(a) The probability that X, = 1 will be =1/2
(b) The probability that X, = 1 given X,= 1 will be =2/3
(c) The probability that in the first 4 trials you get (at least) three white balls in a row will be=2/5
(d) The expected value of the number of white balls in 4 trials will be=2
(e) The variance of the number of white balls in 4 trials will be=2
A box starts with 2 balls; [ black and 1 white, x draw on these balls are supposed to be uniformly at random then we will replace it with 2 of the same colour. The Process repeats for Each i=1,2,3..........
Let x_1=1, if we draw a white ball on trial 1
The Property of the x_1 is
The Event where The drawn fall is white =A
Let the number of white balls in 4 trials is denoted by 'x'.
[tex]P(x=0) P\left(A^c A^c A^c A^c\right) . \\=1 / 2 \times 3 / 3 \times 3 / 4 \times 4 / 5=1 / 5 . \\P(x-1)=P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right)+P\left(A^c A^c A^c A^c\right) \\=1 / 2 \times 1 / 3 \times 1 / 4 \times 3 / 5+1 / 4 \times 1 / 3 \times 2 / 3 \times 3 / 5+1 / 2 \times 2 / 3 \times 1 / 4 \times 3 / 5+1 / 2 \times 2 / 3^2 \times 3 / 4 \times 1 / 5 . \\=\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20} . \\=4 \times \frac{1}{20}=1 / 5 . \\[/tex]
[tex]\therefore P(x=2)=1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 .[/tex]
[tex]$\begin{aligned} \therefore P(x=2) & =1 / 2 \times 2 / 3 \times 1 / 4 \times 2 / 5 \times 4 / 2=6 \times 1 / 3=1 / 5 . \\ P(x=3) & =1 / 2 \times 2 / 3 \times 3 / 4 \times 1 / 5 \times 4 / 3 . \\ & =1 / 20 \times 4=1 / 5 . \\ P(x=4) & =1 / 2 \times 2 / 3 \times 2 / 4 \times 4 / 5=P(\text { AAAA })=1 / 5 .\end{aligned}$[/tex]
(a)
[tex]P\left(X_2=1\right) & =P(A A)+P\left(A^C A\right) . \\& =1 / 2 \times 2 / 3 \times 1 / 2 \times 1 / 3 . \\& =2 / 6+1 / 6=3 / 6=1 / 2 . \\P\left(X_4=1\right)= & P(A A A)+P\left(A A A A^{\prime} A\right)+P\left(A^C A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P \\& \left.\quad\left(A^{\prime} A A A\right)+P\left(A^{\prime} A^{\prime} A\right)+P\left(A^A A A\right)\right) \\[/tex]
[tex]= & 1 / 5+1 / 20+1 / 20+1 / 20+1 / 20+1 / 30+1 / 30+1 / 20 . \\= & 1 / 5+4 / 20+3 / 20 .=2 / 5+1 / 10 . \\= & \frac{4+1}{10}=5 / 10=1 / 2 .[/tex]
[tex]$\therefore$[/tex] Probability that x_2=1 is equal with probability that x_4 >1
(b) Probability that x_2=1 given x_4=1
[tex]$$\begin{aligned}& =P\left(x_2=1 / x_{4=1}\right)=\frac{P\left(x_2=1 \& x_4=1\right)}{P\left(x_4=1\right) .} \\& =\frac{P(A A A A)+P\left(A A A^{\prime} A\right)+P(A A A A)+P\left(A^C A A^C A\right)}{1 / 2} \\& =2 \times(1 / 5+1 / 20+1 / 20+1 / 30] \\& =2 \times[1 / 5+1 / 10 \times 1 / 30] \\& =2 \lambda\left[\frac{6+30+1}{30}\right] \\& =2 \times \frac{10}{30} .=2 / \mathrm{3} .\end{aligned}$$[/tex]
(c) Probability that in that the nuts is 3 which is P(x=3)+P(x=4) is [tex]=1 / 5+1 / 5=2 / 5[/tex]
(d) Expected volume of number of white ball is 4 trial is,
[tex]$$\begin{gathered}{[0 \times 1 / 5+1 \times 1 / 5+2 \times 1 / 5+3 \times 1 / 5+3 \times 1 / 5+4 \times 1 / 5]} \\=\frac{1+2+3+4}{5}=10 / 5=2 .\end{gathered}$$[/tex]
(e)
[tex]E\left(x^2\right) & =0^2 \times 1 / 5+1^2 \times 1 / 5+2^2 \times 1 / 5+3^2 \times 1 / 5 .+4^2+1 / 5 . \\& =\frac{1+4+9+16}{5 .} \\& =30 / 51=6 . \\\therefore var/x =E\left(x^2\right)-E[(x)]^2 . \\& =6-2^2 =6-4=2[/tex]
[tex]$\therefore$[/tex] The variance of the number of white balls in 4 trails =2
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A mining company wants to test a claim concerning the mean weight of their silver nuggets. They are testing the null hypothesis that the true mean is 3 ounces against the alternative that the mean is less than 3 ounces. The p-value for the hypothesis test was determined to be 0.002. Which of the following is a correct interpretation of this p-value?
a. The null hypothesis would not be rejected at either the 0.05 or 0.01 level b. The null hypothesis would be rejected at a 0.01 level but not at a 0.05 level. c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels. d. The null hypothesis would be rejected at a 0.05 level but not at a 0.01 level
The correct answer is c. The null hypothesis would be rejected at both the 0.05 and 0.01 levels.
A p-value is a probability of obtaining a result that is at least as extreme as the one observed in the sample data, given that the null hypothesis is true. The smaller the p-value, the less likely it is that the observed result occurred by chance, and the more likely it is that the null hypothesis is false.
In this case, the p-value of 0.002 is less than both the 0.05 and 0.01 significance levels, which means that it is highly unlikely that the observed result occurred by chance if the null hypothesis is true. Therefore, the null hypothesis should be rejected at both the 0.05 and 0.01 levels.
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Solve for interior angles
Answer:
(x+17)°=25° <---Smallest Angle
(7x-16)°=40°
115°=115°
Step-by-step explanation:
Because the angles in a triangle add up to 180°, 115°+(x+17)°+(7x-16)°=180°
Now we can solve algebraically.
115°+(x+17)°+(7x-16)°=180°
115+x+17+7x-16=180
Rearrange:
115+17-16+7x+x=180
Solve:
115+1+8x=180
116+8x=180
8x=180-116
8x=64
x=8
Now we can fill x in to find the measure of the angles.
(x+17)°
(8+17)°
=25°
(7x-16)°
56-16
=40°
Check:
40+25+115
65+115
5+175
=180°, so our angles add up.
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Find the derivative a. by evaluating the integral and differentiating the result b. by differentiating the integral directly. d/dx sin t dt a. Evaluate the integral and differentiate the result to find the derivative, d/dx sin t dt = (Simplify your answer.) b. Differentiate the integral directly to find the derivative. d/dx sin t dt = (Simplify your answer.)
The result of derivative by evaluating the integral and differentiating is 2sinx.
What is derivative?The function itself is the derivative of a function's integral. But only in the case of indefinite integrals is this always the case. Only when the lower limit of the integral is a constant and the higher limit is the variable we are differentiating with, is the derivative of a defined integral of a function the function itself.
The function itself is the derivative of an indefinite integral of a function. Specifically, d/dx f(x) dx = f (x)
d/dx ∫x -x (sin t) dt
⇒ d/dx [- cos t] x -x
⇒ - d/dx [cos x - cos (-x)]
⇒ - d/dx [ 2 cos x]
⇒ -2 d/dx [cos x]
⇒ -2 [- sin x]
⇒ 2 sin x
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a large university is divided into six colleges, with most students graduating from four of these colleges. the following bar chart gives the distribution of the percent graduating from the four most popular colleges in 2003. the percent of students graduating from either engineering or business is:
A.) ~30%
B.) ~40%
C.) ~50%
D.) Over ~60%
The percentage of students graduating from engineering or business
is ~50%
as per given in the questions
An university is divided into 6 colleges
with which the most of the students graduating from the four of the colleges given in the graph below
the percentage of students who are interested in biological science colleges are 20%
the percentage of students who are interested in mathematics colleges are 10%
the percentage of students who are interested in Engineering colleges are 20%
the percentage of students who are interested in business colleges
are 30%
from the graph, graduating from either Engineering or Business
is = 20% + 30% = 50%
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Abdel wants to spend $12 on beans and rice.
- beans, b, cost $5 per pound.
- rice, r, cost $2 per pound.
Answer:
1. 2 pounds of beans and 1 pound of rice
2. 0.6 pounds of beans and 9 pounds of rice
3. b pounds of beans and (12-b)/2 pounds of rice
Step-by-step explanation:
1. You know that 2 pounds of beans costs 2*5 so $10. Then you subtract 12-10 to get 2.
2 pounds of rice
2. You multiply 0.6 by 5, and then you subtract that from 12, getting 9. then you divide by 2 (cost of rice per pound) getting 4.5 pounds of rice
code a function definition for a function named shiftdiagonal which does the following: 1) accepts an x coordinate, y coordinate and amount to shift them by. 2) increments the x and y coordinates by the amount.
As per the condition for defining the function with name shiftdiagonal , we need to define the function with two parameter (x,y,z). Then the function ultimately increments the values in x and y by z and returns the updated values of x, y.
What is a function in programming?Simply said, a function is a "block" of code that you may reuse again rather than having to write it out several times. Programmers can divide an issue into smaller, more manageable parts, each of which can carry out a specific job, using functions. The specifics of how a function operates can virtually be forgotten once it has been built. By abstracting the specifics, the programmer may concentrate on the broad picture.
How do we define a function in python?In Python 'def' keyword is used to define functions.
for example:- def function_name( ):
The code for a function definition to fulfill the conditions put by the question(using python) is given below:
def shiftdiagonal(x , y, z):
x = x + z
y = y + z
return x,y
In the above code z is supposed to be the amount to shift x and y by.
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help please
In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
The value of c in the triangle is 14.
How to angles of triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
In the triangle LMN, m ∠L = (3c + 66)°. The exterior angle to ∠L measures 72 degrees.
Therefore, let's find c.
Hence, the sum of the exterior angle and the interior angle is 180 degrees.
Therefore,
72 + 3c + 66 = 180
3c = 180 - 66 - 72
3c = 42
divide both sides by 3
c = 42 / 3
Therefore,
c = 14
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Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate. f(x) =3x^2 + 2x - 3, a = - 0.9 Set the center of the linearization as x = L(X) =
The linearization of the given function near x = -0.9 is approximated by the linear equation -x - 7, with the center of the linearization at x = -1. This equation is obtained by evaluating the function and its derivative at x = -1, then using them to approximate the value of the function at x = -0.9.
The linearization of the given function f(x) = 3x^2 + 2x - 3 near the point x = -0.9 is a linear equation that approximates the value of the function at the point. To obtain the linearization, we must first choose a suitable integer near -0.9 at which the function and its derivative are easy to evaluate. In this case, we choose x = -1 as the center of the linearization. To obtain the linearization equation, we evaluate the function and its derivative at x = -1, then use them to approximate the value of the function at x = -0.9. This results in the linear equation -x - 7. This equation allows us to approximate the value of the function at x = -0.9 without having to calculate the value of the function directly.
f(-1) = 6
f'(-1) = -1
Linearization: f(x) ≈ f(-1) + f'(-1)(x + 1)
= 6 - 1(x + 1)
= -x - 7
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The following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation = 17.49 + 1.0334x. For these data SSE = 1541.4. Click on the webfile logo to reference the data. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).
$ ______
b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals).
($_____, $_____)
c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
($_____, $_____)
The estimated regression equation for the given data is y = 17.49 + 1.0334x.Create a 95% confidence interval for the median entertainment spending for all cities with $89/day room rates.
a. Estimate the amount of money that will be spent on entertainment in a city with a $89 daily hotel fee (to 2 decimals).
$106.55
b. Create a 95% confidence interval for the average entertainment spending for all cities with $89 daily room rates (to 2 decimals).
($102.61, $110.49)
c. A hotel in Chicago costs $128 on average per night. Create a 95% prediction interval for Chicago's entertainment spending (to 2 decimals).
($132.42, $143.75)
The estimated regression equation for the given data is y = 17.49 + 1.0334x. For a particular city that has a daily room rate of $89, the predicted amount spent on entertainment is $106.55. The 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 is ($102.61, $110.49). For Chicago, which has an average room rate of $128, the 95% prediction interval for the amount spent on entertainment is ($132.42, $143.75).
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[(b-3)/(b^2+2b)]+[b/(4b+8)] simplify
The simplified expression of [(b - 3)/(b² + 2b)] + [b/(4b + 8)] is (b² - 12 + 4b)/[(4b)(b + 2)]
How to simplify the expression?From the question, we have the following parameters that can be used in our computation:
[(b-3)/(b^2+2b)]+[b/(4b+8)]
Rewrite the exponents
[(b - 3)/(b² + 2b)] + [b/(4b + 8)]
So, we have
(b - 3)/(b² + 2b) + b/(4b + 8)
Factor out b and 4
(b - 3)/b(b + 2) + b/4(b + 2)
Factor out 1/(b + 2)
1/(b + 2) * ((b - 3)/b + b/4)
So, we have
1/(b + 2) * (4(b - 3) + b²)/(4b)
This gives
1/(b + 2) * (4b - 12 + b²)/(4b)
Rewrite as
1/(b + 2) * (b² - 12 + 4b)/(4b)
Lastly, we have
(b² - 12 + 4b)/[(4b)(b + 2)]
Hence, the solution is (b² - 12 + 4b)/[(4b)(b + 2)]
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can someone help me figure out how to solve this problem
Answer:
[tex]r = \frac{3}{4}[/tex]
Step-by-step explanation:
Geometric sequence formula: [tex]a_n = a_1 r^{n-1}[/tex]
From the provided sequence, we know that the first term is -4
The second term is -3
Inserting to value to the formula
( n = 2, since we are using the value of the second term)
[tex]a_2 = -4 * r^{2-1}\\[/tex]
[tex]-3 = -4 * r[/tex]
[tex]r = \frac{-3}{-4}[/tex]
[tex]r = \frac{3}{4}[/tex]
if two dice are rolled one time, find the probability of getting these results a sum of greater than or equal to 11
for two dices, there are 36 possible combinations, the probability of getting these results a sum of greater than or equal to 11 is 3/36 = 12
What is probability and example?
Example: toss a coin 100 times, how many Heads will come up? Probability says that heads have a ½ chance, so we can expect 50 Heads. But when we actually try it we might get 48 heads, or 55 heads ... or anything really, but in most cases it will be a number near 50.
The only way to get 11 or more is getting 5 with one dice and 6 with another or getting 6 with both dices.
Therefore, there are only three combinations that satisfy this condition: (5,6), (6,5), and (6,6).
Since, for two dices, there are 36 possible combinations, the probability is 3/36 = 12
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1. A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability. a) Write down the stochastic matrix M that describes, given a probability vector, the probability that the woman will be at each of the places during the next hour. (b) Find the steady state vector. (This is a probability vector [positive entries that add up to 11 satisfying Mu- [Hint: you should simply assume that λ-1 is an eigenvalue for M (this is guaranteed for all stochastic matrices) and find the corresponding eigenspace. Divide by a suitable constant to get the steady state vector (c) After many hours pass, what are the probabilities that the woman will be at A? B? C? D? (These are recorded in the steady state vector.)
The resulting probability is 100%
How to calculate probability?
The general formula to calculate the probability is
=> P(B) = (n(B)/N(S)
where,
P(B) is the probability of an event 'B'.
n(B) is the number of favorable outcomes of an event 'B'.
n(S) is the total number of events occurring in a sample space.
Given,
A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability.
Here we have given that,
Number of places = 4 (A, B, C, D)
Initial point = A
Point D probability = 100%
For Point B to A probability = 100%
For point C to A or B probability = 50%
For point D to B and C probability = 50%
Now, here we need to find the probabilities that the woman will be at.
Like the women will spend three hours of travelling in the point A, B and C, then the probability of the points are calculated as,
=> 1 + 0.5 + 0.5 - 1
=> 2 - 1 = 1
Therefore, the resulting probability is 100%.
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Find the area of a regular 12-gon inscribed in a unit circle.
The required area of the regular 12-gon is obtained as 3 square units.
What is a regular polygon?A regular polygon can be defined as a polygon having all of its sides and angles equal to one another. The expression for each angle of a regular polygon is 180(n - 2)/n.
The angle between two sides of regular 12-gon is given as below,
180(12 - 2)/12 = 150°.
Now, the area of regular 12-gon is equivalent to the area of sum of 12 triangles.
The angle for the triangle will be 150/2 = 75°.
The diagram for such a triangle is given as below,
Now, OC = 1 × Sin B
⇒ OC = Sin 75°
And, BC = 1 × Cos B
⇒ BC = Cos 75°
Then, AB = 2BC = 2Cos 75°
Area of the triangle is given as,
1/2 × base × height
⇒ 1/2 × Sin 75° × 2Cos 75°
⇒ 0.25
Now, the area of the regular 12-gon inscribed in a unit circle is given as,
12 × 0.25 = 3 square units.
Hence, the area of a regular 12-gon inscribed in a unit circle is 3 square units.
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Stock Market Worksheet 1
You need to show your work in order to receive full credit.
Business Organization
1. James invests $10,000 in a partnership with 3 other people. One of those people also invested
$10,000 and the other two invested $90,000 each. What percent of the business does James
own?
I would give whoever answers this all my 330 points please help
The percentage of the business that James owns, given the amount he invested into the partnership, is 5 %
How to find the percentage owned ?To find the percentage of the business that James owns, you first need to find the total amount invested into the business by all the partners. That amount is :
= 10, 000 + 10, 000 + 90, 000 + 90, 000
= $ 200, 000
The percentage of the business owned by James is :
= Amount invested by James / Total amount invested by partnership
= 10, 000 / 200, 000
= 5 %
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a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t). the function t(t) can be expressed as t(t)
The function t(t) can be expressed as t(t) = xt where x refers the number of stocks and t refers the number of days.
In math, the term function refers an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Here we have given that a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week, t(t).
And we need to find the function t(t) can be expressed.
While we looking into the given question, we have identified the that the function that represents the situation is written as t(t).
In this one t refers the number of days in the week they spend on the tesla stocks.
And here let us consider x be the number of stocks did the a brokerage firm keeps track.
So, the resulting function is written as,
=> t(t) = xt.
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Given the functions, g(x), graphed below and f(x)=√x+1-3. Which statement about the functions is true?
f(x) and g(x) are both even functions.
Only g(x) is an even function.
f(x) and g(x) are both odd functions.
Only f(x) is an odd function.
Put the value where the variable is, read the graph, and do the arithmetic.
g(2) = 3f(2) -2 = 3(-1) -2
g(2) = -5
What does a variable mean?In a mathematics problem or experiment, a variable is a quantity that can change. To indicate a variable, we often use a single letter. Generic symbols used frequently for variables include the letters x, y, and z.
In the example, what is the variable?A trait that is measurable and capable of taking on several values is known as a variable. There are many variables, including height, age, wealth, province of birth, academic standing, and kind of dwelling. Two categories—categorical and numeric—can be used to categorize variables.
Here,
Given : f(x)=√x+1-3
for odd ,
f(-x) = √-x+1-3
f(-x) ≠ -f(x)
Thus it is not odd function.
f(x) is an even function.
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find a recurrence relation an that counts the number of ways to climb n stairs if you can take either 1 star or 3 strais at a time
The recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.
What is a recurrence relation?
A recurrence relation is an equation that defines a sequence of values in terms of the preceding terms of the sequence. It is a mathematical tool used to define a sequence of numbers, functions, or other mathematical objects in a recursive manner.
To find a recurrence relation that counts the number of ways to climb n stairs if you can take either 1 star or 3 stairs at a time, we can use the following steps:
Identify the base cases. In this case, the base cases are the number of ways to climb 0 stairs (an = 1) and the number of ways to climb 1 stair (an = 1).
Determine the recurrence relation. For n > 1, the number of ways to climb n stairs is equal to the number of ways to climb n-1 stairs (taking 1 stair at a time) plus the number of ways to climb n-3 stairs (taking 3 stairs at a time). Therefore, the recurrence relation is:
an = an-1 + an-3
Use the base cases and the recurrence relation to determine the values of an for the desired range of n.
For example, to determine the values of an for n = 0, 1, 2, 3, 4, and 5, we can use the following table:
n | an
0 | 1
1 | 1
2 | an-1 + an-3 = 1 + 1 = 2
3 | an-1 + an-3 = 2 + 1 = 3
4 | an-1 + an-3 = 3 + 2 = 5
5 | an-1 + an-3 = 5 + 3 = 8
Hence, the recurrence relation an = an-1 + an-3 counts the number of ways to climb n stairs if you can take either 1 stair or 3 stairs at a time.
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Solve the systems of equations: 3x+2y=4
-2x+2y=24
Please show work for how you solved for x and y
Answer:
The solution to the system of equations is x = 28, y = -40.
Step-by-step explanation:
To solve a system of equations, we need to find values for the variables that will make both equations true.One way to do this is to eliminate one of the variables by making the coefficients equal and opposite, then solve for the remaining variable.For example, in this system of equations, we can eliminate the y variable by adding the two equations together:3x + 2y = 4
-2x + 2y = 24
---------
x = 28
Now that we have an equation in terms of x, we can substitute this value back into either of the original equations to solve for y. Let's substitute it into the first equation:3x + 2y = 4
3(28) + 2y = 4
84 + 2y = 4
2y = -80
y = -40
the solution to the system of equations is x = 28, y = -40.
The volume of box is actually 2.300 L. A student makes several measurements to determine the volume of the box. Which of the following measurements listed below is least accurate? A) 2.280L B) 2.291L c) 2.400L D) 2.302L E) 2.300L
Answer:
C) 2.400L
Step-by-step explanation:
A) 2.280L - 2.300L = -0.020L
B) 2.291L - 2.300L = -0.009L
C) 2.400L - 2.300L = 0.100L
D) 2.302L - 2.300L = 0.002L
E) 2.300L - 2.300L = 0.000L
The greatest difference in absolute value between the measurement and the actual volume is 0.100L.
Answer: C)
The 20-cm-diameter disk in the figure can rotate on an axle through its center.
What is the net torque about the axle?
If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94
As we can see here,
20N force which is passing through the center O will not produce any torque about point O
For 30N force which is acting at 45 angles with the x−axis, its x−component will pass through the origin, hence its horizontal component will also not cause any torque about O
Hence, torque because of 20N force which is acting in a tangential direction :
τ1=r⊥F=0.1×30=3N-m
Torque produced by y component of 30N force acting at angle 45:
τ2=r⊥F=0.05×30sin45∘
=0.05×30×1/√2=1.5/√2Nm⨀
Torque produced by 20N force acting in negative y direction:
τ3=r⊥×F=0.05×20
τ=1Nm⨀
Hence, the Net torque produced on O
τnet=τ1+τ2+τ3
τnet=−3+(1.5/√2)+1
τnet=−0.94Nm
or
|τnet|=0.94Nm
So If the 20-cm-diameter disk in the figure can rotate on an axle through its center then the net torque about the axle will be 0.94
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Write a system of equations for the problem below. You do not have to solve the system. Use x for the number of one-dollar bills, y for the number of five-dollar bills, and z for the number of ten-dollar bills. Top equation: Molly has one-dollar bills, five-dollar bills, and ten-dollar bills in her wallet that are worth a total of . 96 Second Equation: If she had one more one-dollar bill, she would have just as many one-dollar bills as she has fives and tens combined. Third Fquation: She has bills total
In view of Molly's three types of bills
Therefore the first equation is [tex]1x+5y+10z=96[/tex]
Therefore the second equation is [tex]x+1=y+z[/tex]
Therefore the third equation is [tex]x+y+z=23[/tex]
As per the details share in the above question as as follow,
x for the no, of $1 bills
y for the no. of $5 bills.
z for the no. of $10 bills.
We have to find the first, second and third equations.
Therefore worth of x $1 bills is [tex]1 \times x[/tex]
So of y for the no. of $5 bills is [tex]5 \times y[/tex]
And z for the no. of $10 bills is [tex]10 \times z[/tex]
The total worth in molly wallet is $96.
So the equation will be,
[tex]1x+5y+10z=96[/tex]
Now further is molly has one more $1 bill then the number of $1 bill will be same as.
Therefore the second equation is [tex]x+1=y+z[/tex]
Now she had 23 bills,
We also know that she has one-dollar, five-dollar, and ten-dollar notes, with x denoting the quantity of each, Y the number of the five-dollar bill, and Z the number of the ten-dollar bill.
Therefore the third equation is [tex]x+y+z=23[/tex]
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The Shaffer family started on a trip in their car with 18 gallons of gasoline. The car uses 2 gallons of gasoline every hour. If t represents the number of hours spent driving and g represents the number of gallons of gasoline left in the car, which equation could be used to calculate the value of g, if 0 ≤t ≤9
Multiple Choice
g = 18 - 2t
g = 18t - 2
g = 2t - 18 g = 2t + 18
Answer:
g = 18 - 2t
Step-by-step explanation:
They start with 18 gal.
To find how much gas they use while driving:
(2 gal/hr)(t hr)
Subtract that amount from the 18 gal they had in the tank to start with.
g = 18 gal - (2 gal/hr)(t hr)
Express the number as a product of two fractions 2/5
The number as a product of two fractions is 4/2 * 1/5
How to express the number as a product?From the question, we have the following parameters that can be used in our computation:
Fractions = 2/5
To express it as a product of two fractions, we start with the following equation (first split)
Fractions = 2/1 * 1/5
Express 2 as 4/2
So, we have the following representation
Fractions = 4/2 * 1/5
Hence, the fraction products is 4/2 * 1/5
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A consumer group claims that the mean annual consumption of high fructose corn syrup by a person in the United States is 48.8 pounds. A random sample of 120 people in the United States has a mean annual high fructose com syrup consumption of 49.5 pounds. Assume the population standard deviation is 3.6 pounds. At alpha = 0.05, can you reject the claim? Identify the null and alternative hypotheses. Identify which hypothesis is the claim. Use the sample statistics given to find the standardized test statistics: z and P. Make a decision to reject or fail to reject the null hypothesis. Interpret your decision in the context of the original claim.
the result we get is statistically significant. We reject the null hypothesis.
The null hypothesis in the given question is 'the mean annual consumption of high fructose corn syrup by a person in the United States is 48.8 pounds' and the alternative hypothesis in the given question is 'the population standard deviation is 3.6 pounds.'
Population mean = 48.8 pounds
Sample size = 120
Sample mean = 49.5 pounds
Population standard deviation = 3.6
α = 0.05
The standardized statistic z is:
z = (Sample mean - Population mean) x (√n / standard deviation)
z = (49.5 - 48.8) x (√120/3.6)
z = 2.13
The standardized statistic P is:
P = 2 - 2 x Φ(z)
P = 2 - 2 x 0.983
P = 0.034
Since, the result we get is statistically significant. We reject the null hypothesis.
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Line 1 passes through the points (-20, -4) and (-11,-4).
Line 2 is perpendicular to Line 1 and passes through the
point (-17, -14).
What is the equation of Line 2?
something noteworthy is that, the y-coordinate for Line 1 is the same, well that simply means that Line 1 is a horizontal line, anything perpendicular to a horizontal line is simply a vertical line, Check the picture below.
Which design? The following situations all require inference about a mean or means. Identify each as (1) a single sample, (2) matched pairs, or (3) two independent samples. Explain your answers.
(a) You want to estimate the average age of your store’s customers.
(b) You do an SRS survey of your customers every year. One of the questions on the survey asks about customer satisfaction on a seven-point scale with the response 1 indicating "very dissatisfied" and 7 indicating "very satisfied." You want to see if the mean customer satisfaction has improved from last year.
(c) You ask an SRS of customers their opinions on each of two new floor plans for your store.
As per the sampling, the resulting values of
(a) Single sample design
(b) two independent samples
(c) matched pairs
What is meant by sampling?
In math, sampling is the process of selecting the group that you will actually collect data from in your research.
Here we have find in Which design the following situations all require inference about a mean or means.
By looking into the given statement, (a) You want to estimate the average age of your store’s customers.
Here this is a single sample design and the only sample we need here is the store’s customers.
Where as (b) You do an SRS survey of your customers every year. One of the questions on the survey asks about customer satisfaction on a seven-point scale with the response 1 indicating “very dissatisfied’’ and 7 indicating “very satisfied.’’ You want to see if the mean customer satisfaction has improved from last year.
In this is the two independent samples design. Because in this case we compare the customer satisfaction of two groups of customers. And the first group is the customers from last year and the other is the group from this year.
Finally, (c) You ask an SRS of customers their opinions on each of two new floor plans for your store.
Here we have a matched-pair design in this case because one group of people gave opinions on two new floor plans.
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according to carfax, the value of a new vehicle can drop by 20 percent after the first 12 months of ownership. then, for the next four years, you can expect your car to lose roughly 10 percent of its value annually. use the depreciation rates listed by carfax to find the value of a brand new ford f-150 valued at 63,580 after 5 years. round to the nearest dollar.
The value of the brand new Ford F-150 after five years is approximately 32,435 dollars. Rounded to the nearest dollar, the value of the Ford F-150 after five years is 32,000 dollars.
The value of a new vehicle after the first 12 months of ownership is given by the equation:
value after 12 months = value at time of purchase × (1 - depreciation rate)
In this case, the value of the vehicle at the time of purchase is 63,580, and the depreciation rate is 20%. Plugging these values into the equation gives us:
value after 12 months = 63,580 × (1 - 0.20) = 50,864
The value of the vehicle after five years is given by the equation:
value after 5 years = value after 12 months × [tex](1 - depreciation rate)^n[/tex]
where n is the number of years after the first 12 months of ownership. In this case, n is 4 (5 years - 1 year).
Plugging the values for the value after 12 months, the depreciation rate, and n into the equation gives us the following:
value after 5 years = 50,864 × [tex](1 - 0.10)^4[/tex] = 32,435
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What’s a pattern for determining 10% of a number?
To take 10% of something, move the decimal point one spot to the left
Examples:
10% of 12.3 is 1.2310% of 567.89 is 56.789i need help??!!!!!!!
Answer:
Triangle RST rises 4 units and runs 8 units.
Triangle XYZ rises 3 units and runs 6 units.
The slope of line b is 1/2.
Step-by-step explanation:
Triangle RST rises 4 units and runs 8 units.
Triangle XYZ rises 3 units and runs 6 units.
The slope of line b is 1/2.
(2, 0) and (8, 3)
m = 3-0/8-2
m = 3/6
m = 1/2