Given the expressions:
[tex]\begin{gathered} \frac{4^5}{4^2} \\ \text{and} \\ \frac{4^2}{4^5} \end{gathered}[/tex]we can use the following property for exponents in quotients:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]in this case, we have the following:
[tex]\begin{gathered} \frac{4^5}{4^2}=4^{5-2}=4^3 \\ \text{and} \\ \frac{4^2}{4^5^{}}=4^{2-5}=4^{-3} \end{gathered}[/tex]then, the difference between both expressions is that when they are simplified, they get opposite signs on their exponents.
The equation y + 2 = 5(x – 4) represents a linear function. What is the y-intercept of the equation?
Answer:
-22
Step-by-step explanation:
Hello!
We can convert it into Slope-Intercept form: [tex]y = mx + b[/tex]
m = slopeb = y-interceptConverty + 2 = 5(x - 4)y + 2 = 5x - 20y = 5x - 22The y-intercept is -22.
Mai is filling her fish tank water flows into the tank at a constant rate. 2.&- 0.5 1.6 time (minutes) water (gallons) 0.5 0.8 1 x1.6 1.6 x1.6 4.8 25 G 3 40 1) How many gallons of water will be in the fish tank after 3 minutes? Explain or show your reasoning. 2) How long will it take to fill the tank with 40 gallons of water? Explain or show your reasoning. 3) What is the constant of proportionality? What does it tell us about this situation?
Given
x = 0.5; y = 0.8
The constant of proportionality has to be calculated to estimate the other values.
The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.
So, in this exercise,
[tex]\begin{gathered} 0.8=k\cdot0.5 \\ \frac{0.8}{0.5}=k \\ k=1.6 \end{gathered}[/tex]y = 1.6y
(1) From this, we can estimate the value of y when x = 3.
[tex]\begin{gathered} y=1.6\cdot3 \\ y=4.8\text{gallons} \end{gathered}[/tex](2) If we want how long it will take to fill the tank with 40 gallons:
[tex]\begin{gathered} 40=1.6\cdot x \\ \frac{40}{1.6}=x \\ 25=x \end{gathered}[/tex]It will take 25 minutes.
(3) Finally, the constant of proportionality is 1.6 (as calculated above).
It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.
i need help please and thank youthere are 2 pictures bc i couldn’t get it all in 1!
we have the system
y < -2x^2+4x-2
The solution for this inequality is the shaded area below the vertical dashed parabola
and
[tex]y\ge\frac{2}{3}x-3[/tex]the solution for this inequality is the shaded area above the solid line y=(2/3)x-3
therefore
the solution for this system of inequalities
Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3
see the attached figure to better understand the problem
I need some help with this
The product is:
(7*10⁵)*(3*10²) = 2.1*10⁸
So the correct option is D
The quotient is:
(2*10⁵)/(4*10²) = 5*10²
So the correct option is B.
How to get the products?
Here we want to get the product between numbers in scientific notation, the first one is:
a) (7*10⁵)*(3*10²)
We can rewrite this as:
(7*10⁵)*(3*10²) = (7*3)*(10⁵*10²) = (21)*(10⁵⁺²) = 21*10⁷
In scientific notation we can have only one digit at the left of the decimal point, so we can rewrite:
21*10⁷ = 2.1*10⁸
So the correct option is D.
b) Now the quotient is:
(2*10⁵)/(4*10²) = (2/4)*(10⁵*10²) = 0.5*10⁵⁻² = 0.5*10³
Again, we need to have a single digit in the left of the decimal point:
0.5*10³ = 5*10²
The correct option is B.
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i need help with this question parts 3 - 7
Answer:
i also don't know
Step-by-step explanation:
i also don't know..,......
The table to right gives the projections of the population of a country from 2000 to 2100.Answer parts (a) through (c).
c.
As found in part (a), the data in the table can be represented by the linear model as follows,
[tex]f(x)=2.928x+270.641[/tex]Here, 'x' is the number of years after year 2000.
To find: The population in 2080 as predicted by the model.
The value of 'x' corresponding to the year 2080 can be obtained as follows,
[tex]\begin{gathered} x=2080-2000 \\ x=80 \end{gathered}[/tex]Substitute the value of 'x' in the model for population,
[tex]\begin{gathered} f(80)=2.928\cdot(80)+270.641 \\ f(80)=234.24+270.641 \\ f(80)=504.881 \\ f(80)\approx504.9 \end{gathered}[/tex]Thus, the population in 2080 will be 504.9 million approximately, as predicted by the linear model.
Find the a) domain, b) x-intercept and c) y - intercept: 1) f(x) = 3x-12 2x+4 2x+9 2) f(x) = x²-16 3) f(x) = x2-9
Answer
Check Explanation
Explanation
Before we start answering, we should first explain what these terms stand for
- Domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
- x-intercept
The x-intercept refers to the value of x when the value of y or f(x) = 0, that is, the value of x at which the graph of the function crosses the x-axis. To obtain this, we just solve for x when y or f(x) = 0
- y-intercept
The y-intercept refers to the value of y or f(x) when the value of x = 0, that is, the value of y when it crosses the y-axis. To obtain this, we just substitute 0 for x and solve for f(x)
We can now solve
[tex]f(x)=\frac{3x-12}{2x+4}[/tex]- For the domain, we can tell that x can take on any real number value and provide an answer for f(x) except the point where the denominator of this is equal to 0. At the point where the denominator is 0, f(x) will tend to infinity.
2x + 4 = 0
2x = -4
Divide both sides by 2
(2x/2) = (-4/2)
x = -2
So, the domain of this function is all real number values for x except x = -2
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when f(x) = 0} \\ 0=\frac{3x-12}{2x+4} \\ \text{Cross multiply} \\ 3x-12=0\times(2x+4) \\ 3x-12=0 \\ 3x=12 \\ \text{Divide both sides by 3} \\ \frac{3x}{3}=\frac{12}{3} \\ x=4 \end{gathered}[/tex]The x-intercept = 4.
In coordinate form, the x-intercept is (4, 0)
- For the y-intercept, we just solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{3x-12}{2x+4} \\ \text{when x = 0} \\ f(x=0)=\frac{3(0)-12}{2(0)+4} \\ f(x)=\frac{0-12}{0+4}=\frac{-12}{4}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the second question
[tex]f(x)=\frac{2x+9}{x-3}[/tex]- The domain will be all real number values of x except when (x - 3) = 0
x - 3 = 0
x = 3
The domain will be all real number values of x except when x = 3.
- For the x-intercept, we just solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ when\text{ f(x) = 0} \\ 0=\frac{2x+9}{x-3} \\ \text{Cross multiply} \\ 2x+9=0 \\ 2x=-9 \\ x=-4.5 \end{gathered}[/tex]The x-intercept = -4.5
In coordinate form, the x-intercept = (-4.5, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{2x+9}{x-3} \\ \text{when x = 0} \\ f(x=0)=\frac{0+9}{0-3}=\frac{9}{-3}=-3 \end{gathered}[/tex]The y-intercept = -3
In coordinate form, the y-intercept is (0, -3)
For the third question
[tex]f(x)=\frac{x^2-16}{x^2-9}[/tex]- For the domain, we first solve for when x² - 9 = 0
x² - 9 = 0
x² = 9
x = ±√9
x = ±3
x = +3 or -3
The domain of this function is all real number values of x except when x = +3 and x = -3
- For the x-intercept, we solve for x when f(x) = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when f(x) = 0} \\ 0=\frac{x^2-16}{x^2-9} \\ \text{Cross multiply} \\ x^2-16=0 \\ x^2=16 \\ x=\pm\sqrt[]{16} \\ x=\pm4 \\ x=+4_{} \\ or\text{ x = -4} \end{gathered}[/tex]The x-intercepts are at -4 and +4.
In coordinate form, the x-intercept are (-4, 0) and (4, 0)
- For the y-intercept, we solve for f(x) when x = 0
[tex]\begin{gathered} f(x)=\frac{x^2-16}{x^2-9} \\ \text{when x = 0} \\ f(x)=\frac{0-16}{0^{}-9}=\frac{-16}{-9}=1.7778 \end{gathered}[/tex]The y-intercept = (16/9) = 1.7778
In coordinate form, the y-intercept is (0, 1.7778)
Hope this Helps!!!
Faith borrowed $2250 for home repairs. She paid back 24 payments of$132 each. How much did she pay in interest on the loan?a. $87.71b. $2,520c. $918d. $4.38
• We are given that Faith paid $132 for 24 months.
So; 132 * 24 = $3168
• Since we know that Faith initially borrowed $2250
Interest paid = $3168 - $2250
= $918
• Option C is the correct choice.
You begin at the origin and travel 5 units to the right and then vertically 3 units. You will be at what ordered pair?
In a x-y coordinate plane of you moves to the right it increase the value of x and if you moves vertically it increases the value of y.
The ordered pair is (x,y)
For the given moves: (5,3)35+3(8-4)
(please explain how you did it)
Answer:47
Step-by-step explanation: First multiply 3x8=24 then subtract 3x4=12 from it. Which will get you 12 then add 35 to 12 which will get you 47.
35 + 3(8-4) = ?
Do the parentheses first : 8 - 4 = 4
= 35 + 3(4)
Then multiply- that's the one that is in parentheses : 3 x 4 = 12
= 35 + 12
Then just straight up add : 35 + 12 = 47
35 + 3(8-4) = 47
So ? = 47
Solve the equation 3x - 4y = 16 for x.16 4OA. X-B. x1643C. X= 4y + 16O D. x= 3(16+47)
To solve for x, first, we add 4y to the equation:
[tex]\begin{gathered} 3x-4y+4y=16+4y, \\ 3x=16+4y\text{.} \end{gathered}[/tex]Now, we divide by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{16+4y}{3}, \\ x=\frac{16+4y}{3}\text{.} \end{gathered}[/tex]Answer:
[tex]x=\frac{16+4y}{3}\text{.}[/tex]ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The
quadratic function h(t) = − 16t² + 84t+ 72 models the ball's height about the ground, h(t), in feet, t
seconds after it was thrown. Please help me identify the height of the ball in feet and how many seconds it takes to hit the ground
The height of the ball was 182.25 feet and it took 6 seconds for the ball to hot the ground.
Given that:-
Quadratic equation:-
[tex]h(t)=-16t^2+84t+72[/tex]
We have to find the ball's height, in feet and how many seconds it takes to hit the ground.
Differentiating the given equation, we get
dh/dt=-32t + 84
Putting dh/dt = 0, we get,
-32t + 84 = 0
t = 84/32 = 21/8 seconds
Putting t = 21/8, we will get the maximum height that the ball will reach.
Hence,
[tex]h(21/8)=-16(21/8)^2+84(21/8)+72[/tex]
h(21/8) = -16(441/64)+84(21/8)+72 = -110.25 + 220.50 +72 = 182.25 feet
At h = 0, the ball will have hit the ground.
Hence, we can write,
[tex]h(t) = 0 = -16t^2+84t+72[/tex]
Dividing -4 from the equation, we get,
[tex]4t^2-21t-18=0[/tex]
Using middle term split theorem, we can write,
[tex]4t^2-24t+3t-18=0\\[/tex]
4t(t-6)+3(t-6) = 0
(t-6)(4t+3) = 0
Hence, the values of t can be:-
t = 6, -3/4
As the time cannot be negative, hence the ball will hit the ground after 6 seconds.
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A biologist wants to determine the effect of a new fertilizer on tomato plants. What would be the control?All PlantsPlants not treated with the Fertilizer.The FertilizerPlants treated with the Fertilizer.
Remember that the control variable does not change in the experiment or in any study.
So the control here will be all the plants because you can not control the type of the plant.
Answer:b
Step-by-step explanation:
8. Three consecutive even numbers have a sum where one half of that sum is between 90 and 105. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality. a. (n+(n+2)+(n+4) < −90 or −(n+(n+2)+(n+4)) > 105 b. n-62 or n > 68 a. 90 < 2(n + (n + 2) + (n + 4)) < 105 b. 13 ≤ n ≤ 15.5 a. 90 < ¹² (n + (n +2)+(n+ 4))
Given:
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
Required:
To write an inequality to find the three numbers and to solve the inequality.
Explanation:
(a)
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
[tex]90<\frac{1}{2}(n+(n+2)+(n+4))<105[/tex](b)
[tex]undefined[/tex]if the probability of drawing an A or B is 9/25, what is the probability of the complementary event?
If an event has a probability of "A", then the complementary event will have a probability of "1 - A".
Given, the probability of an event is 9/25, we can easily find the probability of the complementary event. Shown below:
[tex]\begin{gathered} 1-\frac{9}{25} \\ =\frac{25}{25}-\frac{9}{25} \\ =\frac{16}{25} \end{gathered}[/tex]The correct answer is:
[tex]\frac{16}{25}[/tex]= The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 82. If state A has more counties than state B, how many counties does each state have? State A has counties.
State A have 42 counties and State B have 40 counties.
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant
Let,
x = The number of counties of state B
x + 2 = The number of counties of State A
It's given, The sum of counties of state A and state B is 82
so, the equation become is linear.
The linear equation will be,
x + (x + 2) = 82
solve for x,
2x + 2 = 82
2x = 82 - 2
2x = 80
x = 80/2
x = 40 (counties of State B)
put the value in x in x + 2,
40 + 2 = 42 (counties of State A)
Therefore, State A have 42 counties and State B have 40 counties.
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The distance to your brother's house is 481 miles, and the distance to Disneyland is 518 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to Disneyland to take?
Answer:
364/7 = 260/d
Cross multiply.
364d = 1820
d = 5 hours
Miles per hour, mph = miles/hour
364 miles/7 hours = 52 mph
260 miles/52 mph = 5 hours
a loaf of sandwich bread contains 24 slices. which of these tables correctly shows the ratios of different of loaves of bread to the number of total slices they contain
We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.
Therefore, we have that the only table that follows this is the table that has:
If we have:
2/48 = 1/24
3/72 = 1/24
4/96 = 1/24
The ratio of loaves to slices is the same, that is, 1 / 24.
Henry has 3 3/5 metres of rope, and Sam has a piece of rope that is 1 1/2 metres
shorter. What is the total amount of rope that the boys have together?
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
The answer to the puzzle is 21 divided by ten.
What factors make a number rational?
It is possible to express rational numbers in the form pq, where p and q are integers and q0. Fractions cannot have a negative numerator or denominator, which is what distinguishes them from rational numbers.
Rates and ratios compare two different numbers. Simply put, a rate is a particular kind of ratio. The distinction is that a rate involves comparing two numbers.
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#3b. Two bicyclists ride in the same direction. The first bicyclist rides at a speed of 8 mph.One hour later, the second bicyclist leaves and rides at a speed of 12 mph. How long will thesecond bicyclist have traveled when they catch up to the first bicyclist?I’m
Answer:
2 hours
Explanation:
[tex]\text{Speed}=\frac{Dis\tan ce}{Time}[/tex]The first bicyclist rides at a speed of 8 mph. Therefore:
[tex]\begin{gathered} 8=\frac{d}{t} \\ \implies d=8t \end{gathered}[/tex]One hour later, the second bicyclist leaves and rides at a speed of 12 mph.
Therefore, the time of the second bicyclist = (t-1) hours.
Therefore:
[tex]\begin{gathered} 12=\frac{d}{t-1} \\ \implies d=12(t-1) \end{gathered}[/tex]Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.
So:
[tex]\begin{gathered} 8t=12(t-1) \\ 8t=12t-12 \\ 8t-12t=-12 \\ -4t=-12 \\ \frac{-4t}{-4}=\frac{-12}{-4} \\ t=3\text{ hours} \end{gathered}[/tex]Therefore, the second bicyclist will have traveled for:
(t-1) = (3-1) =2 hours.
Two legs of a step ladder are each 4 metres long. The angle formed between the two legs is 30degrees.Make a labelled scale drawing of the ladder using the scale Icm=0.5 metres and fill in the blanksbelow.
assume the figure as two step ladder
7. Principal = $39,300, Rate = 4.5%, Time = 6 months. What will that total principal + interest payment be rounded to the nearest dollar? o Lidhe total amount of
Given :
Principal = $39,300,
Rate = 4.5% = 0.045
Time = 6 months = 6/12 year = 0.5 year
Assume simple interest
So,
interest = Principal * rate * time = 39,300 * 0.045 * 0.5 = 884.25
So, the total = Principal + interest = 39,300 + 884.25 = 40,184.25
Rounding the answer to the nearest dollar
So, the total = $40,184
If g(x)=f(x)−1, then g(x) translates the function f(x) 1 unit _[blank]_.Which word correctly fills in the blank in the previous sentence?A. upB. leftC. downD. right
To answer this question, we need to remember the rules of transformations of functions, the rules are shown below:
From the table, we notice that if we subtract a number we are performing a vertical translation down.
Therefore, the correct word to fill the blank is down and the correct option is C.
Need help pleaseI was bad at math in school so lwant to learn
The probability of an event is expressed as
[tex]Pr(\text{event) =}\frac{Total\text{ number of favourable/desired outcome}}{Tota\text{l number of possible outcome}}[/tex]Given:
[tex]\begin{gathered} \text{Red}\Rightarrow2 \\ \text{Green}\Rightarrow3 \\ \text{Blue}\Rightarrow2 \\ \Rightarrow Total\text{ number of balls = 2+3+2=7 balls} \end{gathered}[/tex]The probability of drwing two blue balls one after the other is expressed as
[tex]Pr(\text{blue)}\times Pr(blue)[/tex]For the first draw:
[tex]\begin{gathered} Pr(\text{blue) = }\frac{number\text{ of blue balls}}{total\text{ number of balls}} \\ =\frac{2}{7} \end{gathered}[/tex]For the second draw, we have only 1 blue ball left out of a total of 6 balls (since a blue ball with drawn earlier).
Thus,
[tex]\begin{gathered} Pr(\text{blue)}=\frac{number\text{ of blue balls left}}{total\text{ number of balls left}} \\ =\frac{1}{6} \end{gathered}[/tex]The probability of drawing two blue balls one after the other is evaluted as
[tex]\begin{gathered} \frac{1}{6}\times\frac{2}{7} \\ =\frac{1}{21} \end{gathered}[/tex]The probablity that none of the balls drawn is blue is evaluted as
[tex]\begin{gathered} 1-\frac{1}{21} \\ =\frac{20}{21} \end{gathered}[/tex]Hence, the probablity that none of the balls drawn is blue is evaluted as
[tex]\frac{20}{21}[/tex]You flip a coin 3 times. Let's fill out a tree diagram to see allof the possible outcomes.What is the probabilitythat you will flip a headsall 3 times?
Answer
Explanation
Given:
You flip a coin 3 times.
To determine the tree diagram to see all of the possible outcomes when you flip a coin 3 times, we first note that we can get either Heads or Tails. So the tree diagrams is shown below:
The possible outcomes would be:
HHH, HHT,HTH,HTT,THH,THT,TTH,TTT
We can notice that there are 8 possible outcomes. But, the number of cases to get exactly 3 heads is just 1.
Hence, the probability of getting 3 heads is:
Probability = 1/8 =0.125
Therefore, the probability that you flip a heads all 3 times is 0.125.
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator).
Given the system of equations
[tex]\begin{gathered} x+4y-z=20-----1 \\ 3x+2y+z=8-----2 \\ 2x-3y+2z=-16-----3 \end{gathered}[/tex]We can solve for x, y and z below.
Explanation
Step 1: Find the value of z using the substitution method
[tex]\begin{gathered} \begin{bmatrix}x+4y-z=20\\ 3x+2y+z=8\\ 2x-3y+2z=-16\end{bmatrix} \\ Isolate\text{ for x in equation 1} \\ x=20-4y+z \\ \mathrm{Substitute\:}x=20-4y+z\text{ in equation 2 and 3} \\ \begin{bmatrix}3\left(20-4y+z\right)+2y+z=8\\ 2\left(20-4y+z\right)-3y+2z=-16\end{bmatrix} \\ sinplify \\ \begin{bmatrix}-10y+4z+60=8 \\ -11y+4z+40=-16\end{bmatrix} \\ Isolate\text{ for y in}-10y+4z+60=8 \\ -10y=8-4z-60 \\ y=\frac{8-4z-60}{-10} \\ y=\frac{-4z-52}{-10} \\ y=\frac{2\left(z+13\right)}{5} \\ \mathrm{Substitute\:}y=\frac{2\left(z+13\right)}{5}\text{ in }-11y+4z+40=-16 \\ \begin{bmatrix}-11\cdot \frac{2\left(z+13\right)}{5}+4z+40=-16\end{bmatrix} \\ simplify \\ \begin{bmatrix}\frac{-2z-286}{5}+40=-16\end{bmatrix} \\ multiply\text{ through by 5} \\ -2z-286+200=-80 \\ isolate\text{ for z} \\ -2z=-80-200+286 \\ -2z=6 \\ z=\frac{6}{-2} \\ z=-3 \end{gathered}[/tex]Step 2: Find y
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3\text{ in}\mathrm{\:}y=\frac{2\left(z+13\right)}{5} \\ y=\frac{2(-3+13)}{5} \\ y=\frac{2(10)}{5} \\ y=4 \end{gathered}[/tex]Step 3: Find z
[tex]\begin{gathered} \mathrm{Substitute\:}z=-3,\:y=4\text{ in }x=20-4y+z \\ x=20-4\cdot \:4-3 \\ x=1 \end{gathered}[/tex]Answer: The solutions to the system of equations are
[tex]x=1,\:z=-3,\:y=4[/tex]Answer the following question by creating an exponential equation? 1. On the day a rumor was started, 4 people knew about the rumor. The next day, and onward, the number of people who knew about the rumor doubled. On what day did 800 people know about the rumor?
Given
Series of numbers
first day = 4
second day = 8
Third day = 16
4, 8, 16, ...
From the exponential sequence
First term a = 4
common ratio r = second term/first term
= 8/4 = 2
r = 2
[tex]undefined[/tex]Susan is putting 11 colored lightbulbs into the string of lights that are three blue light bulbs to yellow light bulbs and six orange light bulb how many distinct orders of lightbulbs are there is two lightbulbs of the same color are considered identical(not distinct)
Using combinations, the number of ways is 36,036.
How to find a number of ways?Combinations are a method of calculating the total outcomes of an event where the order of the outcomes is irrelevant. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n represents the total number of items and r represents the number of items chosen at a time.How many distinct orders of light bulbs are there?
Since we have given thatNumber of white light bulbs = 5Number of orange light bulbs = 6Number of blue light bulbs = 2Total number of light bulbs = 13So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
Therefore, using combinations, the number of ways is 36,036.
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Sarah wants to take a vacation that will cost 2,562 if sarah plans to save for 9 months, then how much needs to be saved per month
Let:
x = Number of months
y = Total savings
a = Savings per month
so:
[tex]\begin{gathered} y=ax \\ where \\ y=2562 \\ x=9 \\ so\colon \\ 2562=9a \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{2562}{9} \\ a\approx284.67 \end{gathered}[/tex]She needs to save approximately $284.67 per month