hundredth as needed.)
We can calculate the number of people suffering malnutrition in the world by using the Rule of three:
If 200 is the total population, then 28 suffer from malnutrition.
Then, if the total population is 6.9 billion people, x suffer from malnutrition:
\(\begin{gathered} 200\longrightarrow28 \\ 6.9\longrightarrow x=6.9\cdot\frac{28}{200}=6.9\cdot0.14=0.966\approx0.97 \end{gathered}\)Answer: The number of people of the world's population that suffer from malnutrition is 0.97 billion.
9. Ryan is remodeling his kitchen floor, which is 110 square feet. He used
31.5 tiles in his kitchen. If Ryan wants to remodel his bathroom, which is 28
square feet, approximately how many tiles would he need? *
Answer:
8 tiles
Step-by-step explanation:
For the kitchen floor, each title that ryan used has an area approximately of 110/31.5 ≈ 3.49 square feet
For his bathroom, Ryan would need about: 28/3.49 ≈ 8 titles
Here is the histogram of a data distribution. All class widths are 1.
Which of the following numbers is closest to the mean of this distribution?
A. 7
B. 5
C. 9
D. 4
E. 3
Considering the given histogram, the mean of the data-set is closest to:
B. 5.
What is an histogram?An histogram is a graph that shows the number of times each element of x was observed.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
Hence, considering the histogram, the mean is given by:
M = (1x1 + 2x2 + 3x3 + 4x1 + 5x1 + 6x2 + 7x3 + 8x1 + 9x1)/(1 + 2 + 3 + 1 + 1 + 2 + 3 + 1 + 1) = 4.87.
Which is closest to 5, hence option B is correct.
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f(x)=2x^2-3x+7 evaluate f(-2)
Answer:
Step-by-step explanation:
Find two linear functions p(x) and q(x) such that (p (f(q(x)))) (x) = x^2 for any x is a member of R?
Let p(x)=kpx+dp and q(x)=kqx+dq than
f(q(x))=−2(kqx+dq)2+3(kqx+dq)−7=−2(kqx)2−4kqx−2d2q+3kqx+3dq−7=−2(kqx)2−kqx−2d2q+3dq−7
p(f(q(x))=−2kp(kqx)2−kpkqx−2kpd2p+3kpdq−7
(p(f(q(x)))(x)=−2kpk2qx3−kpkqx2−x(2kpd2p−3kpdq+7)
So you want:
−2kpk2q=0
and
kpkq=−1
and
2kpd2p−3kpdq+7=0
Now I amfraid this doesn’t work as −2kpk2q=0 that either kp or kq is zero but than their product can’t be anything but 0 not −1 .
Answer: there are no such linear functions.
select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. calculate the mean for your sample.
The mean for the sample is 14.5.
We are asked to select a random sample of size 2 by writing the five numbers in this population on slips of paper, mixing them, and then selecting two. We then have to calculate the mean for the sample. The given numbers are: 12, 17, 8, 13, and 20. Therefore, there are five numbers in the population.
Now, we have to choose any two numbers randomly from the population. Let us suppose that we select 12 and 17 randomly from the population. Therefore, the sample will be {12, 17}. Now, we have to calculate the mean of the sample.
The formula to calculate the mean is: mean = sum of all numbers in the sample / total number of items in the sample. The sum of 12 and 17 is 12 + 17 = 29. Therefore, the sum of all numbers in the sample is 29. Also, the total number of items in the sample is 2.
Therefore, we can calculate the mean as: mean = 29 / 2mean = 14. 5. Therefore, the mean for the sample is 14.5.
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for the simple harmonic motion equation d=2 sin(pi/3t) what is the period
For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.
The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.
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What is the slope of the line that contains the points (1,4) and (4,8)
Answer:
i think 4/3 is the answer
Identify the intercepts of the equation 2x-5y=30
Answer:
see explanation
Step-by-step explanation:
to find the x- intercept, where the line crosses the x- axis, let y = 0 in the equation and solve for x
2x - 5(0) = 30
2x = 30 ( divide both sides by 2 )
x = 15 ← x- intercept
to find the y- intercept, where the line crosses the y- axis, let x = 0 in the equation and solve for y
2(0) - 5y = 30
- 5y = 30 ( divide both sides by - 5 )
y = - 6 ← y- intercept
Find each product by factoring the tens.
7 × 3, 7 × 30, and 7× 300
The products by factoring the tens are: 7 × 3 = 21, 7 × 30 = 210, and 7 × 300 = 2,100.
To find each product by factoring the tens, we need to separate the given number into its tens and ones place values, and then multiply the tens by the given factor.
7 × 3:
The number 7 has a tens place value of 0, so there are no tens to factor. To find the product, simply multiply 7 by 3:
7 × 3 = 21.
7 × 30:
The number 30 has a tens place value of 3.
To find the product, multiply 7 by 3:
7 × 3 = 21.
Since there is a tens place value of 3, we add a zero to the end:
21 + 0 = 210.
7 × 300:
The number 300 has a tens place value of 30.
To find the product, multiply 7 by 30:
7 × 30 = 210.
Since there is a tens place value of 30, we add two zeros to the end:
210 + 00 = 21,000.
Therefore, the products by factoring the tens are:
7 × 3 = 21,
7 × 30 = 210,
7 × 300 = 21,000.
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Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)
Component 3 must be started on day 197 to meet the delivery date of day 200.
To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.
(a) Backward schedule:
Operation | Work Center | Time (hours) | Start Day
--------------------------------------------------------
Final Assembly | Work Center 1 | 1 | 200
Sub-assembly 1 | Work Center 2 | 2 | 199
Component 4 | Work Center 3 | 3 | 197
Component 2 | Work Center 4 | 4 | 196
Component 3 | Work Center 5 | 3 | ????
(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.
From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.
Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.
Hence, component 3 must be started on day 197 to meet the delivery date of day 200.
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the diagonal of a square is 50cm long. how long are the sides of the square?
URGENT!!! Pls HELP
When dividing fractions that are represented in same terms, their quotient is simply the quotient of their numerators.
Write an equation that demonstrates this.
Answer: see below
Step-by-step explanation:
The result is the quotient of the numerators because the denominators cancel out.
\(\text{Consider}\ \dfrac{2}{7}\div \dfrac{3}{7}\\\\\\=\dfrac{2}{7}\times \dfrac{7}{3}\\\\\\\text{Cross-cancel the 7's:}\\=\dfrac{2}{3}\)
9 1/10
Step-by-step explanation:
2 3/5 / 2/7 = 13/5 x 7/2 = 91/10 = 9 1/10
What transformation rule would represent a shift of 3 units to the right and 4 units down?
Group of answer choices
The transformation of the shifts is (x + 3, y - 4)
Describing the transformation of the shiftsFrom the question, we have the following parameters that can be used in our computation:
Shift of 3 units to the rightShift of 4 units downAssuming a point on the coordinate plane is represented as
(x, y)
When shifted to the right by 3 units, we have
(x + 3, y)
When shifted down by 4 units, we have
(x + 3, y - 4)
Hence, the transformation of the shifts is (x + 3, y - 4)
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the slope of the line...................
Answer:
Y=0/0
Step-by-step explanation: since their is no fall or rise in the slope it is 0
Paul had some candy to give his five children. He first took ten pieces for himself and then evenly divided the rest among his children. Each child received three pieces. With how many pieces did he start>
Answer:
25 pieces
Step-by-step explanation:
let c = amt of candy
(c - 10 ) / 5 = 3
cross-multiply:
c-10 = 15
c = 25
(X+5)/2 = (2x-1)/3 what’s x?
Answer:
x= 3x=17/4
Step-by-step explanation:
a)work out 7/9 x 5 2/5 b)1 3/4 x 4 1/6
a. 4 1/5
b. 7 7/24
Please see the attached picture for full solution
hope it helps
Good luck on your assignment
Consider the function that assigns to each positive number x the value
Do you think this function is linear or nonlinear?
Develop a list of inputs and outputs for this function. Organize your work using the table below. Then, answer the questions that follow.
Input (x)
Output (y)
0.1
1/10 .
0.2
1/5
0.4
2/5
0.5
1/2
0.8
4/5
1
0
1.6
8/5
2
0
2.5
5/2
4
0
5
0
Plot the inputs and outputs as ordered pairs defining points on the coordinate plane.- You will do this on the peardeck or a piece of paper.
What shape does the graph of the points appear to take?
Find the rate of change using rows 1 and 2 from the table above.
Find the rate of change using rows 2 and 3 from the table above.
Find the rate of change using any two other rows from the table above.
Return to your initial claim about the function. Is it linear or nonlinear? Justify your answer with as many pieces of evidence as possible.
Answer:
The Answer should be: 40 49 60 8 54
\
95 82 40 18 39
94 72 23 70 39
24 55 6 48 40
16 100 67 93 83
2 59 97 66 28
51 81 81 6 1
29 59 34 15 65
100 94 100 70 64
87 33 20 79 76
47 56 83 58 1
36 14 71 87 26
13 4 67 26 76
85 44 55 99 64
89 50 13 10 29
62 76 82 51 71
69 13 76 3 46
71 5 51 81 15
53 94 47 55 61
6 23 97 99 46
3 87 45 49 72
87 14 32 29 22
84 60 17 4 95
100 51 39 77 87
31 97 11 80 94
78 61 38 79 35
87 67 11 21 70
82 43 19 74 42
58 90 24 8 3
61 3 63 84 1
15 67 79 31 83
28 27 93 46 39
76 7 57 82 97
35 38 73 6 88
24 95 20 90 73
17 49 4 63 63
100 3 23 52 80
17 61 39 68 63
67 27 16 81 84
81 37 43 82 34
97 54 8 32 78
99 77 20 71 17
21 42 52 48 8
46 75 71 55 74
11 48 80 39 30
76 50 52 89 100
19 10 57 21 79
58 53 99 99 11
24 59 72 16 52
91 84 36 21 22
72 44 52 56 29
96 78 57 91 47
72 42 35 79 99
44 51 76 93 16
16 36 63 82 63
42 36 82 86 30
63 42 78 75 50
65 2 50 21 32
10 23 26 96 96
61 13 16 37 58
3 30 99 93 1
54 43 8 94 13
62 54 76 14 40
12 22 68 57 24
83 16 36 2 66
49 68 65 88 2
19 36 17 89 59
51 68 100 39 75
67 27 50 87 100
12 87 65 2 1
47 61 50 36 29
64 37 68 3 99
20 83 98 91 77
53 35 37 78 89
87 79 73 20 49
19 36 23 58 29
76 4 18 44 61
65 25 84 11 3
99 97 74 92 97
9 47 73 47 8
35 96 15 65 16
93 5 48 53 28
59 23 7 47 50
20 73 26 86 92
21 10 99 91 32
32 35 63 47 25
3 87 75 9 5
4 75 15 79 43
62 33 6 23 70
81 37 96 93 33
49 72 20 47 61
30 51 67 77 16
51 11 66 68 36
49 45 29 10 98
92 39 36 89 57
74 70 77 13 94
78 1 80 33 85
34 82 27 1 97
59 99 72 82 20
73 67 35 69 68
61 83 15 77 72
31 90 77 9 71
96 96 30 75 87
40 97 78 26 16
41 5 4 57 82
50 94 11 1 94
2 72 71 6 77
89 12 22 68 82
2 35 88 11 43
54 46 9 30 95
7 90 63 13 70
10 15 49 97 73
12 7 86 24 69
91 99 40 51 18
2 79 91 19 97
99 9 66 86 92
70 34 77 31 95
89 25 68 70 57
65 36 4 24 95
36 48 92 44 62
69 84 41 52 92
84 20 66 23 73
16 85 44 17 2
9 90 58 28 90
53 41 42 15 37
18 87 53 21 57
55 25 24 5 57
93 24 17 37 63
8 92 68 68 20
100 69 45 73 11
100 79 27 99 36
44 38 10 100 27
35 32 10 28 70
53 67 81 26 97
9 42 22 1 91
61 70 80 16 38
87 91 49 1 12
57 1 22 12 24
71 88 72 42 23
67 41 20 89 14
24 1 40 41 78
86 77 23 57 96
65 90 27 1 5
59 61 39 34 28
47 83 80 84 44
29 79 94 52 86
32 39 49 100 74
31 87 65 59 47
41 53 99 79 50
83 32 70 69 27
73 69 56 20 99
26 96 14 49 66
42 94 78 88 43
38 93 62 70 97
6 84 59 86 17
20 3 100 52 71
96 71 52 65 30
39 60 100 100 10
82 52 88 39 98
82 28 91 71 33
15 32 7 100 51
40 15 51 42 70
59 54 26 47 74
98 26 42 18 96
40 76 89 79 94
61 70 21 95 18
37 25 99 91 30
86 22 87 18 53
76 57 41 71 52
10 54 35 36 36
53 14 95 5 45
49 98 16 40 8
81 67 54 82 76
83 83 94 37 76
86 23 57 42 79
63 35 88 75 100
26 70 35 35 14
64 24 98 76 46
86 65 59 76 49
70 96 65 57 30
80 1 54 19 93
28 44 11 63 24
61 27 76 6 62
44 22 24 69 58
21 92 44 100 68
82 78 74 4 100
3 52 94 18 91
32 9 95 94 40
67 57 62 46 36
91 24 22 70 17
71 74 66 2 48
86 41 52 66 54
33 99 23 40 81
65 32 16 54 48
18 79 67 4 42
9 47 13 27 59
57 80 24 51 32
86 1 95 17 83
47 38 3 27 26
21 50 99 14 66
40 74 98 16 92
9 15 21 33 87
35 91 50 7 26
22 56 27 77 92
14 81 54 40 63
84 15 48 72 75
70 50 37 48 66
34 12 17 98 51
47 2 33 39 86
10 87 57 6 95
25 74 70 44 57
91 10 34 21 99
21 81 61 87 88
19 38 73 50 11
97 63 83 28 74
7 91 44 32 56
53 98 100 51 70
86 79 18 22 45
46 28 59 76 23
21 57 67 24 16
30 22 12 65 23
51 12 62 39 97
60 49 31 68 21
84 24 66 5 24
64 63 57 12 1
58 79 1 5 62
52 15 69 26 40
17 43 32 73 79
79 25 41 98 46
50 14 91 5 93
23 65 55 85 80
71 62 14 79 53
30 5 88 30 18
2 45 41 45 99
89 13 35 96 12
58 1 71 25 38
73 53 89 63 69
67 93 72 1 17
12 96 12 86 75
1 17 77 92 5
40 78 15 82 5
75 5 34 39 71
80 4 80 13 55
69 44 61 57 45
52 5 49 27 74
76 95 68 93 45
30 75 52 1 51
43 11 43 65 69
3 3 12 4 83
96 58 45 31 89
71 28 49 89 41
31 13 45 86 89
85 61 5 72 60
20 14 19 36 6
29 64 41 40 74
66 16 7 42 15
20 42 72 66 63
97 90 33 47 84
97 81 5 33 58
72 23 25 84 1
17 60 34 51 43
3 29 96 90 37
39 28 43 17 52
99 23 85 93 27
9 10 90 19 30
2 77 6 88 17
45 85 59 60 64
32 11 70 52 2
100 33 22 12 62
42 93 37 5 55
54 70 49 81 4
40 29 45 13 84
83 63 30 46 23
34 19 44 35 8
90 71 19 100 9
28 87 52 6 11
26 14 23 3 13
57 89 82 12 56
69 63 22 3 8
40 38 2 5 4
64 66 52 8 4
62 71 41 39 58
42 76 98 65 33
92 16 48 29 44
8 96 98 74 57
22 12 15 46 10
50 34 75 2 8
40 22 100 21 16
22 60 38 94 81
32 42 65 45 93
23 93 85 64 6
36 12 94 4 79
97 9 96 26 35
12 19 56 4 67
15 47 72 78 74
30 78 100 83 69
24 50 39 87 93
47 11 4 32 15
35 26 9 14 60
11 56 88 84 47
3 28 47 40 67
3 2 94 16 68
28 76 21 86 97
23 85 8 68 49
63 67 82 66 36
20 21 56 91 6
61 24 92 47 89
32 5 83 37 46
70 56 69 41 14
68 52 84 19 9
19 96 54 46 5
23 26 49 79 31
98 48 7 88 56
78 72 82 62 47
3 35 60 95 28
17 34 63 32 81
57 58 88 23 72
25 85 46 36 35
46 26 73 91 63
Find the limit (if it exists). (If an answer does not exist, enter DNE.) limx→9−f(x), where f(x)={2x+2x<9
,936−2x,x>9
Therefore, the answer is DNE.
The function \(f(x) = { 2x + 2, x < 9 936 - 2x, x > 9\)
We need to find the limit of f(x) as x approaches 9- (left-hand limit).
Let's first find the right-hand limit:\(lim x→9+ f(x)= lim x→9+ (936 - 2x) = 936 - 2(9) = 918\)
Now, let's find the left-hand limit:\(lim x→9- f(x) = lim x→9- (2x + 2)= 2(9) + 2= 20\)
As the left-hand limit is not equal to the right-hand limit, the limit does not exist.
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Which of the following is equal to the opposite of -45?
O-(-45)
O-45
O-1-451
O-145!
Step-by-step explanation:
A o option
-(-45)
hope it helps
Find the first five terms of the recursive sequence.
The first five terms of the recursive sequence are 4.5, -27, 162, -972 and 5832
How to determine the first five terms of the recursive sequence.From the question, we have the following parameters that can be used in our computation:
an = -6a(n - 1)
a1 = -4.5
The above definitions imply that we simply multiply -6 to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a(2) = -6 * 4.5 = -27
a(3) = -6 * -27 = 162
a(4) = -6 * 162 = -972
a(5) = -6 * -972 = 5832
Hence, the first five terms of the recursive sequence are 4.5, -27, 162, -972 and 5832
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jackson and ginger are both learning to ride a bike. Jackon can travel y = 4x miles. and ginger travels y = 3x + 15
We can say that the distance travelled and minutes spent biking will be equal for both of them if they bike for 15 minutes.
What is the general equation of a straight line?The general equation of a straight line is of the form -
y = mx + c
where -
[m] is slope of line
[c] is y - intercept
Given are Jackson and Ginger who are learning to ride a bike. Jackson can travel (y = 4x) miles and ginger can travel (y = 3x + 15) miles.
Both the equations represent a straight line, plot the graph for both the lines. The point of intersection of these two lines will represent the point when the distance between and minutes spent biking are same for both Jackson and Ginger.
Refer to the graph attached. Both of these graphs intersect at (15, 60).
Therefore, we can say that the distance travelled and minutes spent biking will be equal for both of them if they bike for 15 minutes.
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[ The complete question is attached with the answer ]
What is the value of this expression when a = 4, b= -5, and c= -7?
a + 2bc
3a ?
Answer:
1) -66
2)
Step-by-step explanation:
Given:
a=4
b=-5
c=-7
=a+2bc
=4+2*-5*7
=4+(-10*7)
=4-70
=-66
=3a
=3(4)
=12
Hope this helps ;) ❤❤❤
Answer:
-66, 12
Step-by-step explanation:
4+2 times-5 times -7 times
-70+4= 66
The gamma function of is defined as . using the transformation , derive the gamma distribution with parameters and . hence find and
The gamma distribution with parameters $\alpha$ and $\beta$ is a probability distribution that can be derived using the transformation $x = \beta y$.
The probability density function of the gamma distribution is:
f(x; α, β) = \frac{(\beta x)^{\alpha - 1} e^{-\beta x}}{\Gamma(\alpha)}
where $\alpha$ is the shape parameter and $\beta$ is the rate parameter.
The derivation is as follows:
* The gamma function is defined as:
Γ(α) = \int_0^{\infty} x^{\alpha - 1} e^{-x} dx
* Using the transformation $x = \beta y$, we get:
Γ(α) = \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy
* We can then write the probability density function of the gamma distribution as:
f(x; α, β) = \frac{1}{\Gamma(\alpha)} \int_0^{\infty} (\beta y)^{\alpha - 1} e^{-\beta y} \beta dy
* This is the same as the probability density function of the gamma distribution with parameters $\alpha$ and $\beta$.
The mean and variance of the gamma distribution can be found using the following formulas:
E(X) = \alpha \beta
Var(X) = \alpha \beta^2
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Find the result of |x-1|=2
The absolute value of x minus one is equal to two. Therefore, x must be either one greater than two (x = 3) or one less than two (x = 1).
One less than x results in a value of two in absolute terms. As a result, x minus 1 has an absolute value of 2, which is a positive number. The separation of an integer from zero is its absolute value. As a result, x minus 1 is two units from zero in absolute terms. As x minus one has an absolute value of two, its real value must either be two or a negative two. That is to say, x must either be one more than two (x = 3) or one less than two (x = 1).In order to confirm this, let's look at a few examples. If x = 3, then |x - 1| = |2 - 1| = |1| = 1 which is not equal to two. Therefore, x = 3 is not the answer we are looking for. On the other hand, if x = 1, then |x - 1| = |1 - 1| = |0| = 0 which is not equal to two. Therefore, x = 1 is also not the answer we are looking for. The only two possible solutions for the equation |x - 1| = 2 are x = 3 and x = 1. Therefore, the result of |x - 1| = 2 is that x must be either one greater than two (x = 3) or one less than two (x = 1)
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