Because the object is moving slowly toward the bottom and the positive y-direction points upward, the object has a positive value for ay.
Motion is the shift in an object's location with regard to time. Motion can be quick or slow, but motion is still present. Due to the significance of motion in the physical world, it is crucial that we pay proper attention to the study of motion. Generally speaking, the following phrases are used to describe motion
DistanceDisplacementSpeedTimeWith the use of equations and derivations, understanding the numerical of physics can be tedious, but with the aid of graphs, it is both entertaining and simple to understand what the answer is describing.
Since they are used in nearly all of the topics in physics, graphs are essential. Give us more information about various graphs in this article.
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Mark has a batting average of 0.155. What is the probability that he has fewer than 3 hits in his next 6 at bats?
Since the probability that a player gets a hit on any given at bat is independent of the other at bats, we can find the probability that Mark has fewer than 3 hits in his next 6 at bats by simply multiplying the probability of getting a hit on each at bat. Since Mark has a probability of 0.155 of getting a hit on any given at bat, he has a probability of (0.155)^3 of getting exactly 3 hits in his next 6 at bats. Therefore, the probability that he has fewer than 3 hits in his next 6 at bats is 1 - (0.155)^3 approx 0.76
Answer:
The probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.
Step-by-step explanation:
A batting average is the number of hits a player has divided by the number of times they have been at bat. In this case, Mark has a batting average of 0.155, which means that he has hit 0.155 of the times he has been at bat.
To find the probability that Mark will have fewer than 3 hits in his next 6 at bats, we can use the binomial probability formula. The formula for binomial probability is:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where "n" is the number of trials, "x" is the number of successes, "p" is the probability of success on a single trial, and "1-p" is the probability of failure on a single trial.
In this case, the number of trials is 6, the number of successes is 3, and the probability of success on a single trial is 0.155. Plugging these values into the formula, we get:
P(3) = (6 choose 3) * 0.155^3 * (1-0.155)^(6-3)
To calculate the probability that Mark will have fewer than 3 hits in his next 6 at bats, we need to sum the probabilities of 0, 1, and 2 hits. We can use the binomial probability formula to calculate the probability of each of these outcomes, and then add them together to find the total probability.
For 0 hits, the probability is:
P(0) = (6 choose 0) * 0.155^0 * (1-0.155)^(6-0) = 0.009
For 1 hit, the probability is:
P(1) = (6 choose 1) * 0.155^1 * (1-0.155)^(6-1) = 0.054
For 2 hits, the probability is:
P(2) = (6 choose 2) * 0.155^2 * (1-0.155)^(6-2) = 0.141
Adding these probabilities together, we get the total probability that Mark will have fewer than 3 hits in his next 6 at bats:
P(0 or 1 or 2) = 0.009 + 0.054 + 0.141 = 0.204
Therefore, the probability that Mark will have fewer than 3 hits in his next 6 at bats is approximately 0.204.
The tickets in a box have an average value of 75, and the SD is 10. A total of 25 draws are made at random with replacement from this box.
(Answer below in percent to the nearest whole percent; do not enter the % sign.)
Find the chance that the average of the draws will be in the range 73 to 77. Answer:
The chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.
Given that,
The average ticket value per box is 75, while the standard deviation is 10. With replacement from this box, 25 random draws are conducted in total.
We have to find the chance that the average of the draws will be in the range 73 to 77.
We know that,
Take
μ=75,σ=10
X₁=73, X₂=77
We need to compute P(73≤X≤77)
The corresponding p-values are calculated by using control limit theorem
Z=X-μ/σ
Z₁=73-75/10=-2/10=-1/5
Z₂=77-75/10=2/10=1/5
We get,
P(73≤X≤77)
P(-1/5≤z≤1/5)
P(z≤1/5)-P(z≤-1/5)
0.6826
Therefore, the chance that the average of the draws will be in the range 73 to 77 is 0.6826 when the average ticket value per box is 75, while the standard deviation is 10.
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if we know the value of b, the slope of the regression line, we can accurately guess the value for the correlation coefficient without looking at the scatterplot or making any calculations.
Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.
Regression and correlation techniques can be used to establish links between variables.
Every day, we refer to any form of association as a "correlation," using that word.
To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.
Although regression illustrates how the variables are related,
Correlation and regression analysis can be shown graphically using scatter plots.
According to the question,
If we know the value of the slopes of the regression line say byx and bxy
We can Calculate the value of Correlation coefficient by using the relation
=> r = √(byx × bxy)
Hence , Yes We can accurately guess the value of correlation when slope of regression line is given
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To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 47 numbers (1 through 47 ). The order in which the selection is made does not matter. How many different selections are possible?
Answer:
Step-by-step explanation:
nCr = n! / r!(n-r)!
n=46
r=6
=46!/6!(46-6)!
=46!/[6!(40)!]
=(46*45*44*43*42*41*40!)/(6*5*4*3*2*1)(40!)
Cancel out 40!
=46*45*44*43*42*41/(6*5*4*3*2*1)
=6744109680/720
=9366819
Possible different selection 9366819
*the data set `normtemp` (**usingr**) contains measurements of 130 healthy, randomly selected individuals. the variable `temperature` contains normal body temperature. does the data appear to come from a normal distribution? if so, perform a $t$-test to see if the commonly assumed value of 98.6 degrees fahrenheit is correct. (studies have suggested that 98.2 degrees fahrenheit is more accurate.)*
A 90% confidence interval places the true mean normal body temperature between 98.14269 and 98.35577.
library(UsingR)
attach(normtemp)
print(normtemp)
hist(normtemp$temperature)
shapiro.test(normtemp$temperature)
qqnorm(normtemp$temperature)
qqline(normtemp$temperature)
We can observe that the data follows a normal distribution from the histogram and q plot.
The points in the q plot fall on a straight line and correspond to a normal distribution.
P-value = 0.2332, P>0.05, from the Shapiro test
hence, we fail to reject null htpothesis.
On accepting the null hypothesis we get to know that the data follows normal distribution.
The output for the given code will be ,
data: normtemp$temperature
t = 1527.9, df = 129, p-value < 2.2e-16
alternative hypothesis: true mean ≠0
90 percent confidence interval:
98.14269 98.35577
sample estimates:
mean of x
98.24923
Therefore , we can conclude that ,
The true mean normal body temperature is believed to be between 98.14269 and 98.35577 with a 90% confidence interval.
98.6 is not included in the 90% confidence interval.
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Can someone please solve a, b, c, and d? Thanks.
a) The variables are;
d = the number of hours walking his neighbor's dog.
c = the number of hours washing cars
b) The system of inequalities are;
6c + 7.5d ≥ 75
d + c ≤ 15
c) The two possible combinations are; (5, 10) and (10, 5)
d) Yes it will be sufficient
How to solve a system of equations?We are told that;
Tom is going to walk his neighbors dog for $6 an hour. Thus;
Money from walking neighbor's dog = $6 per hour
Money from car wash = $7.5 per hour
Total Number of hours of work not more than 15 hours
a) Let d represent the number of hours walking his neighbor's dog.
Let c represent the number of hours washing cars
b) Thus, money from walking neighbor's dog = 6c
Money from car wash = 7.5d
Therefore;
Total money saved = 6c + 7.5d
Since total number of hours of work is not more than 15 hours, then we have the inequality;
d + c ≤ 15
Tom needs to make at least $75 to cover prom expenses and so we have the inequality as;
6c + 7.5d ≥ 75
The system of inequalities represents this solution are;
6c + 7.5d ≥ 75
d + c ≤ 15
From the graph, the shaded part in between both lines provides the possible number of hours which we have as possibly; (5, 10) and (10, 5)
If he works 10 hours washing neighbors dogs and 3 hours on the cars, he will earn;
6(3) + 7.5(10) = $84
This is sufficient.
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3. Directions
Drag and drop the correct answer choice to each answer blank.
The map shows five proposed routes and distances for a new state highway between Camden and U.S. Highway 99.
Proposed Routes for State Highway 1001
Crestview
220
sssssssssssss
Camden
What is the order of these distances from least to greatest?
Distances for Different
Proposed Routes (km)
675
16
40
√2,111
586
13
10√17
The order of the distances, from least to greatest, is given by the following option:
D. 40, 675/16, 586/13, square root of 2,111, 10 square root of 27.
How to order the distances?To order the distances, we have to find them all in the same format.
For this problem, I will use the decimal format for all the distances, meaning that:
The fraction is converted to decimal dividing the numerator by the denominator.The square root is converted to decimal with a calculator.Then the decimal distances are given as follows:
675/16 = 42.1875 km.40 km.square root of 2111 = 45.95 km.586/13 = 45.08 km.10 square root of 27 = 51.96 km.Then option D orders the distances correctly.
Missing InformationThe problem is given by the image shown at the end of the answer.
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HELP IM IN K12 THERS MORE OF THESE
Answer: y=6x
Step-by-step explanation: You have to find the relationship between x and y. For this, 1 (x) times 6 = 6 (y). 2 (x) times 6 = 12 (y). This pattern will repeat in this table for eternity, so the relationship is y=6x.
Fred is (x-1)years old now. how old is he if his age in 8 years time will be three times his age 4 years ago
Answer: Fred will be 3(x-5) years old in 8 years, which is 3x-15 years old.
We know that x-1=3x-15, so x=16.
Fred is 16 years old now.
Step-by-step explanation:
Fred's age four years ago was (x - 5), Fred will be (x+7) years old in 8 years. Fred is currently eight years old.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Given that Fred is (x-1) years old
i) Fred age 4 years ago
Subtract 4 years from the present age
x -1 - 4
x - 5
So, Fred's age 4 years ago is (x - 5)
ii) Add 8 years to the present age
(x-1) + 8
(x+7)
So, Fred's age after 8 years from now is (x+7) years
iii) By the given statement
⇒ (x+7) = 4 [ x - 5 ]
We can then solve for x by expanding the right side of the equation:
⇒ x + 7 = 4x - 20
Then, we can combine like terms to get:
⇒ 4x - x = 20 + 7
⇒ 3x = 27
⇒ x = 9
Fred's present age = (x-1) = 9 - 1 = 8 years
Thus, Fred's current age is 8 years.
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The question seems to be incomplete the correct question would be:
Fred is (x-1) years old now How old: (1) was he 4 years ago. (ii) will he be 8 years from now? (ii) is he now, if his age in 8 years time will be three times his age 4 years ago?
applying the law of cross-cutting relations to the rock pictured above, what is the order (first to last) in which the rock units a-d formed? note that all of the dark-colored rock should be considered part of unit d. group of answer choices a, b, c, d a, c, b, d d, c, b, a d, a, c, b b, c, a, d
unit D must be the youngest rock unit and the order of formation must be A, B, C, D
The Law of Cross Cutting Relations states that any feature (such as a fault or a like) that cuts across a rock unit must be younger than the rock unit.
In the picture, the dark colored rock (unit D) cuts across all of the other rock units (A, B, and C).
Therefore, unit D must be the youngest rock unit and the order of formation must be A, B, C, D.
Therefore, the order of formation is A, B, C, D.
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6x2 + 36x + 3 in standard form
The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 4 sin(Ït) + 4 cos(Ït), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period.
(a) Find the average velocity during each time period.
(i) [1, 2] ? cm/s
(ii) [1, 1.1] ? cm/s
(iii) [1, 1.01] ?cm/s
(iv) [1, 1.001] ?cm/s
(b) Estimate the instantaneous velocity of the particle when t = 1 ? cm/s
The average velocity during [1,2] time period is 6cm/s.
This looks like an exercise that's building toward the idea of a derivative.
These calculations are done best with a calculator, but here's how the first interval is used:
Average velocity = (position at 2 - a position at 1) / (2 - 1)
It's really distance divided by time!
Position at t = 2: 4sin(2[tex]\pi[/tex])+3cos(2[tex]\pi[/tex])=4(0)+3(1)=3
Position at t = 1: 4sin([tex]\pi[/tex])+3cos([tex]\pi[/tex])=4(0)+3(-1)=-3
So over the interval [1, 2], the average velocity is [tex]\frac{3-(-3)}{2-1} =\frac{6}{1} =6[/tex]
∴ Average velocity=6cm/s
I used a spreadsheet to calculate the average velocity over the other intervals and a couple of shorter ones, too. (See attached image.)
As these intervals get shorter (the right endpoint is approaching 1), the average velocity gets closer and closer to the instantaneous velocity. An estimate would be -12.6.
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translate the sentence into an equation. Three times the sum of a number and 4 is 8 .
Answer: 3(x+y)+4=8
simplified: 3x+3y=4
Step-by-step explanation:
three times x (the first number) & y (the second number) & 4. Which means +4. is 8. which means =8
3(x+y)+4=8
what is the value of n in the equation 1.5x10^12=(5x10^5)(3x10^n
Answer:
n = 6
Step-by-step explanation:
(5 x [tex]10^{5}[/tex]) ( 3 x [tex]10^{n}[/tex]) = 1.5[tex]10^{12}[/tex]
(5x3) ([tex]10^{5+n}[/tex]) = 1.5 x[tex]10^{12}[/tex]
15 x ([tex]10^{5+n}[/tex]) = 1.5 x [tex]10^{12}[/tex]
1.5 x [tex]10^{1}[/tex] ([tex]10^{5+n}[/tex]) = 1.5 X [tex]10^{12}[/tex]
1.5 X [tex]10^{1}[/tex] X [tex]10^{5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]
1.5 X [tex]10^{1+5+N}[/tex] = 1.5 X [tex]10^{12}[/tex]
1.5 X [tex]10^{6 + 6}[/tex] = 1.5 X [tex]10^{12}[/tex]
1.5 X [tex]10^{12}[/tex] = 1.5 X [tex]10^{12}[/tex]
Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing. How much is the total amount paid for the used car plus expenses?
The total amount paid for the used car plus expenses will be $6,914.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Zaida purchased a used car for $6,500.
State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Now,
Since, Zaida purchased a used car for $6,500. State tax was 4%, 100 point inspection was $72, $45 for license plate, and $37 for state emissions testing.
Hence, The total amount paid for the used car plus expenses is,
⇒ $6500 + 4% of 6500 + $72 + $45 + $37
⇒ $6500 + $260 + $154
⇒ $6,914
Thus, The total amount paid for the used car plus expenses = $6,914
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1. if he flips the bottle ten times, how many do you expect to land right side up? justify by either plugging into the formula or using complete calculator notation. round answer to 4 decimal places.
I expect to land right side up using probability is 2.
What is Probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.
Probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy, has given these ideas an axiomatic mathematical formalization.
I expect to land right side up using probability is 10(0.2)
so that the answer is 2.
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The research participant is an active partner in the endeavor to develop new methodologies that give voice to those who have been silenced previously. Which of the following statements contained within Feminist Standpoint Theory relates to this statement?We can only know women's experience by attending to women's interpretations of this experience.
The statement contained within FST that agrees with the statement that the research participant is an active partner in the endeavor is: We can only know women's experiences by paying attention to women's own interpretations of these experiences.
FST stands for Food Science and Technology. It is scientific journal reviewed by peers. It acknowledges all the branches of science and technology that deal with packaging and engineering of foods and food products.
Research is the detailed and in-depth study of any subject that includes discovering facts about it as well as inventing new facts. It includes learning from the existing facts and generating new knowledge.
Therefore, the research is the only detailed way for FST.
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The one-to-one function is defined below.
Please help with this answer i’m struggling.
Answer:
<=> (8+9y)x=-y+9
<=> 8x+9yx+y=9
<=> y(9x+1)=9-8x
<=> y=(9-8x)/(9x+1)
domain: 9x+1 [tex]\geq[/tex] 0 <=> x [tex]\geq[/tex] -1/9 => R / {-1/9}
range: R/{-8/9} (horizontal asymptot)
Write the equation of the line described below in slope-intercept form.
Find the equation of the line that is perpendicular to the line y=-4 x-3 and passes through the point (10,6).
y = -1/4x + 34/4 is the equation of the line which is perpendicular to the line y = -4x - 3
Given,
The line, y = -4x - 3
Point, (x₁, y₁) = (10, 6)
We have to find the equation of line that is perpendicular to the given line;
Here,
Slope of the line, m = -1/4 (Because the line is perpendicular)
We have to find the equation line by using the formula;
y - y₁ = m(x - x₁)
Here,
y - 6 = -1/4(x - 10)
y - 6 = -1/4x + 10/4
y = -1/4x + 10/4 + 6
y = -1/4x + 34/4
That is,
The equation of the line perpendicular to the given line is y = -1/4x + 34/4
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At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
Step 1: We need to test the given hypothesis.
We can take x1- x2 to represent the difference between the jumping and relaxed times.
[tex]H0: u1 = u2\\H1: u1 \neq u2[/tex]
Step 2: Simplification
We need to find the mean and standard deviation of both samples.
[tex]u1 = 32.375, s1 = 9.620477\\u2 = 30.625, s2 = 8.331309[/tex]
The differences between the jumping and relaxed times are calculated:
[tex]5, 7, 2, 1, -2, 2, 2, -3[/tex]
The number of differences is ∑(8, i-1) = [tex](d_{i} - \alpha ) ^{2}[/tex] = 75.5
Standard deviation differences are:
[tex]\sqrt{\frac{75.5}{7} }[/tex] = 3.284
The standard error is SE = 1.161
Using this, we can find the value of the test statistic t:
[tex]t = \frac{u1 - u2}{SE}[/tex] = 1.507
Using this and the graph, we get that the p value is 0.17554.
Therefore, since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.
Since p-value is greater than α = 0.05, we cannot reject the hypothesis H0, and we can conclude that it is insufficient evidence to conclude that the average difference is not zero.
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Myesha and her children went into a bakery that sells cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30 to spend and must buy at least 16 cupcakes and cookies altogether. If xx represents the number of cupcakes purchased and yy represents the number of cookies purchased, write and solve a system of inequalities graphically and determine one possible solution.
The system of the equation is written as
xx + yy ≥ 16
$4.25xx + $0.75yy ≤ $30
the graph is attached and the solution from the graph is (5.1, 10.9)
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
If xx represents the number of cupcakes purchased
yy represents the number of cookies purchased
cupcakes for $4.25 each and cookies for $0.75 each. Myesha has $30
$4.25xx + $0.75yy = $30
buy at least ( ≥ ) 16 cupcakes and cookies altogether
xx + yy ≥ 16
The simultaneous equation
xx + yy ≥ 16
$4.25xx + $0.75yy = $30
One solution from the graph is (5, 11)
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8. A chemist wishes to create 1.5 litres of 12% acid solution. He uses.
two types of stock solutions, one with 30% acid content and another with
10% acid content. How much of each does he need?
The quantity of 30% acid content and 10% acid content used is 0.15 liters and 1.35 liters respectively
How much of each acid content is needed?Let
30% acid content = x10% acid content = yx + y = 1.5
0.3x + 0.1y = 1.5 × 0.12
0.3x + 0.1y = 0.18
x + y = 1.5
0.3x + 0.1y = 0.18
From (1)
x = 1.5 - y
Substitute into (2)
0.3x + 0.1y = 0.18
0.3(1.5 - y) + 0.1y = 0.18
0.45 - 0.3y + 0.1y = 0.18
- 0.3y + 0.1y = 0.18 - 0.45
-0.2y = -0.27
divide both sides by -0.2
y = -0.27 / -0.2
y = 1.35
Substitute into (1)
x + y = 1.5
x + 1.35 = 1.5
x = 1.5 - 1.35
x = 0.15
Therefore, 0.15 30% acid content and 1.35 10% acid content is needed.
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Electric charge produces a vector field called the electric field, which represents the force on a unit positive charge placed at the point. Two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another. The divergence of Ē is proportional to the density of the electric charge (that is, the charge per unit volume), with a positive constant of proportionality The electric held at the point 7 as a result of a point charge at the origin is К? E (7) - 11 71 Calculate div Ë for 7 7. 2 div
As per the constant of proportionality, the electric held at the point 7 as a result of a point charge at the origin is К.
What is meant by constant of proportionality?
In math, constant of proportionality refers the ratio that relates two given values in what is known as a proportional relationship.
Here we have given that electric charge produces a vector field called the electric field, which represents the force on a unit positive charge placed at the point. Two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another. The divergence of Ē is proportional to the density of the electric charge.
Here we need to find the positive constant of proportionality The electric held at the point.
As per the definition of the constant of proportionality, we have identified the following values from the given question,
Here we know that the two positive or two negative charges repel one another, whereas two charges of opposite sign attract one another.
And the divergence of Ē is proportional to the density of the electric charge.
So, based on these details, the point 7 as a result of a point charge at the origin is К.
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3x + 2y = 4
-2x + 2y = 24
The answer is (-4,8) I just need someone to solve it please
Ryan delivers flowers to two customers. He drives for 12 minutes at an average speed of
40 miles per hour to reach his first customer. He then drives for 15 minutes at an average
speed of 50 miles per hour to reach his second customer. During the 27 minutes of driving
time, how many total miles does Ryan drive?
Answer:20.5 miles
Step-by-step explanation:
the formula for distance, rate (speed), and time is
Distance=rate×time
D=40 (this is the speed he was going for the first customer) × [tex]\frac{12}{60}[/tex] (time)
the time is 12/60 because we the speed was in miles per HOUR and the time was in miles per MINUTE. To convert minutes to hours, we divide by 60.
D=40× [tex]\frac{12}{60}[/tex]
D=48/6
D=8 miles
Second trip:
D= 50×[tex]\frac{15}{60}[/tex]
D=50×[tex]\frac{1}{4}[/tex] (15/60 simplified is 1/4)
D= 12.5 miles
ANSWER: 8 miles + 12.5 miles = 20.5 miles
Graph: y ≥ 6
Is (6,2) a solution? yes or no
Is ( -2,5) a solution? yes or no
Answer:
both of them are incorrect so the answer is no
Step-by-step explanation:
If the value of y grater than 6 or equal to 6 it should be 6 or above but in (6,2) the value of y is 2 and x=6 so the value of y is less than 6
and in (-2,5) the value of x is -2 and y=5 , again the value of y is not above 6 so the answer is no for both.
Solve the system of linear equations
The value of x and y for the given linear equations are as follows.
For question8: x=4,y=-1
For question9 :x=-1.2, y=-(111/37)
What is linear equations?An equation in which is the highest power of to the variables 1 is knowns as the linear equation. Mathematically: it is an algebraic equations that can be also written in the form of ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.
Question 8
5x+4y=16------- eq1
-2x-4y=-4-------ea 2
5x=16-4y
X=(16-4y)/5
X=4(4-y)/5
Now substitute the value of x in equations 2
-2x-4y=-4
-2(4(4-y)/5)-4y=-4
-2(16-4y)/5-4y=-4
(-32+8y)/5-4y=-4
-32+8y-20y=-20
8y-20y= -20+32
-12y=12
y=-1
Now substitue the value of y in following equation
5x+4y=16
5x+4(-1)=16
5x-4=16
5x=4+16
x=20/5
x=4
Question 9
-5x+y=3-------------eq 1
3x-8y=24-------------eq2
-5x=-3-y
-5x= -(3+y)
x=(3+y)/5
Now substitute the value of x in equation 2
3(3+y)/5-8y=24
(9+3y)/5-8y=24
9+3y-40y=24
3y-40y=120-9
y=-(111/37)
Now substitue the value of y in following equation
-5x+y=3
-5x+(-111/37)=3
-185x-111=111
-185x=222
x= -222/185
x= -1.2
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let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. show that has student t distribution with $d$ degrees of freedom.
let z be standard normal random variable. let v be chi-squared random variable with d degrees of freedom. let x and v be independent random variables. [tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]
Let [tex]$X$[/tex]and [tex]$V$[/tex] be independent random variables.
[tex]$X \sim N(0,1)$[/tex] , [tex]$V \sim \chi^2(d)$[/tex]
We know that for a standard normal random variable [tex]$X$[/tex] and a [tex]$\chi^2$[/tex] random variable [tex]$V$[/tex] with [tex]$d$[/tex] degrees of freedom, the random variable [tex]$T$[/tex] given by:
[tex]$T = \frac{X}{\sqrt{\frac{V}{d}}}$[/tex]
has a student t-distribution with d degrees of freedom.
This can be seen by the following calculation:
[tex]$f_T(t) = \int_{-\infty}^{\infty} f_X(xt)\frac{1}{\sqrt{2\pi v}}e^{-\frac{v}{2}}\frac{v^{d/2}}{\Gamma(d/2)}\frac{1}{v^{d/2}}e^{-\frac{v}{2d}t^2}dv$[/tex]
[tex]$= \frac{1}{\sqrt{2\pi}}\int_{0}^{\in[/tex]
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Select Strong association, Weak association, or Moderate association to correctly classify each correlation coefficient. Correlationcoefficient Strongassociation Weakassociation Moderate association 0.45 0.95 -0.8 0.10
The correlation coefficient is,
0.45 is a moderate association0.95 and -0.8 are both the strong association0.10 is weak associationThis is the interpretation of the correlation coefficient,
A scatter plot's correlation coefficient evaluates the association between two variables.If the correlation coefficient's sign is positive, the two variables tend to increase or decrease in the same direction. If variable X increases, variable Y increases; conversely, if variable X reduces, variable Y increases. If the correlation coefficient's sign is negative, the two variables have an inverse relationship. This curve or line slopes downward. A correlation coefficient of +1 or -1 is a perfect association. The two variables are totally associated.A strong relationship is defined as a correlation coefficient that is less than +1 but more than 0.7. A coefficient between -0.7 and -1 would be the same.A moderate link is indicated by a correlation coefficient of +0.5 or -0.5. There is no correlation when the correlation coefficient is zero. A correlation coefficient of 0 is a null association.A weak relationship is 3;. similar when the correlation coefficient ranges from -3 to 0.To read more about Correlation coefficient
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Suppose replacing and using a gas furnace costs $5, 000 upfront and $100 per
month in gas. An alternative is an electric heat pump, which costs $7,000 up front
and $75 per month in electricity. These equations would be
C= 100t + 5000 and C= 75t + 7000.
What does the point of intersection represent?
a) The point in time where the cheaper option will become the more expensive
option.
Ob) The cost of installing either system.
Oc) The point in time where the rate of change is the same.
d) The time in months where you'd have to make another replacement.
The point of intersection of the equations C = 100t + 5000 and C = 75t + 7000 represents the the point in time where the cost of installing either will be the same.
What is Linear Equations?Linear equations are equations where the right hand side and left hand side involves expressions with one or more variables for which the highest degree of the variable being 1.
We have two linear equations given,
C = 100t + 5000 and C = 75t + 7000.
The point of intersection of these linear equations will be when both the equations are equal.
100t + 5000 = 75t + 7000
100t - 75t = 7000 - 5000
25t = 2000
t = 2000/25
t = 80
This is the point in time where the cost of installing either will be the same, that is after 80 months.
Cost of installing = (100 × 80 ) + 5000 = 13,000
Or = (75 × 80) + 7000 = 13000
Hence the point of intersection of these equations represent the point in time where the cost of installing either will be the same.
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