Answer:
a) [tex]\hat p=\frac{148}{4167}=0.036[/tex]
b) [tex]0.0355 - 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.030[/tex]
[tex]0.0355 + 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.041[/tex]
Step-by-step explanation:
The sample proportion have the following distribution
[tex]\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
Part a
The estimated proportion for this case can be calculated like this:
[tex]\hat p=\frac{148}{4167}=0.036[/tex]
Part b
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing we got:
[tex]0.0355 - 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.030[/tex]
[tex]0.0355 + 1.96\sqrt{\frac{0.036(1-0.036)}{4167}}=0.041[/tex]
According to the data given:
The best point estimate of the population proportion p is 0.036.The 95% confidence interval for the proportion of adverse reactions is (0.03, 0.042).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]\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 z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
Out of 4167 patients treated with the drug, 148 developed the adverse reaction of nausea, hence:
[tex]n = 4167, \pi = \frac{148}{4167} = 0.036[/tex]
The best point estimate of the population proportion p is 0.036.
95% confidence level
So [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{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}} = 0.036 - 1.96\sqrt{\frac{0.036(0.964)}{4167}} = 0.03[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.036 + 1.96\sqrt{\frac{0.036(0.964)}{4167}} = 0.042[/tex]
The 95% confidence interval for the proportion of adverse reactions is (0.03, 0.042).
A similar problem is given at https://brainly.com/question/16807970
Suppose that g(x) = f(x) - 2. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 2 units to the left.
B. The graph of g(x) is vertically stretched by a factor of 2.
C. The graph of g(x) is shifted 2 units up.
D. The graph of g(x) is shifted 2 units down.
Answer:
D. The graph of g(x) is shifted 2 units down
Step-by-step explanation:
Since we are modifying b in f(x) = mx + b, we are dealing with vertical movement up and down. Since it is -2, we are moving down 2.
I need help plz someone help me solved this problem I need help ASAP! I will mark you as brainiest!
Answer: k = -9
Step-by-step explanation:
kx² - 12x - 4 = 0
In order to have exactly one solution, it must be a perfect square.
Assume k is negative and factor out a negative 1.
-1(kx² + 12x + 4) = 0
[tex]\bigg(\sqrt{kx^2}+\sqrt4\bigg)^2=0\\\\[/tex]
The middle term = 12x [tex]= 2(\sqrt{kx^2})(\sqrt4)[/tex]
12x = 4x√k
3 = √k
9 = k
-1(9x² + 12x + 4) = 0
-9x² - 12x - 4 = 0
k=-9
Is the area of this shape approximately 24 cm* ? If not give the correct area.
311
101
True
False
Answer:
19.2 feet square
Step-by-step explanation:
We khow that the area of an octagon is :
A= 1/2 * h * P where h is the apothem and p the perimeter
A= (1/2)*1.6*(3*8) = 19.2 feet squarea line pass through the point (4,-2) and has a slope of 1/2 what is the value of (-4,a)
Answer:
if you are trying to find the value of a then a= -6
Step-by-step explanation:
i used the information along with desmos graphing calculator and i graphed the line and got the second point (-4,-6)
Answer:
a=-6
Step-by-step explanation:
slope=(y2-y1)/x2-x1)
1/2=(a-(-2))/(-4-4)
1/2=(a+2)/-8
a+2=1/2×-8=-4
a=-4-2=-6
A researcher records the amount of time (in minutes) that parent child pairs spend on social networking sites to test whether they show any generational differences. From the following findings in APA format, interpret these results by stating the research design used (repeated measures or matched pairs), the sample size, the decision, and the effect size. Parents spend significantly less time on social networking sites compared their children (MD = -42 minutes),t(29)=4.021,p<.05,d=0.49.(a) What research design was used? (Repeated measures or matched pairs?)(b) What is the sample size? (n = ?)
Answer:
(a) matched pair design
(b) n = 30
(c) Reject the null hypothesis.
Step-by-step explanation:
The complete question is:
A researcher records the amount of time (in minutes) that parent child pairs spend on social networking sites to test whether they show any generational differences. From the following findings in APA format, interpret these results by stating the research design used (repeated measures or matched pairs), the sample size, the decision, and the effect size. Parents spend significantly less time on social networking sites compared their children (MD = -42 minutes),t(29)=4.021,p<.05,d=0.49.(a) What research design was used? (Repeated measures or matched pairs?)(b) What is the sample size? (n = ?)(c) What is the decision? (Retain or reject the null?)
Solution:
(a)
It s provided that the researcher records the amount of time (in minutes) that parent-child pairs spend on social networking sites.
This implies that the data collected is in the form of paired data.
Thus, the research design that was used was matched pair design.
(b)
Consider the t-statistics provided:
t (29) = 4.021
The number 29 in the bracket is the degrees of freedom.
The degrees of freedom for a matched pair design is,
df = n - 1
Compute the value of n as follows:
df = n - 1
29 = n - 1
n = 29 + 1
n = 30
Thus, the sample size is n = 30.
(c)
The p-value of the test is:
p < 0.05
The p-value of the test is less than the 5% significance level.
This implies that the null hypothesis will be rejected at 5% significance level.
Describe the transformations.
I NEED HELP PLEASE, THANKS! :)
Answer:
Option D
Step-by-step explanation:
x is given to be 4 in this case, so all we would have to is plug it into the following function -
[tex]f ( x ) = \left \{ {{x - 2, x < 4 } \atop {x + 2, x \geq 4 }} \right[/tex]
Through substitution, you would receive the following function -
[tex]f ( x ) = \left \{ {{2, 4 < 4 } \atop 6, 4 \geq 4 }} \right[/tex]
Now the graph proves that this function is closer to 4, and thus proves that the y - coordinate is about 2 at the same time. However, the graph is cut off, so the limit doesn't exists.
31
z – 40-12
2
Solution
Answer:
31z-162
Step-by-step explanation:
[tex]-40-122=-162[/tex]
[tex]=31z-162[/tex]
i have a question what is 2 plus 2 i will really live it if you respond
Hi there! Hopefully this helps!
------------------------------------------------------------------------------------------------
2 + 2 = 4.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You can simply find this answer by getting two of your fingers on your left hand, getting two MORE fingers of your right hand, and counting them. You will end up with 4.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You could multiply 2 two times, like this:
2 x 2 = 4.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You could split the numbers into parts and add them back together, like this:
2 = 1 + 1.
+
2 = 1 + 1.
=
1 + 1 + 1 + 1 = 4.
Answer:
4
Step-by-step explanation:
problem is if you dont have a fingers... you cant physically count 2 + 2
anyway... just add them using your brain = 2 + 2 makes 4
Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
Find the area
O 60 square meters
O 120 square meters
O None of these
O 156 square meters
Answer:
120 m²
Step-by-step explanation:
We khow that the area of a triangle is the product of the lenght and the wight
let x be the width
the pythagorian theorem : x²+8²= 17² x² = 17²-8² x²= 225 x= 15so the lenght is 15
A= 15*8 = 120 m²Answer:
120 square meters
Step-by-step explanation:
The missing leg of the right triangle is found from the Pythagorean theorem:
diagonal² = length² + width²
length² = diagonal² -width²
length = √(17² -8²) = √(289 -64) = √225 = 15
So, the rectangle is 8 m by 15 m and has an area that is ...
A = LW = (15 m)(8 m) = 120 m²
What does the denominator of this rational expression represent? Jessica is organizing a guided tour of the rain forest. The average profit per person that the touring company makes is given by the rational expression , where is the number of people going on the tour.
Complete Question
Jessica is organizing a guided tour of the rain forest. The average profit per person that the touring company makes is given by the rational expression 18x+35/x, where x is the number of people going on the tour. What does the denominator of this rational expression represents?
Answer:
Number of people going on the tour
Step-by-step explanation:
Given that the average profit per person [tex]=\dfrac{18x+35}{x}[/tex]
[tex]\text{Average}=\dfrac{\text{Sum of Total Items}}{\text{Number of Items}}[/tex]
Therefore:
[tex]\text{Average Profit}=\dfrac{(18x+35)\text{ profit}}{x\text{ persons}}[/tex]
The denominator, x represents the number of people going on the tour.
Answer:
btw 35/x represents epresents a fixed cost, like a cover charge for the tour, that is not affected by the number of people attending the tour. So, the quotient 35/x represents the profit that the tour company makes from the cover charge per person.
Step-by-step explanation:
PLATO
state which triangle congruence postulate explains that the triangles are congruent
Answer:
Step-by-step explanation:
Angle-angle-side since they have two similar angles and one common sideIf 16 ounces of bulk rice costs $2.50, how much would 24 ounces cost?Also, could you tell me how much it costs per ounce?
Answer:
24 oz costs $3.75
The rice cost per oz is $0.16
Step-by-step explanation:
Step 1: Set up proportion
16/2.5 = 24/x
Step 2: Cross multiply
16x = 24(2.5)
Step 3: Solve
16x = 60
x = 15/4 or 3.75
Identifico el nombre de la propiedad a la que hacen referencia las siguientes expresiones:
Hacen falta las expresiones para poder responder a tu pregunta, estuve investigando y adjuntaré una imagen que hace referencia a tus preguntas, espero no equivocarme.
Si este es el caso, son 9 expresiones y el nombre de cada propiedad es:
1. Inverso aditivo (Sumar un número por su opuesto el resultado es 0)
2. Ley conmutativa (El orden de los factores no altera el producto)
3. Ley asociativa (Agrupar los términos sin alterar el resultado)
4. Ley de la identidad, (Sumar un número con 0 se obtiene el mismo número)
5. Ley distributiva (La misma respuesta cuando multiplicas un conjunto de números por otro número que cuando se hace cada multiplicación por separado)
6. Ley distributiva
7. Ley distributiva
8. Ley asociativa
9. Ley conmutativa
PLSSS PEOPLE I NEED HELP
Answer:C
Step-by-step explanation:
The vertical line test
A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose that the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time t 0, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.
a) Write an initial value problem that models the mass of the drug in the blood for t20.
b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.
c) What is the steady-state mass of the drug in the blood?
d) After how many minutes does the drug mass reach 90% of its stead-state level?
Answer:
a) [tex]\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}[/tex]
b) [tex]\mathbf{x = 2000 - 2000e^{-0.015t}}[/tex]
c) the steady state mass of the drug is 2000 mg
d) t ≅ 153.51 minutes
Step-by-step explanation:
From the given information;
At time t= 0
an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500
The inflow rate is 0.06 L/min.
Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant.
The objective of the question is to calculate the following :
a) Write an initial value problem that models the mass of the drug in the blood for t ≥ 0.
From above information given :
[tex]Rate _{(in)}= 500 \ mg/L \times 0.06 \ L/min = 30 mg/min[/tex]
[tex]Rate _{(out)}=\dfrac{x}{4} \ mg/L \times 0.06 \ L/min = 0.015x \ mg/min[/tex]
Therefore;
[tex]\dfrac{dx}{dt} = Rate_{(in)} - Rate_{(out)}[/tex]
with respect to x(0) = 0
[tex]\mathbf{\dfrac{dx}{dt} = 30 - 0.015 x}[/tex]
b) Solve the initial value problem and graph both the mass of the drug and the concentration of the drug.
[tex]\dfrac{dx}{dt} = -0.015(x - 2000)[/tex]
[tex]\dfrac{dx}{(x - 2000)} = -0.015 \times dt[/tex]
By Using Integration Method:
[tex]ln(x - 2000) = -0.015t + C[/tex]
[tex]x -2000 = Ce^{(-0.015t)[/tex]
[tex]x = 2000 + Ce^{(-0.015t)}[/tex]
However; if x(0) = 0 ;
Then
C = -2000
Therefore
[tex]\mathbf{x = 2000 - 2000e^{-0.015t}}[/tex]
c) What is the steady-state mass of the drug in the blood?
the steady-state mass of the drug in the blood when t = infinity
[tex]\mathbf{x = 2000 - 2000e^{-0.015 \times \infty }}[/tex]
x = 2000 - 0
x = 2000
Thus; the steady state mass of the drug is 2000 mg
d) After how many minutes does the drug mass reach 90% of its stead-state level?
After 90% of its steady state level; the mas of the drug is 90% × 2000
= 0.9 × 2000
= 1800
Hence;
[tex]\mathbf{1800 = 2000 - 2000e^{(-0.015t)}}[/tex]
[tex]0.1 = e^{(-0.015t)[/tex]
[tex]ln(0.1) = -0.015t[/tex]
[tex]t = -\dfrac{In(0.1)}{0.015}[/tex]
t = 153.5056729
t ≅ 153.51 minutes
Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
Pls help with this area question
Answer:
1
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = 2πrh
The total area is that added to the areas of the two circular bases:
A = 2πr² +2πrh
We want the ratio of these to be 1/2:
LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr
Multiplying by 2(r+h) gives ...
2h = r+h
h = r . . . . . subtract h
So, the desired ratio is ...
h/r = h/h = 1
The ratio between height and radius is 1.
Translate and solve.
17. The absolute value of three times a number, n, is greater than 15.
Answer:
3n>15
Step-by-step explanation:
So basically, this three times a number, 3n, is greater than 15. So, this is 3n>15.
If George is 33 1/3% richer than Pete, than Pete is what percent poorer than George?
Answer:
25%
Step-by-step explanation:
George is 33[tex]\frac{1}{3}[/tex]% ([tex]\frac{100}{3}[/tex]%) richer than Pete. Let Pete's percentage of wealth be 100%.
Thus George percentage of wealth = 100% + [tex]\frac{100}{3}[/tex]%
= [tex]\frac{400}{3}[/tex]%
= 133[tex]\frac{1}{3}[/tex]%
Pete's percent poorer than George can be determined by;
= [tex](\frac{100}{3})[/tex] ÷ [tex](\frac{400}{3} )[/tex] × 100
= [tex](\frac{100}{3})[/tex] × [tex]\frac{3}{400}[/tex] ×100
= 0.25 × 100
= 25%
Pete is 25% poorer than George.
graph y=8 sec1/5 Ø the answers are graphs I am just unsure of how to answer
Answer:
Use a graphing calc.
Step-by-step explanation:
There are 7 students in a class: 5 boys and 2 girls.
If the teacher picks a group of 4 at random, what is the probability that everyone in the group is a boy?
Answer:
4/7
Step-by-step explanation:
5+2=7
7 children
4 boys Out of 7 children
Answer:1/7
Step-by-step explanation:
Khan academy
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this? (it's not 15)
Answer: 20
Step-by-step explanation:
I guess that we want to distribute all the 7 candies between 4 kids
We have 3 options:
first 3, 2, 1 and 1. (the number of candies that each kid gets)
The possible permutations in this case:
if we leave the 3 fixed, the ones do are equal, so the permutations are only given by the change in the kid that gets 2 candies, we have 3 permutations for this.
And for the fixed 3, we have 4 possible places where we can fix it, so the total number of combinations is:
c = 3*4 = 12.
and the second option is (2, 2, 2, 1)
Here the only change is the kid that gets only one candy, we have 4 options in this case:
c = 4.
the third option is (4, 1, 1, 1)
Here the only change is the kid that gets 4 candies, and we have 4 options for this, so we have 4 combinations:
c = 4.
Then the total number of possible combinations is:
C = 12 + 4 + 4 = 20
Which equation represents the statement below?
Thirteen less than a number is forty-two.
Select one:
a. n – 13 = 42
b. 42 – 13 = n
c. 13 – n = 42
d. 13 – 42 = n
The answer is option A
Step-by-step explanation:
Thirteen less than a number is written as
n - 13
Equate it to 42
We have
n - 13 = 42
Hope this helps you
Estimate the area under the graph of f(x)=2x^2-12x+22 over the interval [0,2] using four approximating rectangles and right endpoints.
Answer:
The right Riemann sum is 21.5.
The left Riemann sum is 29.5.
Step-by-step explanation:
The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the right endpoints:
[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]
The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the left endpoints:
[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]
Help me please! I need an answer!
Answer: [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
Inversely proportional means a x b = k --> b = k/a
Given that a₁ = 2 --> b₁ = k/2
Given that a₂ = 3 --> b₂ = k/3
[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]
Write the comparison below as a ratio in simplest form using a fraction, a colon, and the word to. 11 oz to 5 oz
A small combination lock on a suitcase has 3 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 3 digits with no repeats, what is the probability of a person guessing the right combination?
Answer:
0.14% probability of a person guessing the right combination
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the numbers are selected is important. For example, 1,3,2 is a different combination than 3,1,2. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Desired outcomes:
One right combination, so [tex]P = 1[/tex]
Total outcomes:
10 numbers from a set of 3. So
[tex]P_{(10,3)} = \frac{10!}{(10-3)!} = 720[/tex]
What is the probability of a person guessing the right combination?
[tex]p = \frac{D}{T} = \frac{1}{720} = 0.0014[/tex]
0.14% probability of a person guessing the right combination
Express it in slope-intercept form.
Answer:y=3/2x-3
Step-by-step explanation: the slope of the graph is (y2-y1)/(x2-x1)
If we take points (0,-3) (2,0) the slope would be (0--3)/(2-0) = 3/2
And the y-intercept of the slope is -3