Jack wants to pack three different colored shirts for a trip. If he has seven colors to choose from, how many different selections of shirts can he make
In the context of probability, an experiment is a process:
First, he has to decide on a pair of shirts and he has 7 different colors to choices.
A value between 0 and 1, inclusive, describes the relative possibility (chance or likelihood) that an event will occur.
For each of those choices he has a choice of 7 different shirts, so that gives him 3 times 7 = 21 different shirts.
For each of those 21 possibilities, he has 21 times 3 = 63 different outfits, and some of them may be acceptable to wear in public.
It is simply,3*3*7=64 ways.
The number of favorable outcomes is divided by the number of possible outcomes.
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Describe the transformations necessary to transform f(x) into g(x)
a) f(x)= √x; g(x)= √3x -1
b) f(x)=[tex]x^4[/tex]; g(x)= [tex]2(x-3)^4[/tex]
Using translation concepts, the transformations are given as follows:
a) The function is horizontally compressed by a factor of 3 and shifted down one unit.
b) The function is shifted right 3 units and vertically stretched by a factor of 2.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The transformations are:
x -> 3x, hence the function is horizontally compressed by a factor of 3.y -> y - 1, hence the function is shifted down one unit.Item b:
The transformations are:
x -> x - 3, hence the function is shifted right 3 units.y -> 2y, hence the function is vertically stretched by a factor of 2.More can be learned about translation concepts at https://brainly.com/question/4521517
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if 251 base x =100, find x
If [tex]251_x\equiv100_{10}[/tex], then this translates to the equation
[tex]251_x = 2x^2 + 5x + 1 = 100[/tex]
Solve for [tex]x[/tex].
[tex]2x^2 + 5x = 99[/tex]
[tex]2\left(x^2 + \dfrac52 x\right) = 99[/tex]
[tex]2 \left(x^2 + \dfrac52 x + \dfrac{25}{16}\right) - \dfrac{25}8 = 99[/tex]
[tex]2 \left(x + \dfrac54\right)^2 = \dfrac{817}8[/tex]
[tex]\left(x + \dfrac54\right)^2 = \dfrac{817}{16}[/tex]
[tex]x + \dfrac54 = \pm \dfrac{\sqrt{817}}4[/tex]
[tex]x = \dfrac{-5\pm\sqrt{817}}4[/tex]
though it is a bit unusual (but not entirely out of the question) to have an irrational base number system.
In case you meant [tex]100_2[/tex] on the right side, then [tex]100_2 = 2^2 = 4_{10}[/tex], so that
[tex]2x^2 + 5x + 1 = 4 \\\\ 2x^2 + 5x - 3 = 0 \\\\ (x+3) (2x-1) = 0 \\\\ x=-3 \text{ or } x = \dfrac12[/tex]
which at first glance seem like more reasonable choices of base.
He length of the hypotenuse of a right triangle is 24 inches. if the length of one leg is 8 inches, what is the approximate length of the other leg? 16.0 inches 18.4 inches 22.6 inches 25.3 inches
Answer:
22.6
Step-by-step explanation:
a^2 + b^2 = c^2 We know one of the legs and the hypotenuse. The hypotenuse must be c. The leg that we do know can be a or b. It is our choice. I am going to let it be a
8^2 + b^2 = 24^2 Plug in the numbers that I know
64 + b^2 = 576 Square the numbers that I know
b^2 = 512 Subtract 64 from both sides
b = 22.6 Put this in your calculator to find the square root and round.
Turn 12 ¾= to a decimal
Answer:
12.75
Step-by-step explanation:
Turn 12 ¾ = to a decimal
¾ = 0.75
12 + 0.75
12.75
4^x + 3 = 7 using the change of base formula log y =
log y/log b
Answer:
x=1
Step-by-step explanation:
It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:
log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3
4^x=4
log(4)4^x=log(4)4 (both logs are base 4 in this case to free the x)
x=log(4)4
x=log(10)4/log(10)4 (both logs are base 10 in this case)
x=1
Change base is definitely unnecessary in this problem
Check all that are Solutions are there inequality
The solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595
Number line is a arrangements of numbers on a straight line A number line has zero on its centerAll the numbers lie on the left-hand side of 0 are negative numbersAll the numbers lie on right-hand side of 0 are positive numbersWhen we move from left to right, the numbers are increasing When we move from right to left, the numbers are decreasingGiven the inequality is x>-2
Solution of the inequality is greater than -2
0, 4 2/5, 1.999, 347.595 are the solutions of given inequality.
Hence, the solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595
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help me please im in a rush
Answer: 390 m².
Step-by-step explanation:
[tex]Surface \ area = 11*13+11*12+11*5+2*\frac{12*5}{2}=11*(13+12)+11*5+12*5=\\ =11*25+5*(11+12)=275+5*23=275+115=390\ (m^2).[/tex]
What is the missing number in this sequence: 1 , 3, ___ , 10 , 15 , 21 ?
Please explain it step-by-step
Answer:
6
Step-by-step explanation:
the sequence increases by 1,2,3,4,5,6 each time, thus it is 6
The doubling period of a bacteria population is 10 minutes. At time t = 110 minutes, the bacterial population was 800.
What was the initial population at time t = 0? Round to the nearest whole number and give an un-rounded decimal.
Find the size of the bacteria population after 4 hours. Round to the nearest whole number and give an un-rounded decimal.
The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the bacteria population at time t. a represent the initial population at t = 0. Since the doubling period of a bacteria population is 10 minutes, hence:
[tex]y=a(2)^\frac{t}{10}[/tex]
At time t = 110 minutes, the bacterial population was 800. Hence:
[tex]800=a(2)^\frac{110}{10} \\\\a = 0.39[/tex]
At 4 hours (240 minutes):
[tex]y=0.39(2)^\frac{240}{10} =6553600[/tex]
The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600
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Which of the following completes the two-column proof below?
Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:
1. ∠1≅∠2 (Given)
2. p∥q (?)
3. p⊥r (?)
4. q⊥r (?)
The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
What is the Converse of Corresponding Angles Theorem?According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.
Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.
We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.
The missing reasons in the proof are:
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
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factorise fully
-x-10
The factorized expression of -x - 10 is -(x + 10)
How to factorize the expression?The expression is given as:
-x - 10
Factor out -1 from the expression
-1(x + 10)
Rewrite as:
-(x + 10)
Hence, the factorized expression of -x - 10 is -(x + 10)
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Each week, Adam deposits money into his savings account. The graph below models the scenario.
(Graph is in the image below)
A) How much money does Adam deposit each week?
B) How did you determine the answer?
C) Use an alternate strategy to determine the amount of money Adam deposits each week.
Adam's weekly money deposit is a linear relation with a slope of $6 per week.
A) Money deposited by Adam each week is $6.
B) The answer can be determined by observing the graph provided to us, in which the point representing 1 week on the x-axis is intersected by the point representing $6 on the y-axis. This helps us determine that Adam's weekly deposit is $6.
C) An alternative strategy of calculating the slope can be used.
The slope can be calculated in the following way:
m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
Thus slope of this line can be calculated as,
m = (12 - 6)/(2 - 1) = 6/1 = 6 {Since, the line passes through the points (2, 12) and (1, 6)}.
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Which of the following best describes a parabola?
A.The locus points equidistant from a given line of symmetry and focus.
B.The locus of points equidistant from two given points.
C.The locus of points equidistant from a given directrix and focus.
D.The locus of points equidistant from a center.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.
What is a Parabola?A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.
The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.
Therefore, The correct option is C.
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Please help ASAP
Please help ASAP
Please help ASAP
Using proportions, it is found that:
Unit price for the 11.3 ounce package: $0.33 per ounce.Unit price for the 29.3 ounce package: $0.31 per ounce.The 29.3 ounce package is the better deal.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The unit price is given by the cost divided by the number of ounces, and the better deal is given by the deal with the lowest unit price.
Hence, for the 11.3 ounce package:
u = 3.68/11.3 = $0.33 per ounce.
For the 29.3 ounce package:
u = 8.98/29.3 = $0.31 per ounce.
Due to the lower unit cost, the 29.3 ounce package is the better deal.
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Using the quadratic formula, solve for "t" in
the function: 0= -16t2 + 5t + 104. Keep in
mind that time CANNOT be "negative'!!!
t = 1.1 s
t = 1.9 s
t=2.71 s
t=2.2 s
Here is a prism.
Its face is made from 6 identical squares
with side length 2 cm.
Work out the volume of the prism.
Height 2cm
Width 12 cm
Answer:
The required volume of the prism is 48 cubic centimeters
Volume of a prism.The formula for calculating the volume of a prism is expressed as:
V = lwh
where l is the side length
w is the width
h is the height
Given the following
l = 2 cm.
Height 2cm
Width 12 cm
Substitute
V = 2(2)(12)
V = 48 cubic centimeters
Hence the required volume of the prism is 48 cubic centimeters
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In the figure below, ⎯⎯⎯⎯⎯⎯⎯⎯,⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯, and ⎯⎯⎯⎯⎯⎯⎯⎯⎯ are medians of △. If KC = 108 and OC = 2n+10, then n=
The question was incomplete. Below you will find the missing content.
In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=
The picture is attached below.
The value of n is 31.
The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.
The intersection of all 3 medians of the triangle is called the centroid.
As we know centroid divides the median in the ratio of 2:1.
In the given picture,
Medians of triangle △ABC are AM, BL, and CK.
So the centroid of the triangle is O.
Given that KC= 108
As the centroid O divides the line KC in 2:1.
Let OC=2x
KO= X
As KC= KO+OC
⇒ 108= x+2x
⇒ 3x=108
⇒ x=108/3
⇒ x=36
Then OC= 2x= 2*36= 72
As given in the question OC= 2n+10
putting the value of OC in above equation
⇒ 72= 2n+10
⇒ 2n= 72-10
⇒ 2n=62
⇒ n=62/2
⇒n=31
Therefore the value of n is 31.
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A trapezoid has bases measuring 5cm and 9cm, and an area of 42cm. Find the height
The height of the trapezoid is 6 cm
How to find the height?The given parameters are:
Bases = 5cm and 9cm
Area = 42 square cm
The height is calculated using
Area = 0.5 * (Sum of bases) * Height
So, we have:
42 = 0.5 * (5 + 9)* Height
This gives
42 = 7* Height
Divide through by 7
Height= 6
Hence, the height of the trapezoid is 6 cm
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Matthew thought he could make 19 free throws, but he only made 13. What was his percent error? Hint: Percent error = Prediction - Actual Actual x 100 Round to the nearest percent. [ ? 1% Matthew thought he could make 19 free throws , but he only made 13 . What was his percent error ? Hint : Percent error = Prediction - Actual Actual x 100 Round to the nearest percent . [ ? 1 %
Answer:
[tex]\huge\boxed{\sf 46.2\%}[/tex]
Step-by-step explanation:
Prediction = 19 throws
Actual = 13 throws
Percent Error:[tex]\displaystyle =\frac{Predication -Actual}{Actual} \times 100 \%\\\\= \frac{19-13}{13} \times 100 \%\\\\= \frac{6}{13} \times 100 \%\\\\= 0.462 \times 100 \%\\\\= 46.2\%\\\\\rule[225]{225}{2}[/tex]
Find the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2. a. r= 6/1+2 sin theta b. r= 6/1-2 sin theta c. r= 3/ 1- 2 cos theta d. r= 1/3+2 cos theta
The required polar equation of a conic is given be: [tex]r = \frac{6}{1-2sin\Theta }[/tex]. option b is correct.
For a conic we have directrix = 3 and eccentricity = 2
What is polar equation?Polar equation can be identified as of the form of x= a+b.sinФ.
Which contain simple variable along with trigonometric operators.
Here,
Standard polar equation for the conic is given as,
[tex]r=\frac{ep}{1-esin\theta}[/tex]
By putting given values
[tex]r = \frac{6}{1-2sin\Theta }[/tex].
Thus, the required polar equation for the conic is [tex]r = \frac{6}{1-2sin\Theta }[/tex].
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Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.
After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.
Cannot be determined from the information given.
False
True
Minerva's account balance will be about $100 , it is True and Option A is the correct answer.
What is meaning of Compounded annually ?Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.
It is given that
Principal Amount = $50
From the graph attached in the answer which was missing in the question ,
It can be confirmed that after 12 years
Minerva's account balance should be about $100.
Therefore it is True and Option A is the correct answer.
The graph missing is attached
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math!! please helpp!!!
What is the y intercept of the line below?
( i attached an image)
a) -3
b) 1/3
c) 4
d) (-1.5,0)
e) -1.5
f) (4,0)
g) 3
Answer:
f (4,0)
Step-by-step explanation:
Hope it helps!!!
y=4
x=0
⊱_______________________________________________________⊰
Answer:
4Step-by-step explanation:
[tex]\large\displaystyle\begin{gathered} \sf{The \ y-intercept \ is \ the \ point \ where \ the \ graph \ intercepts \ the \ y \ axis. \\ \sf{Thus, \ assuming \ that \ each \ little \ square \ represents \ one \ unit, \ the \ y-intercept} \\ \sf{is \ 4} \end{gathered}[/tex]
done !!
⊱_______________________________________________________⊰
CαlligɾαρhγFind the missing value.
Answer:
The correct answer is 6
Step-by-step explanation:
x/10=3/5
then cross multiply
it will now give
5x=30
x=6
For the following exercises, find the x- and y-intercepts of the graphs of each function.
28. f(x) = −2| x +1 | + 6
The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.
What are the x- and y-intercepts of the graph of the function?It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.
Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;
x -intercept is;
0 = -2(x+1) + 6
2x = -2 +6
2x = 4
x = 4/2 = 2
y-intercept is;
y = -2(0+1) +6
y = 4.
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Suppose a circle has a radius of 13 inches. How far would a 24 inch chord be from the center of the circle? (Hint: Draw a diagram)
PLEASE PLEASE HELPPPP
Answer:
24 Inches
Step-by-step explanation:
Its 24 Inches away from the centre lol
Answer:
Step-by-step explanation:
Directions
Draw a circleDear a chord with a length of 24 inside the circle. You just have to label it as 24Draw a radius that is perpendicular and a bisector through the chordDraw a radius that is from the center of the circle to one end of the chord.Label where the perpendicular radius to the chord intersect. Call it E.You should get something that looks like the diagram below. The only thing you have to do is put in the point E which is the midpoint of CB.Givens
AC = 13 inches Given
CB = 24 inches Given
CE = 12 inches Construction and property of a midpoint.
So what we have now is a right triangle (ACE) with the right angle at E.
What we seek is AE
Formula
AC^2 = CE^2 + AE^2
13^2 = 12^2 + AE^2
169 = 144 + AE^2 Subtract 144 from both sides.
169 - 144 = 144-144 + AE^2 Combine
25 = AE^2 Take the square root of both sides
√25 = √AE^2
5 = AE
Answer
The 24 inch chord is 5 inches from the center of the circle.
In the diagram, JKLM∼EFGH. Find the perimeter of each polygon.
The perimeter of polygon JKLM = 85 units
The perimeter of polygon EFGH = 34 units.
What is the Perimeter of a Polygon?The perimeter of polygon JKLM = JK + KL + LM + JM
The perimeter of polygon EFGH = EF + FG + GH + EH
Find the missing lengths using the similarity theorem:
JK/EF = KL/FG = LM/GH = JM/EH
Plug in the values
20/8 = KL/11 = LM/3 = 30/EH
20/8 = KL/11
KL = (20 × 11)/8 = 27.5
20/8 = LM/3
LM = (20 × 3)/8
LM = 7.5
20/8 = 30/EH
EH = (30 × 8)/20
EH = 12
The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units
The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.
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e
7 cm
Find the value of x to 3
significant figures.
x
12 cm
8 cm
Answer:
12.0 to 3 dig digs You must include the 0 to get 3 significant figures.
Step-by-step explanation:
Comment
This is a Pythagorean Problem. Use the formula
c ^2 = a^2 + b^2
Givens
a = 8 - 7 = 1 cm
b = 12 cm
c = ?
solution
c^2 = 1^2 + 12^2
c^2 = 1 + 144
c^2 = 145 Take the square root of both sides
√c^2 = √145
c = 12.04
c = 12.0 to 3 sig digs.
Write an algebraic expression for this statement.
A stick [tex]l[/tex] feet long is broken into two parts, one of which is twice as long as the other. How long is the shorter piece?
**Please Help, Respond soon....Will mark brainliest for correct answer**
The algebraic expression is 2/3(2y + y)
How to determine the expressionThe length of the 2/3 feet long
It is broken into two parts x and y
If x is twice the length of y, we have
x = 2y
The algebraic expression is 2/3/x + y , if x = 2y
We have that,
2/3(2y + y)
Thus, the algebraic expression is 2/3(2y + y)
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Please help me out i will mark you brainlest
The appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
What are the trig values?Given the equation and interval.
tanθ = -3, [ π/2 < θ < π ]
First, we use the definition of tangent to determine the known sides of the unit circle right triangle.
Note that; the quadrant determines the sign of each values.
tanθ = opposite / hypotenuse
We can use Pythagoras theorem to find the hypotenuse of the unit circle right triangle as the opposite and adjacent sides are known.
Hypotenuse = √( opposite² + adjacent² )
Hence, we have;
Hypotenuse = √( [3]² + [-1]² )
Hypotenuse = √( 9 + 1 )
Hypotenuse = √10
1) To find sinθ
sinθ = opposite / hypotenuse
sinθ = 3/√10
We simplify
sinθ = 3/√10 × √10/√10
sinθ = 3√10 / 10
[tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex]
2) cosθ
cosθ = adjacent / hypotenuse
cosθ = -1 / √10
Simplify
cosθ = -1 / √10 × √10/√10
cosθ = -√10 / 10
[tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex]
3) cotθ
cotθ = adjacent / opposite
cotθ = -1 / 3
[tex]cot\theta= -\frac{1}{3}[/tex]
4) secθ
secθ = hypotenuse / adjacent
secθ = √10 / -1
[tex]sec\theta=-\sqrt{10}[/tex]
5) cscθ
cscθ = hypotenuse / opposite
cscθ = √10 / 3
[tex]csc\theta= \frac{\sqrt{10} }{3}[/tex]
Therefore, the appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
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