Answer:
21.27 years
Step-by-step explanation:
22800 = 9900(1.04^t)
22800/9900 = 1.04^t
76/33 = 1.04^t
ln(76/33) = t×ln(1.04)
t = 21.27
Answer: it will take 20.83 years.
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 9900
A = 22800
r = 4% = 4/100 = 0.04
Therefore,
22800 = 9900 x 2.7183^(0.04 x t)
22800/9900 = 2.7183^0.04t
2.3 = 2.7183^0.04t
Taking ln of both sides, it becomes
Ln 2.3 = 0.04t ln2.7183
0.833 = 0.04t
t = 0.833/0.04
t = 20.83 years
Which table shows a proportional relationship between a and b?
Answer:
B
Step-by-step explanation:
I first went through starting with A and took 3-9 (since it’s in the first box) I got -6 . You then divide 3 and 9 by -6 and report your answer.
I got 3/-6 = -.5 and And 9/-6 = -1.5
I then moved onto 4 and 12, I took the difference 4-12 and got -11.
4/-11 = -0.36 and 12 /-11 = -1.09
Since these answers are not the all the same I moved onto B
I took 20-25 = -5
20/-5 = -4 and 25/-5 = -5
Next numbers
24-30 = -6
24/6 = 4 and 30/6= 5
Next number
32-40= -8
32/-8 = -4
40/-8 = -5
( when putting this in fraction form it would be -4/-5 and that turns positive.) making this table proportioned unlike the other ones
Answer: option B is the correct answer.
Step-by-step explanation:
If two variables are proportional, a change in the value of one variable would cause a corresponding change in the value of the other variable. This means that both variables are related by a constant of proportionality, k.
Looking at the given tables,
For table A,
9/3 = 12/4 but not equal to 20/5
The relationship is not proportional.
For table B,
25/20 = 30/24 = 40/32 = 1.25
The relationship is proportional.
For table C,
12/4 = 15/5 but not equal to 24/6
The relationship is not proportional.
For table D,
4/3 = 16/12 but not equal to 9/6
The relationship is not proportional.
A building contractor buys 7070% of his cement from supplier A and 3030% from supplier B. A total of 9595% of the bags from A arrive undamaged, while 7070% of the bags from B arrive undamaged. Find the probability that anan undamagedundamaged bag is from supplier Upper AA.
Title:
The answer is [tex]\frac{133}{174}[/tex].Step-by-step explanation:
Let the building contractor bought 1000 cement in total.
70% of 1000 = 700 cements were from A and (1000 - 700) = 300 cements were from B.
The number of undamaged bag from A was 95% of 700 = [tex]\frac{95}{100} \times700 = 7\times95 = 665[/tex] and the number of undamaged bags from B was 70% of 300 = [tex]\frac{70}{100} \times300 = 210[/tex].
Total undamaged bags were (665 + 210) = 870.
The probability that an undamaged bag is from A is [tex]\frac{665}{870} = \frac{133}{174}[/tex].
PLEASE HELP URGENT MY MOM WILL GROUND ME IF I DONT FINISH THIS LOL
What coordinates on the unit circle are associated with the angle measure?
Drag coordinates into each box to match the angle measure.
Step-by-step explanation:
Hope it helps you in your learning process.
[tex]\frac{23\pi}{3}[/tex] corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].
[tex]-\frac{3\pi}{4}[/tex] corresponds to [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].
-150 degree corresponds to [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].
Rewrite as:
[tex]\frac{23\pi}{3}=\frac{18\pi+5\pi}{3}=6\pi+\frac{5\pi}{3}[/tex].
We know that [tex]\frac{5\pi}{3}[/tex] corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex]. So [tex]\frac{23\pi}{3}[/tex] also corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].
[tex]-\frac{3\pi}{4}[/tex] has same position as: [tex]-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}[/tex].
So the corresponding point to it is [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].
From unit circle 150 degree corresponds to [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].
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This is the correct method of recording numerical information from an experiment.
Answer:
Data-table is the correct approach of recording numerical information from an experiment
Step-by-step explanation:
A data-table is a group of related facts arranged in labeled rows and columns and is used to record information. Its purpose is to help sort, analyze and compare data gathered from a science experiment or research project. Knowing how to create a data table demonstrates skills in organizing information in a meaningful way and provides a learning base to progress to more sophisticated ways to track data.
What steps should be used to find the range of a set of data? Put the values in order, then locate the value that is far away from every other value. Subtract the maximum and minimum values. Add all of the values together, then divide the sum by the number of values. Add the two middle values together, then divide the sum by two.
Answer:
Subtract the maximum and minimum values.
Step-by-step explanation:
The range of a data set is the interval that contains all values in the set and is determined as the difference between the maximum and the minimum values within the data set. Therefore, in order to find the range of a set of data, simply subtract the maximum and minimum values.
Answer:
Subtract the maximum and minimum values.
Step-by-step explanation:
At a convention, there are 8 mathematics instructors, 13 computer science instructors, 4 statistics instructors, and 6 physics instructors. If an instructor is selected, fint the probability of getting a physics or a statistics instructor.
Answer:
0.323
Step-by-step explanation:
Number of mathematics instructors=8
Number of Computer Science instructors=13
Number of Statistics instructors=4
Number of Physics instructors=6
Total Attendance = 8+13+4+6=31
Probability of Getting a Physics Instructor=6/31
Probability of Getting a Statistics Instructor=4/31
Pr (Getting a Physics OR Statistics Instructor)
=Probability of Getting a Physics Instructor+
Probability of Getting a Statistics Instructor
=6/31+4/31=10/31=0.323
Cathy fills a 10-cup bucket with pond water. She uses a 2-cup jar to scoop out water from the pond and pours it into her bucket. How many times does cathy need to scoop water from the pond to fill the bucket?
Answer:
5
Step-by-step explanation:
Very early in your study of multiplication tables, you learned that ...
5 × 2 = 10
Cathy must fill the 2-cup jar 5 times to transfer a total of 10 cups.
Final answer:
To fill a 10-cup bucket using a 2-cup jar, Cathy must scoop water from the pond 5 times, as 10 divided by 2 equals 5.
Explanation:
The question is how many times Cathy needs to scoop water from the pond with a 2-cup jar to fill her 10-cup bucket.
To find the answer, we simply divide the total capacity of the bucket by the capacity of the jar. So, the calculation would be:
Calculate the total number of cups needed: 10 cups (capacity of the bucket).
Calculate the number of cups per scoop: 2 cups (capacity of the jar).
Divide the total number of cups by the number of cups per scoop: 10 cups/ 2 cups per scoop
= 5 scoops.
Cathy needs to scoop water from the pond 5 times to fill her 10-cup bucket.
A country has 50 million people, 30 million of whom are adults. Of the adults, 5 million are not interested in working, another 5 million are interested in working but have given up looking for work, and 5 million are still looking for work. Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time. What is this country's labor force participation rate? 83.3% 75% 50% 66.7%
Answer:
66.7%
Step-by-step explanation:
Given that
Total population = 50 million
Adults = 30 million
Those not interested in working = 5 million
Those interested in working but given up on searching = 5 million
Those searching = 5 million
Those working part time = 5 million
Those working full time = 10 million
Recall that
Labour force participation rate = (number of people actively participating in labour ÷ total number of people eligible) × 100
Number of people actively participating in labour = employed + unemployed
Employed = 10 million full time + 5 million part time
= 15 million
Unemployed = 5 million. Those searching.
Thus,
People actively participating in labour = 15 + 5= 20 million.
Total number of eligible people = total number of adults = 30 million
Therefore
Labour participation rate = (20/30) × 100
= 0.66667 × 100
= 66.6667
Approximately 66.7%
A school wishes to form three sides of a rectngular playground using 480 meters of fencing. The playground borders the school building, so the fourth side does not need fencing.
Answer:
Step-by-step explanation:
If you were talking about how many meters of fencing the school would need it would be 160 meters. The reason i say this is because if you were to divide the 3 sides of the playground by 48o meters of fencing you would get 160 meters of fencing. If this is not the answer your looking for than please state the question next time. THANK YOU
The function of area will be A(x) = x( 480 - 2x)
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The perimeter is given P = 480 meters
Since the one of the sides does not need fencing, the perimeter would be:
P = 2x + y
Make y the subject;
y = P -2x
Substitute 480 for P;
y = 480 - 2x
The area of a rectangular fence is:
Area = xy
Substitute ;
A = x( 480 - 2x)
Express as a function
A(x) = x( 480 - 2x)
Hence, the function of area will be A(x) = x( 480 - 2x)
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Using the distributive property to find the product (y - 4x)(y ^ 2 + 4y + 16) results in a polynomial of the form y ^ 3 + 4y ^ 2 + ay - 4x * y ^ 2 - axy - 64x . What is the value of a in the polynomial?
Answer:
a=16
Step-by-step explanation:
The distributive property states that
[tex]a(b+c)=ab+ac[/tex]
Therefore using the distributive property
[tex](y - 4x)(y ^ 2 + 4y + 16)[/tex]
=[tex]y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)[/tex]
Expanding the brackets
[tex]y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x[/tex].....(i)
Comparing with the form
[tex]y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x[/tex]-----(ii)
The coefficient of y in (i) is 16 which corresponds to a and the likewise the coefficient of xy
Therefore, a=16
Answer:
C.) 16
Step-by-step explanation:
Evaluating each geometric series described. Find the sum A1=-3, An=-196608, r=4 Answer choices: A) 1 B)-285886 C)-262143 D)-339855 S=
Answer:
(C)-262143
Step-by-step explanation:
For a geometric series, the nth term
[tex]A_n=ar^{n-1}[/tex] where a= first term, r=common ratio.
If [tex]A_1=a=-3[/tex] , r=4 and [tex]A_n=-196608[/tex]
then from [tex]A_n=ar^{n-1}[/tex]
-196608=-3 X [tex]4^{n-1}[/tex]
[tex]4^{n-1}=\frac{-196608}{-3} =65536\\4^{n-1}=4^8[/tex]
Since the bases are the same, the powers are equal
n-1=8
n=8+1=9
Therefore the Sum of the geometric series
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] (This form is used because r>1)
[tex]S_n=\dfrac{-3(4^{9}-1)}{4-1}[/tex]
[tex]S_n=\dfrac{-3(262144-1)}{3}=\dfrac{-3(262143)}{3}=-262143[/tex]
#2 math help needed
Answer:
Step-by-step explanation:
False. Asymptotes are the walls that the function can't get over. This wall has no gaps or holes, nor does it have a gate. The function has to stay on one side of the asymptote in order for it to be a legit asymptote. Since our function is both above and below the dotted line, the dotted line is not an asymptote.
Horace is a professional hair stylist. Let CCC represent the number of child haircuts and AAA represent the number of adult haircuts that Horace can give within 777 hours. 0.75C+1.25A \leq 70.75C+1.25A≤70, point, 75, C, plus, 1, point, 25, A, is less than or equal to, 7 Horace gave 555 child haircuts. How many adult haircuts at most can he give with the remaining time? Choose 1 answer:
Answer:
At most 2 adult haircuts
Step-by-step explanation:
The equation given is:
[tex]0.75C+1.25A \leq 70[/tex]
This equation dictates the number of haircuts Horace gives in 7 hours.
Horace gave 5 child haircuts (C=5). So, that would make the equation:
[tex]0.75C+1.25A \leq 7\\0.75(5)+1.25A \leq 7\\3.75+1.25A \leq 7\\1.25A \leq 7 - 3.75\\1.25A \leq 3.25\\A \leq \frac{3.25}{1.25}\\A \leq 2.6[/tex]
This means Horace can give LESS THAN or EQUAL to 2.6 haircuts.
2.6 haircuts doesn't make sense, so the maximum would be "2" haircuts.
Atmost 2 adult haircuts
PLEASE HELP...
Write a simplified polynomial expression in standard form to represent the area of the rectangle below:
A picture of a rectangle is shown with one side labeled as 2 x minus 2 and another side labeled as x plus 4.
2x2 + 3x − 20
2x2 + 13x − 1
2x2 + 13x − 20
2x2 + 3x − 1
The area of the given rectangle is of the standard form option 1.[tex]2x^{2} + 3x - 20[/tex].
Step-by-step explanation:
Step 1:
The parameters needed to determine the area of a rectangle are the base length and the width.
The base length of this rectangle is [tex]2x-5[/tex] units while its width is [tex]x+4[/tex] units.
The area of a rectangle is determined by multiplying the base length with the width.
Step 2:
The area of the rectangle [tex]= (length)(width).[/tex]
Here length is [tex]2x-5[/tex] units and the width is [tex]x+4[/tex] units.
The area of the rectangle[tex]= (2x-5)(x+4) = 2x^{2} + 8x -5x-20 = 2x^{2} + 3x - 20.[/tex]
So the area of the given rectangle is of the standard form [tex]2x^{2} + 3x - 20[/tex] which is the first option.
To find the area of the rectangle, we need to multiply the expressions for the lengths of its sides. The sides are given as [tex]\(2x - 2\) and \(x + 4\).[/tex]
First, write the expressions for the sides of the rectangle:
- One side is[tex]\(2x - 2\)[/tex]
- The other side is[tex]\(x + 4\)[/tex]
To find the area, multiply these two expressions:
[tex]\[(2x - 2)(x + 4)\][/tex]
Use the distributive property (also known as the FOIL method for binomials) to expand this product:
[tex]\[(2x - 2)(x + 4) = 2x(x) + 2x(4) - 2(x) - 2(4)\][/tex]
Simplify each term:
[tex]\[= 2x^2 + 8x - 2x - 8\][/tex]
Combine like terms:
[tex]\[= 2x^2 + 6x - 8\][/tex]
So, the polynomial expression in standard form representing the area of the rectangle is:
[tex]\[2x^2 + 6x - 8\][/tex]
Given the options:
- 2x^2 + 3x − 20
- 2x^2 + 13x − 1
- 2x^2 + 13x − 20
- 2x^2 + 3x − 1
None of these options exactly match our result of [tex]\(2x^2 + 6x - 8\),[/tex] indicating a potential error in the problem statement or options provided. The correct simplified polynomial expression for the area, based on the given side lengths, is[tex]\(2x^2 + 6x - 8\).[/tex]
Identify the sample chosen for the study. The number of hours a group of 12 children in Mrs. Smith's kindergarten class sleep in a day. Answer2 Points The 12 children selected in Mrs. Smith's kindergarten class. All children in Mrs. Smith's kindergarten class. The number of hours children sleep.
Answer:
The 12 children selected in Mrs. Smith's kindergarten class.
Step-by-step explanation:
In this case, the population studied are all children in Mrs Smith's kindergarten class, the sample chosen for the study are the 12 children selected in Mrs. Smith's kindergarten class, and the analyzed variable is the number of hours children sleep.
Therefore, since the question asks for the sample, the answer is The 12 children selected in Mrs. Smith's kindergarten class.
DONT SKIP PLZ HELP IM DESPERATE
Answer:
C
Step-by-step explanation:
The slope = rise over run
If you count the blocks, you'll see it goes down 5 for every 6 to the right it goes.
There are about 320 million residents on the United States if 38% of them live in the south,estimate how many live in other areas of the United States?
Answer:
198,400,000
Step-by-step explanation:
Total Approximate Number of Residents in the United States = 320 million
38 per cent of the total number of residents live in the South
That means, as a percentage, 100%-38%=62% live in other areas of the Unjted States.
[tex]62 \% of 320 million[/tex] = [tex]\frac{62}{100}X320000000[/tex]=198,400,000.
Therefore a total of about 198,400,000 live in other areas of the United States.
CAN I GET SOME HELP AND NOT SKIPPED?
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-2, 2) and point (4, 4) rounded to the nearest tenth?
1 unit
5.7 units
4 units
6.3 units
Answer:
The last one: 6.3 units.
Answer: 6.3 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 4
x1 = - 2
y2 = 4
y1 = 2
Therefore,
Distance = √(4 - - 2)² + (4 - 2)²
Distance = √6² + 2² = √36 + 4 = √40
Distance = 6.3 units
Graph the relation. Is the relation a function? Why or why not?
{(–1, 1), (–2, 1), (–2, 2), (0, 2)}
No; a range value has two domain values.
Yes; there is only one range value for each domain value.
No; a domain value has two range values.
Yes; there is only one domain value for each range value.
Answer:
No; a range value has two domain values.
Step-by-step explanation:
Output has to be unique for all inputs.
Output for -2 is not unique
Answer:
No; a range value has two domain values
Step-by-step explanation:
The volume v of any cube with a side length s can be deermind using the formula v=s^3 what is the volume in the cubic cenitermeters of a cube with a side length of 2.3 cenimeters
Answer:
12.167[tex]cm^3[/tex]
Step-by-step explanation:
The volume of any solid shape is the quantity or capacity it can contain. For example, if you have a closed tin of milf that is filled to the brim, the volume of the tin is the quantity of milk that is in the tin.
Given any cube with side length s, the Volume V=[tex]s^3[/tex]
If the cube has a side length of 2.3 centimeters
Volume=[tex]s^3[/tex]= s X s X s = 2.3 X 2.3 X 2.3=12.167[tex]cm^3[/tex]
Volume of the Cube = 12.167[tex]cm^3[/tex]
Answer: 12.167 cubic centimeters
Step-by-step explanation:
If sample variance is computed by dividing SS by n, then the average value of the sample variances from all the possible random samples will be _______ the population variance.
Answer:
Less than
Step-by-step explanation:
Sample variance is computed by dividing the Sum of Squares (SS) by the number of samples (n).
Population variance is computed by dividing the Sum of Squares (SS) by the difference between the number of samples and 1 (n-1).
After computing, it would be found that the sample variance is less than the population variance.
The average of sample variances, computed by dividing the Sum of Squares by sample size (n) from all possible samples, will be less than the population variance.
Explanation:If sample variance is computed by dividing Sum of Square (SS) by sample size (n), then the average value of the sample variances from all possible random samples would be biased. In fact, it will be less than the actual population variance. This is commonly known as Bessel's correction in statistics. For an unbiased estimate of the population variance, we should rather divide the SS by degrees of freedom (n-1), not by the sample size n. So, when you average the sample variances, obtained by dividing by n from all possible samples, the result will be less than the population variance.
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Please help dont skip
What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?
4.1 units
17 units
4.6 units
1.4 units
Answer:
1.4 units
Step-by-step explanation:
Which equation is the inverse of y = 9x2 – 4? y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds
The inverse of the equation y = 9x² − 4 is found by switching x and y and solving the equation for the new y. The correct inverse function after simplification is y = ±√(x / 9 + 4).
Explanation:To find the inverse of the equation y = 9x2 − 4, you need to switch the roles of x and y and then solve for y once again. Here is a step-by-step explanation:
Replace y with x and x with y to get x = 9y2 − 4.Add 4 to both sides to isolate the perfect square term: x + 4 = 9y2.Divide both sides by 9 to get (x + 4) / 9 = y2.Take the square root of both sides note that there are always two solutions when taking a square root, a positive and a negative: y = ±√((x + 4) / 9).Finally, simplify to express y: y = ±√(x / 9 + 4/9).Comparing the result with the choices given, we find that y = ±√(x / 9 + 4) is the correct inverse function.
Margie needs to know the square footage for the first floor of the condo her client wants to make an offer on. The kitchen is 10 feet by 15 feet, the living/dining combo is 20 feet by 25 feet, and the office and sunroom are each 10 feet by 10 feet. What’s the total square footage?
Answer: the total square footage is
850 ft³
Step-by-step explanation:
The kitchen is 10 feet by 15 feet. This means that the volume of the kitchen would be
10 × 15 = 150 ft³
The living/dining combo is 20 feet by 25 feet. This means that the volume of the living/dining combo would be
20 × 25 = 500 ft³
The office and sunroom are each 10 feet by 10 feet. This means that the volume of the office would be
10 × 10 = 100 ft³
Also, the volume of the sunroom would be
10 × 10 = 100 ft³
Therefore, the total square footage is
150 + 500 + 100 + 100 = 850 ft³
Quiz 2 Problem The double number line shows that 444 bottles of water cost 101010 dollars at a music festival. Based on the ratio shown in the double number line, how much does 333 bottles of water cost? dollars Report a problem
Answer:
Cost of 3 bottles will be $7.5.
Step-by-step explanation:
Given:
According to double number line.
Cost of 4 bottles = $10
Based on this we need to find the cost of 3 bottles of water.
Solution:
Now we know that;
4 bottles = $10
1 bottle = Cost of 1 bottle
By using Unitary method we get;
Cost of 1 bottle = [tex]\frac{10}{4}=\$2.5[/tex]
So we can say that;
Cost of n bottles = [tex]\$2.5n[/tex]
Cost of 3 bottles = [tex]\$2.5\times 3 = \$7.5[/tex]
Hence Cost of 3 bottles will be $7.5.
Now we have drawn the double number line.
Bottom line(Line 1) will be number of bottles:
1 2 3 4 5 6
Top line (Line 2) will be the cost of corresponding bottles:
2.5 5 7.5 10 12.5 15
Answer:
$7.5 Dollars
Step-by-step explanation:
The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50.
Now, to find the cost of 3 water-bottles, we have to multiply.
$2.50 * 3 = $7.50.
So, the answer to this question is 3 bottles = $7.50
(Hope this helps!)
Use the polygon tool to draw a rectangle with a length of 4 units and a height of 2 units one of the sides of the rectangle falls on like ef and the rectangle had a vertex of e each segment on the grid represents 1 unit
Answer:
Step-by-step explanation:
Please find the attached photo for your reference how to draw the rectangle.
1. From on point E and draw a segment 2 units long because the height is 2 units and be vertical.
2. Draw horizontally a line 4 units long (the length) to the right
3. Draw a line upwards 2 units long, at that point it must be at the same height than point E.
4. Draw a 4-units line to the left, and you will be back on point E, the rectangle done.
Answer:
Over here
Step-by-step explanation:
According to a study published by a group of University of Massachusetts sociologists, approximately 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems. Find the probability that among the next 8 users from this state who are interviewed, (a) exactly 3 began taking Valium for psychological problems;(b) at least 5 began taking Valium for problems that were not psychological.
Answer:
(a) 0.124
(b) 0.174
Step-by-step explanation:
We are given that 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems.
The Binomial distribution probability is given by;
P(X = r) = [tex]\binom{n}{r}p^{r}(1-p)^{n-r}[/tex] for x = 0,1,2,3,.......
Here, n = number of trials(samples) which is 8 in our case
r = no. of success
p = probability of success which is probability of users who take
Valium for psychological problems of 0.60 in our case
(a) Let X = users taking Valium for psychological problems
So, P(X = 3) = [tex]\binom{8}{3}0.6^{3}(1-0.6)^{8-3}[/tex]
= [tex]56 * 0.6^{3}*0.4^{5}[/tex] = 0.124
(b) Since, it is given that 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems which means 40% of the Valium users in the state of Massachusetts take Valium for problems which are not psychological.
i.e., in this case p = 0.40
So, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
= [tex]\binom{8}{5}0.4^{5}(1-0.4)^{8-5} + \binom{8}{6}0.4^{6}(1-0.4)^{8-6} + \binom{8}{7}0.4^{7}(1-0.4)^{8-7} + \binom{8}{8}0.4^{8}(1-0.4)^{8-8}[/tex]
= [tex]56 * 0.4^{5} * (0.6)^{3} + 28 * 0.4^{6} * (0.6)^{2} + 8 * 0.4^{7} * (0.6)^{1} + 1 * 0.4^{8}[/tex]
= 0.174
Using the binomial probability formula, we can determine the probabilities requested in the question. For example, the probability that exactly 3 of the next 8 users began taking Valium for psychological problems is computed using the formula for binomial probability with n=8, k=3, and p=0.60, and the probability that at least 5 began taking Valium for other reasons is computed analogously with p=0.40.
Explanation:This question relates to the concepts of binomial probability and combinatorics. It asks about the probability that certain conditions are met among a specific set of Valium users.
First, to find the probability that exactly 3 of the next 8 users began taking Valium for psychological problems, we would use the formula for binomial probability: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). Here, n=8 (the total number of trials), k=3 (the number of successful trials we're looking for), and p=0.60 (the probability of a single successful trial).
Calculating, we get P(X=3) = C(8, 3) * (0.60^3) * ((1-0.60)^(8-3))
For the second part of the question, we want to find the probability that at least 5 out of the 8 users began taking Valium for reasons other than psychological issues. This is equivalent to 1 - the probability that 4 or fewer of the 8 users took it for non-psychological reasons.
The same binomial probability formula can be used, with n=8, p=0.40 (since the probability of a single user taking Valium for non-psychological reasons is 1 - 0.60 = 0.40), and k taking values from 0 to 4. The probabilities are computed for each k and then summed. The result is then subtracted from 1 to get our desired probability, given by: P(X>=5) = 1 - Σ [P(X=k) from k=0 to 4]
Learn more about Binomial Probability here:https://brainly.com/question/33993983
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A particle is moving horizontally along the x-axis. Its position (in ft) is: s(t)=t^3-18t^2+33t+14 where t is in sec.
Find the time at which the particle switches from moving left to moving right.
t= ___ sec.
Answer:
t=11 sec
Step-by-step explanation:
The position of the particle moving along the x-axis is given by:
[tex]s(t) = {t}^{3} - 18 {t}^{2} + 33t + 14[/tex]
The velocity is given by:
[tex]s'(t) = 3 {t}^{2} - 36{t} + 33[/tex]
If s'(t)>0 then the particle is moving right.
[tex]3 {t}^{2} - 36{t} + 33 \: > \: 0 \\ {t}^{2} - 12{t} + 11\: > \: 0[/tex]
[tex] \implies \: t \: < \: 1 \: or \: t \: > \: 11[/tex]
This means that the particle is moving left when
[tex]1 \: < \: t \: < \: 11[/tex]
The particle changes direction at time t=1 or t=11
Assume the supply curve shifts to the right by a given amount at each price. The price in the market will decline the most if demand is more price-_____ and supply is more price-_____. elastic; elastic inelastic; elastic elastic; inelastic inelastic; inelastic
Answer: c. price inelastic and supply is more price-inelastic.
Step-by-step explanation:
Inelastic price describes the consumers static habit of purchasing irrespective of the rise or fall in price.
Supply inelastic : This is a sitiuation when percentage change in supply is less than a percentage change in price.
PLLLZ HELP Find the coefficient of the indicated term in each expansion. (2x – y)4, x2y2 term
4
24
48
12
Coefficient of [tex]x^2y^2[/tex] = 24
Solution:
Given that:
[tex](2x - y)^4[/tex]
We have to find the coefficient of [tex]x^2y^2[/tex] term
Use the following algebraic formula
[tex](a-b)^4 = a^4 - 4a^3b+6a^2b^2-4ab^3+b^4[/tex]
From given,
[tex](2x - y)^4[/tex]
Where,
a = 2x
b = y
Therefore, by using formula, we get,
[tex](2x - y)^4 = (2x)^4 - 4(2x)^3(y) + 6(2x)^2(y)^2 - 4(2x)(y)^3 + y^4\\\\Simplify\\\\(2x - y)^4 = 16x^4 - 32x^3y + 24x^2y^2-8xy^3 + y^4[/tex]
Find the coefficient of [tex]x^2y^2[/tex]
From above simplified expression,
coefficient of [tex]x^2y^2[/tex] = 24
Answer:
24
Step-by-step explanation: