Answer:
Step-by-step explanation:
a) The first derivative helps considering f decreases or increases. Also, when f'(x) = 0, the function gets local max/min depends on how it acts.
The second derivative helps determining the concave up/down.
At x = -5, f"(-5) = -1 <0 That means the function f have concave down. Also, it shows f increases before -5 and decreases after -5.
Hence f'(-5) = 0 shows f gets maximum at -5.
b) At the point where f" =0, the function has a reflecting point and we need more information to determine if f has a local max/min there.
Using concepts of critical points, it is found that:
a) At x = −5, f has a local maximum.
b) At x = 1, f has neither a maximum nor a minimum.
-----------------------
A critical value of a function f(x) is a value of [tex]x^{\ast}[/tex] for which: [tex]f^{\prime}(x^{\ast}) = 0[/tex].
The second derivative test is also applied:
If [tex]f^{\prime\prime}(x^{\ast}) > 0[/tex], [tex]x^{\ast}[/tex] is a minimum point.If [tex]f^{\prime\prime}(x^{\ast}) < 0[/tex], [tex]x^{\ast}[/tex] is a maximum point.If [tex]f^{\prime\prime}(x^{\ast}) = 0[/tex], [tex]x^{\ast}[/tex] is neither a maximum nor a minimum point.Item a:
[tex]f^{\prime}(-5) = 0, f^{\prime\prime}(-5) = -1[/tex], thus, a maximum point, and the correct option is:At x = −5, f has a local maximum.
Item b:
[tex]f^{\prime}(1) = 0, f^{\prime\prime}(1) = 0[/tex], thus, neither a maximum nor a minimum point, and the correct option is:At x = 1, f has neither a maximum nor a minimum.
A similar problem is given at https://brainly.com/question/16944025
Indicate in standard form equation of the line passing through the given 
Answer:
x - 3y= -14
Step-by-step explanation:
Slope is rise over run
m = (6-5)/(4-1) = 1/3
we write in slope-intercept form:
y = 1/3x + b
solve for b by plugging in either point
i'm going to plug in H
5 = 1/3 + b
b = 14/3
we get our equation
y = 1/3x + 14/3
now re-write it in standard form
-1/3x + y = 14/3
make it pretty
x - 3y = -14
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
670
Step-by-step explanation:
2003-814=1189
1189-519=670
Answer: The third number is 670.
Step-by-step explanation:
The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.
814 + 519 + x = 2003 where x is the third number
1333 + x = 2003
-1333 -1333
x = 670 So the third number is 670
Check:
814 + 670 + 519 = 2003
2003 = 2003 so yes again 670 is the third number.
Determine whether the sampling method is independent or dependent. A stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks. He randomly selects 13 energy stocks and computes the rate of return for the past year.
Answer:
The sampling method is independent.
Step-by-step explanation:
Samples are said to be dependent when the data chosen in one sample has an effect on the data to be chosen in the other sample, while samples are said to be independent if the data chosen in one sample has no effect on the data to be chosen on the other sample.
Here, the stock analyst wants to know if there is a difference between the mean rate of return from energy stocks and that from financial stocks, so, he randomly selects 13 energy stocks. Since the energy stocks he chose were randomly selected, it means the data he selected from the energy stock will not dictate the type of data to be selected from the financial stock. Thus, the sampling method is said to be independent.
Solve x2 - 4x - 7 = 0 by completing the square. What are the solutions?
Answer:
[tex]x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2-4x-7=0\\\mathrm{Solve\:with\:the\:quadratic\:formula}\\Quadratic\:Equation\:Formula\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\mathrm{For\:}\quad a=1,\:b=-4,\:c=-7:\quad x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}\\x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2+\sqrt{11}[/tex]
[tex]x=\frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:1\left(-7\right)}}{2\cdot \:1}:\quad 2-\sqrt{11}\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\x=2+\sqrt{11},\:x=2-\sqrt{11}[/tex]
The result of which expression will best estimate the actual product of (-4/5)(3/5)(-6/7)(5/6)
Answer:
[tex]\frac{12}{35}[/tex]
Step-by-step explanation:
[tex]\frac{-4}{5} * \frac{3}{5} * (\frac{-6}{7} ) * \frac{5}{6}[/tex]
[tex]\frac{(-4) * 3}{5 * 1} * \frac{(-1)}{7} \\\\\frac{12}{35}[/tex]
Please answer this correctly
Answer:
10-19 ⇒ 3
50-59 ⇒ 4
Answer:
# of ties # of racks
10-19 3
50-59 4
Step-by-step explanation:
Using the Stem and Leaf plot, our data is:
11, 12, 16
21
32, 34, 36, 37, 39
41, 45
51, 52, 53, 56
# of ties # of racks
10-19 3 (11, 12, 16)
50-59 4 (51, 52, 53, 56)
What is the next pattern ?
What is the slope of a line that is perpendicular to the line y = -1/2x + 5?
the answer choices are
-2
-1/2
1/2
2
Answer:
2
Step-by-step explanation:
as you can see the slope of the line y = -1/2x + 5 is -1/2
the slope m of any line perpendicular to it should verify : -1/2×m = -1
-1/2×m = -1
→ multiply both sides by -2
m = 2
What single decimal multiplier would you use to increase by 7% followed by a 4% decrease?
Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93
Step-by-step explanation:
Find the equation for the plane through the points Upper P 0 (5 comma 4 comma 5 ), Upper Q 0 (negative 5 comma negative 1 comma negative 4 ), and Upper R 0 (negative 2 comma 1 comma negative 2 ). The equation of the plane is nothing.
Answer:
The equation of the plane is
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 7y - 5z + 13 = 0
Step-by-step explanation:
Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).
We can calculate the equation of the plane through those points as
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.
The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.
For this question,
P = (5, 4, 5)
Q = (-5, -1, -4)
R = (-2, 1, -2)
PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)
= (-10î - 5ĵ - 9ķ)
PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)
= (-7î - 3ĵ - 7ķ)
PQ × PR is then
| î ĵ ķ |
|-10 -5 -9|
|-7 -3 -7|
= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]
= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)
= 8î - 7ĵ - 5ķ
Hence, (a, b, c) = (8, -7, -5)
And using point P as (x₀, y₀, z₀) = (5, 4, 5)
The equation of the plane is
a(x - x₀) + b(y - y₀) + c(z - z₀) = 0
8(x - 5) - 7(y - 4) - 5(z - 5) = 0
8x - 40 - 7y + 28 - 5z + 25 = 0
8x - 7y - 5z = 40 - 28 - 25 = -13
8x - 7y - 5z + 13 = 0
Hope this Helps!!!
WILL GIVE BRAINLIEST HELP ASAP
Answer:
x = -3
Step-by-step explanation:
1.8 - 3.7x = -4.2x +.3
Add 4.2x to each side
1.8 - 3.7x +4.2x= -4.2x+4.2x +.3
1.8 +.5x = .3
Subtract 1.8 from each side
1.8 +.5x -1.8 = .3 -1.8
.5x = -1.5
Divide each side by .5
.5x/.5 = -1.5/.5
x = -3
Answer:
x=-3
Step-by-step explanation:
In order to solve this equation, we have to isolate x. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides.
1.8-3.7x= -4.2x +0.3
3.7x is being subtracted from 1.8 (-3.7x). The inverse operation of subtraction is addition. Add 3.7x to both sides.
1.8-3.7x+3.7x= -4.2x+3.7x+0.3
1.8= -4.2x+3.7x+0.3
1.8= -0.5x+0.3
0.3 is being added to -0.5x. The opposite of addition is subtraction. Subtract 0.3 from both sides.
1.8-0.3= -0.5x+0.3-0.3
1.8-0.3 = -0.5x
1.5=-0.5x
-0.5 and x are being multiplied (-0.5*x= -0.5x). The opposite of multiplication is division. Divide both sides by -0.5.
1.5/-0.5=-0.5x/-0.5
1.5/-0.5=x
-3=x
What is the difference? Negative 6 minus (11)
Answer:
-17
Step-by-step explanation:
-6-11=-17
Answer:
the answer is -17
Step-by-step explanation:
Researchers want to compare the effectiveness of an extract of St. John's Wort with placebo in outpatients with major depression. They recruited 200 adult outpatients diagnosed as having major depression and having a baseline Hamilton Rating Scale for Depression (HAM-D) score of at least 20. Participants were randomly assigned to receive either St. John's Wort extrat, 900 milligrams per day (mg/day) for 4 weeks, increased to 1200 mg/day in the absence of an adequate response thereafter, or a placebo for 8 weeks. The response variable was the change on the HAM-D over the treatment period. After analysis of data, it was concluded that St. John's Wort was not effective for treatment of major depression.
Required:
a. What type of experimental design this is?
b. What is the population that is being studied?
c. What is the response variable in this study?
d. What are the treatments?
e. Identify the experimental units.
f. What is the control group in this study?
Answer:
a) Experimental Design: Randomised Experimental Design
b) Population : All Adult outpatients diagnosed with major depression
c) Responsive Variable : Effectiveness of extracts on depression patients' HAM-D rating
d) Treatments : John Wart extracts or Placebo
e) Experimental units : 200 adult outpatients diagnosed with major depression having HAM-D score > 20
Step-by-step explanation:
a) Randomised Experimental Design is being used : As experimental units are randomly assigned to any of the experimental groups, each receiving different treatments
b) Population refers to the entire group of objects or individuals, to whom the experiment research can be applied. So, all adult outpatients diagnosed with major depression as per HAM-D depression score are population
c) Responsive variable is the dependent variable being affected by independent variables. It is effectiveness of extracts on depression patients, ie change in change on the HAM-D depression rating
d) Treatments are the ways or objects with which experimental units are treated. These are John wart extracts or Placebo
e) Experimental units are the selected sample people or objects for experiment conduct. These are '200' adult outpatients diagnosed with major depression, having a baseline Hamilton Rating Scale for Depression (HAM-D) score > 20
A typical classroom is a rectangle with dimensions of 20 feet wide by 25 feet long, and the area needed for each person in the room is approximately 28 square feet, what fraction of the total area in a classroom is needed for each person? What is the largest number of people that would fit in an average sized classroom while practicing good social distancing?
Answer:
A fraction of 0.056 of the classroom is needed for each student.
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
Step-by-step explanation:
We have a classroom that is a recatngle with dimensions of 20 feet wide by 25 feet long.
The total area of the classroom is:
[tex]A=w\cdot l=20\cdot25=500[/tex]
As the area of the classromm is 500 square feet and we need 28 square feet for each student, the fraction that is needed for each student is:
[tex]f=\dfrac{A_{\text{student}}}{A_{\text{classroom}}}=\dfrac{28}{500}=0.056[/tex]
A fraction of 0.056 of the classroom is needed for each student.
The largest number of students that would fit in an average sized classroom while practicing good social distancing can be calculated dividing the area of the classroom by the area needed for each student. This is equal to the inverse of the fraction calculated previously:
[tex]n=\dfrac{1}{f}=\dfrac{1}{0.056}\approx17.86[/tex]
A typical classroom can acomodate up to 17 persons while practicing good social distancing.
Please help . I’ll mark you as brainliest if correct! Only the one marked with an X is wrong . I don’t get it
Answer:
(x+7)² = 9
Step-by-step explanation:
x² + 14x + 40 = 0
(x² + 14x) + 40 = 0
(x² +14x +49) + 40 - 49 = 0
(x+7)² - 9 = 0
(x+7)² = 9
Hope this helps!
Answer:
(x+7)² = 9
Step-by-step explanation:
A sample of 500 nursing applications included 60
from men. Find the 90% confielence interval
for the
true proportion of men who applied to the nursing
program.
Answer:
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 500
sample proportion
[tex]p = \frac{x}{n} = \frac{60}{500} = 0.12[/tex]
Level of significance ∝= 0.90 or 0.10
90% confidence interval for the true proportion of men who applied to the nursing program.
[tex](p - Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} } , p + Z_{\frac{0.10}{2} } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](p - Z_{0.05 } \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.05 } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.12 - 1.645 \sqrt{\frac{0.12(1-0.12)}{500} } , 0.12 + 1.645 \sqrt{\frac{0.12(1-0.12)}{500} })[/tex]
On calculation , we get
( 0.12 - 0.02326 , 0.12 + 0.02326)
(0.09674 ,0.14326)
Final answer:-
90% confidence interval for the true proportion of men who applied to the nursing program.
(0.09674 ,0.14326)
The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest.
Height of eruption
62 33 50 90
80 50 40 70
50 63 74 53
55 64 60 60
78 70 43 82
Required:
Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. The values closest to the middle are_________inches and_______inches.
Answer:
[tex] Median = \frac{60+60}{2}=60[/tex]
And we see that the closest values to 60 are 62 and 63 and then the answer would be:
The values closest to the middle are 62 inches and 63 inches.
Step-by-step explanation:
We have the following dataser given:
62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82
We can sort the values from the lowest to the highest and we got::
33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90
Now we see that we have n=20 values and the values closest to the middle and we can use the middle as the median and for this case the median can be calculated from position 10 and 11th and we got:
[tex] Median = \frac{60+60}{2}=60[/tex]
And we see that the closest values to 60 are 62 and 63 and then the answer would be:
The values closest to the middle are 62 inches and 63 inches.
The values closest to these middle elements are 60 and 63 inches
The dataset is given as:
62 33 50 90 80 50 40 70 50 63 74 53 55 64 60 60 78 70 43 82
Next, we sort the data elements in ascending order
33 40 43 50 50 50 53 55 60 60 62 63 64 70 70 74 78 80 82 90
The length of the dataset is 20.
So, the elements at the middle are the 10th and the 11 elements.
From the sorted dataset, these elements are: 60 and 62
Hence, the values closest to these middle elements are 60 and 63
Read more about median at:
https://brainly.com/question/14532771
In 2014, 2.756 billion dollars of e-cigarettes were sold worldwide. Fill in the table with the 2014 sales amount written in millions of dollars.
Answer:
$2756 million
Step-by-step explanation:
2.756×10⁹ = 2756×10⁶
Sales in 2014 were $2756 million.
_____
Comment on the question
In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Since they are similar, hence taking proportionality,
CA/CB = d1/d2
Cross Multiplying
We get
CA × d2 = CB × d1
OR
d1×CB = d2 × CA
x/x-2+x-1/x+1=-1
I'm having trouble figuring this out, an explanation on how to solve would suffice.
Answer:
x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Step-by-step explanation:
Solve for x over the real numbers:
x - 2 + x/x + 1 - 1/x = -1
x - 2 + x/x + 1 - 1/x = x - 1/x:
x - 1/x = -1
Bring x - 1/x together using the common denominator x:
(x^2 - 1)/x = -1
Multiply both sides by x:
x^2 - 1 = -x
Add x to both sides:
x^2 + x - 1 = 0
Add 1 to both sides:
x^2 + x = 1
Add 1/4 to both sides:
x^2 + x + 1/4 = 5/4
Write the left hand side as a square:
(x + 1/2)^2 = 5/4
Take the square root of both sides:
x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
7x + 6y + 4z = 10
3x + 3y + 3z - 1
4x + 4y + 4z = 2
Part: 0/2
Part 1 of 2
Evaluate the determinants D, Dx Dy and Dz.
D=
Dx=
Dy=
Dz=
Answer:
D = 0 , Dx = 4 , Dy = -6 , Dz = 2
Step-by-step explanation:
As per cramer's rule,
D = | 7 6 4 | = 0
| 3 3 3 |
| 4 4 4 |
Dx = | 10 6 4 | = 4
| 1 3 3 |
| 2 4 4 |
Dy = | 7 10 4 | = -6
| 3 1 3 |
| 4 2 4 |
Dz = | 7 6 10 | = 2
| 3 3 1 |
| 4 4 2 |
Is f(x) continuous at x equals 4? Why or why not? A. No, f(x) is not continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. Yes, f(x) is continuous at x equals 4 because f (4 )exists. C. No, f(x) is not continuous at x equals 4 because f (4 )is undefined. D. Yes, f(x) is continuous at x equals 4 because ModifyingBelow lim With x right arrow 4 f (x )equals f (4 ).
Corrected Question
Is the function given by:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
continuous at x=4? Why or why not? Choose the correct answer below.
Answer:
(D) Yes, f(x) is continuous at x = 4 because [tex]Lim_{x \to 4}f(x)=f(4)[/tex]
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
A function to be continuous at some value c in its domain if the following condition holds:
f(c) exists and is defined.[tex]Lim_{x \to c}$ f(x)[/tex] exists. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]At x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Therefore: [tex]Lim_{x \to 4}f(x)=f(4)=2[/tex]
By the above, the function satisfies the condition for continuity.
The correct option is D.
A newspaper posted this question on its web "How often do you seek medical information online?" Of 1072 Internet users who chose to respond, 38% of them responded with "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method? What term is used to describe this type of survey? Select all that apply.
What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond?
a. The respondents are a census.
b. The respondents are a population.
c. The respondents are a voluntary response sample.
d. The respondents are a self-selected sample.
What is wrong with this type of sampling method?
a. The survey question is "loaded," or intentionally worded to elicit a desired response.
b. It is too expensive.
c. Many people may choose not to respond to the survey.
d. Responses may not reflect the opinions of the general population.
e. It is too time consuming
Answer:
1. Option c
2. Option d
Step-by-step explanation:
This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.
This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.
Part A: The respondents are a voluntary response sample (Option C)
Part B: Responses may not reflect the opinions of the general population (Option D)
The total number of internet users = 1072
Percentage of the total number of people that chose to respond = 38%
Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.
Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.
In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples
The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population
Learn more on sampling methods here: https://brainly.com/question/16587013
If Romeo earns 8% more than Juliet, Romeo’s salary is how many times Juliets salary?
A) 1.08
B) 0.92
C) 80
D) 108
Answer:
1.08
Step-by-step explanation:
If Romeo earns 8% more than Juliet,
Example?
If Juliet earns $80
80x8% = 6.40 So his pay would be 80 + 6.40
If you times 80 by 1.08 (this would also be 108%) you would get $86.40
Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. Group of answer choices
Answer:
(71.28, 78.72)
Step-by-step explanation:
We have the following information from the statement:
mean (m) = 75
sample standard deviation (sd) = 5
Sample size (n) = 13
Significance level (alpha) = 1 - 0.98 = 0.02
Degrees of freedom for t-d (df) = n - 1 = 13 - 1 = 12
The critical value would be:
t (alpha / 2) / df = T (0.01) / 12 = 2,681 (this for the table)
Margin of error equals:
E = t (alpha / 2) / df * sd / n ^ (1/2), replacing:
E = 2,681 * 5/13 ^ (1/2)
E = 3.72
Therefore, the interval of 98% confidence interval would be:
75 + 3.72 = 78.72
75 - 3.72 = 71.28
(71.28, 78.72)
Borachio eats at the same fast food restaurant every day. Suppose the time X between the moment Borachio enters the restaurant and the moment he is served his food is normally distributed with mean 4.2 minutes and standard deviation 1.3 minutes. Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Answer:
26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 4.2, \sigma = 1.3[/tex]
Find the probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
This is 1 subtracted by the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 4.2}{1.3}[/tex]
[tex]Z = 0.615[/tex]
[tex]Z = 0.615[/tex] has a pvalue of 0.7308.
1 - 0.7308 = 0.2694
26.94% probability that when he enters the restaurant today it will be at least 5 minutes until he is served.
Match each linear equation with the name of its form.
y=-x+8
slope-intercept form
2x - 5y = 9
standard form
y + 6 = -3(x - 1)
point-slope form
Answer:
y + 6 = -3(x - 1) - Point Slope
y=-x+8 - Slope Intercept
2x - 5y = 9 - Standard
Step-by-step explanation:
Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]
y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.
Slope-intercept form is: [tex]y=mx+b[/tex]
y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.
This only leaves 2x - 5y = 9, which is in standard form.
All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
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.
We have to given that;
All the expressions are,
1) y = -x + 8
2) 2x - 5y = 9
3) y + 6 = -3(x - 1)
Now, All the correct linear equation with the name of its form are,
1) y = -x + 8 = Slope-intercept form
2) 2x - 5y = 9 = Standard form
3) y + 6 = -3(x - 1) = Point-slope form
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help *URGENT* PLZ..........
Answer:
2, -1/2
Step-by-step explanation:
2m²-3m-2=0
2m² - 4m + 1m - 2=0
2m(m-2)+(m-2)=0
(2m+1)(m-2)=0
2m+1=0 ⇒ m= -1/2
m-2=0 ⇒ m=2
A study of the effect of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it takes to fall asleep. These data are obtained:
Smokers: 69.3 56.0 22.1 47.6 53.2 48.1 52.7 34.4 60.2 43.8 23.2 13.8
Non-Smokers: 28.6 25.1 26.4 34.9 28.8 28.4 38.5 30.2 30.6 31.8 41.6 21.1 36.0 37.9 13.9
Which group having greater value of relative dispersion and why?
Answer:
The group that has greater value of relative dispersion is the smokers group, as the coefficient of variationof their data is bigger than the coefficient of variation of the non-smokers group data.
CV smokers: 0.387
CV non-smokers: 0.234
Step-by-step explanation:
We will calculate the relative dispersion of each data set with its coefficient of variation (ratio of the standard deviation to the arithmetic mean).
Then, first we calculate the mean and standard deviation for the smokers data:
Mean: 43.7
Standard deviation: 286.5
[tex]M_s=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_s=\dfrac{1}{12}(69.3+56+22.1+47.6+53.2+. . .+13.8)\\\\\\M_s=\dfrac{524.4}{12}\\\\\\M_s=43.7\\\\\\s_s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_s)^2\\\\\\s_s=\dfrac{1}{11}((69.3-43.7)^2+. . . +(13.8-43.7)^2)\\\\\\s_s=\dfrac{3152}{11}\\\\\\s_s=286.5\\\\\\[/tex]
The mean and standard deviation for the non-smokers is:
Mean: 30.3
Standard deviation: 50.9
[tex]M_n=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M_n=\dfrac{1}{15}(28.6+25.1+26.4+34.9+28.8+. . .+13.9)\\\\\\M_n=\dfrac{453.8}{15}\\\\\\M_n=30.3\\\\\\s_n=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M_n)^2\\\\\\s_n=\dfrac{1}{14}((28.6-30.3)^2+. . . +(13.9-30.3)^2)\\\\\\s_n=\dfrac{713.3}{14}\\\\\\s_n=50.9\\\\\\[/tex]
Now, we can calculate the coefficient of variation:
CV smokers:
[tex]CV_s=\dfrac{s_s}{M_s}=\dfrac{16.9}{43.7}=0.387[/tex]
CV non-smokers:
[tex]CV_n=\dfrac{s_n}{M_n}=\dfrac{7.1}{30.3}=0.234[/tex]
Multiply or divide as indicated x^10/x^4
Answer:
X^6
Step-by-step explanation:
