Using the Fundamental Counting Theorem, it is found that Samantha has 24 different outfits to choose from.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with n1 ,n2 , n3, ..... nn ways to be done, each thing independent of the other, the number of ways they can be done is:
N= n1*n2*n3.....nn
In this problem:
For the pants, there are 2 options, hence n1=2 .
For the t-shirts, there are 2 outcomes, hence n2=2.
For the shoes, there are 9 outcomes, hence n3=6.
Thus, the total number of outfits is given by:
N = 2 x 2 x 6 = 24.
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Pablo invested in a savings bond for 3 years and was paid simple interest at an annual rate of 4%. The total interest that he earned was
$48. How much did he invest?
If necessary, refer to the list of financial formulas.
Answer:
400
Step-by-step explanation:
=
1
We know that:
3 R=4% 1 = 48
T =3 R = 4% into formula 48 2 Substitute
1=Prt
48= Prt
Solve the equation:
3 × 0.04x= 48
3
X = 400
so Pablo invested 400$
10.8 divided by 0.09
Answer: 120
Step-by-step explanation:
[tex]\displaystyle\\10.8:0.09=\\\\\frac{10.8}{0.09}=\\\\\frac{10.8(100)}{0.09(100)}=\\\\\frac{1080}{9} =\\\\\frac{9(120)}{9}=\\\\120[/tex]
on a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. if there are 60 juniors on the team, how many students in total are on the team? a. 90 b. 140 c. 150 d. 180 e. 210
The total number of students that are on the team is e. 210 if the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6
As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;
Freshmen = 1x
Sophomores = 3x
Juniors = 4x
Seniors = 6x
As the number of juniors on the team is 60, therefore;
4x = 60
To determine the value of x we divide both sides by 4;
4x/4 = 60/4
x = 15
Now the total number of students can be found by substituting the value of x;
1x + 3x + 4x + 6x
1(15) + 3(15) + 4(15) + 6(15) = 210
Hence, the total number of students on the team is 210.
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show how to transform the weight function of a weighted matroid problem, where the desired optimal solution is a minimum-weight maximal independent subset, to make it a standard weighted-matroid problem. argue carefully that your transformation is correct.
To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w
We build the transformation, i.e, a new weight function, as follows: We want the elements with maximum weight to have minimum weight and. In other words, two weight functions need to be mutually opposite in this sense. Therefore, if we denote the maximum weight of all the elements with w ∗ : w ∗ = max w(x) x ∈ S we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly. Since we want the weight function to be strictly positive, we finish our construction with: w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)
Using equation (1) we can derive the following expression for the weight w ′
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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w
We build the transformation,
or a new weight function, as follows:
We want the elements with maximum weight to have minimum weight a In other words, two weight functions need to be mutually opposite in this sense.
Therefore, if we denote the maximum weight of all the elements with
w ∗ : w ∗ = max w(x) x ∈ S
we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly.
Since we want the weight function to be strictly positive, we finish our construction with:
w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)
Using equation (1) we can derive the following expression for the weight w ′
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3. Masani is testing 25 g of fertilizer. She of the plans to give each test plant 0.4 g fertilizer and have 8 g left over for future tests. Solve the equation 0.4n+ 8 = 25 to find the number of plants Masani car use in her
Answer:
Step-by-step explanation:
So, you have to isolate the variable. Think of it as finding how many plants she gave fertilizer to. 0.4n+8=25, when moving the 8 to the other side, it becomes negative. 0.4n=25-8. 0.4n=17. You then find the variable n. think of it as dividing 17 by 0.4 or multiplying n a certain number of times to find the number of plants.17/0.4 is 42.5. therefore, she gave 42 plants fertilizer, depending on what your teacher wanted to count. If she says round down, 42. If she wants to round up, 43. If she wants to be specific, 42.5. I would personally put the decimal.
Given that f(x)=2x + 1 and g(x)=3x-1/2x+1
(a) evaluate f(1/2) and g(-1)
Answer:
a)
f(1/2) = 2
g(-1) = -3/2
Step-by-step explanation:
for f(x) = 2x + 1 substitute the x with 1/2
2(1/2) + 1 then solve
1+1
2
for g(x) = 3x - 1/2x + 1 substitute with -1
3(-1) - 1/2(-1) +1 then solve
-3 + 1/2 + 1
-3/2
Which phrase best describes the graph of this equation? 3x+3y^2+6y+3=0
The screenshot has the answer!!
The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.
The given equation is 3x+3y²+6y+3=0.
What is the parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Left
Vertex: (0, -1)
Focus: (-1/4, -1)
Axis of symmetry: y=-1
Directrix: x = 1/4
The coordinate points to plot (2, 0.41), (-2, -2.41), (-1, 0), (-1, -2) and (0, -1).
The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.
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30g 25´into second please solve its optional math question please solve it carefully its my project so question is 30grade25´ into second.
Answer:
Step-by-step explanation:
30.25g=296.6511625 m/s^2
1. Multiply.
0.7 times 100 equals what number?
A. 7
B. 70
C. 700
D. 7,000
2.Multiply.
0.13 times 10,000 equals what number?
A. 13
B. 130
C. 1,300
D. 13,000
3. Multiply.
0.63 times 0.01 equals what number?
A. 0.0063
B. 0.063
C. 0.63
D. 6.3
4. Divide.
0.37 divided by 100 equals what number?
A. 0.00037
B. 0.0037
C. 0.037
D. 0.37
5. Divide.
0.8 divided by 0.01 equals what number?
A. 8
B. 80
C. 800
D. 8,000
The various values using mathematical operations are;
1) B: 70
2) C: 1300
3) A: 0.0063
4) B: 0.0037
5) B: 80
How to use mathematical operations?
1) We want to multiply 0.7 times 100.
Now, 0.7 can be expressed as 0.7 = 7/10. Thus;
0.7 * 100 = 7/10 * 100 = 70
2) We want to multiply 0.13 by 10000.
0.13 can be expressed as;
0.13 = 13/100. Thus;
0.13 * 10000 = 13/100 * 10000 = 1300
3) We want to multiply 0.63 times 0.01.
They can be expressed as;
63/100 * 1/100 = 63/10000 = 0.0063
4) Divide 0.37 by 100.
0.37 can be expressed as 37/100. Thus;
0.37/100 = 37/100 ÷ 100
= 37/100 * 1/100 = 37/10000 = 0.0037
5) Divide 0.8 divided by 0.01.
They can be expressed as;
8/10 ÷ 1/100
= 8/10 * 100/1
= 80
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The population of a fish farm is modeled by the equation where t is time in yearsP(t) = 1250/ 2+3e ^ -0.6tpart one)part two)part three)part four)part five)
The Solution:
Given the equation that modeled the population of fish after time (t) in years as below:
[tex]p(t)=\frac{1250}{2+3e^{-0.6t}}[/tex]part 1:
We are to find the initial population of fish. This means we are to find the value of p when t = 0.
[tex]p(0)=\frac{1250}{2+3e^{-0.6(0)}}=\frac{1250}{2+3e^0}=\frac{1250}{2+3}=\frac{1250}{5}=250\text{ fish}[/tex]Part 2:
We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.
Note: double of 250 fish is 2x250 = 500 fish.
[tex]\begin{gathered} p(t)=\frac{1250}{2+3e^{-0.6t}} \\ \\ \text{Where P(t)=500, and t=?} \end{gathered}[/tex][tex]\begin{gathered} 500=\frac{1250}{2+3e^{-0.6t}} \\ \text{Cross multiplying, we get} \\ \\ 500(2+3e^{-0.6t})=1250 \\ \text{ Dividing both sides by 500, we get} \\ \\ \frac{500(2+3e^{-0.6t})}{500}=\frac{1250}{500} \end{gathered}[/tex][tex]\begin{gathered} 2+3e^{-0.6t}=2.5 \\ \text{ Collecting the like terms, we get} \\ 3e^{-0.6t}=2.5-2 \\ 3e^{-0.6t}=0.5 \end{gathered}[/tex]Dividing both sides by 3, we get
[tex]\begin{gathered} \frac{3e}{3}^{-0.6t}=\frac{0.5}{3} \\ \\ e^{-0.6t}=\frac{1}{6} \end{gathered}[/tex]Taking the natural log of both sides, we get
[tex]undefined[/tex]which equation describes the line that is perpendicular to y=1/3x+2
Answer:
y= -3x+1
Step-by-step explanation:
Describe and correct the error a student made when graphing y + 5 = - 3/4 (x - 8).
The student's first error was in step 1.
Step 1 should involve plotting a point at (0, 1).
Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).
Step 3, connecting the points with a line was correct.
In this question, we have been given an equation of line y + 5 = - 3/4 (x - 8)
We need to describe and correct the error a student made when graphing y + 5 = - 3/4 (x - 8).
Consider given equation.
y + 5 = - 3/4 (x - 8)
y + 5 = - 3/4 x - (-3/4) 8
y + 5 = -3/4 x + 6
y = (-3/4)x + 6 - 5
y = -3/4 x + 1
Here,
slope(m) = (-3/4)
and y-intercept (c) = (0, 1)
Therefore, the student's first error was in step 1.
Step 1 should involve plotting a point at (0, 1).
Step 2 should involve plotting a point 3 units down and 4 units right from the point in step 1, at (4, -2).
Step 3, connecting the points with a line was correct.
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4/7x = 28 solve for x simplify your answer as much as possible
I WILL USE CROSS MULTIPLICATION
[tex] \frac{4}{7x} = 28 \\ 4 = 28(7x) \\ 196x = 4 \\ \frac{196x}{196} = \frac{4}{196} \\ x = \frac{1}{49} [/tex]
ATTACHED IS THE SOLUTION
Answer:
16
Step-by-step explanation:
7x=28x4
7x=112
x=112/7
x=16
MATH PLEASE HELP!!!
Let f(x) be given by the (large) graph to the right. On a piece of paper, graph and label each. function listed below.
y = f((1/2)x))
y=2f(2x)
y = f(2x)
original function y=f(x) is attached
y = f(2x) ⇒ Shrink the graph of function f(X) by half horizontally .
What is function and example?
A function is a type of rule that produces one output for a single input.This is represented by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.Four main categories can be used to classify various types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.y = f((1/2)x)) ⇒ Stretch the graph of f(x) horizontally by factor 2 .
y=2f(2x) ⇒ Shrink the graph of f(X) by half horizontally .
Shrink the graph twice ( vertically) .
y = f(2x) ⇒ Shrink the graph of f(X) by half horizontally .
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Help me I need help because I need help
Answer:
6.3 * 10^3
Step-by-step explanation:
6.3 * 10^3
:]
Island bank is advertising a special 1.55% APR for long -term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily. What will the annual percentage yield be for mannys account to the nearest hundredth of a percent .
The annual percentage yield is 1.55% for any account if the interest is compounded daily.
Given that Island bank is advertising a special 1.55% APR for long-term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily.
Principal (P) = $40000
Interest rate(r) = 1.55% = 0.0155
Number of periods (n) = 365
The formula for Annual Percentage Yield (APY) for an account that is compounded continuously is given as
APY = [1 + (r/n)ⁿ - 1]
Substitute the values in the formula to get
= [1 + (0.0155/365)³⁶⁵ - 1]
= [1 + 0.000042)³⁶⁵ - 1]
= [1.000042]³⁶⁵- 1
= 1.015448 - 1
= 1.55%
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Can someone please help me on question 42 (7th grade math) pls and thank u :)
Answer:
Answer down below!
Step-by-step explanation:
(Part a):
So we have the information that after 20 minutes, the submarine descended 480 feet.
To find how many feet it descended per minute, all we need to do is divide 480 and 20 which will give us 24
Every 1 minute, the submarine descended 24 feet.
(Part b):
Now that we have how many feet it descended per minute, we have to make an expression that goes along with it.
Our unknown variable in this case will have to have to be the feet.
We can use the letter f to express that. We can also use the letter m to express our minutes in the end
So after 24(f) = m
(Part c):
After 5 Minutes: 120 ft
After 10 Minutes: 240 ft
After 15 Minutes: 360 ft
After 18 Minutes: 432 ft
Determine the quotient of
3/7 divided by 2/3
Johnny was building a tree house. The boards for the floor are 8.89 centimeters wide. He will use 18 boards to cover the floor. How wide is the floor of the treehouse?
Answer:
1422.5778
Step-by-step explanation:
8.89x8.89=79.0321. 79.0321x18=1422.5778
Given g (x) = 3x+5 determine x for g (-2)
Answer:
-1
Step-by-step explanation:
when you change g[×] to g[-2] , 3x+5 change to 3[-2] +5
f(x) = 1x g(x) = x − 4 Can you evaluate (g ○ f)(0)?
The evaluation of the composite function (g o f)(0) is -4
How to solve composite function?A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function below:
f(x) = 1x
g(x) = x - 4
Let's find (g o f)(0)
Therefore,
(g o f)(x) = g(f(x))
Hence,
(g o f)(0) = g(f(0))
f(0) = 1(0) = 0
Therefore, let's substitute f(0) in g(x)
(g o f)(0) = 0 - 4
(g o f)(0) = - 4
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17. An Uber ride costs a flat rate of $7 and you are charged $.65 per mile. What
is the algebraic expression for this situation? How much would it cost for 15
miles?
*
The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.
What are expressions?A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11 written as 8 + 3.So, the flat rate is $7 and we're charged $0.65 per mile:
Let, 'x' be the number of miles traveled.Then the suitable expression will be:
0.65x = 7Cost if we traveled 15 miles:
So, 0.65x = y where x = 15.
0.65x = y0.65(15) = y9.75 = yIt would cost $9.75 for 15 miles.
Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.
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May someone please help me! I have to submit this tonight and do not know how to do it or the answer may you please help me thank you.
x3 + 11x2 – 3x – 33 by grouping
Answer:
-3
Step-by-step explanation:
It was quite easy
Answer:
Step-by-step explanation: factor out x2
from the expression x2 (x+11) -3x-33
Factor out-3 from the expression x2 (x-+11) -3(x+11)
Factor out x+11 your solution is x2 (x+11) (x-3).
Hilda went hiking and used the app on her phone to track her progress. When she looked back, she discovered she had hiked up 530 feet, down 602 feet, up 1003 feet, and down 89 feet to get to the lake. What is her elevation in relation to where she started?
The elevation is 848 feet.
What is meant by elevation?The word elevation is often used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying aeroplanes or orbiting satellites, and depth is used to describe locations below the surface.
A geographical feature's elevation is determined by how high it is above the mean sea level (MSL). Accordingly, elevation is the distance between the height that corresponds to the ocean's surface and the top of the feature.
Given:
Hilda hiked up 530 feet,
down 602 feet,
up 1003 feet,
and down 89 feet to get to the lake.
Taking all similar cases together
Hiked up
= 530 + 1003
= 1533 feet
and, hiked down
=602+83
= 685
Thus, the elevation is
= 1533 - 685
= 848
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a vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol. How much distance will it cover 2 liters of petrol
8.32 Km is the distance of how much it would be covered
A unit rate means a quantity at a rate of one of something.
The distance traveled with 2 liters of petrol is 47.9 km.
What is a unit rate?A unit rate means a quantity at a rate of one of something.
It is written with a denominator of one.
Example:
Man can walk 6km in 2 hours.
In one hour a man can walk 3 km.
We have,
A vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol.
This can be written as:
524/25 km = 7/8 liters
Multiply both sides by 8/7
8/7 x 524/25 km = 1 liter
23.95 km = 1 liter _____(1)
Now,
Multiply 2 on both sides of (1)
2 x 1 liter = 2 x 23.95 km
2 liter = 47.9 km
Thus,
The distance traveled with 2 liters of petrol is 47.9 km.
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suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin that lands on heads with some unknown probability p that need not equal to 1 2 . consider the following procedure for accomplishing your task
The probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.
Given that, we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2.
What is the probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
The following procedure for accomplishing our task are:
1. Flip the coin.
2. Flip the coin again.
From here will know that the coin is first flipped twice
3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails
But if the outcomes of the two flip are different i.e., they did not land on both heads or both did not land on tails , then we will consider such an outcome.
Let the probability of head = p
so P(head) = p
the probability of tail be = (1 - p)
This kind of probability follows a conditional distribution.
Therefore, the probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.
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"Your question is incomplete, probably the complete question/missing part is:"
Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:
1. Flip the coin.
2. Flip the coin again.
3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.
(a) Show that the result is equally likely to be either heads or tails.
(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?
) To stay healthy, Emily decided to walk for 4
5
mile every
day. She walked 2
5
mile to work and walked 1
4
mile at
lunchtime. How much more does she need to walk after
dinner if she wants to meet her target distance?
If she wants to meet her target distance 3/20 steps need to be taken.
Emily made the decision to walk 4/5 kilometers every day in order to keep healthy. She walked a distance of 2/5 miles to work and a distance of 1 mile for lunch.
The desired range is 4/5 miles.
walked for 2/5 miles and for 1/4 miles.
Total miles walked is [tex]\frac{2}{5} + \frac{1}{4}[/tex]
= [tex]\frac{13}{20}[/tex]
Mileage walked overall is +
LCD is 20
add the fractions after matching the denominators
The desired range is 4 to 5 miles.
Now deduct the distance you walked from the goal distance.
[tex]\frac{4}{5} - \frac{13}{20} \\\\\frac{16}{20} - \frac{13}{20} \\\\\frac{3}{20}[/tex]
the required walking distance is 3/20
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Please help asap
Word definitions you can use
Rigid Transformations
Sequence of Transformations
Translations (slide) -
Reflection (flip)
The best description for the sequence of transformation used is; Rigid Transformations.
What is the type of transformation?
In mathematics, a rigid transformation is defined as a geometric transformation of a defined Euclidean space that does not change or preserves the Euclidean distance that is between every pair of points. Examples of this rigid transformations are rotations, translations, reflections e.t.c
Now, from the given transformation, the first thing to notice is that the transformation does not change the distance between pair of points in the diagram. Secondly, it is neither only a translation nor reflection as it is more than one transformation that was used and so it can be described as a rigid transformation.
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please I need the asnwers with explanation as soon as possible