Answer: 73.55%
Step-by-step explanation:
p = (100-a) e^-b(0.07)
we have a = 20 and b =1.2
= (100-20) e^-(1.2)(0.07)
= 80(e^-0.084)
= 80(0.919431)
= 73.55%
Answer:
The correct answer is 93.6%
Step-by-step explanation:
Got it right on Edge 2020
A scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours. How many hours will it take for the bacteria colony to decrease to 1000? Round your answer to the nearest tenth of an hour.
Answer:
3.3 hours.
Step-by-step explanation:
We have been given that a scientist is testing a new antibiotic by applying the antibiotic to a colony of 10,000 bacteria. The number of bacteria decreases by 75% every two hours.
Since number of bacteria is decreasing exponentially, so we will use exponential decay function.
[tex]y=a*b^x[/tex], where,
a= Initial value,
b = For decay b is in form (1-r), where r is rate in decimal form.
Let us convert our given rate in decimal form.
[tex]75\%=\frac{75}{100}=0.75[/tex]
As number of bacteria is decreasing every 2 hours, so number of bacteria decreased in 1 hour will be x/2.
Upon substituting our given values in above formula we will get,
[tex]y=10,000(1-0.75)^{\frac{x}{2}}[/tex]
To find the number of hours it will take to for the bacteria colony to decrease to 1000, we will substitute y = 1,000 in our equation.
[tex]1,000=10,000(0.25)^{\frac{x}{2}}[/tex]
Let us divide both sides of our equation by 10,000.
[tex]\frac{1,000}{10,000}=\frac{10,000(0.25)^{\frac{x}{2}}}{10,000}[/tex]
[tex]0.1=(0.25)^{\frac{x}{2}}[/tex]
Let us take natural log of both sides of our equation.
[tex]ln(0.1)=ln((0.25)^{\frac{x}{2}})[/tex]
[tex]ln(0.1)=\frac{x}{2}*ln(0.25)[/tex]
[tex]-2.302585=\frac{x}{2}*-1.386294[/tex]
[tex]x=\frac{-2.302585}{-1.386294}*2[/tex]
[tex]x=1.660964*2[/tex]
[tex]x=3.3219\approx 3.3[/tex]
Therefore, it will take 3.3 hours for the bacteria colony to decrease to 1000.
Final answer:
It will take 4 hours for the bacteria colony to decrease from 10,000 to 1,000, considering a 75% decrease every two hours.
Explanation:
To find out how many hours it will take for the bacteria colony to decrease from 10,000 to 1,000 with a 75% decrease every two hours, we can use the formula for exponential decay: [tex]N = N0(1 - r)^t[/tex], where N is the final amount, N0 is the initial amount, r is the rate of decrease (expressed as a decimal), and t is the time in units of the rate's period (in this case, every two hours).
Here, N0 = 10,000, N = 1,000, and r = 0.75. Plugging the values into the formula gives [tex]1,000 = 10,000(1 - 0.75)^t.[/tex]Simplifying, we find [tex](1 - 0.75)^t = 0.1.[/tex]
Solving for t, we find that t equals 2 cycles or 4 hours, because the bacteria population decreases by 75% every 2 hours, and it takes 2 cycles for the population to reach 1,000 from 10,000.
check my answer?
what are the real and imaginary parts of the complex number?
-7+8i
the real part :: -7 ( my answer )
the imaginary part :: 8i ( my answer )
Answer:
The real part is -7
The imaginary part 8i
Step-by-step explanation:
A complex number is in the from a +bi
The real part is a and the imaginary part is bi
-7+8i
The real part is -7
The imaginary part 8i
Math help!
What is the value of a?
Answer:
a = 8
Step-by-step explanation:
Put the given information into the function equation and solve for a.
f(x) = a/(x-h) +k . . . . for (h, k) = (4, 2) and (x, y) = (12, 3)
3 = a/(12 -4) +2 . . . . . . . givens substituted in
1 = a/8 . . . . . . subtract 2
8 = a . . . . . . . multiply by 8
What is the value of x?
5
6
2
-2
Answer:
x= -2
Step-by-step explanation:
The distance from one end of the line to the other is -3x-1.
Counting on the number line we count 6 units. Setting them equal we get
-3x-1 = 5
Add 1 to each side
-3x-1+1 = 5+1
-3x = 6
Divide each side by -3
-3x/-3 = 6/-3
x = -2
Which points lie on more than one plane? M and R A and S X and Y M and S
Answer:
Points X and Y lie on more than one plane.
Step-by-step explanation:
From the figure attached we have to find the points which lie on more than one plane.
M and R :
These are the points which lie on only one plane painted in yellow color.
A and S
These points lie on a plane perpendicular to the plane painted in yellow color.
X and Y :
These points lie on both the planes, painted in yellow color and the plane perpendicular to this.
M and S :
Point M lies on a plane in yellow color and point S lies on a plane perpendicular to the yellow plane.
Therefore, points X and Y lie on more than one plane.
Monday Janel and $16 for two hours of babysitting getting paid the same rate she earns $40 for babysitting on Saturday how many hours did you know babysit on Saturday
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $48.00 , how much will a 19 foot length with 3 inches diameter cost?
Answer:
$273.60
Step-by-step explanation:
The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing.
i.e [tex]C\propto L\cdot D[/tex]
i.e [tex]C=k\cdot L\cdot D[/tex]
A 5 foot or 60 inches length with diameter 2 inches costs $48.00, so
[tex]\Rightarrow 48=k\times 60\times 2[/tex]
[tex]\Rightarrow k=\dfrac{48}{60\times 2}=0.4[/tex]
Now the equation becomes,
[tex]C=0.4\cdot L\cdot D[/tex]
So the cost of a 19 foot or 228 inches length with 3 inches diameter is,
[tex]C=0.4\times 228\times 3=\$273.60[/tex]
Based on the polynomial remainder theorem, what is the value of the function when x=-5
f(x)=x^4+9x^3+17x^2-8x+50
Answer: 15
Step-by-step explanation:
Using synthetic division:
-5 | 1 9 17 -8 50
| ↓ -5 -20 15 -35
1 4 -3 7 15 ← this is the remainder
Check:
f(x) = x⁴ + 9x³ + 17x² - 8x + 50
f(-5) = (-5)⁴ + 9(-5)³ + 17(-5)² - 8(-5) + 50
= 625 - 1125 + 425 + 40 + 50
= 15
1. What is the value of x? Show your work to justify your answer.
2. What is the value of the exterior angle? Show your work to justify your answer.
Answer:
see explanation
Step-by-step explanation:
the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is
2x + 4 = x + 60 ( subtract x from both sides )
x + 4 = 60 ( subtract 4 from both sides )
x = 56
exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°
An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
a. chocolate chosen
b. strawberry chosen
c. vanilla chosen
d. ice cream on a cone
e. ice cream in a cup
Find the probability that the ice cream was sold on a cone and was strawberry flavor
Answer:
Step-by-step explanation:
Sales of the chocolate ice cream is 45%, 30% for strawberry and 25% (100%-45%-30%) of vanilla.
Percentages of cone sales for chocolate, strawberry and vanilla are 75%, 60% and 40%respectively.
A. Probability chocolate chosen: 45%=0.45
B. Probability strawberry chosen: 30%=0.30
C. Probability vanilla chosen:25%=0.25
D. Probability ice cream on a cone: 75%×45%+60%×30%+40%×25%
=0.75×0.45+0.60×0.30+0.40×0.25
=0.3375+0.18+0.1
=0.6175
E. Probability ice cream in a cup: 1- Probability ice cream in a cone
=1-0.6175
=0.3825
Probability that the ice cream sold on a cone and was strawberry flavoured is : 30%×60%
=0.30×0.60
=0.18
Answer: 0.18.
Step-by-step explanation: Let us define the following events
A= event that chocolate chosen,
B=event that strawberry chosen,
C=event that vanilla chosen,
D=event of choosing ice-cream on a cone
and
E=event of choosing ice-cream on a cup.
Then, according to the given information, we have
P(A)=0.45, P(B)=0.30, P(C)=0.25, P(A\D)=0.75, P(B\D)=0.60 and P(C\D)=0.40.
Therefore, the probability that the ice-cream was sold on a cone and was strawberry flavour is given by
[tex]P(B\cap D)=P(B)\times 0.60\\\Rightarrow P(B\cap D)=0.30\times 0.60\\\Rightarrow P(B\cap D)=0.18.[/tex]
Thus, the required probability is 0.18.
Quentin has 6 5/8 feet of lumber but needs another 2 3/4feet to complete the project he's working on. How much total wood will the project have used when finished?
Answer:
Total wood required for the project will be 9 3/8 feet.
Step-by-step explanation:
As given in the question Quentin has lumber of length = 6 5/8
feet =53/8 feet.
Now Quentin needs more lumber = 2 3/4 feet =11/4 feet or 22/8 feet.
So we can get total wood required by adding these two figures
That is = 53/8 + 22/8
= (53 +22)/8
= 75/8
= 9 3/8 feet
Answer:
[tex]The\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
Step-by-step explanation:
As given
[tex]Quentin\ has\ 6 \frac{5}{8}\ feet\ of\ lumber\ but\ needs\ another\ 2 \frac{3}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
i.e
[tex]Quentin\ has\ \frac{53}{8}\ feet\ of\ lumber\ but\ needs\ another\ \frac{11}{4}\ feet\ to\ complete\ the\ project\ he's\ working\ on.[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53}{8} + \frac{11}{4}[/tex]
L.C.M of (8,4) = 8
Than
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 11\times 2}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used =\frac{53 + 22}{8}[/tex] [tex]Total\ wood\ will\ the\ project\ have\ used =\frac{75}{8}[/tex]
[tex]Total\ wood\ will\ the\ project\ have\ used = 9 \frac{3}{8}[/tex]
[tex]Therefore\ the\ total\ wood\ will\ the\ project\ have\ used\ be\ 9 \frac{3}{8}.[/tex]
13. Find a cubic function with the given zeros. 7, -3, 2
[tex]\bf \begin{cases} x=7\implies &x-7=0\\ x=-3\implies &x+3=0\\ x=2\implies &x-2=0 \end{cases}~\hspace{7em}(x-7)(x+3)(x-2)=\stackrel{y}{0} \\\\\\ (x^2-4x-21)(x-2)=y \\\\\\ x^3-4x^2-21x-2x^2+8x+42=y\implies x^3-6x^2-13x+42=y[/tex]
help!!
1.does y vary directly with x? If it does, write an equation for the direct variation.
x|y
−3|2.25
1 |−0.75
4 |−3
Answer:
y = -.75 x
Step-by-step explanation:
To determine if y varies directly with x, we look at y/x and see if it is a constant
y/x = 2.25/-3 = -.75
= -.75/1 = -.75
=-3/4 = -.75
Since it is a constant, it has direct variation. The constant of variation is -.75
y = -.75 x
Please help on this one ?
1 ║ 1 2 -3 2
1 3 0
--------------------------------------------------------------------
1 3 0 [tex]\boxed{2}[/tex]
⇒ The Remainder is 2
The arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. When programming the robot, let the complex number d represent the direction the robot is facing. As the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. At the start of the maze, what is the value of d?
Answer:
d=1
Step-by-step explanation:
If North is i and South is -i
East is 1 and West is -1
The robot is facing East as it enters the maze, it will have a starting value of 1
Answer:
The value of d at the start of the maze will be 1 because 1 represents East .
Points A and B on the coordinate grid below show the positions of two midfield players of a soccer team: Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point A is located 1 unit to the left and 3.5 units down. From the origin, point B is located 1 unit to the right and 3.5 units down. Which statement best describes the relationship between the positions of the two midfield players? B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the y-axis; only the signs of the y-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the x-coordinates of A and B are different. B is A reflected across the x-axis; only the signs of the y-coordinates of A and B are different.
Answer:
Point B is Point A reflected across the y-axis.
Step-by-step explanation:
Answer:
B is A reflected across the y-axis; only the signs of the x-coordinates of A and B are different.
Step-by-step explanation:
When a point is reflected across the y-axis, the x-coordinate of the point is negated. Algebraically,
(x, y)→(-x, y)
Point A is located at (-1, -3.5) and point B is located at (1, -3.5). The only difference between the two points is that the x-coordinate is negated; this means it is a reflection through the y-axis.
As a membership fee a health club charges a one-time amount of $40 in charges $25 for each month the total fee after M months is $240 what is the value of M
The equation for this problem is x=25(m)+40
If the value of x=240, then the value of m=8.
Find the missing value
8
14
45
15
Answer:
The correct option is B.
Step-by-step explanation:
From the given figure it is nices that the length of sides AB, BC and AC are 20, 22 and 35. The line AD is angle bisector.
Let the missing value be x.
The Triangle Angle Bisector Theorem states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
Since AD is angle bisector, therefore
[tex]\frac{AB}{AC}=\frac{BD}{CD}[/tex]
[tex]\frac{20}{35}=\frac{22-x}{x}[/tex]
[tex]20x=35(22-x)[/tex]
[tex]20x=770-35x[/tex]
Add 35x both sides.
[tex]55x=770[/tex]
Divide both sides by 55.
[tex]x=\frac{770}{55}[/tex]
[tex]x=14[/tex]
Therefore, second option is correct.
What is the first step in simplifying the following expression: 2 + 3(4 + 5×2) − 8 + 3^2
Question options:
2 + 3
5 x 2
3^2
4 + 5
Answer:
5 x 2 inside the parenthesis
Step-by-step explanation:
We need an order of operations to ensure we always arrive at the correct answer. It gives us a consistent way to work with numbers. We use the mnemonic device like PEMDAS to remember the correct order.
P-parenthesis
E-exponents
M-multiplication
D-division
A-add
S-subtract.
We apply them left to right doing inner operations before outer operations.
There fore our first step is in the parenthesis and multiplication because it is the inner most operations. 5 x 2 inside the parenthesis.
A fruit stand has to decide what to charge for their produce. They need \$10$10 for 44 apples and 44 oranges. They also need \$12$12 for 66 apples and 66 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?
Answer: No, we can't find a unique price for an apple and an orange.
Step-by-step explanation:
Since we have given that
Cost of 4 apples and 4 oranges = $10
Cost of 6 apples and 6 oranges = $12
We need to find the unique price for an apple and an orange.
According to question, our equations will be
[tex]4x+4y=\$10\\\\6x+6y=\$12[/tex]
since it is equation of parallel lines, as
[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}\\\\\frac{4}{4}=\frac{6}{6}\neq \frac{10}{12}[/tex]
Hence, No, we can't find a unique price for an apple and an orange.
Kellyanne bought a pair of shoes that cost $98.00. Sales tax on the shoes was 7.5%. What was the total cost of the shoes including tax?
Answer:
105.35
Step-by-step explanation:
:)
use the given information to prove that FG=HF
1. EG = HJ (Given)
2. EG = EF + FG, HJ = HF + FJ (Seg. Add. Prop.)
3. EF + FG = HF + FJ (Subst. Prop.)
4. EF = FJ (Given)
5. FG = HF (Subtraction Prop.)
It's challenging to demonstrate that FG equals HF as these may represent different elements or variables in different mathematics or physics contexts. At its simplest, FG seems to represent the gravitational force between two masses, and HF would need to represent the same force to hold true.
The equation given seems to pertain to gravitational forces where FG represents the gravitational force between two masses, electron and proton.
Given that FG = GMM where G is the gravitational constant (6.67×10-¹1 N·m²/kg²), m and M represent the masses of the electron and proton, to prove that FG=HF, it implies that HF represents the same gravitational pull.
However, without more detailed context or information, I can't further demonstrate or prove that FG does equal HF as these terms may refer to different elements or variables in different contexts of mathematics or physics problems.
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If there are 1.61 kilometers in a mile and also 5280 feet in a mile, the how many feet are there in 3 kilometers
Answer:
9,839 ft
Step-by-step explanation:
How much money should be deposited today in an account that earns 3 % compounded semiannually so that it will accumulate to $8000 in three? years
To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the compound interest formula.
Explanation:To calculate the amount that should be deposited today in an account that earns 3% compounded semiannually to accumulate to $8000 in three years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, the future value (A) is $8000, the interest rate (r) is 3% or 0.03, the number of compounding periods per year (n) is 2 (semiannual compounding), and the number of years (t) is 3. Plugging these values into the formula, we get:
A = P(1 + r/n)^(nt)
$8000 = P(1 + 0.03/2)^(2*3)
$8000 = P(1 + 0.015)^(6)
$8000 = P(1.015)^(6)
To find the value of P, we divide both sides of the equation by (1.015)^6: P = $8000 / (1.015)^6. Using a calculator, we find that P ≈ $7383.42. Therefore, approximately $7383.42 should be deposited today in the account.
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If you flip a coin or roll a 6-sided die, what is the probabilty that you will flip a tails and roll a 2?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
P(tail) = [tex]\frac{1}{2}[/tex]
P(2) = [tex]\frac{1}{6}[/tex]
P(tail and 2 ) = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{12}[/tex]
What is the value of A in the matrix equation below?
Answer:
Option (b) is correct.
The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Step-by-step explanation:
Given : A matrix form,
[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]
we have to find the value of matrix A
Consider the given matrix form,
[tex]A+\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}[/tex]
when A + B = C
Then A = C - B
That is
[tex]A=\begin{pmatrix}0&-5&6&10\\ \:3&0&-2&7\end{pmatrix}-\begin{pmatrix}3&9&-1&-8\\ \:16&-2&3&13\end{pmatrix}[/tex]
Subtract the elements in the matching position, we get,
[tex]A=\begin{pmatrix}0-3&\left(-5\right)-9&6-\left(-1\right)&10-\left(-8\right)\\ 3-16&0-\left(-2\right)&\left(-2\right)-3&7-13\end{pmatrix}[/tex]
Simplify, we get,
[tex]A=\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Thus, The matrix A is [tex]\begin{pmatrix}-3&-14&7&18\\ -13&2&-5&-6\end{pmatrix}[/tex]
Please help me with these problems
Answer:
1.a=2
2. C x=2 and x=-3
Step-by-step explanation:
The standard form for the quadratic function is
ax^2 +bx+c
so we need to rewrite the function to be in this form
2x^2 -10 = 7x
Subtract 7x from each side
2x^2 -7x-10 = 7x-7x
2x^2 -7x-10 = 0
a =2, b= -7 c=-10
2. The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
2x^2 + 2x=12
Lest get the equation in proper form
2x^2 + 2x-12 = 12-12
2x^2 +2x-12 =0
a=2 b=2 c=-12
Lets substitute what we know
-2 ± sqrt(2^2 -4(2)(-12))
----------------------------
2(2)
-2 ± sqrt(4+96)
----------------------------
2(2)
-2 ± sqrt(100)
----------------------------
4
-2 ± 10
----------------------------
4
-2 + 10 -2-10
----------- and --------------
4 4
8/4 and -12/4
2 and -3
Write the equation of a line that is perpendicular to the given line and that passes through the given point. y-3=-1/5(x+2); (-2, 7)
A. y=5x+7
B. y=5x+17
C. y=(1/5)x-2
D. y=-2x+3
Plz answer quickly!! Thank you :) <3
To find the equation of a line perpendicular to a given line, find the negative reciprocal of the slope and use the point-slope form of a line.
Explanation:To find the equation of a line that is perpendicular to the given line and passes through the given point, we first need to determine the slope of the given line. The given line has a slope of -1/5, which is the negative reciprocal of the slope we want for the perpendicular line. The negative reciprocal of -1/5 is 5/1 or 5. Now we have the slope of the perpendicular line and a point it passes through (-2, 7), we can use the point-slope form of a line to find the equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values, we get: y - 7 = 5(x - (-2))
y - 7 = 5(x + 2)
y - 7 = 5x + 10
y = 5x + 10 + 7
y = 5x + 17
Therefore, the equation of the line that is perpendicular to the given line and passes through the given point (-2, 7) is y = 5x + 17. Option B is the correct answer.
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The correct answer is B. y=5x+17.
To write the equation of a line that is perpendicular to the given line y-3=-1/5(x+2) and that passes through the point (-2, 7), first, we need to find the slope of the given line and then determine the slope of the perpendicular line, which will be the negative reciprocal of the given line's slope. The slope of the given line is -1/5, so the slope of the line perpendicular to it will be 5 (since the negative reciprocal of -1/5 is 5).
Next, we use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes. Plugging in our slope of 5 and the point (-2, 7), the equation becomes:
y - 7 = 5(x - (-2))
Expand and simplify to solve for y:
y - 7 = 5x + 10
y = 5x + 17
The correct answer is B. y=5x+17.
Write an addition equation that will have a new thousand, a new hundred, and a new ten. Then solve. Explain how you chose your numbers.
Answer:
1987 + 1257 = 3247
Step-by-step explanation:
We are going to use a base number to start from. That number is 1,987 where the thousand is 1, the hundred is 9 and the ten is 8.
Then we are going to add 1,257 which will be 3,247. Thus we will have a new thousand which is 3 (formerly 1), a new hundred which is 2 (formerly 9), and finally, a new ten which is 5 (formerly 7).
1987 + 1257 = 3247 gives you a new thousand, a new hundred and a new ten.
Answer:
Step-by-step explanatcagion:
If William has 5 different shirts and 7 different pairs of pants, how many different combinations could he wear?
The question is asking how many different outfit combinations William can form if he has 5 shirts and 7 pants. It's a simple multiplication of the two numbers (5*7) resulting in 35 different combinations. Therefore, William could wear a different outfit for 35 days without repeating.
Explanation:The subject of this question is combinatorics, a branch of mathematics concerned with counting, both as a means and an end. In this specific context, we are looking at the number of different combinations that William can wear with the clothes he has. Since each shirt can be worn with any pair of pants, this translates into a simple product calculation.
William has 5 different shirts and 7 different pairs of pants. So, the total number of combinations of outfits he can put together is calculated by multiplying these numbers together. Hence, 5 shirts * 7 pants = 35 combinations.
This means that if William chooses a different combination each day, he could go for 35 days without wearing the same outfit twice.
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