Work Shown:
(9^x)/(3^y)
( (3^2)^x )/(3^y)
( 3^(2x) )/( 3^y )
3^(2x-y)
3^2 .... use the equation 2x-y = 2
9
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
-----------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
-----------------
The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
-----------------
The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
which terms are like terms in the following expression ? 6x + 8xy - 3x + 9y + 4x^2
Answer:
[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]
Step-by-step explanation:
Like terms have identical variables and exponents, the coefficients don’t have to be the same.
The like terms from the expression are 6x and -3x.
Step-by-step explanation:
Hey, there!!
6x and -3x are like terms.
Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"
6x and -3x has "x" common in them so, The answer is 6x and -3x.
Hope it helps..
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results:
Analysis of Variance
Source df SS MS F P
Factor 3 28.17 9.39 5.37 0.010
Error 15 26.26 1.75
Total 18 54.43
A) Reject H0 if F >
B) For the 0.05 level of significance, is there a difference in the mean difference in the mean number of months before a raise was anted among the four CPA firms?
Answer:
A) Reject H0 if F > 5.417
B) we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
Step-by-step explanation:
A) From the table, we can see that we have df1 = 3 and df2 = 15. And we are given a significance level of α = 0.01
We are also given f-value of 1.75
Thus,from the f-distribution table attached at significance level of α = 0.01 and df1 = 3 and df2 = 15, we have;
F-critical = 5.417
Normally, we reject H0 if F > 5.417
But in this case, F is 1.75 < 5.417 and so we conclude that we do not reject H0 at the 0.01 level of significance
B) for 0.05 level of significance, df1 = 3 and df2 = 15, from the 2nd table attached, we have;
F-critical = 3.2874
Again the f-value is less than this critical one.
Thus, we fail to reject the null hypothesis and conclude that we do not have sufficient evidence at 0.05 level of significance to support the claim that there is a difference in the mean number of months before a raise was granted among the four CPA firms
Ae
A Man travels distance
84km in Ihr 20mins. Find
His speed average find-
Answer:
1.05km/min
Step-by-step explanation:
[tex]Distance = 84 km\\\\Time = 1hr 20 min= 80minuttes\\\\Average \: Speed = \frac{Distance}{Time} \\\\A.S =\frac{84}{80} \\\\A.S = 1.05km/min[/tex]
we, know that
➺ Average Speed = Total Distance/Total Time taken
where,
Total Distance = 84km = 84000mTotal time = 1hr20mins = 4800sec♛ Substituting these values ♛
◗Average Speed = Distance/Time
◗Average Speed = 84000/4800
◗Average Speed = 840/48
◗Average Speed = 70/4
◗Average Speed = 17.5m/s
Hence, Average Speed of the man is 17.5m/sWhich is the simplified form of (StartFraction 2 a b Over a Superscript negative 5 Baseline b squared EndFraction) Superscript negative 3? Assume a not-equals 0, b not-equals 0. StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction StartFraction a Superscript 6 Baseline Over 4 b EndFraction StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction
Answer:
[tex]\dfrac{b^3}{8a^{18}}[/tex] matches the first choice
Step-by-step explanation:
[tex]\left(\dfrac{2 a b}{a^{-5}b^2}\right)^{-3}=(2a^{1-(-5)}b^{1-2})^{-3}=(2a^6b^{-1})^{-3}\\\\=2^{-3}a^{6(-3)}b^{-1(-3)}=8^{-1}a^{-18}b^3=\boxed{\dfrac{b^3}{8a^{18}}}[/tex]
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
Answer:
A
Step-by-step explanation:
just took the pretest! good luck!
A chicken soup recipe calls for 13 cups of chicken stock how much is this in quarts
Answer:
3.25 US Quarts
Step-by-step explanation:
how to write this in number form The difference of 9 and the square of a number
Answer:
9-x^2
Step-by-step explanation:
The difference of means subtracting. the first number is 9 and the second is x^2, so you get 9-x^2
Which ordered pair is a solution to the following linear system? y = x y = –x
Answer:
(2,2) (-1,-1)
Step-by-step explanation
i think this is there answer im sorry if im wrong
identify(describe) each part of the ellipse as labeled by a letter
Answer: see below
Step-by-step explanation:
A) y has the smaller radius so this is the Minor Axis
B) y has the smaller radius so these are the CoVertices
C) x has the bigger radius so these are the Vertices
D) This is the Center of the ellipse.
F & G) These are the Foci (plural for Focus)
H) x has the bigger radius so this is the Major Axis
Find the zeros of the quadratic function f(x) = 1/2(x- 7)^2 – 8
Answer:
x = 11 or 3
Step-by-step explanation:
f(x) = (1/2)(x- 7)² – 8
to find the zeros, we equate f(x) = 0
f(x) = 0
(1/2)(x- 7)² – 8 = 0 (add 8 to both sides)
(1/2)(x- 7)² = 8 (multiply both sides by 2)
(x- 7)² = (8)(2)
(x- 7)² = 16
x-7 = ±√16
x-7 = ±4
hence,
x - 7 = 4
x = 4 + 7
x = 11
or
x - 7 = -4
x = -4 +7
x = 3
Answer:
x = 11 or 3
Step-by-step explanation:
I confirmed the answer in grandpoint.
What is the most precise name for quadrilateral ABCD with vertices A(–5,2), B(–3, 5),C(4, 5),and D(2, 2)?
Answer: ABCD is a parallelogram.
Step-by-step explanation:
First we plot these point on a graph as given in attachment.
From the attachment we can observe that AD || BC || x-axis .
also, AB ||CD, that will make ABCD a parallelogram , but to confirm we check the property of parallelogram "diagonals bisect each other" , i.e . "Mid point of both diagonals are equal".
Mid point of AC= [tex](\dfrac{-5+4}{2},\dfrac{2+5}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]
Mid point of BD= [tex](\dfrac{-3+2}{2},\dfrac{5+2}{2})=(\dfrac{-1}{2},\dfrac{7}{2})[/tex]
Thus, Mid point of AC=Mid point of BD
i.e. diagonals bisect each other.
That means ABCD is a parallelogram.
Answer: ABCD is a parallelogram.
Step-by-step explanation:
First, we plot these points on a graph as given in the attachment. From the attachment, we can observe that AD || BC || x-axis. Also, AB ||CD, which will make ABCD a parallelogram, but to confirm, we check the parallelogram property "diagonals bisect each other," i.e., "Midpoint of both diagonals is equal."
The midpoint of AC=. The midpoint of BD=. Thus, the Midpoint of AC=Mid point of BD diagonals bisects each other. That means ABCD is a parallelogram.
expanded notation 13.62
Answer:
thirteen point six two
Describe the transformation from triangle DEF to triangle D′E′F′ in the figure. Question 17 options:
A) Transformation down 8 units and right 6 units
B) Rotation 90° counterclockwise about the origin
C) Reflection about the origin
D) Rotation 90° clockwise about the origin
Answer:
C) Reflection about the origin
Step-by-step explanation:
DE points to the right and slightly down. D'E' points to the left and slightly up. The segments are parallel, not perpendicular, so represent a rotation of 180°, not 90°. If the figure were subject only to translation, these segments would point in the same direction.
The transformation is a reflection about the origin (C). (This is equivalent to a rotation of 180°.)
You are certain to get a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusiv
Answer:
If something is guaranteed, it has a probability of 100%, or 1.
Step-by-step explanation:
A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)
Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.
What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.
So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled
The probability of getting a red card is 1.
No matter how you shuffle the cards, the no of cards will remain the same.
Therefore, it will not affect the probability.
What is probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
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Does anyone know how to find the area of this problem?
Answer:
Step-by-step explanation:
2x2=4 4x1=4
Answer:
7units²
Step-by-step explanation:
I cut the shape into smaller shapes, found the area of each smaller shape, then added those areas together to find the total area for the whole shape :)
PLEASE PLEASE PLEASE HELP ME ANSWER THIS QUESTION QUICK!! The picture of the question is down below.
Answer:
1. 2 -- x-axis represents time, each vertical line represents 2 hours. (8 lines, 16 hours total)
2. 10 --- y-axis represents number of customers. (5 lines, 52 customers total. points go just above 5th line)
hope this helps :)
michaela has h hair ties. michaela's sister has triple the number of hair ties that michaela has. choose the expression that shows how many hair bows michaela's sister has
Answer:
[tex]S = 3 h[/tex]
Step-by-step explanation:
Let M represent Michaela hair tier and S represents Michaela sister's
Given
M = h
S = Triple of M
Required
Determine an expression for S
From the given parameters, we have that;
S = Triple of M
Mathematically, this implies;
[tex]S = 3 * M[/tex]
Substitute h for M
[tex]S = 3 * h[/tex]
[tex]S = 3 h[/tex]
Hence, the expression for Michaela sister' is [tex]S = 3 h[/tex]
Three guests check into a hotel room. The manager says the bill is $30, so each guest pays $10. Later the manager realizes the bill should only have been $25. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests.
On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. As the guests aren't aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.
As each guest got $1 back, each guest only paid $9, bringing the total paid to $27. The bellhop kept $2, which when added to the $27, comes to $29. So if the guests originally handed over $30, what happened to the remaining $1?
Answer:
the manager has it
Step-by-step explanation:
this sounds more like a riddle than a math question
Answer:
This was so confusing and I had to use like 3 sheets of paper
Step-by-step explanation:
$25 + $2 + $1 + $1 + $1 = $30.
So the manager has it, the point is to change the numbers so your brain gets confused.
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n
Complete Question
Determine whether the normal sampling distribution can be used. The claim is p < 0.015 and the sample size is n=150
Answer:
Normal sampling distribution can not be used
Step-by-step explanation:
From the question we are told that
The null hypothesis is [tex]H_o : p = 0.015[/tex]
The alternative hypothesis is [tex]H_a : p < 0.015[/tex]
The sample size is n= 150
Generally in order to use normal sampling distribution
The value [tex]np \ge 5[/tex]
So
[tex]np = 0.015 * 150[/tex]
[tex]np = 2.25[/tex]
Given that [tex]np < 5[/tex] normal sampling distribution can not be used
Based on the normal sampling assumption, the product of the sample size and the proportion must be greater than or equal to 5. Hence, since, the condition isn't met, then the normal sampling cannot be used.
Given the Parameters :
Proportion, p = 0.015Sample size, n = 150Test if np ≥ 5 :
(150 × 0.015) = 2.252.25 < 5
Hence, np < 5 ;
Hence, the normal sampling distribution cannot be used.
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What is the domain of f(x)=2/5x+6
Answer:
Look at that picture
Step-by-step explanation:
Without using technology, describe the end behavior of f(x) = −3x4 + 7x2 − 12x + 13.
Answer:
11 over 13
Step-by-step explanation:
first, you deal with multiplication;
x = -12 + 14 - 12x + 13
second, deal with addition;
x = -2 - 12x + 13
third, take -12 to the other side then the negative changes to positive;
12x + x = -2 + 13
fourth, add them then simplify;
13x = 11
ans is 11 over 13
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste?
A. none of these
B. Let “1,2,3” represent preferring the toothpaste and “0,4,5,6,7,8,9” represent not recommending the toothpaste.
C. Let “1,2,3” represent preferring the toothpaste and “4,5,6,7,8,9” represent not recommending the toothpaste.
D. Let “0,1,2” represent preferring the toothpaste and “3,4,5,6,7,8” represent not recommending the toothpaste.
Reset Selection
Answer:
b
Step-by-step explanation:
only b has 10 didgets. it could be a since the didgets aren't very random, but then again, i think it's b
Let favorable event“1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
Three out of every ten dentists recommend a certain brand of fluoride toothpaste. Which assignment of random digits would be used to simulate the random sampling of dentists who prefer this fluoride toothpaste to determine.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
While going throughout the option in options C and D number so the sample is not equal to 10 so both the statement is false. Option B is the correct option because the sample space is also equal to 10 and the number of the favorable events is also 3 which is mentioned in the question.
Thus, let favorable event “1,2,3” represent preferring the toothpaste and sample space “0,4,5,6,7,8,9” represent not recommending the toothpaste. Option B is correct.
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Which option is correct and how would one solve for it?
Answer:
-3/5, -1, -5/3, -3, -7
Step-by-step explanation:
Let x go from 1 to 5
x =1 (1+2)/(1-6) = 3/-5 = -3/5
x =2 (2+2)/(2-6) = 4/-4 = -1
x =3 (3+2)/(3-6) = 5/-3 = -5/3
x =4 (4+2)/(4-6) = 6/-2 = -3
x =5 (5+2)/(5-6) = 7/-1 = -7
(2²)³+(2³)²/4
Simplificar
━━━━━━━☆☆━━━━━━━
▹ Answer
80
▹ Step-by-Step Explanation
(2²)³ + (2³)² ÷ 4
Rewrite:
2⁶ + 2⁶ ÷ 2²
Divide:
2⁶ + 2⁴
Factor:
(2² + 1) * 2⁴
Evaluate:
(4 + 1) * 2⁴
Calculate:
5 * 16
= 80
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Please answer my question
Step-by-step explanation:
The inequality shows by line is
i) 1<=x<=6
OR,
x is an positive integer.
A researcher would like to test the claim that the mean lung capacity of middle-aged smokers is less than the mean lung capacity of senior citizen nonsmokers. Independent random samples of 34 middle-aged smokers and 34 senior citizen nonsmokers will be used in a hypothesis test of this claim, and it is believed that the standard deviations of the lung capacities in the populations of middle-aged smokers and senior citizen nonsmokers are the same. Which test statistic formula should be used for this test
Answer:
The respiratory system extends from the nose and upper airway to the alveolar surface of the lungs, where gas exchange occurs. Inhaled tobacco smoke moves from the mouth through the upper airway, ultimately reaching the alveoli. As the smoke moves more deeply into the respiratory tract, more soluble gases are adsorbed and particles are deposited in the airways and alveoli. The substantial doses of carcinogens and toxins delivered to these sites place smokers at risk for malignant and nonmalignant diseases involving all components of the respiratory tract including the mouth.
The Triangle shown below has an area of 12 Units^2.
Find X
10
6
Answer:
4
Step-by-step explanation:
I got it right on Khan
The value of x is 4.
What is Triangle?A triangle is a polygon in two dimensional geometry. I has three sides and three angles along with three vertices.
Area of a triangle = [tex]\frac{1}{2}[/tex] × b × h
where b is the base of the triangle and h is the length of height of the triangle.
The given triangle is an obtuse triangle which has an angle equal to greater than 90 degrees. So the height of the triangle is found by drawing a perpendicular line from the base to the opposite vertex.
Here, height = x and base length = 6
Area = 12 units²
[tex]\frac{1}{2}[/tex] × 6 × h = 12
6 × h = 12 × 2
6 × h = 24
h = 24/6
h = 4 units.
Hence the length of the height which is x is 4 units.
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Find s. Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.
Answer:
s is [tex]s =15.3[/tex]
Step-by-step explanation:
From the question we are told that
The data is
Generally the mean is evaluated as
[tex]\= x = \frac{84+ 85+ 83+ 63+ 61+100+ 98}{7}[/tex]
[tex]\= x = 82[/tex]
The standard deviation is mathematically represented as
[tex]s = \frac{\sum (x- \= x)^2}{n-1}[/tex]
[tex]s =\sqrt{ \frac{ (84-82)^2+ (85-82)^2 +( 83-82 )^2 +(63-82) ^2 + ( 61-82)^2,+ (100-82)^2 + (98-82)^2}{7-1}}[/tex]
[tex]s =15.3[/tex]
logx - logx-1^2=2log(x-1)
Answer:
x is approximately 2.220744
Step-by-step explanation:
This can be simplified a little using properties of logarithms, and then solve it by graphing:
[tex]log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)[/tex]
So we use a graphing tool to find the intersection point of the graph of [tex]log(x)[/tex], and the graph of [tex]4\,log(x-1)[/tex]
Please see attached image for the graph and solution.
The value of x is approximately 2.220744
Answer:
x = 2.32011574011
Step-by-step explanation:
The problem with your original equation is that it is a long way of saying ...
log(x) -log(x) -1 = 2log(x-1)
0 -1 = 2log(x-1)
which has the solution ...
-1/2 = log(x -1)
1/√10 = x -1
x = 1 + 1/√10 ≈ 1.3162278
__
We have asked for clarification, and what we got was ...
[tex]\log{(x)}-\log{(x-1^2)}=2\log{(x-1)}[/tex]
which, again, is a long way of saying ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
The other reasonable interpretation of your 'clarified' equation is ...
[tex]\log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}[/tex]
which you already have an answer to. You have declared that a "misconception."
So, we are left with the interpretation that the equation you want a solution to is ...
[tex]\log{(x)}-\log{(x-1)}=2\log{(x-1)}[/tex]
_____
When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...
[tex]f(x)=\log{(x)}-3\log{(x-1)}[/tex]
A graphing calculator shows that f(x) = 0 when ...
x ≈ 2.32011574011
__
If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).
Help please!!! Thank you
Answer:
B: 54
Step-by-step explanation:
for the first digit: 1 or 3 (2 choices)
for the second digit: 0, 1, or 3 (3 choices)
for the third digit: 0, 1, or 3 (3 choices)
for the forth digit: 0, 1, or 3 (3 choices)
2×3×3×3=54
Answer:
B) 54
Step-by-step explanation:
There are 3 numbers, but in the fourth positon (tens of thousands) if i put the zero no give value, then, in this position only have 2 options:
2*3*3*3 = 54
