y=×^2+23
Answer letter B
×=y-23
find the missing sides. Brainliest!!
Answer:
1. x = 28; y = 14√3
2. x = 9√2
Step-by-step explanation:
For these, it is helpful to remember that the side lengths of a 30°-60°-90° triangle have the ratio 1 : √3 : 2, and those of a 45°-45°-90° triangle have the ratio 1 : 1 : √2.
1. 14 is the shortest side, and x is the longest side, so ...
x = 2·14 = 28
y = (√3)·14 = 14√3
__
2. 18 is the longest side and x is the shortest side of this 45°-45°-90° triangle, so ...
x·√2 = 18
x = 18/√2 = 18·(√2)/2 = 9√2
13 ? start fraction, 13, divided by, 10, end fraction of a number is what percentage of that number?
Answer:
The percentage is [tex]130\%[/tex]
Step-by-step explanation:
Let
x-----> the number
we have
[tex]\frac{13}{10}x=1.3x[/tex]
To find the percentage multiply by 100
[tex]1.3*100=130\%[/tex]
What term describes this polygon ?
Answer:
Step-by-step explanation:
The last one
I hope I helped you.
Polygons are closed figures based on a plane that are characterized by their sides and angles. Without an image or description of the polygon, it's impossible to identify the specific polygon indicated.
Explanation:In mathematics, polygons are divided based on many factors such as the number of sides, length of sides, angle measures, etc. However, without the image or description of the polygon, I can't definitively tell what polygon you're referring to. For example, a polygon could be anything from a triangle (3 sides) to a decagon (10 sides). Remember, a polygon is basically a closed figure formed by three or more sides in a plane.
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Tom had $56. He bought a soda for $2 and 2 cookies for $3. Which expression correctly shows the total money Tom has left? A. $56 + (?$2) + (?$3) B $56 + (?$2) ? (?$3) C $56 ? (?$2) ? (?$3) D $56 ? (?$2) + (?$3)
C ($56) - ($2) - ($3)
Answer:
I believe it's A
Step-by-step explanation:
Sorry if wrong ;-;
Please answer at least one of these questions!! Please state which question you answered too. Will give brainliest!
Answer:
15. 4.9 cm
17. 6.63 cm
Step-by-step explanation:
15. A perpendicular bisector is a segment which divides another in half. Since JH is 9.8 then each of the two segments it divides into is 4.9.
17. The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.
a² + b² = c²
Here a is unknown, b = 10 and c = 12.
a² + 10² = 12²
a² + 100 = 144
a² = 44
a = √44 = 6.63
Solve by using proper methods. Show your work.
Determine the principal P that must be invested at 7%, compounded monthly, so that $200,000 will be available for retirement in 15 years?
Answer:
$70,201.38
Step-by-step explanation:
To determine the principal amount, we can use the formula:
[tex]P=\dfrac{A}{(1+\frac{r}{n})^{nt}}[/tex]
A = $200,000
r = 7% or 0.07
t = 15 years
n = 12
Now let's substitute our values.
[tex]P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}[/tex]
[tex]P=\dfrac{200,000}{(1.00583333333)^{12(15)}}[/tex]
[tex]P=70,201.38[/tex]
So the principal needed to get 200,000 in 15 years is $70,201.38.
translate inequality: "half of the sum of a number and five is a maximum of ten"
Answer:
[tex]\frac{1}{2} (x+5)\leq 10[/tex]
Step-by-step explanation:
Half the sum of (1/2 * ) a number and five (x + 5) is a maximum of 10 (less than or equal to).
Answer:[tex]\frac{x+5}{2}\leq 10[/tex]
Step-by-step explanation:
upper text bottom text left text right text this is for min word req problem in picture
Replace x in the second equation with the value of x from the first one.
x = -3y
x + y = -6
-3y + y = -6
Simplify:
-2y = -6
Divide both sides by -2:
y = -6 / -2
y = 3
Now replace Y with 3 in one of the equations to solve for x:
x = -3y = -3(3) = -9
X = -9, Y = 3
(-9,3)
The volume of a prism is 48 cubic centimeters. If the length is 2 centimeters and the width is 4 centimeters. What is the height?
Answer:
6
Step-by-step explanation:
volume is (lwh) since youre trying to find the height just multiply the 2 and 4 together to get 8. Then divide 8 by 48 to get your height.
A real estate broker's base salary is $18,000. She earns a 4% commission on total sales. How much must she sell to earn $55,000 total? Show your work and explain your reasoning in the space provided below.
The salary of the real estate broker = $18,000
Commission earned on total sales = 4% or 0.04
Total income earnings = $55,000
Let the total sales be = x
Equation becomes :
[tex]18000+0.04x=55000[/tex]
[tex]0.04x=55000-18000[/tex]
[tex]0.04x=37000[/tex]
[tex]x=925000[/tex]
Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.
To earn $55,000 total, the real estate broker must sell $925,000 in total.
Explanation:To find out how much the real estate broker must sell to earn $55,000 total, we need to consider both her base salary and her commission. Let's set up an equation to solve for the total sales needed:
$18,000 + 0.04x = $55,000
Subtracting $18,000 from both sides gives:
0.04x = $37,000
Dividing both sides by 0.04 gives:
x = $925,000
Therefore, the real estate broker must sell $925,000 in total to earn $55,000.
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23 points help asap!
Find the unit price and choose the better buy.
80 oz bottle of cleaner for $13.60
70 oz bottle of cleaner for $13.30
90 oz bottle of cleaner for $18.00
60 oz bottle of cleaner for $10.80
Answer:
60
Step-by-step explanation:
ITS THE BEST ONE
an 80 oz bottle of cleaner for $13.60 is the better buy because usually it would be about $40 for that size bottle
[tex](x-4)^{2} ^+(y-3)^{2} =16[/tex]
Find the center and radius
(explanation please, I need help)
an equation for a circle has formula
(x-m)² + (y-n)² = r²
where (m,n) is its center
and r is its radius
so, the equation has center (4,3) and radius 4
the equation is derived from the pythagorean theorem
Find the inverse function of that problem! Please!!
Answer:
[tex]y=\frac{\sqrt{x} -8}{-2}[/tex]
Step-by-step explanation:
To find an inverse, switch x and y values in the equation. Then solve for y.
[tex]F(x) = (8-2x)^2\\x = (8-2y)^2\\\sqrt{x} = 8 - 2y\\\sqrt{x} -8 = -2y\\\frac{\sqrt{x} -8}{-2} =y[/tex]
An elevator has a placard stating that the maximum capacity is 23252325 lblong dash—1515 passengers. So, 1515 adult male passengers can have a mean weight of up to 2325 divided by 15 equals 155 pounds.2325/15=155 pounds. If the elevator is loaded with 1515 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 155155 lb. (Assume that weights of males are normally distributed with a mean of 161 lb161 lb and a standard deviation of 31 lb31 lb.) Does this elevator appear to be safe?
Answer:
0.7734; no, it does not.
Step-by-step explanation:
To find this probability we will use a z-score. We are dealing with the probability of a sample mean being larger than a given value; this means we use the formula
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar in this problem is 155, as that is the sample mean we are trying to find the probability of. Our mean, μ, is 161 and our standard deviation, σ, is 31. Our sample size, n, is 15. This gives us
[tex]z=\frac{155-161}{31\div \sqrt{15}}=\frac{-6}{8.0042}=-0.75[/tex]
Using a z table, we see that the area under the curve less than this, corresponding with probability less than this value, is 0.2266. This means that the probability of the sample mean being larger than this is
1-0.2266 = 0.7734, or 77.34%.
Since there is a 77.34% chance of the passengers having a mean weight that is too heavy, this elevator is not safe.
The probability that the elevator is overloaded using the normal distribution principle is 0.7870
Given the Parameters :
Mean, μ = 161Standard deviation, σ = 31 Sample size, n = 15X = 155Using the relation :
Zscore = (xbar - μ) ÷ (σ/√(n))
Zscore = (155 - 161) ÷ (31/√15)
Zscore = - 0.796
The probability that lift is overloaded can be expressed thus :
P(Z ≥ - 0.796) = 1 - P(Z ≤ - 0.796)
Using a normal distribution table ; PP(Z ≤ - 0.796) = 0.2130
P(Z ≥ - 0.796) = 1 - 0.2130
P(Z ≥ - 0.796) = 0.7870
Therefore, the probability that weight is overloaded is 0.7870
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Holly has a rectangular garden that measures 12 m wide by 14 m long. She wants to increase the area to 255 m? by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.
Answer:
255 square meters
Step-by-step explanation:
Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508
So the width becomes
12 * 1.2320134508 = 14.7841614091
and the length becomes
14 * 1.2320134508 = 17.2481883107
That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters
Answer: The answer is 17
Step-by-step explanation:
The quarterly returns for a group of 51 mutual funds are well modeled by a Normal model with a mean of 7.4% and a standard deviation of 3.4%. Use the 68-95-99.7 Rule to find the cutoff values that would separate the following percentages of funds, rather than using technology to find the exact values. a) the highest 50% b) the highest 16% c) the lowest 2.5% d) the middle 68% a) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals 50% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% b) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xgreater than or equals nothing% B. xless than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% c) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.) A. xless than or equals nothing% B. xgreater than or equals nothing% C. nothing%less than or equalsxless than or equals nothing% d) Select the correct choice and fill in any answer boxes in your choice below. (Round to one decimal place as needed.)
Answer:
A) x ≥ 0.074; B) x ≥ 0.108; C) x ≤ 0.006; D) 0.04 ≤ x ≤ 0.108
Step-by-step explanation:
68% of data will fall within 1 standard deviation of the mean; 95% of data will fall within 2 standard deviations of the mean; and 99.7% of data will fall within 3 standard deviations of the mean.
Breaking this down, we find that 34% of data fall from the mean to 1 standard deviation above the mean; 13.5% of data fall from 1 standard deviation above the mean to 2 standard deviations above the mean; 2.35% of data fall from 2 standard deviations above the mean to 3 standard deviations above the mean; and 0.15% of data fall above 3 standard deviations above the mean.
The same percentages apply to the standard deviations below the mean.
The highest 50% of data will fall from the mean to the end of the right tail. This means the inequality for the highest 50% will be x ≥ 0.074, the mean.
The highest 16% of data will fall from 1 standard deviation above the mean to the end of the right tail. This means the inequality for the highest 16% will be x ≥ 0.074+0.034, or x ≥ 0.108.
The lowest 2.5% of data will fall from 2 standard deviations below the mean to the end of the left tail. This means the inequality for the lowest 2.5% will be x ≤ 0.074-0.034-0.034, or x ≤ 0.066.
The middle 68% will fall from 1 standard deviation below the mean to 1 standard deviation above the mean; this means the inequality for the middle 68% will be
0.074-0.034 ≤ x ≤ 0.074+0.034, or
0.04 ≤ x ≤ 0.108
The cutoff values using the 68-95-99.7 Rule for the given mutual funds data are calculated. The highest 50% lies between 4.0% and 10.8%, the highest 16% lies between 0.6% and 14.2%, the lowest 2.5% lies between -2.8% and 17.8%, and the middle 68% lies between 4.0% and 10.8%.
Explanation:The cutoff values can be found using the 68-95-99.7 Rule, which states that approximately 68 percent of the data lies within one standard deviation of the mean, 95 percent lies within two standard deviations, and 99.7 percent lies within three standard deviations. With a mean of 7.4% and a standard deviation of 3.4%, we can determine the cutoff values:
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(4CQ) Determine whether the series 3/2+9/8+27/32+...is convergent or divergent.
Answer:
The series is convergent ⇒ answer (a)
Step-by-step explanation:
* The series is 3/2 + 9/8 + 27/32 + ........
- It is a geometric series with:
- first term a = 3/2 and common ratio r = 9/8 ÷ 3/2 = 3/4
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = 3/4
∴ r < 1
∴ The series is convergent
Anvi designs a game in which a player either wins or loses 4 points during each turn. Which equation represents all numbers of points(p), a player may have after his or her first turn of the game?
p = 4
p = -4
|p| = 4
|p| = -4
Will mark the brainliest answer to the first person to correctly answer it
Answer: c) | p | = 4
Step-by-step explanation:
A player wins 4 (+4) or loses 4 (-4) points so you are looking for an answer that is ±4.
| p | = 4 → p = 4, p = -4
Simplify the expression. log(1/7)
Answer:
d. [tex]\frac{1}{7}[/tex]
Step-by-step explanation:
The given logarithm is
[tex]10^{\log(\frac{1}{7})}[/tex]
Recall that the common logarithm has a base of 10.
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}[/tex]
Recall also that;[tex]p^{(\log_pa)}=a[/tex]
[tex]10^{\log(\frac{1}{7})}=10^{\log_{10}(\frac{1}{7})}=\frac{1}{7}[/tex]
Determine the slope of the line that has the following coordinates: (-3, 6) (4,-2)
Answer: [tex]m=-\frac{8}{7}[/tex]
Step-by-step explanation:
To calculate the slope of the line that has the coordinates given in the problem you must use the formula shown below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Given the points (-3, 6) (4,-2), when you substitute them into the eequation shown above, you obtain that the slope is the following:
[tex]m=\frac{-2-6}{4-(-3)}\\m=-\frac{8}{7}[/tex]
Answer:
[tex] - \frac { 8 } { 7 } [/tex]
Step-by-step explanation:
We are given the following two points on a line and we are to find the slope of this line:
(-3, 6) and (4,-2)
We know the formula of the slope is given by:
[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]
Substituting the given coordinates in the above formula to get:
Slope = [tex] \frac { - 2 - 6 } { 4 - - 3 } = - \frac { 8 } { 7 } [/tex]
You have 6 large candy bars. You want to split each one into thirds. How many candy bar pieces will you then have?
Answer:
[tex]18\ pieces[/tex]
Step-by-step explanation:
step 1
Divide each large candy bar into thirds
so
[tex]\frac{1}{3}[/tex]
Now for each large candy bar you have 3 pieces of [tex]\frac{1}{3}[/tex]
step 2
Find the total number of candy bars pieces by proportion
[tex]\frac{1}{3}\frac{bar}{pieces} =\frac{6}{x}\frac{bar}{pieces}\\ \\x=6*3\\ \\x=18\ pieces[/tex]
Final answer:
To determine the total number of candy bar pieces after splitting 6 large bars into thirds, you multiply 6 by 3 resulting in 18 pieces.
Explanation:
The student's question is about dividing candy bars into thirds. If you start with 6 large candy bars and want to split each one into thirds, you end up with 6 groups of 3 pieces. To find the total number of candy bar pieces, you multiply the number of candy bars by the number of pieces you want to make from each bar, which is:
6 bars × 3 pieces per bar = 18 pieces.
Therefore, after splitting all the large candy bars into thirds, you will have a total of 18 candy bar pieces.
Triangle ABC has vertices at A(–2, 3), B(–3, –6), and C(2, –1). Is triangle ABC a right triangle? If so, which angle is the right angle? No, the triangle has no right angles. Yes, the right angle is angle A. Yes, the right angle is angle B. Yes, the right angle is angle C.
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).
Recall the slope formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line going through AC is
[tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]
The slope of the line going through BC s
[tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]
The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]
This means line AC is perpendicular to BC at C.
Hence the triangle ABC is right angled at C.
Answer:
Yes, the right angle is angle C.
Step-by-step explanation:
Find the point of intersection of the lines: y = 4x + 1 and y = – 2x + 4 A. (2 , 9) B. ( 1 2, 3 ) C. (1 , 2) D. ( 1 4, 2)
Answer:
B. (1/2, 3)
Step-by-step explanation:
It is perhaps easiest to try the point values in the equations.
A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer
B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer
we need go no further since we have the answer
To find the point of intersection, solve the system of equations formed by the two lines. Substituting x=1 into either equation gives y=5. Therefore, the point of intersection is (1,5).
Explanation:To find the point of intersection of two lines, we need to solve the system of equations formed by the two lines. In this case, the equations are y = 4x + 1 and y = -2x + 4.
Setting the equations equal to each other, we have 4x + 1 = -2x + 4. Solving for x, we get x = 1.
Substituting x = 1 into either of the original equations, we find y = 4(1) + 1 = 5. Therefore, the point of intersection is (1, 5).
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Which is true about the functional relationship shown in the graph?
Answer:
D
Step-by-step explanation:
For linear graphs, we say that the y-axis (y) is a function of the x-axis (x).
The y-axis shows earnings and the x-axis shows time worked (in hours). Thus, we can say that earnings is a function of the number of hours worked.
Looking at the answer choices, D is the correct choice.
Answer:
D
Step-by-step explanation:
I got it correct on A P E X
The following shape is NOT a polygon because:
Answer:
The shape includes a curve.
Step-by-step explanation:
A polygon consists of joined straight lines - no curves.
I dont understand anything
Answer:
D
Step-by-step explanation:
Answer:
The correct answer options are D and E.
Step-by-step explanation:
We are to determine whether which of the given data sets in the answer options are continuous.
For this, we need to know what a continuous data set is.
A data set which have no definite end to its value but keep on continuing.
Here, the data sets given in A, B and C have definite starting and ending points.
While D and E are continuous sets as its values are continuing.
Which situation describes DEPENDENT events? A) A die is rolled, the outcome is recorded, then a coin is tossed. B) A die is rolled, the outcome is recorded, then the same die is rolled again. C) A spinner is spun once, the outcome is recorded, then it is spun again. D) A card is drawn from a deck, then a second card is drawn from the same deck. Eliminate
Answer:
the answer is D
Step-by-step explanation:
Abott simplified an expression. His work is shown below.
Step 1
Step 2
Step 3
Step 4
45.5
In which step did Abott make his first mistake?
step 1
step 2
step 3
step 4
Mark this and return
Save and Exit Next Submit
Abott make his first mistake in step 2
Further explanationCalculation operations include multiply, divide, add, substract, etc.
In mathematical operations we can use the order of operation / calculation according to the principle of PEMDAS
P: Parentheses ⇒ ( ) E: Exponents (powers, square roots, etc.)⇒√,² MD: Multiplication and Division ⇒ x and : AS: Addition and Subtraction ⇒ + and -Multiplication and division or addition and subtraction are interchangeable/rank equally so the calculations/equation operations should be done from left to right
Abbot expression :
9.5 : 0.25 + + 4(0.25+0.5) + 6
Step 1 : 9.5 : 0.25 + + 4(0.75) + 6
Step 2 : 38 + 10(0.75)
Step 3 : 38 + 7.5
Step 4 : 45.5
From the Abott steps it can be concluded that the error occurred in step 2, because the number 4 must be multiplied first with the number in parentheses (ie 0.75)
The correct steps should:
step 1: Step 1: 9.5: 0.25 + 4 (0.75) + 6
Step 2: 38 + 3 + 6
Step 3: 38 + 9
Step 4: 47
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PEMDAS
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Answer:
Its B
Step-by-step explanation:
Match each expression to its equivalent expression with a rational denominator.
Answer: BCDA
Step-by-step explanation:
[tex]\dfrac{1}{\sqrt[4]{3x^3y^5}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\bigg(\dfrac{\sqrt[4]{3^3xy^3} }{\sqrt[4]{3^3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{\sqrt[4]{3^3xy^3} }{y(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3^3xy^3} }{3xy^2}}\quad Option\ B[/tex]
[tex]\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\bigg(\dfrac{\sqrt[4]{3xy^3} }{\sqrt[4]{3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{3\sqrt[4]{3xy^3} }{x^2y^3(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3xy^3} }{x^3y^4}}\quad Option\ C[/tex]
[tex]\dfrac{2}{\sqrt[6]{2x^7y^5}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\bigg(\dfrac{\sqrt[6]{2^5x^5y} }{\sqrt[6]{2^5x^5y}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{2\sqrt[6]{32x^5y} }{x(2xy)}\\\\\\\boxed{=\dfrac{\sqrt[6]{32x^5y} }{x^2y}}\quad Option\ D[/tex]
[tex]\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\bigg(\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{4\sqrt[6]{2xy^3} }{y(2xy)}\\\\\\\boxed{=\dfrac{2\sqrt[6]{2xy^3} }{xy^2}}\quad Option\ A[/tex]
Pete’s parents are offering to pay him a weekly allowance for doing his chores. They’ve given him two different payment options for a period of 15 weeks.
Option 1: $20 every week
Option 2: A penny in the first week, and then double the amount from the previous week in each week after that. So, 1 penny in the first week, 2 pennies in the second week, 4 pennies in the third week, and so on.
Which one is the better option for Pete? Explain why.
Find the total of each option to see which one is better.
Option 1:
$20 every week for 15 weeks = 15 x 20 = $300 total.
Option 2:
Week 1 you have 1 penny.
Week 2 you would have 1 +2 = 3 pennies.
Week 3 you would have 3 + 4 = 7 pennies.
From this we can see a pattern of 2^x - 1 where x is the number of weeks.
So in 15 weeks he would have 2^15 - 1 = 32767 pennies.
100 pennies equal $1
32767 / 100 = $327.67
The second option is better because he ends up with more money.