Which statement about the following equation is true?
2x2-9x+2-1
Complete Question:
Which statement about the following equation is true?
[tex]2x^2-9x+2 = -1[/tex]
A) The discriminant is less than 0, so there are two real roots
B) The discriminant is less than 0, so there are two complex roots
C) The discriminant is greater than 0, so there are two real roots
D) The discriminant is greater than 0, so there are two complex roots
Answer:
C) The discriminant is greater than 0, so there are two real roots
Step-by-step explanation:
The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes
[tex]2x^2 - 9x + 3 = 0[/tex]
For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]
If the discriminant D is greater than 0, the roots are real and different
If the discriminant D is equal to 0, the roots are real and equal
If the discriminant D is less than 0, the roots are imaginary
For the quadratic equation under consideration, a = 2, b = -9, c = 3
Let us calculate the discriminant D
D = (-9)² - 4(2)(3)
D = 81 - 24
D = 57
Since the Discriminant D is greater than 0, the roots are real and different.
Answer:
Step-by-step explanation:
C) The discriminant is greater than 0, so there are two real roots
Rafael made 20,000 in taxable income last year. Suppose the income tax rate is 15% for the first 8000 plus 17% for the amount over 8000. How much must Rafael pay in income tax for the last year?
The answer is 3,240
Explanation:
To calculate the total income tax, it is necessary to calculate what is the 15% of 8000, and 17% for the remaining money, which is 12.000 (20,000 - 8,000= 12,000). Considering the statement specifies the 15% is paid for the first 8,000 and from this, the 17% is paid. Now to know the percentages you can use a simple rule of three, by considering 8000 and 12000 as the 100%. The process is shown below:
1. Write the values
[tex]8000 = 100[/tex]
[tex]x = 15[/tex] (the percentage you want to know)
2. Use cross multiplication
[tex]x =\frac{8000 x 15 }{100}[/tex]
[tex]x = 1200[/tex]
This means for the first 8000 the money Rafael needs to pay is 1,200
Now, let's repeat the process for the remaining money (12,000)
[tex]12000 = 100\\\\[/tex]
[tex]x = 17[/tex]
[tex]x = \frac{12000 x 17}{100}[/tex]
[tex]x = 2040[/tex]
Finally, add the two values [tex]1200 + 2040 = 3240[/tex]
A subscription for 15 magazines cost $45. the same company is offereing 25 magazines for $70. which is a better deal? why?
Answer:
25 magazines for $70. (For why, read explanation)
Step-by-step explanation:
We can find the unit price of each of these deals by dividing the cost and the quantity.
[tex]\frac{45}{15}[/tex] = 3, so the first deal is $3 per magazine.
[tex]\frac{70}{25}[/tex] = 2.8, so the second deal is $2.80 per magazine.
Therefore, 25 magazines for $70 is a better deal.
Hope this helped!
Based on past experience, it is estimated that a restaurant will serve 122 guests on a weekday evening. This is an example of which type of probability
Answer: Experimental probability.
Step-by-step explanation:
This starts as "based on past experience."
So we can suppose that this estimation is obtained by looking at the mean of the number of guests on the past N weekday evenings. (With N a large number, as larger is N, more data points we have, and a better estimation can be made)
Then, this would be an experimental probability, because it is obtained by repeating an experiment (counting the number of guests on weekday evenings) and using that information to make an estimation.
Need Answers ASAP!!!! (due today)
Answer:
1.
a. 20 m²: barn door is 5m x 4m
b. 468 m²:surface area of barn
i. left and right barn walls: 2(15 x 7) = 210
ii. back wall: 7 x 8 = 56
iii. front wall: (7 x 8) - 20* = 36
*20 for the barn door
iv. front of roof: (4 x 4) / 2 = 8 x 2* = 16
*I split the triangle into 2 smaller triangles
v. sides of roof: 2(5 x 15) = 150
2.
a. 15 m²: silo door is 3m x 5m
b. 244.18 m²: surface area of silo
i. SA(silo)=2πrh+2πr²
ii. SA(silo) = 2π(2.5)(14) + 2π(2.5)²
iii. SA(silo) = 259.18
iv. SA(silo - door) = 259.18 - 15
v. SA(silo - door) = 244.18
3.
a. 712.18 m²: total surface area painted red
i. add both surface areas: 468 + 244.18 = 712.18 m²
hope this helps :)
A circle is centered at CC-1, -3) and has a radius of 6.
Where does the point P(-6, -6) lie?
Choose 1 answer:
Inside the circle
On the circle
Outside the circle
Answer:
outside the circle i think
Step-by-step explanation:
Answer:
inside the circle
Step-by-step explanation:
Two professors in the mathematics building have offices that are consecutive odd numbers with a sum of 14,600. What are the official numbers of these two professors?
Answer: 7299, 7301
Step-by-step explanation:
x + x + 2= 14,600
2x = 14,598
x = 7,299
Therefore, the office numbers are 7299 and 7301
Explain how using dot paper helps in drawing perspective drawings.
Answer:
Dot paper helps to understand and bring in the big picture in perspective drawing.
Step-by-step explanation:
Dot paper helps to understand patterns and features of the big picture. It helps to understand patterns at various intervals. Drawing with perspective helps to understand the big idea. Perspective reveals your point of view and helps gravitate your idea of the spatial onto paper. You can express linear perspectives.
You can use your principles of perspective drawing to create a perception of your world and your world view through your art.
I need help with this problem.
________________________Alike______________________
→ Both of the lines are proportional meaning they go through the origin.
→ Both of the lines have a positive slope meaning the slope goes towards the top right corner.
__________________________________________________
_____________________Difference_____________________
→ The 2 lines have different slopes, the first one has a slope of 1/3x whereas the 2nd one has a slope of 3x.
→ The points that create the lines are totally different, no two points are the same.
__________________________________________________
Brainliest for the correct awnser!!! The function is not an example of a rational function. True or false?
Answer:
true
Step-by-step explanation:
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
What is the solution to the following system of equations?
|3x - 2y = 12
[6x - 4y= 24
It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0)
URGENT!! The quotient of the rational expressions
Answer:
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]Option C is the correct option
Step-by-step explanation:
[tex] \frac{x}{3x - 1} \div \frac{x - 2}{2x} [/tex]
To divide by a fraction, multiply by the reciprocal of that fraction
[tex] \frac{x}{3x - 1} \times \frac{2x}{x - 2} [/tex]
Multiply the fractions
[tex] \frac{2 {x}^{2} }{(3x - 1)(x - 2)} [/tex]
Multiply the parentheses
[tex] \frac{2 {x}^{2} }{3x(x - 2) - 1(x - 2)} [/tex]
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 6x - x + 2 } [/tex]
Collect like terms
[tex] \frac{2 {x}^{2} }{3 {x}^{2} - 7x + 2 } [/tex]
Hope this helps...
Best regards!!
The average student loan debt for college graduates is $25,800. Suppose that that distribution is normal and that the standard deviation is $14,150. Let X = the student loan debt of a randomly selected college graduate. Round all probabilities to 4 decimal places and all dollar answers to the nearest dollar The middle 20% of college graduates' loan debt lies between what two numbers?
Please Help! Look at Screenshot for question.
Answer:
C
Step-by-step explanation:
A modified box plot does not include the outliers in the whiskers, instead they are points outside of the whiskers
5,25,33,34,34,37,37,40,42,45,45,46,46,49,73
This data has 2 outliers 5 and 73 so we have 2 choices for a modified box plot D or D
The lowest value outside of the outliers is 25 , so C would be the logical choice
D has the lower end of the whisker too close to the outlier
If the image is blurry the answer choices are -1,0,1,2,and 3. The question says select each correct answer
Answer:
12Step-by-step explanation:
There is no algebraic way to solve such an equation. It can be simplified to ...
[tex]-2x-6=-2^x-6\\\\2x-2^x=0\qquad\text{add $2x+6$}[/tex]
This has solutions at x=1 and x=2 as shown in the attached graph.
__
The second attachment shows the functions graphed on the same graph.
In the United States, the mean age of men when they marry for the first time follows the normal distribution with a mean of 24.7 years. The standard deviation of the distribution is 2.8 years. For a random sample of 60 men, what is the likelihood that the age when they were first married is less than 25.2 years
Answer:
The likelihood is [tex]P(X < 25.2) = 0.91668[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 24.7 \ years[/tex]
The standard deviation is [tex]\sigma = 2.8 \ years[/tex]
The sample size is [tex]n = 60 \ men[/tex]
The consider random value is x = 25.2 years
Given that mean age is normally distributed, the likelihood that the age when they were first married is less than x is mathematically represented as
[tex]P(X < x) = P( \frac{X - \mu }{\sigma_{\= x }} < \frac{x - \mu }{\sigma_{\= x }} )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma_{\= x}} = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < x) = P(Z< \frac{x - \mu }{\sigma_{\= x }} )[/tex]
Where [tex]\sigma_{\= x }[/tex] is the standard error of the sample mean which mathematically evaluated as
[tex]\sigma_{\= x } = \frac{ \sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \frac{ 2.8 }{\sqrt{ 60 } }[/tex]
[tex]\sigma_{\= x } = 0.3615[/tex]
So
[tex]P(X < 25.2) = P(Z< \frac{ 25.2 - 24.7 }{0.3615} )[/tex]
[tex]P(X < 25.2) = P(Z< 1.3831 )[/tex]
From z-table the value for P(Z< 1.3831 ) is [tex]P(Z < 1.3831 ) = 0.91668[/tex]
So
[tex]P(X < 25.2) = 0.91668[/tex]
In right triangle ABC, 2B is a right angle, AB = 48 units, BC = 55 units, and AC = 73 units.
literally please help me
Answer:
73/55
Step-by-step explanation:
The cosecant (csc) is one of the reciprocal functions:
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
So, if we can find the sine, we can find the cosecant.
__
The mnemonic SOH CAH TOA reminds you that the sine is ...
Sin = Opposite/Hypotenuse
The above tells you that ...
Csc = 1/Sin = Hypotenuse/Opposite
The hypotenuse of your triangle is AC = 73. The side opposite angle θ is BC = 55. So, the ratio you want is ...
csc(θ) = 73/55
Answer:
[tex]csc (\theta)=\frac{33}{55}[/tex]
Step-by-step explanation:
Hello!
1) The cosecant function is the inverse the sine function. So we can write:
[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]
2) The sine function is the side opposite angle to [tex]\angle \theta[/tex] over the hypotenuse:
[tex]sin(\theta)=\frac{55}{33}[/tex]
3) So, remembering operations with fractions then the cosecant is:
[tex]csc \theta = \frac{1}{\frac{55}{33} } =1 \times \frac{33}{55}[/tex]
[tex]csc (\theta)=\frac{33}{55}[/tex]
What is the solution for x in the given equation? (root)9x+7+ (root)2x=7 A. x = 18 and x = 2 B. x = 18 C. x = 2 D. x = 18 and x = -2
Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
select the inequality that represents the relationship desribed below the sum of three times a number and seven is greater than four times the number
Answer:
There are many combinations based on the number you chose to subtract from both sides.
Step-by-step explanation:
Let the number be x.
According to the question,
3 x+7 > 4 x
We get, 3 x+1=4 x-6, after subtracting 6 from both sides.
3 x+1=4 x-6
4 x- 3 x=6+1
x=7
You will get the same answer if you subtract 3 x or 7 or any other number from both sides.
Thank you!
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
Limits for B scores
( 79,2 ; 92 )
Step-by-step explanation:
The interval we are looking for is between 6 % and 59%
p₁ = 6 % p₁ = 0,06
As this point is at the right tail of the bell we better look for
p = 1- 0,06 p = 0,94
In z-table z score for 0,94062 is: z₁ = 1,56 ( 0,94062 ≈ 0,94 )
Doing the same to find z₂ score for 59% or 0,59
In z-table again
p = 0,59
z₂ = 0,023
Now we know
1,56 * σ = x₁ - 79
1,56*8,4 + 79 = x₁
x₁ = 92,10 or x₁ = 92
And
0,023*8,4 + 79 = x₂
x₂ = 79,19 or x₂ = 79,2
Please help me identify the rays!!!!
Answer:
D (The last choice)
Step-by-step explanation:
We know that rays are lines with a dot on one side and an arrow on the other. WE also know that lines have two arrows on each end. Keeping this in mind, we can identify which line segments and rays and lines.
g Refer to these data for the next set of questions: The JMP output is below. Use it to answer the following questions. Write the estimated regression equation. Test for a significant linear regression at the α = 0.05 level of significance At x=, find the 95% confidence interval for μY|x, and verbally explain the answer. At x = 12, compute a 95% CI for μY|x, and verbally explain the answer. How do you explain the different widths of the intervals in parts (c) and (d)?
Player A finished first in a tournament at a golf club with a score of −9, or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par. What was the difference in scores between Player A and Player B?
Answer:
18
Step-by-step explanation:
since you want the difference in scores, you want to take the absolute value of the difference
9 - (-9) = 9+9 = 18
The difference in scores between Player A and Player B is 18.
How do we calculate the difference?The difference between two numbers is found by subtracting the smaller number from the greater number.
How do we solve the given question?We are informed that Player A finished first in a tournament at a golf club with a score of −9 or nine strokes under par. Tied for 46th place was player B, with a score of +9, or 9 strokes over par.
We are asked for the difference in scores between Player A and Player B.
The score of Player A = -9.
The score of Player B = 9
Since Player B's score > Player A's score,
To calculate the difference in their scores, we subtract player A's score from player B's score.
∴ Difference = 9 - (-9)
or, Difference = 9 + 9
Difference = 18.
∴ The difference in scores between Player A and Player B is 18.
Learn more about the difference at
https://brainly.com/question/25421984
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use what you know about zeros of a function and end behavior of a graph that matches the function f(x) = (x+3)(x+2)(x-1)
Answer:
The zeros are x=-3,-2,1
end behavior is one up one down
Step-by-step explanation:
The zeros are x=-3,-2,1
The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.
The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gasemissions?
Type A Type B Type C
7.6 6.2 6.4
6.1 7.6 7.5
6.1 6.7 7.4
6.7 7.5 6.6
7.4 7.7 6.1
7.4 7.5 7.5
5.9 5.8 6.6
5.9 6.8 6.3
6.2 7.3
7.4
What are the hypotheses for this test?
A. H0: μ1 = μ2 = μ3
H1: μ1 ≠ 2μ ≠ μ3
B. H0: μ1 = μ2 = μ3
H1: At least one of the means is different from the others.
C. H0: μ1 ≠ μ2 ≠ μ3
H1: μ1 = μ2 = μ3
D. H0: At least one of the means is different from the others.
H1: μ1 = μ2 = u3
Determine the test statistic.
F = ________
What is the critical F value?
F = _________
Identify the P-value.
P-value = __________
What is the conclusion of the test?
_________ the null hypothesis. Conclude that the type of vehicle ______________ appear to affect the amount of greenhouse gas emissions for these three types.
Answer:
1.
A. H0 : μ1 = μ2 = μ3
Ha : μ1 ≠ 2μ ≠ μ3
2. Test Statistics = 95%
3. Critical F-Value = 3.76
4. P-Value = 2.32
5. Conclusion : Reject the null hypothesis
6. Type of vehicle does effect the amount of green house gas emissions.
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
A. H 0 μ1 = μ2 = μ3
Ha μ1 ≠ 2μ ≠ μ3
2. Test Statistics is 95%
3. Critical F-Value is 3.76.
4. P-Value is 2.32.
5. Conclusion Reject the null hypothesis.
6. Type of vehicle does effect the amount of green house gas emissions.
The correct order of the steps of a hypothesis test is given below.
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
All steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
For more details on hypothesis test follow the link:
https://brainly.com/question/10758924
Suppose that the probability distribution below shows the number of colleges that children of celebrities applied to in 2018. Compute the standard deviation for the number of college applications.
x 0 2 4 6
P(x) 0.4 0.3 0.2 0.1
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma = 2.45[/tex]
Step-by-step explanation:
From the given data we can compute the expected mean for each random values as follows
[tex]E(X) = \sum [ X * P(X = x )]\\\\ X \ \ \ \ \ \ X* P(X =x )\\ 0 \ \ \ \ \ \ \ \ \ \ 0* 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2 * 0.3 = 0.6 \\ 4 \ \ \ \ \ \ \ \ \ \ 4 * 0.2 = 0.8\\ 6 \ \ \ \ \ \ \ \ \ \ 6* 0.1 = 0.6[/tex]
So
[tex]E(x) = 0 + 0.6 + 0.8 + 0.6[/tex]
[tex]E(x) = 2[/tex]
The
[tex]E(X^2) = \sum [ X^2 * P(X = x )]\\\\ X \ \ \ \ \ \ \ \ \ \ X^2 * P(X=x ) \\ 0 \ \ \ \ \ \ \ \ \ \ 0^2 * 0.4 = 0 \\ 2 \ \ \ \ \ \ \ \ \ \ 2^2 * 0.3 = 12 \\ 4 \ \ \ \ \ \ \ \ \ \ 4^2 * 0.2 = 3.2 \\ 6 \ \ \ \ \ \ \ \ \ \ 6^2 * 0.1 = 3.6[/tex]
So
[tex]E(X^2) = 0 + 1.2 + 3.2 + 3.6[/tex]
[tex]E(X^2) = 8[/tex]
Now the variance is mathematically evaluated as
[tex]Var (X) = E(X^2 ) -[E(X]^2[/tex]
Substituting value
[tex]Var (X) = 8-4[/tex]
[tex]Var (X) = 6[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{Var(x)}[/tex]
[tex]\sigma = \sqrt{4}[/tex]
[tex]\sigma = 2[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE FILE ATTATCHED
Answer:
1. [tex] P(x) [/tex] ÷ [tex] Q(x) [/tex]---> [tex] \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex]---> [tex]\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}[/tex]
3. [tex] P(x) - Q(x) [/tex]---> [tex] \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) [/tex] --> [tex] \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Step-by-step explanation:
Given that:
1. [tex] P(x) = \frac{2}{3x - 1} [/tex]
[tex] Q(x) = \frac{6}{-3x + 2} [/tex]
Thus,
[tex] P(x) [/tex] ÷ [tex] Q(x) [/tex] = [tex] \frac{2}{3x - 1} [/tex] ÷ [tex] \frac{6}{-3x + 2} [/tex]
Flip the 2nd function, Q(x), upside down to change the process to multiplication.
[tex] \frac{2}{3x - 1}*\frac{-3x + 2}{6} [/tex]
[tex] \frac{2(-3x + 2)}{6(3x - 1)} [/tex]
[tex] = \frac{-3x + 2}{3(3x - 1)} [/tex]
2. [tex] P(x) + Q(x) [/tex] = [tex] \frac{2}{3x - 1} + \frac{6}{-3x + 2} [/tex]
Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:
[tex] \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{12x - 2}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} [/tex]
3. [tex] P(x) - Q(x) [/tex] = [tex] \frac{2}{3x - 1} - \frac{6}{-3x + 2} [/tex]
[tex] \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} [/tex]
[tex] \frac{-24x + 10}{(3x - 1)(-3x + 2)} [/tex]
[tex] = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} [/tex]
4. [tex] P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} [/tex]
[tex] P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} [/tex]
[tex] P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} [/tex]
Composite functions involve combining multiple functions to form a new function
The functions are given as:
[tex]P(x) = \frac{2}{3x - 1}[/tex]
[tex]Q(x) = \frac{6}{-3x + 2}[/tex]
[tex]P(x) \div Q(x)[/tex] is calculated as follows:
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}[/tex]
Express as a product
[tex]P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}[/tex]
Divide 2 by 6
[tex]P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}[/tex]
Multiply
[tex]P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}[/tex]
Hence, the value of [tex]P(x) \div Q(x)[/tex] is [tex]\frac{-3x + 2}{3(3x - 1)}[/tex]
P(x) + Q(x) is calculated as follows:
[tex]P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}[/tex]
Factor out 2
[tex]P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) + Q(x) is [tex]\frac{2(6x -1)}{(3x - 1)(-3x + 2)}[/tex]
P(x) - Q(x) is calculated as follows:
[tex]P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}[/tex]
Take LCM
[tex]P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}[/tex]
Open brackets
[tex]P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}[/tex]
Collect like terms
[tex]P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}[/tex]
[tex]P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}[/tex]
Factor out -2
[tex]P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) - Q(x) is [tex]\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}[/tex]
P(x) * Q(x) is calculated as follows:
[tex]P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}[/tex]
Multiply
[tex]P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}[/tex]
Hence, the value of P(x) * Q(x) is [tex]\frac{12}{(3x - 1)(-3x + 2)}[/tex]
Read more about composite functions at:
https://brainly.com/question/10687170
The surface area of a given cone is 1,885.7143 square inches. What is the slang height?
Answer:
If [tex]r >> h[/tex], the slang height of the cone is approximately 23.521 inches.
Step-by-step explanation:
The surface area of a cone (A) is given by this formula:
[tex]A = \pi \cdot r^{2} + 2\pi\cdot s[/tex]
Where:
[tex]r[/tex] - Base radius of the cone, measured in inches.
[tex]s[/tex] - Slant height, measured in inches.
In addition, the slant height is calculated by means of the Pythagorean Theorem:
[tex]s = \sqrt{r^{2}+h^{2}}[/tex]
Where [tex]h[/tex] is the altitude of the cone, measured in inches. If [tex]r >> h[/tex], then:
[tex]s \approx r[/tex]
And:
[tex]A = \pi\cdot r^{2} +2\pi\cdot r[/tex]
Given that [tex]A = 1885.7143\,in^{2}[/tex], the following second-order polynomial is obtained:
[tex]\pi \cdot r^{2} + 2\pi \cdot r -1885.7143\,in^{2} = 0[/tex]
Roots can be found by the Quadratic Formula:
[tex]r_{1,2} = \frac{-2\pi \pm \sqrt{4\pi^{2}-4\pi\cdot (-1885.7143)}}{2\pi}[/tex]
[tex]r_{1,2} \approx -1\,in \pm 24.521\,in[/tex]
[tex]r_{1} \approx 23.521\,in \,\wedge\,r_{2}\approx -25.521\,in[/tex]
As radius is a positive unit, the first root is the only solution that is physically reasonable. Hence, the slang height of the cone is approximately 23.521 inches.
A group of 59 randomly selected students have a mean score of 29.5 with a standard deviation of 5.2 on a placement test. What is the 95% confidence interval for the mean score, , of all students taking the test
Answer:
The 95% confidence interval for the mean score, , of all students taking the test is
[tex]28.37< L\ 30.63[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 59[/tex]
The mean score is [tex]\= x = 29.5[/tex]
The standard deviation [tex]\sigma = 5.2[/tex]
Generally the standard deviation of mean is mathematically represented as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{5.2 }{\sqrt{59} }[/tex]
[tex]\sigma _{\= x} = 0.677[/tex]
The degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 59 -1[/tex]
[tex]df = 58[/tex]
Given that the confidence interval is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha =[/tex]5%
[tex]\alpha = 0.05[/tex]
Now the critical value at this significance level and degree of freedom is
[tex]t_{df , \alpha } = t_{58, 0.05 } = 1.672[/tex]
Obtained from the critical value table
So the the 95% confidence interval for the mean score, , of all students taking the test is mathematically represented as
[tex]\= x - t*(\sigma_{\= x}) < L\ \= x + t*(\sigma_{\= x})[/tex]
substituting value
[tex](29.5 - 1.672* 0.677) < L\ (29.5 + 1.672* 0.677)[/tex]
[tex]28.37< L\ 30.63[/tex]