To determine how long it will take for $10,000 to triple with a continuous compounded interest rate of 5.5%, we use the continuous compound interest formula. Solve the equation for t by taking the natural logarithm of both sides and dividing by the interest rate, which yields t = ln(3) / 0.055.
Explanation:The subject at hand deals with Continuous Compound Interest. The formula used to calculate this is A = Pe^(rt), where A is the final amount, P is the initial principal, r is the yearly interest rate and t is the time in years.
In this case, the initial principal P is $10,000, the final amount (A) we want is $30,000 (because we want to triple the money), and the rate r is 5.5% or 0.055 as a decimal. We want to find t.
Plugging into the formula, we get 30000 = 10000 * e^(0.055t). Dividing both sides by 10000 yields 3 = e^(0.055t). If we take the natural log (ln) of both sides, the equation simplifies to ln(3) = 0.055t. Finally, solving for t, we get t = ln(3) / 0.055.
This will give you the number of years it'll take for the money to triple at an interest rate of 5.5% compounded continuously.
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what are the zeros of the function f(x) = x^2 + 2x- 8 / x^2 - 2x - 8
Answer:
x=-4 and x=2
Step-by-step explanation:
You are given the function
[tex]f(x)=\dfrac{x^2+2x-8}{x^2-2x-8}[/tex]
The zeros of the function are those value of x, for which [tex]f(x)=0[/tex]
First, find x for which function is undefined
[tex]x^2-2x-8\neq0\\ \\x^2-4x+2x-8\neq 0\\ \\x(x-4)+2(x-4)\neq 0\\ \\(x-4)(x+2)\neq 0\\ \\x\neq 4\text{ and }x\neq -2[/tex]
Now find points at which f(x)=0:
[tex]f(x)=0\Rightarrow x^2+2x-8=0\\ \\x^2+4x-2x-8=0\\ \\x(x+4)-2(x+4)=0\\ \\(x-2)(x+4)=0\\ \\x=2\text{ or }x=-4[/tex]
For both these values (x=-4 and x=2) function f(x) is defined, then x=-4 and x=2 are zeros of the function.
Final answer:
To find the zeros of the given function, set the numerator equal to zero and solve for x. The zeros are x = -4 and x = 2.
Explanation:
We can notice that both the numerator and denominator share the same factors (x² - 2x - 8). This means that f(x) is undefined where the denominator is zero.
Therefore, the zeros of the function f(x) = x² + 2x - 8 / x² - 2x - 8 can be found by setting the numerator equal to zero and solving for x.
By factoring the numerator and denominator, it becomes easier to identify the zeros.
x² - 2x - 8 = 0
Factoring the expression:
(x - 4)(x + 2) = 0
Therefore, the zeros of the function f(x) are x = 4 and x = -2.
TIMED HURRY PLS!
Maria determined that these expressions are equivalent expressions using the values of x=3 and x=7. Which statements are true? Check all that apply.
Answer:
We have the following equations:
5 + 3x - 2 and x + 2(x+1) + 1
Before checking the statements. Let's solve the syste of equations:
5 + 3x - 2 = x + 2(x+1) + 1
5 + 3x - 2 = x + 2x+2 + 1
3x + 3 = 3x + 3
Both equations are equivalent. Now, let's judge the statements:
1. The expressions are only equivalent when evaluated with odd values.
Given that the both expression are the same, the expressions are equivalent for ALL values.
Therefore, the statement IS FALSE ❌
2. The expressions are only equivalent for x=3 and x=7.
Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.
Therefore, the statement IS FALSE ❌
3. The expressions should have been evaluated with one odd value and one even value.
If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.
Therefore, the statement IS FALSE ❌
4. The expressions have equivalent values when x=6.
Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).
Therefore, the statement IS TRUE ✅
5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.
Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.
Therefore, the statement IS FALSE ❌
6. The expressions have equivalent values for any value of x.
Given that the both expression are the same, the expressions are equivalent for ALL values of x.
Therefore, the statement IS TRUE ✅
7. When x=10, both expressions have a value of 33
Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.
Therefore, the statement IS TRUE ✅
Answer:
D,F,G
Step-by-step explanation:
It Makes Sense.
Consider the following formula used to estimate the height, h, of a seedling after w weeks since planting: h = (1/5)w + (8/5). Which of the following represents the formula that could be used to find the number of weeks since planting using the height, h, of the seedling?
A. w = 5h - (8/5)
B. w = 5h - 8
C. w = h/5 - 8
D. w = h/5 - 8/5
[tex]\bf h=\cfrac{1}{5}w+\cfrac{8}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(h)=5\left( \cfrac{1}{5}w+\cfrac{8}{5} \right)}\implies 5h=w+8\implies 5h-8=w[/tex]
The equation that can be used to find the number of weeks since planting is (b) w = 5h - 8
How to determine the equation of the number of weeks?The equation is given as:
h = (1/5)w + (8/5)
Multiply through by 5
5h = w + 8
Subtract 8 from both sides
5h - 8 = w
Make w the subject
w = 5h - 8
Hence, the equation that can be used to find the number of weeks since planting is (b) w = 5h - 8
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A water tank is a cylinder with radius 40 cm and depth 150 m
150 cm
40 cm
It is filled at the rate of 0.2 litres per second.
1 litre = 1000 cm3
Does it take longer than 1 hour to fill the tank?
3.142×40^2×150=753,982.237
if1sec =0.2litres
what about 753.982=
753.982×1/0.2
=22.80
To determine if filling a tank takes longer than an hour, calculate the tank's volume, convert it to liters, and then divide by the fill rate. With a 240π liter capacity and a 0.2 L/s fill rate, it takes approximately 1.05 hours, thus longer than 1 hour.
To determine if it takes longer than 1 hour to fill a water tank with a radius of 40 cm and depth of 150 cm at a rate of 0.2 liters per second, we first calculate the volume of the tank and then the total time required to fill it at the given rate.
Step 1: Calculate the Volume of the Tank
Volume of a cylinder = πr²h, where r is the radius and h is the height.
Here, r = 40 cm and h = 150 cm.
Volume = π(40²)(150) = π(1600)(150) = 240000π cm³.
Step 2: Convert the Volume to Liters
Since 1 liter = 1000 cm³, the volume in liters = 240000π / 1000 = 240π liters.
Step 3: Calculate the Filling Time
Time = volume / rate = 240π / 0.2 = 1200π seconds.
To convert to hours, divide by 3600 (the number of seconds in an hour).
Total time in hours = 1200π / 3600 = π/3 hours, which is approximately 1.05 hours.
Since it takes approximately 1.05 hours to fill the tank, it does take longer than 1 hour to fill the tank.
HELP PLZ
What is the shape of the following cross section????
Answer:
Triangle
Step-by-step explanation:
Look at the shape of the red part
The shape of the triangle is the cross-section part of the given figure. Thus, option A is correct.
How to find the shape inscribed in a square?The cross-section part of the given figure could be the shape fro the inscribed figure.
Here we can see that the three-dimensional figure inscribed in the square is a cone.
The right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
But for the plane of the square, the triangle is the cross-section part of the given figure.
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Solve this system of equations by elimination:
8x+9y=48
12x+5y=21
Answer:
Let's solve your system of equations by elimination.
8x+9y=48;12x+5y=21
Steps:
Multiply the first equation by 5,and multiply the second equation by -9.
5(8x+9y=48)
−9(12x+5y=21)
Becomes:
40x+45y=240
−108x−45y=−189
Add these equations to eliminate y:
−68x=51
Then solve−68x=51for x:
−68x /−68 = 51 /−68 (Divide both sides by -68)
x= −3 /4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
8x+9y=48
Substitute
−3 /4
8x+9y=48:
8( −3 /4 )+9y=48
9y−6=48 (Simplify both sides of the equation)
9y−6+6=48+6 (Add 6 to both sides)
9y=54
9y /9 = 54 /9 (Divide both sides by 9) y=6
Answer: x= −3 /4 and y=6
Hope This Helps! Have A Nice Day!!
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. You order a large pizza, and it cost $16.49. Describe the pizza you ordered.
Math sequences number patterns
Answer:
see explanation
Step-by-step explanation:
(a)
Note the squared value in column 3 which is the square of 1 more than the row number, that is
row 2 → (2 + 1)² →3²
row 3 → (3 + 1)² → 4²
Find the square root of 676 = 26 → (25 + 1)² = 26²
Hence the row number is 25
(b)
The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]
row number is n then n(n + 2) + 1 = n² + 2n + 1
A 2-pound bottle of barbecue sauce costs $22.40. What is the price per ounce
Answer:
The answer is $0.69. This is because there are 32 ounces in the bottle, and $22.08/32=0.69, or $0.69.
Step-by-step explanation:
please help me cause I really need it!!
The equation would be h = 25 + m
^^^The reason this is the equation is because the amount of time it takes to do the homework is the 25 min of reading AND the m of completing math problems
Insert 20 in for m and solve for h
h = 20 + 25
h = 45
Insert 25 in for m and solve for h
h = 25 + 25
h = 50
Hope this helped!
~Just a girl in love with Shawn Mendes
Write x^3/2 in radical form
Answer:
Step-by-step explanation:
I think you meant x^(3/2). This breaks down in at least two ways:
[x^3]^(1/2), or √(x^3)m or √x³), or
[x^(1/2)]^3 = (√x)^3
To write [tex]x^{3/2}[/tex] in radical form, rewrite it as (√x)³or √(x³). This utilizes the relationship between fractional exponents and radicals.
To write [tex]x^{3/2}[/tex] in radical form, we can use the relationship between exponents and radicals. In general, the expression [tex]x^{a/b}[/tex] can be written in radical form as the b-th root of x raised to the power 'a'. So, applying this rule to the given expression.
[tex]x^{3/2}[/tex]
Step-by-Step Explanation:
Rewrite the exponent 3/2 as a fraction where the numerator is the power and the denominator is the index of the root.So, [tex]x^{3/2}[/tex] can be written as the square root of x raised to the power of 3.This translates to: (√x)³ or equivalently, [tex](x^{3})^{1/2}[/tex] which means the square root of x cubed.Therefore, the radical form of [tex]x^{3/2}[/tex] is √x³ or (√x)³.
Find the surface area of the pyramid shown to the nearest whole number get brainlists
Answer
914 m^2 to the nearest whole number.
Step-by-step explanation:
The area of the hexagonal base is made up of 6 congruent triangles so its area = 6* 1/2 base* height
= 6 * 1/2 * 12 * 6√3
= 216-√3 m^2.
The area of each slanting triangle = 6 * 15 m^2 so the lateral area of the pyramid
= 6*6*15= 540 m^2
Total surface area = 540 + 216√3
= 914.12 m^2.
hope this helps
and to make it simpler its C or 914.12
If a product is normally retails for $40 and we give you a six dollar discount what percentage is your discount are we giving you
Answer:
The discount is 15% because 6/40 = 0.15 and a percent is multiplied by 100 so the answer is 15%.
To find the percentage discount, subtract the discount amount from the original price and divide by the original price, then multiply by 100.
Explanation:To find the percentage discount, we need to calculate the amount of the discount first. The discount is given as $6, so we subtract $6 from the original price of $40 to get $34. To find the percentage, we divide the discount amount by the original price and multiply by 100. In this case, the discount percentage would be (6/40) * 100 = 15%.
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Hello anyone can do this? Please put answer in points(x,y)
Answer:
Check the attached graph
Step-by-step explanation:
Given that slope of the line is m = 1
And the line passes through the point (-3,5).
Now we need to graph the line using above information. So begin by graphing the point (-3,5).
Slope means rise/run
Then slope = 1 means rise/run=1=1/1
means move point 1 unit up then 1 unit right
then new point is at (-2,6).
Now draw a line joining both points to get the final graph.
How do I solve this math problem
Answer:
Cross Multiply.
Step-by-step explanation:
Multiply the denominator (3) of one side and the numerator (n).
Then, multiply the numerator (2) of on side and the denominator (4) of the other.
3n = 8
You divide both sides by 3 to have n be by itself, equaling ~2.6 or 8/3.
If a data set has many outliers, which measure of central tendency would be the BEST to use?
A) mean
B) median
C) mode
D) range
Mode could work but I believe the best answer would be median.
Answer:
median
Step-by-step explanation:
Median is correct. One extreme outlier can "drag" the mean up or down, while it would have little or no effect on the median.
One timer is set to ring every 48 seconds. Another timer is set to ring every 2 minutes 15 seconds. They rang together at 7 p.m. When is the next time that the timers will ring together? Include your reasoning and calculations to justify your answer
Answer:
8:16 p.m.
Step-by-step explanation:
You have to find LCM(a,b), where a=48 seconds and b=95 seconds (2 minutes 15 seconds).
1.
[tex]48=2\cdot 24=2\cdot 2\cdot 12=2\cdot 2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 2\cdot 3=2^4\cdot 3.[/tex]
2.
[tex]95=5\cdot 19.[/tex]
3.
[tex]LCM(48,95)=2^4\cdot 3\cdot 5\cdot 19=4560\text{ seconds }=76\text{ minutes }=1\text{ hour }16 \text{ minutes. }[/tex]
If they rang together at 7 p.m, then the next time that the timers will ring together will be after 1 hour 16 minutes that is 8:16 p.m.
Answer:
8:16 p.m.
Step-by-step explanation:
You have to find LCM(a,b), where a=48 seconds and b=95 seconds (2 minutes 15 seconds).
1.
2.
3.
If they rang together at 7 p.m, then the next time that the timers will ring together will be after 1 hour 16 minutes that is 8:16 p.m.
What is the distance between points (7, -4) and (7, 9)?
Answer:
13Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (7, -4) and (7, 9). Substitute:
[tex]d=\sqrt{(7-7)^2+(9-(-4))^2}=\sqrt{0+13^2}=\sqrt{13^2}=13[/tex]
Used [tex]\sqrt{a^2}=a[/tex]
can a triangle have sides with the given lengths? 2ft, 7ft, 12ft
Answer:yes
Step-by-step explanation:
2+7=9
12+2=14
12+7=19
Answer:
No
Step-by-step explanation:
the sum of two sides has to be greater than the third side
2+7=9 9 isn't greater than 12
What is a solution for both equations y=x+3 and -2x+y=1
Answer:
(2, 5)
Step-by-step explanation:
Given the 2 equations
y = x + 3 → (1)
- 2x + y = 1 → (2)
Substitute y = x + 3 into (2)
- 2x + x + 3 = 1
- x + 3 = 1 ( subtract 3 from both sides )
- x = - 2 ( multiply both sides by - 1 )
x = 2
Substitute x = 2 into (1) for corresponding value of y
y = 2 + 3 = 5
Solution is (2, 5)
Answer: y=5, x=2
Step-by-step explanation:
What is the discriminant of 3x2 + 6x = 2?
Answer: x = 1/6 or 1.6667
Steps3x * 2 + 6x = 2
Multiply the numbers: 3 * 2 = 6
6x + 6x = 2
Add similar elements: 6x + 6x = 12x
12x = 2
Divide both sides by 12
12x / 12 = 2 / 12
Simplify
x = 1/6
Answer: The required discriminant of the given quadratic equation is 60.
Step-by-step explanation: We are given to find the discriminant of the following quadratic equation :
[tex]3x^2+6x=2\\\\\Rightarrow 3x^2+6x-2=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the discriminant of a quadratic equation [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]D=b^2-4ac.[/tex]
For the given equation (i), we have
a = 3, b = 6 and c = -2.
Therefore, the discriminant of the given equation will be
[tex]D=b^2-4ac=6^2-4\times3\times(-2)=36+24=60.[/tex]
Thus, the required discriminant of the given quadratic equation is 60.
A shop keeper sold some products the results of the number of products are shown below which product had the greatest percentage of its inventory sold 40 mango jellies out of the 80 jellies 68% of the of the apple juice is sold 0.475 of the cake are sold
Apple juice
Cake
Mango jelly
Answer: Apple Juice
Step-by-step explanation: Right of the bat we know 40 out of 80 is 50%. This is already less then the 68% we are given, so therefore it can't be mango jelly. 0.475 would be made into a percent of 47.5%. We know that the fraction would be 475 over 1000, so we need to move the decimal point once to the left for each number, giving us the percent above. 68% is greater than 47.5, making Apple juice the winned
Apple juice good luck
4. A book club earns $230 for its meetings. They want to divide the money to pay for 7 meetings. When the treasurer types
230 ÷ 7 into a calculator, the number that appears is 32.8571. Where should the treasurer round the answer? Explain.
nearest cent so so 32.86 but since its money and 32.86 times 7 is 230.02 it should be rounded down so the answer will be 32.85
consider the exponential function f(x)=13500×0.89^x Which models the value of Mikaylas scooter, where X represents the number of years since she purchased scooter
part a: is the value of of Mikaylas scooter growing or decaying?
part b: what is the rate of growth or decay?
part c: what does 13500 represent?
Part a: decaying;
Part b: decays 11% each year( 100-89=11);
Part c:the initial value of the scooter ( money spent to buy the scooter)
The value of Mikayla's scooter, modeled by the exponential decay function f(x)=13500x0.89^x, is decaying at a rate of 11% per year. The initial cost of the scooter was $13,500.
Explanation:The function f(x)=13500×0.89^x is an example of an exponential decay function because the base (0.89) is less than 1. So, the value of Mikayla's scooter is decaying.
Part a: The value of the scooter is decaying because the base of the exponential function is less than 1.
Part b: The rate of decay is 11% per year. This comes from the fact that 1 - 0.89 = 0.11 or 11%, signifying the percentage decrease each year.
Part c: 13500 represents the initial value of the scooter. This is how much the scooter was worth when it was first purchased by Mikayla.
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1
The formula for the area of a triangle is A =
bh, where bis
Find the height of a triangle that has an area of 30 square
units and a base measuring 12 units.
the length of the base and h is the height. The equation
solved for his h= 24
3 units
5 units
8 units
9 units
Answer:
height is 5 units
Step-by-step explanation:
We are required to determine the height of a triangle that has an area of 30 square units and a base measuring 12 units.
The formula for the area of a triangle is given as;
[tex]Area=\frac{1}{2}*base*height[/tex]
We plug in the given values and solve for the height;
[tex]30=\frac{1}{2}*12*height\\\\30=6*height\\height=5[/tex]
Answer:
5 units^2
Step-by-step explanation:
The sixth grade chorus has a boy to girl ratio of 3:8 which of the following ratios is equivalent to this ratio?
A) 15 boys to 55 girls
B) 55 boys to 15 girls
C) 40 boys to 15 girls
D) 15 boys to 40 girls
The ratio in option (D), 15 boys to 40 girls is equivalent to 3 : 8.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
The given ratio of boy to girls is 3 : 8.
To find the equivalent ratio to 3:8.
Solve with the help of option,
(A)
15 boys to 55 girls.
The ratio 15 : 55 = 3 : 11
(B)
55 boys to 15 girls,
The ratio 55 : 15 = 11 : 3.
(C)
40 boys to 15 girls,
The ratio 40 : 15 = 8 : 3
(D)
15 boys to 40 girls,
The ratio 15 : 40 = 3 : 8.
The ratio of 15 boys to 40 girls is 3:8.
Hence, the correct option is (D).
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Which is the correct letter answer of the value of the log equation?
Answer:
The value of the single logarithm is -11 ⇒ answer B
Step-by-step explanation:
* Lets revise the rule of the logarithmic functions
# ㏒ a + ㏒ b = ㏒ ab
# ㏒ a - ㏒ b = ㏒ a/b
# ㏒ a^n = n ㏒ a
# ㏒ 1 = 0
* Now lets solve the problem
∵ [tex]log_{b}(\frac{A^{5}C^{2}}{D^{6}})[/tex]
- Change the single logarithm to an expression by change the
multiplication to addition and the division to subtraction
∵ [tex]log_{b}A^{5}=5log_{b}A[/tex]
∵ [tex]log_{b}C^{2}=2log_{b}C[/tex]
∵ [tex]log_{b}D^{6}=6log_{b}D[/tex]
∴ The single logarithm = [tex]5log_{b}A+2log_{b}C-6log_{b}D[/tex]
* Now lets substitute the values
∵ [tex]log_{b}A=3;===log_{b}C=2;===log_{b}D=5[/tex]
- Substitute the values into the expression
∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11
* The value of the single logarithm is -11
Write an expression to represent:
Three more than the product of two and a number xxx.
Answer:
(2x)+3
Step-by-step explanation:
I'm sure most of you just want the answer, but if you want me to educate you, keep reading!!
The product of two and a number x can be written as 2x.
Three more than something means that we add 3 to it.
If we add 3 to 2x, we have 3+2x.
So in conclusion, the answer would be (2x)+3.
Hope this helps! :)
The final value will be 2x+3
How to find the expression?Firstly,
The product of two and a number x can be written as 2x.Three more than something means that we add 3 to it.∴If we add 3 to 2x, we have 3+2x.
So the answer would be (2x)+3.
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Select all expressions that are equivalent to 6x+1-(3x-1)
where are the expressions ?
Answer:
3x + 2
Step-by-step explanation:
Angel and Isaiah have forgotten whose turn it is to mow the lawn. how can they make a fair decision? SELECT ALL THE CORRECT ANSWER
t
Answer:
A and C
Step-by-step explanation:
This question is on probability.
In the first option A, when a coin is tossed, two outcomes are obtained, a head or a tail. Angel to mop can be represented by heads and Isaiah to mow can be represented by tail.In this case, a 50% chance is observed.
In the third option, putting each person's name on a separate piece of paper in a bag has two outcomes to be obtained. The probability of picking a person name is 50%. You can pick a paper with Angel's name or Isaiah's name.The picked name will mow the lawn.
In the second option B, when a coin is flipped twice, we obtain 4 outcomes; HH,HT,TH,TT. If either toss is tail, TT, then Angel mows the lawn.However, there are 3 other outcomes that could occur which will make Isaiah to mow the lawn.In this case it will be unfair because the probability for Angle to mow, P(A)=1/4 where as that for Isaiah to mow P(I)=3/4
In the last option D, the probability of rolling a cube with a number 1 or 6 is 1/6. This is the same for geting a 2,3,4,or 5.Angel will mow if the number is 1 or 6 where as Isaiah will mow if the number is 2,3,4 or 5. This is unfair to Isaiah because geting any number holds a probability of 1/6, while Angels waits for 2 numbers, he waits for 4 numbers.
Answer: Option 1 and 3
Step-by-step explanation:
A fair decision is when both of them have the same probability of winning and losing, in this case, because we have two possible results, we need to find an experiment with a 50/50 chance.
The coin in option 1 is a good option, 50% of the time it will end in tails and 50% of the time it will come up with heads, so this will be a fair decision.
option 3 also works, because we have two pieces of paper, if you draw one, the probability of drawing a specific one is 1/2 (the specific result divide by the total number of possible results) and this is equivalent to 0.5 or 50%.
The other two options have probabilities that are not equal, for example in the fourth option, Angel mows the lawn when the number is 1 or 6, we have 2 out of 6 results where he mows the lawn, this is p = 2/6 = 1/3
then the probability of Isaiah of mowing the lawn is p = 4/6 = 2/3, wich is bigger.