Direct variations have an special characteristic: they can be represented on a plane by a line paassing through the origin (0,0).
The equation of a line has the following shape:
[tex]y=mx+b[/tex]Where x is the slope, and b is the y intercept.
For direct variations, the line passes through the origin; then, the y intercept is 0, therefore b=0.
For direct variations, we can have an associated line with the following shape:
[tex]y=mx[/tex]We can find the value for m knowing 2 points of the line and calculating the slope. One point is (-1,-4); and the other is the origin (0,0).
Now we can calculate the slope by dividing y distance of the points by the x distance of the points:
[tex]m=\frac{0-(-4)}{0-(-1)}=\frac{0+4}{0+1}=\frac{4}{1}=4[/tex]We have calculated the slope to be 4, then the equation representing the direct variation is:
[tex]y=4x[/tex]Any pair of points x,y that satisfy the equation will an element of the direct variation.
Now, we can try each:
With 8,0:
[tex]\begin{gathered} 0=4\cdot8 \\ 0=16 \end{gathered}[/tex]8,0 does not satisfy, therefore it is not an element of the direct variation.
2,8:
[tex]\begin{gathered} 8=4\cdot2 \\ 8=8 \end{gathered}[/tex]2,8 is element of the dierct variation
-2,0:
[tex]\begin{gathered} 0=4\cdot(-2) \\ 0=-8 \end{gathered}[/tex]-2,0 is not part
4,-1:
[tex]\begin{gathered} -1=4\cdot4 \\ -1=16 \end{gathered}[/tex]4,-1 is not part
8,-1:
[tex]\begin{gathered} -1=4\cdot8 \\ -1=32 \end{gathered}[/tex]8,-1 is not part
-2,-8:
[tex]\begin{gathered} -8=4\cdot(-2) \\ -8=-8 \end{gathered}[/tex]-2,-8 is part.
Finally, we can say points (-4,-1), (2,8) and (-2,-8) are part of the direct variation.
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
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.
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
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]= 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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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]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
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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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)HelpWhich equation can be used to solve for x in the following diagram?
The sum of the angles is 90° because is a right angle because the square on the angle means it
then if we sum the angles 30° and 2x° we have 90°
[tex]30+2x=90[/tex]or
[tex]2x+30=90[/tex]then right option is A
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]#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.
ANSWER ASAP!! Raise the monomial to a power: -2m^3n^2t to the power of 4
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
Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.
Given:
Sara's age is represented by S and Ronaldo's age is represented by R.
Since,
Sara is 33 years younger than Ronaldo, then;
S= R - 33
Now, the sum of ages of Sara and Ronaldo is 105 then
[tex]R+S=105[/tex]Hence, from above,
[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]Therefore, second option is correct.
What is the equation in slope-intercept form of the line that passes through the point (1,5) and is parallel to the line represented by 3x-y=4?
Answer:
[tex]3x - 14[/tex]
Step-by-step explanation:
-y= -3x+4
-1 because de y no have a number in front
-1y÷-1= -3x÷-1 4÷-1
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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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.
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.
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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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
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.
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]find the volume or missing value 3ft, 2.5ft, 6ft
The formula to find the volume of a rectangular prism is
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \text{ Where V is the volume}, \\ l\text{ is the length,} \\ w\text{ is the width and} \\ \text{h is the height of the rectangular prism} \end{gathered}[/tex]Graphically,
So, in this case, you have
[tex]\begin{gathered} l=3ft \\ w=2.5ft \\ h=6ft \\ V=l\cdot w\cdot h \\ V=3ft\cdot2.5ft\cdot6ft \\ V=45ft^3 \end{gathered}[/tex]Therefore, the volume of the rectangular prism is 45 cubic feet.
Note:enter your answer and show all steps that you use to solve this problem3.jaoquin buys 3 dozen lightbulbs.after changing the lightbulbs in his house, he has 15 lightbulbs left how many lightbulbs did he use?*btw the not is the same thing to my question I have for number 6*6. the empire state building in new York City is 1,250 feet tall. it has 103 floors. rounded to the nearest whole, what is the height of each floor?
Answer: Number of lightbulbs that he used = 21 lightbulbs
1 dozen of light bulbs = 12 light bulbs
Jaoquin buys 3 dozens
3 dozens of lightbulbs = 3 * 12 lightbulbs
3 dozens of lightbulbs = 36 lightbulbs
This means that :
The number of light bulbs Jaoquin bought = 36
The number of lightbulbs that remain = 15
The number of lightbulbs that he used = (Number of lightbulbs that he buys) - (Number of lightbulbs that remains)
Number of lightbulbs that he used = 36 - 15
Number of lightbulbs that he used = 21 lightbulbs
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!!!
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]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
if a certain number is added to both the numerator and denominator of the fraction 8/9, the result is 6/7. Find the numer.