whats the slope of the graph -4, 5 1,-7.5
Answers
Answer:
Slope (m)= -12.5/5= -2.5
-12.5/5 in fraction form
or
-2.5 in decimal form
Step-by-step explanation:
slope (m)= -12.5/5= -2.5
the points belong as a decreasing linear function
equation: y= -2.5x-5
Related Questions
A student at a four-year college claims that mean enrollment at four-year colleges is higher than at two-year colleges in the United States. Two surveys are conducted. Of the 35 four-year colleges surveyed, the mean enrollment was 5,135 with a standard deviation of 783. Of the 35 two-year colleges surveyed, the mean enrollment was 4,436 with a standard deviation of 553. Test the student's claim at the 0.01 significance level.
NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.)(1) What is the test statistic? (Round your answer to two decimal places.)(2) What is the p-value? (Round your answer to four decimal places.)
Answers
Answer:
Part 1: The statistic
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]
Replacing we got
[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]
Part 2: P value
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{68}>4.31)=0.000022 \approx 0.00002[/tex]
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
Step-by-step explanation:
Data given
[tex]\bar X_{1}=5135[/tex] represent the mean for four year college
[tex]\bar X_{2}=4436[/tex] represent the mean for two year college
[tex]s_{1}=783[/tex] represent the sample standard deviation for four year college
[tex]s_{2}=553[/tex] represent the sample standard deviation two year college
[tex]n_{1}=35[/tex] sample size for the group four year college
[tex]n_{2}=35[/tex] sample size for the group two year college
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the mean enrollment at four-year colleges is higher than at two-year colleges in the United States , the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}\leq 0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}> 0[/tex]
We can assume that the normal distribution is assumed since we have a large sample size for each case n>30. So then the sample mean can be assumed as normally distributed.
Part 1: The statistic
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=35+35-2=68[/tex]
Replacing we got
[tex]t=\frac{(5135-4436)-0}{\sqrt{\frac{783^2}{35}+\frac{553^2}{35}}}}=4.31[/tex]
Part 2: P value
Since is a right tailed test the p value would be:
[tex]p_v =P(t_{68}>4.31)=0.000022[/tex]
Comparing the p value we see that is lower compared to the significance level of 0.01 so then we can reject the null hypothesis and we can conclude that the mean for the four year college is significantly higher than the mean for the two year college and then the claim makes sense
Suppose that there are 100 MBA students in the first-year class. Of these students, 20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience. Suppose that a first-year MBA student is selected at random. (a) What is the probability that this student has at least four years of work experience
Answers
Answer:
(a)0.5
(b)0.625
Step-by-step explanation:
Out of 100 MBA students
20 of them have two years of work experience, 30 have three years of work experience, 15 have four years of work experience, and 35 have five or more years of work experience.Total Sample Space, n(S)=100
(a)Let event A be the event that an MBA student has at least four years of work experience.
n(A)=15+35=50
Therefore:
[tex]P(A)=\dfrac{n(A)}{n(S)} =\dfrac{50}{100}=0.5[/tex]
The probability that this student has at least four years of work experience is 0.5.
(b)Conditional probability that given that a student has at least three years of work experience,this student has at least four years of work experience.
P(at least 4 years|the student has at least three years of experience)
[tex]=\dfrac{50/100}{80/100} =\dfrac{5}{8}=0.625[/tex]
The probability that a randomly selected first-year MBA student has at least four years of work experience is 0.5 or 50%.
Explanation:The question involves the concept of probability in statistics, a part of Mathematics. Here, we are given that there are a total of 100 first-year MBA students. The number of students with at least four years of work experience combines the students with four years and five or more years of work experience. Thus, the students with at least four years of work experience are 15 (four years of work experience) + 35 (five or more years of work experience), which equals 50.
The probability is determined by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability that a randomly selected first-year MBA student has at least four years of work experience is calculated as 50 (students with at least four years' experience) divided by 100 (total students), which equals 0.5 or 50%.
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Find the horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.
y = −3
y = −1
y = 3
y = 1
Answers
Answer:
y = 3
Step-by-step explanation:
y = (3x² + 3x + 6) / (x² + 1)
The power of the numerator and denominator are equal, so as x approaches infinity, y approaches the ratio of the leading coefficients.
y = 3/1
The horizontal asymptote will be;
⇒ y = 3
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The algebraic expression is,
''The horizontal asymptote off of x equals quantity 3 x squared plus 3x plus 6 end quantity over quantity x squared plus 1.''
Now,
We can formulate;
⇒ f (x) = ( 3x² + 3x + 6 ) / (x² + 1)
Hence, We get the horizontal asymptote as;
We know that;
A function f is said to have a horizontal asymptote y = a;
⇒ [tex]\lim_{x \to \infty} f (x) = a[/tex]
So, We get;
⇒ [tex]\lim_{x \to \infty} f (x) = \lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{(3x^2 + 3x + 6)}{x^2 + 1} = \lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)}[/tex]
⇒ [tex]\lim_{x \to \infty} \frac{3x^2 (1+1/x + 6/x^2)}{x^2(1 + 1/x^2)} = 3[/tex]
⇒ y = 3
Thus, The horizontal asymptote will be;
⇒ y = 3
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Which of the following best describes the equation below? y=-6x+7
Answers
Answer:
y=-6x+7 (Negative Slope)
Step-by-step explanation:
This equation is in slope intercept form.
7= y-intercept
-6= slope
This means that when you plot this on a graph, your slope will be negative.
(please break it down for me to understand):)
*I got 0.00040404 on calculator but I need fraction not decimal trying to understand how to get the fraction*
[tex] \frac{1}{50} \times \frac{2}{99} = \frac{1}{2475} [/tex]
Answers
Answer:
1/50 times 2/99 = 2/4950
divide numerator and denominator by 2 and the answer you should get is 1/2475 and in decimal form it equals 0.00040404040404040
Step-by-step explanation:
Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. 500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adults residents of this city who have cell phones.
Answers
Answer:
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 500, \pi = \frac{421}{500} = 0.842[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.
Given :
500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones.95% confidence level.The formula for the confidence interval is given by:
[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex] --- (1)
where the value of p is given by:
[tex]\rm p =\dfrac{421}{500}=0.842[/tex]
Now, the value of z for 95% confidence interval is given by:
[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]
So, the z value regarding the p-value 0.975 is 1.96.
Now, substitute the value of z, p, and n in the expression (1).
[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]
The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.
So, the 95% confidence interval is (0.81,0.874).
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You need tile on one wall in your kitchen. The wall measures 12 feet by 5 feet. The tile cost $2 a square foot. How much money will it cost for the tile on the kitchen wall?
Answers
Answer:
$120
Step-by-step explanation:
Area of wall: 12*5=60 square feet
price = 60*2=$120
3. Find the radius of the object to the right.
Answers
Answer:
2.5 cm
Step-by-step explanation:
The line to the right of the object indicates the diameter. Therefore, the diameter is 5 cm.
The diameter is twice the radius, or
d=2r
We know the diameter is 5, so we can substitute that in for d
5=2r
To solve for r, we need to get r by itself. To do this, divide both sides by 2. This will cancel the 2s on the right.
5/2=2r/2
2.5=r
So, the radius is 2.5 centimeters
6.- Find the area under the standard normal distribution: to the left of z=-1.55.
Answers
Answer:
[tex] P(z<-1.55)=0.0606[/tex]
Step-by-step explanation:
For this case we want to find this probability:
[tex] P(z<-1.55)[/tex]
Because they want the area to the left of the value. We need to remember that the normal standard distribution have a mean of 0 and a deviation of 1.
We can use the following excel code: =NORM.DIST(-1.55,0,1,TRUE)
And we got:
[tex] P(z<-1.55)=0.0606[/tex]
The other possibility is use the normal standard table and we got a similar result.
A camera has a listed price of $778.95 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
$854.90
Step-by-step explanation:
List Price Before Tax = $778.95
Sales Tax Rate = 9.75% = 0.0975
Total Cost of the Camera = ?
Sales Tax = List Price Before Tax x Sales Tax Rate
Sales Tax = $778.95 x 9.75%
Sales Tax = $75.9476
or
Sales Tax = $75.95
Now add the Sales Tax in List Price Before Tax, to compute the Total Cost of the Camera, as follows;
Total Cost of the Camera = Sales Tax + List Price Before Tax
Total Cost of the Camera = $75.95 + $778.95
Total Cost of the Camera = $854.90
Between the years of 1947 and 1956 earthenware jars containing what are known as the Dead Sea scrolls were found in caves along the coast of Jerusalem in the Dead Sea. Upon radiometric testing it was found that the scrolls were wrapped in material that contained about 79 percent of the original carbon-14.archeologists estimated that the scrolls are about 1900 years old. Are they right ?
Answers
Answer:
The scroll is 1949 years old, thus the archeologists are right.
Step-by-step explanation:
The decay equation of ¹⁴C is:
[tex] A = A_{0}e^{-\lambda*t} [/tex] (1)
Where:
A₀: is the initial activity
A: is the activity after a time t = 79%*A₀
λ: is the decay rate
The decay rate is:
[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex] (2)
Where [tex]t_{1/2}[/tex]: is the half-life of ¹⁴C = 5730 y
By entering equation (2) into equation (1) we can find the age of the scrolls.
[tex] A = A_{0}e^{-\lambda*t} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t} [/tex]
Since, A = 79%*A₀, we have:
[tex]\frac{79}{100}A_{0} = A_{0}e^{-\frac{ln(2)}{t_{1/2}}*t}[/tex]
[tex]ln(\frac{79}{100}) = -\frac{ln(2)}{t_{1/2}}*t[/tex]
Solving the above equation for t:
[tex]t = -\frac{ln(79/100)}{\frac{ln(2)}{t_{1/2}}}[/tex]
[tex]t = -\frac{ln(75/100)}{\frac{ln(2)}{5730 y}} = 1949 y[/tex]
Hence, the scroll is 1949 years old, thus the archeologists are right.
I hope it helps you!
Answer:
The hypothesis is correct.
Step-by-step explanation:
Using the half-life equation, the number of years (1,900) can be substituted for t and the half-life (5,730) can be substituted for h. Since the original amount is not known but the percent remaining is known, any value can be used for the original amount. Using 100 will be the easiest. Plugging these values into the equation gives 79.47 remaining. If 79.47 of the original 100 units are left, that is 79.47 percent. Since radiometric dating gives an estimate of age, the archeologists’ hypothesis is correct.
I need to Simplify (3mn)^4
Answers
9514 1404 393
Answer:
81m^4·n^4
Step-by-step explanation:
"Simplify" in this context means "remove parentheses." The applicable rule of exponents is ...
(ab)^c = (a^c)(b^c)
__
[tex](3mn)^4=3^4m^4n^4=\boxed{81m^4n^4}[/tex]
Choose the function that represents the data in the table.
A.Y= 0.5x^2+6
B. Y= 0.5^x+6
C. Y= 0.5x+ 6
D. Y= x^0.5+ 6
Answers
Given:
It is given that the function represents the data in the table.
We need to determine the function.
Slope:
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let us substitute the coordinates (1,6.5) and (4,8) in the above formula, we get;
[tex]m=\frac{8-6.5}{4-1}[/tex]
[tex]m=\frac{1.5}{3}[/tex]
[tex]m=0.5[/tex]
Thus, the slope is 0.5
y - intercept:
The y - intercept is the value of y when x = 0.
Thus, from the table, when x = 0 the corresponding y value is 6.
Therefore, the y - intercept is [tex]b=6[/tex]
Equation of the function:
The equation of the function can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values [tex]m=0.5[/tex] and [tex]b=6[/tex], we get;
[tex]y=0.5x+6[/tex]
Thus, the equation of the function is [tex]y=0.5x+6[/tex]
Hence, Option C is the correct answer.
The annual energy consumption of the town where Camilla lives in creases at a rate that is onal at any time to the energy consumption at that time. The town consumed 4.4 trillion ually after 5 years. British thermal units (BTUs) initially, and it consumed 5.5 trillion BTUs ann What is the town's annual energy consumption, in trillionso f BTUs, after 9 years?
Answers
Answer:
6.575 trillion BTUs
Step-by-step explanation:
Let represent the annual energy consumption of the town as E
The rate of annual energy consumption * energy consumption at time past
dE/dt * E
dE/dt =K
k = the proportionality constant
c= the integration constant
(dE/dt=) kdt
lnE = kt + c
E(t) = e^kt+c ⇒ e^c e^kt e^c is a constant, and e^c = E₀
E(t) = E₀ e^kt
The initial consumption of energy is E(0)=4.4TBTU
set t = 0 then
4.4 = E₀ e⇒ E₀ (1)
E₀ = 4.4
E (t) = 4.4e^kt
The consumption after 5 years is t = 5, e(5) = 5.5TBTU
so,
E(5) = 5.5 = 4.4e^k(5)
e^5k = 5/4
We now take the log 5kln = ln(5/4)
5k(1) = ln(5/4)
k = 1/5 ln(5/4) = 0.04463
We find the town's annual energy consumption, after 9 years
we set t=9
E(9) = 4.4e^0.04463(9)
= 4.4(1.494301) = 6.5749TBTUs
Therefore the annual energy consumption of the town after 9 years is
= 6.575 trillion BTUs
Leah has a 22 ounce coffee. she drinks 7 ounces. enter the percentage of ounces Leah has left of her coffee. round your answer to the nearest hundredth.
Answers
Answer:
The percentage of ounces Leah has left of her coffee is 68.18%.
Step-by-step explanation:
The decrease percentage is computed using the formula:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
It is provided that Leah originally had 22 ounce coffee.
Then she drinks 7 ounces of coffee.
Decrease = 7 ounces
Original = 22 ounces
Compute the percentage of ounces Leah has left of her coffee as follows:
[tex]\text{Decrease}\%=\frac{\text{Original amount - Decrease}}{\text{Original amount}}\times 100[/tex]
[tex]=\frac{22-7}{22}\times 100\\\\=\frac{15}{22}\times 100\\\\=68.1818182\%\\\\\approx 68.18\%[/tex]
Thus, the percentage of ounces Leah has left of her coffee is 68.18%.
This is the question with the answer choices. Is it correct?
Answers
Step-by-step explanation:
A question is asked with options for answers, but in reality, there is only one question stating that it is correct.
PLEASE HELP! IF CORRECT WILL GET BRAINLIST!
Answers
Answer:
2
Step-by-step explanation:
f=1
2 x 1=2
4-2=2
Answer:2
Step-by-step explanation:
If f=1 then that means you are multiplying 2 by 1 which is 2. So that makes your problem 4-2=2
4-2(1)=2
The table shows the relationship, "Taiga reads 250 words Which equation models this relationship?
per minute."
O wm = 250
The independent variable, the number of minutes he
O w = 250m
reads, causes a change in the dependent variable, the
O m = 250w
number of words read.
O w + m = 250
Minutes
(m)
Words
(w)
250
500
750
1000
Answers
9514 1404 393
Answer:
w = 250m
Step-by-step explanation:
As the problem statement tells you, the independent variable, the number of minutes he reads, causes a change in the dependent variable, the number of words read. This is modeled by ...
w = 250m
Answer: B. w = 250m
Step-by-step explanation: i answered the question and got it right :)
A fair dice is rolled.
Work out the probability of getting a multiple of 3.
Give your answer in its simplest form.
Answers
Answer:
2/6 or 1/3
Step-by-step explanation:
3 and 6 are multiples of 3
so that is 2 out of 6 numbers on a fair dice.
Simplify 8(x - 4).
A. 8x-4
B. 8x-32
C. x-32
D. x-4
Answers
If you multiply 8 by each value you get B.
Answer:
8x-32
Step-by-step explanation:
Because 8 multiples X and gives 8x and also multiples-4 and gives you -32
:.8x-32
Sara is watching a movie that is 1hr. And 38 mins. long she has already watched 48mins. If the 6:10pm what time will the movie be over?
Answers
Answer: 7:48pm
Step-by-step explanation:
Convert 1h to mins
[tex]1h(\frac{60min}{1h} )=60min[/tex]
add the 38 extra mins.
60+38=98mins
The movie started at 6:10pm, and she has already watched 48 mins of it.
Add 48 to the time and subtract from the length of the movie.
6:10pm + 48 mins=6:58pm (this is the current time)
98-48=50
Let's add 2 mins to make it 7:00pm.
6:58pm+2mins=7:00pm
50-2=48mins
So now it's 7:00pm and we still have 48 mins to watch. Add that to the time.
7:00pm+48mins=7:48pm
A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $3 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length
Answers
Answer:
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
Step-by-step explanation:
-> materials has a square base of side length, dimension will be: x . x = x²
'y' represents height
->For dimensions of 4 silver plated sides= xy each
->dimensions of the nickel plated top= x²
Volume = yx²
44=yx² => y= 44/x²
Cost of the sides will be( 4 * xy * $3 )
Cost of the top and the bottom will be (2 * x² * $1)
For the Total cost: 12xy + 2x²
substituting value of 'y' in above equation,
=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²
To Minimum critical point => d [cost] / dx = 0
=> - 528/x² + 4x =0
132/x² - x =0
132 - x³ = 0
x³ = 132
Taking cube root on both sides
∛x³ = ∛(132)
x= 5.09
=> y = 44/5.09² =>1.69
Dimensions of the box :
Base= 5.09 cm x 5.09 cm; height = 1.69 cm
1 third plus 1/2 -1/5 equals
Answers
Answer: 0.63333333333
Step-by-step explanation: Use a calculator.
Answer: 19/30
Step-by-step explanation:
You want to find a common denominator that works for all fractions and add a subtract them and the simplify
what is the volume of a cube whose surface area is 294
Answers
Answer: V = 343unit³
Step-by-step explanation:
This is a solid shape problems a three dimensional.
Surface area of a cube = 6s² and the Volume = s³.
Since the surface area is given to be 294, we now use this to calculate the s.
Now,
6s² = 294, now solve for s
s² = 294/6
= 49
s² = 49
Now, to find s, we recalled the laws of indices by taking the square root of both sides
√s² = +/- √49
s. = +/-7unit.
Now to find the volume of the cube, where
V = s³ and s = 7, therefore
V = 7³
= 343unit³
6.8 Use the Normal approximation. Suppose we toss a fair coin 100 times. Use the Normal approximation to find the probability that the sample proportion of heads is (a) between 0.3 and 0.7. (b) between 0.4 and 0.65. Moore, David. Exploring the Practice of Statistics & Student CD (p. 325). W.H. Freeman & Company. Kindle Edition.
Answers
Answer:
(a) The probability that proportion of heads is between 0.30 and 0.70 is 1.
(b) The probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Step-by-step explanation:
Let X = number of heads.
The probability that a head occurs in a toss of a coin is, p = 0.50.
The coin was tossed n = 100 times.
A random toss's result is independent of the other tosses.
The random variable X follows a Binomial distribution with parameters n = 100 and p = 0.50.
But the sample selected is too large and the probability of success is 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of [tex]\hat p[/tex] (sample proportion of X) if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10Check the conditions as follows:
[tex]np=100\times 0.50=50>10\\n(1-p)=100\times (1-0.50)=50>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex]
[tex]\mu_{p}=p=0.50\\\sigma_{p}=\sqrt{\frac{p(1-p)}{n}}=0.05[/tex]
(a)
Compute the probability that proportion of heads is between 0.30 and 0.70 as follows:
[tex]P(0.30<\hat p<0.70)=P(\frac{0.30-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.70-0.50}{0.05})\\[/tex]
[tex]=P(-4<Z<4)\\=P(Z<4)-P(Z<-4)\\=(\approx1)-(\approx0)\\=1[/tex]
Thus, the probability that proportion of heads is between 0.30 and 0.70 is 1.
(b)
Compute the probability that proportion of heads is between 0.40 and 0.65 as follows:
[tex]P(0.40<\hat p<0.65)=P(\frac{0.40-0.50}{0.05}<\frac{\hat p-p}{\sigma_{p}}<\frac{0.65-0.50}{0.05})\\[/tex]
[tex]=P(-2<Z<3)\\=P(Z<3)-P(Z<-2)\\=0.9987-0.0228\\=0.9759[/tex]
Thus, the probability that proportion of heads is between 0.40 and 0.65 is 0.9759.
Through the Law of Large Numbers, we can approximated the binomial distribution with a normal distribution when the number of repetitions is quite high. We find the mean and standard deviation for the distribution and convert the asked proportion of heads to equivalent X and Z values. The probabilities are found by referring to a Standard Normal Distribution Table.
Explanation:Normal Approximation to Binomial DistributionIn this problem, we are dealing with a binomial distribution -- a coin flip with two outcomes, heads or tails. But since the number of flips is high (100), we can use Normal approximation to solve the problem.
Whenever a fair coin is tossed, the chance of getting a head is 0.5. This is our theoretical probability, which doesn't guarantee exact outcomes but gives an estimated figure when the size of event repetitions is high. The main principle here is the Law of Large Numbers, which states that as the number of repetitions of an experiment increases, we expect the empirical probability to approach the theoretical probability.
Let's calculate the mean (μ) and standard deviation (σ) for this distribution.
Mean (μ) = np = 100*0.5 = 50Standard Deviation (σ) = √[np(1-p)] = √[100*0.5*0.5] = 5(a) To find the probability of the sample proportion of heads being between 0.3 and 0.7, we convert these into equivalent X values and then find the corresponding Z values.
X for 0.3 is 0.3*100 = 30X for 0.7 is 0.7*100 = 70We calculate Z for each using Z = (X - μ) / σ. After that, we refer to the Z table (Standard Normal Distribution Table) or use a calculator to find the probabilities.
Repeat similar steps for part (b) for the probabilities between 0.4 and 0.65.
Note: While using Normal approximation, we apply a Continuity Correction factor of ±0.5 depending upon the problem.
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Find the inverse of the function: { (3,5), (1, 6), ( -1, 7), (-3, 8)}
Answers
Answer:
{(5,3) , (6,1), (7,-1), (8,-3)}
Step-by-step explanation:
inverse of (x,y) is (y,x)
inverse of { (3,5), (1, 6), ( -1, 7), (-3, 8)} is
{(5,3) , (6,1), (7,-1), (8,-3)}
Suppose shirts are one of 3 colors (red, blue and green) and pants are either black or brown. An outfit consists of a shirt and pants. What is the minimum number of people that need to be in a room together to guarantee that at least two of them are wearing same-colored outfits
Answers
You solve this question by finding the maximum possible number of different combinations, then adding one extra person.
3 possible shirts * 2 possible pants for each shirt = 6 combinations of pants and shirts.
6 + 1 = 7
Therefore, the minimum is:
7 People
A random sample of n = 4 scores is selected from a population with a mean of 50 and a standard deviation of 12. If the sample mean is 56, what is the z-score for this sample mean?
Answers
The z-score for the sample mean in this case is 0.5, which is calculated using the z-score formula, Z = (X - μ) / σ, where X is the sample mean, μ is the population mean, and σ is the standard deviation.
Explanation:The subject here pertains to the calculation of a z-score, which is a statistical measurement describing a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.
Given the sample mean (56), population mean (50), and standard deviation (12), and the formula for the z-score, which is Z = (X - μ) / σ, we can compute for the z-score as follows:
- X is the raw score which is 56- μ is the population mean which is 50- σ is the population standard deviation which is 12Substituting these values into the equation, we have: Z = (56 - 50) / 12 = 0.5. Hence, the z-score of the sample mean is 0.5.
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A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1 of A IS AT (-1,9) and B (2,0)
Answers
Step-by-step explanation:
A,B, and C are collinear, and B is between A and C. The ratio of AB to BC is 1:1 of A IS AT (-1,9) and B (2,0)
to find out point C use section formula
[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]
A is (-1,9) that is our (x1,y1)
that is our (x2,y2)
ratio is 1:1 that is m and n
Plug in the values in the formula
[tex](\frac{mx_2+nx_1}{m+n} ,\frac{my_2+ny_1}{m+n} )[/tex]
[tex](\frac{1(x_2)+1(-1)}{1+1} ,\frac{1(y_2)+1(9)}{1+1} ) =(2,0)\\\frac{1(x_2)+1(-1)}{1+1}=2\\\frac{1(x_2)+1(-1)}{2}=2\\\\x_2-1=4\\x_2= 5\\\frac{1(y_2)+1(9)}{1+1}=0 \\\frac{1(y_2)+1(9)}{2} =0\\\\y_2+9=0\\x_2= -9[/tex]
Answer C is (5,-9)
Quiz 1
1,700
Possiblem
A circle has a radius of 10. An arc in this circle has a central angle of 72.
What is the length of the arc?
Either enter an exact answer in terms of 7 or use 3.14 for 7 and enter your answer as a decimal.
Skill Sum
Circle basi
Arc measu
Arc length
Ouiz 1
Unit test
4 of 5 •••
Answers
Answer:
Length of arc=4π
Step-by-step explanation:
Length of arc=¤/360 x 2xπxr
Where:
¤=72
r=10
Length of arc=72/360 x 2xπx10
Length of arc=0.2 x 20π
Length of arc=4π