A) The data models a geometric sequence
B) Using a recursive formula, the time she will complete station 5 is; 2
C) Using a explicit formula, the time she will complete station 9 is; 512
How to find the Recursive Formula?A) From the given coordinates (1, 3), (2, 6), (3, 12), (4, 24), we can say that when x increases by 1, y is multiplied by 2. Thus, as the quotient between consecutive terms is the same, the data depicts a geometric sequence.
B) The recursive formula for a geometric sequence with common ratio r and first term a₁ is given by the formula:
f(n) = a₁(r)ⁿ⁻¹
Since a₁ = 2 and r = 1, then we have;
f(1) = 2(1)¹⁻¹
f(1) = 2
f(5) = 2
C) The explicit formula from the calculations above will be;
aₙ = 2ⁿ
Thus;
a₉ = 2⁹
a₉ = 512
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Mr. Wright is investing $1 million. He has options with Bank of Munich, Coralbank, and Lone Star Credit Union.
Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
Lone Star Credit Union is offering an interest rate of 1.75% on all funds invested with them.
Mr. Wright plans to leave whatever funds he invests in the account for 15 years.
ROUND ALL ANSWERS TO THE NEAREST TEN THOUSAND AND DO NOT USE COMMAS IN YOUR RESPONSE.
How much money should Mr. Wright expect to have after 15 years if he invests all of his funds with Coralbank?
How much money would he have if he invests everything with Bank of Munich for the full 15 years?
If he plans carefully and invests his funds to gain the maximum amount of interest across all three institutions, how much money will he have in each bank
after 15 years?
Bank of Munich:
Coralbank
Lone Star Credit Union:
In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97
What is Interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
Given:
Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.
So, After 15 years
First, convert R as a percent to r as a decimal
r = R/100
r = 3/100
r = 0.03 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 500,000.00[tex](1 + 0.03/1)^{(1)(15)[/tex]
A = 500,000.00[tex](1 + 0.03)^{(15)[/tex]
A = $778,983.71
and, for Another $500,000
A = P[tex](1 + r/n)^{nt[/tex]
A = 500,000.00 [tex](1 + 0.00/1)^{(1)(15)[/tex]
A = 500,000.00 [tex](1 + 0.01/1)^{(1)(15)[/tex]
A = $580,484.48
Total he Invests= $ 1,359,468.19
and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.
Then solve the equation for A
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for A
A = P[tex](1 + r/n)^{nt[/tex]
A = 250,000.00[tex](1 + 0.02/1)^{(1)(15)[/tex]
A = 250,000.00 [tex](1 + 0.02)^{(15)[/tex]
A = $336,467.08
and, for Another $750,000 .
A = P[tex](1 + r/n)^{nt[/tex]
A = 750,000.00[tex](1 + 0.0125/1)^{(1)(15)[/tex]
A = 750,000.00 [tex](1 + 0.0125)^{(15)[/tex]
A = $903,621.89
Total he Invests= $ 1,240,088.97
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40 divided by 5 times (24-23)
Apply the ditributive property to factor out the greatet common factor. 60 − 40 y =
The factors by applying distributive property out the greatest common factor is 20(3 - 2y).
Define the term greatest common factor?The largest of these shared factors is the greatest common factor of the two integers.For the stated equation;
= 60 − 40 y
Do the prime factorization of the both numbers-
60 = 2×2×3×5
40 = 2×2×2×5
Thus, the greatest common factor from both numbers is-
2×2×5 = 20
Taking 20 common from both terms in equation-
Using distribute property;
= 20(3 - 2y)
Thus, factors by applying distributive property out the greatest common factor is 20(3 - 2y).
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what was the major flaw in the stanford prison experiment? group of answer choices zimbardo did not use a control group. the respondents wanted to leave, but zimbardo would not let them. the students were not randomly assigned. the study went on too long.
The answer is (a) Zimbardo did not use a control group.
The stanford prison experiment was a two week simulation of a prison environment that examined the effect of situational variables on participants reactions and behaviors.
The Stanford prison experiment, one of the most famous and compelling psychological studies of all time.
The major flaw in the research design of the Stanford prison experiment was that the Zimbardo did not use a control group.
A control group is used to establish a cause-and-effect relationship by isolating the effect of an independent variable. A control group was necessary to study a particular variable in prison. He had no alternative group to compare to measure the results of the experiment.
A control group in an experiment does not receive the treatment. Instead, it serves as a comparison group for the treatments.
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a consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. what is the probability that a car chosen at random will need a) norepairs? b) nomorethanonerepair? c) some repairs?
The probability that a car chosen to random will need:
A) no repairs: 72%
B) No more than one repairs: 89%
C) some repairs: 11%
The total amount of cars that will need some type of repair is 28%; 17% will need to be repaired once + 7% will need to be repaired twice + 4% will need to be repaired more than two times.
The amount of cars that wouldn´t need any type of repairs is the total amount of cars minus the percentage that need some type of repair:
100% - 28% = 72%.
The amount of cars that will need no repairs or only one repair is the total amount of cars minus the percentage that need more than one of repair:
100% - (7% + 4%) = 89%.
The amount of cars that need some repairs is the sum of those cars that need two repairs plus those that need three or more repairs:
7% + 4% = 11%
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given vector u equals open angled bracket negative 11 comma negative 5 close angled bracket and vector v equals open angled bracket 4 comma 8 close angled bracket comma what is projvu?
The value of the vector VU is <44, 40>
Vector:
in math vector consist an object that has both a magnitude and a direction.
Given:-
Here we have the vector v and u with the value of v = <11, 5> and the value of u = <4, 8>.
Now, we have to find the value of VU.
In order to find the value of VU, we have to perform the multiplication operation on the given vector,
In order to perform the multiplication on it, we have to arrange them in the following order,
=> VU = <11, 5> x <4,8>
Now, we have to combine the values like the following,
=> <(11 x 4) , (5 x 8)>
Now, do the multiplication then we get,
=> <44, 40>
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a gardener uses a total of 61.5 gallons of gasoline in one month. Of the total amount of gasoline, 3/5 was used in his lawn mowers. How many gallons of gasoline did the gardener use in his lawn mowers in the one month
Answer:
36.9 gallons were used in one month.
Step-by-step explanation:
In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other:
3 ÷ 5 = 0.6
Then, we can set up this equation to figure out how much gallons of gasoline was used:
0.6 x 61.5 = 36.9
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Answer: 36.9 gallons were used in one month.
Step-by-step explanation:
In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other: 3 ÷ 5 = 0.6
Then, we can set up this equation to figure out how much gallons of gasoline was used: 0.6 x 61.5 = 36.9
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find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 40. b) 48. c) 56. d) 64.
With any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, considering that n is 40:
n = 40 as a positive integer
Probability of not choosing any of the six ideal numbers in a lottery:
C(34 , 6)/C(40 , 6)
The likelihood of choosing none of the six correct integers in a lottery:
1344904/3838380
Probability of not winning a lottery with any of the six correct integers:
0.35
Therefore, with any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.
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Correct question:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)
a) 0.40
b) 0.48
c) 0.56
d) 0.64
e) 0.35
Multiply: (9x + 8) (3x² + x − 1)
O 27x³ + 9x² - 8
O 27x³ + 33x² + 17x + 8
O 3x² + 10x + 7
O 27x³ +33x² - x - 8
Answer:
[tex]\textsf{D)} \quad 27x^3+33x^2-x -8[/tex]
Step-by-step explanation:
Given expression:
[tex](9x+8)(3x^2+x-1)[/tex]
Distribute the parentheses:
[tex]\implies 9x \cdot 3x^2+9x \cdot x+ 9x \cdot (-1) + 8 \cdot 3x^2 + 8 \cdot x +8 \cdot(-1)[/tex]
Simplify:
[tex]\implies 27x^3+9x^2-9x + 24x^2 + 8x -8[/tex]
Collect like terms:
[tex]\implies 27x^3+9x^2+ 24x^2-9x + 8x -8[/tex]
Combine like terms:
[tex]\implies 27x^3+33x^2-x -8[/tex]
melissa makes bracelets at a constant rate. she spends 45 minutes making 25 bracelets. which equation describes the relationship between the time in minutes she spends making bracelets, t, and the total number of bracelets she makes, n?
Answer:09.8990
Step-by-step explanation: take one and add
I went to dinner and the dessert was 17% of the $85 meal. How much did we spend on dessert?
Answer:
$14.45
Step-by-step explanation:
To make the equation easier you would have to make the percent decimal and to do that move it twice to the left. So it would be 0.17 x 85 which is 14.45 and add that dollar sign there. :)
Determine the factors of x2 + 4x - 12.
Answer:
(x+6)(x-)
Step-by-step explanation:
A track and field team was calculating their long jump scores. The long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m. Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m. What score would Alaina have to get to tie the Winning teams score? Show your work.
The score that Alaina would have to get to tie the winning team's score is of:
4.4 meters.
What is the needed score?The combined score of the winning team is given as follows:
25.6 m.
The scores of Alaina's teammates are given as follows:
5.46 m, 4.84 m, 4.92 m, 5.98 m.
Considering Alaina's score, the scores of her team are given as follows:
5.46 m, 4.84 m, 4.92 m, 5.98 m, x m.
In which x is the unknown Alaina's score.
Then their combined scores are given as follows:
5.46 + 4.84 + 4.92 + 5.98 + x = 21.2 + x.
The scores will be tied when they are equal, that is:
21.2 + x = 25.6.
Then the score that Alaina needs is obtained as the subtraction of 25.6 and 21.2, as follows:
x = 25.6 - 21.2
x = 4.4 meters.
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jo adds up all the positive integers from 1 to 100. kate does a similar thing with the first 100 positive integers; however, she first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values. what is the positive difference between jo's sum and kate's sum?
Jo's sum is easy = (100)(101)/2 = 50 * 101 = 5050
Given,
In the question:
Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers.
She first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values.
To find the what is the positive difference between jo's sum and Kate's sum?
Now, According to the question:
Kate would first start with 5 [ since 1 - 4 ] are rounded to 0
Starting with 5 thru 14 she will have ten 10s
15 - 24 she will have ten 20s
25 - 34 she will have ten 30s
.
.
.
.
.
85 - 94 she will have ten 90s
95 - 100 she will have six 100s
So.....her sum is
10 [10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90] + 6 [100]
10 [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100]
10 (10) [ sum of the first nine positive integers ] + 6 [ 100]
100 [ (9)(10) / 2 ] + 6[100]
100 [ 45] + 6[100]
100 [ 45 + 6 ]
100 [ 51 ]
5100
Hence, The positive difference is 5100 - 5050 = 50
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A factory process requires 3 steps to finish a product. The steps each have a mean completion time of u = 10 seconds and a standard deviation of o = 5 seconds. The time it takes to complete each step is independent from the other steps. Let I be the total completion time of the 3 steps on a randomly chosen product.
Answer:
square root 75
Step-by-step explanation:
how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other
In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.
What is meant by Permutation?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.
In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.
We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.
How to solve?
For 8 men in a line: 8! = 40320
In order to separate 2 women, we have to choose 5 out of 9
C(9,5) = 9! / 5!4! = 126
Random place 5 women in the 5 chosen places: 5! = 120
Total ways= 40320 * 126 * 120 = 609638400
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explain why the analysis of differences is important in the confirmation of accounts receivable, even if the misstatements in the sample are not material.
The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.
Here,
Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.
The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.
Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.
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In a class of 25 students, 5 have a cat and 9 have a dog. There are 3 students who have a cat and a dog. What is the probability that a student has a cat given that they do not have a dog?.
The probability that:
A student has a cat and they do not have a dog = 1/8 or 0.125.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for an event's taking place.
Given that,
The number of students in the class = 25
[tex]5[/tex] students have a cat.
[tex]9[/tex] students have a dog.
[tex]3[/tex] students have both a cat and a dog.
The objective is to find the probability that given that they don't have a dog, a student has a cat.
To find the probability that one of the pupils has a cat because there isn't a dog in the class:
First, determine the total number of pupils without a dog..
Since there are 25 students in total and 9 have a dog,
Now, 25 - 9 = 16
So the number of students who do not have a dog = 16
Now, determine the number of students who have both a cat and a dog.
According to the question:
There are 3 students who have both,
Subtract this from the percentage of students who own cats.
Therefore,
5 - 3 = 2
So, there are 2 students who have a cat but not a dog.
[tex]Probability = \frac{\text{(Number of students with only a cat)}}{\text{ (Number of students who do not have a dog)}}[/tex]
Probability = 2 / 16
Probability = 1 / 8
Hence,
The required probability that a student has a cat given that they do not have a dog = 1/8 or 0.125.
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What i the point-lope from the line with lope -1/4 that pae through the point (-2,9)
The equation of the line in point slope form is y = -1/4x + 17/2.
Define the term point slope form?A line's equation written using a single point mostly on line and the line's slope is referred to as the point-slope form. The slope is really the rise over distance, or the proportion of the change there in y values over change in the x values, and the point form is denoted as (x,y).The slope of the equation of the line is given as;
slope m = -1/4
Passing point = (-2,9)
Equation of the line;
y - y1 = m(x - x1)
y - 9 = -1/4(x + 2)
y = -1/4x -1/2 + 9
y = -1/4x + 17/2
Thus, the equation of the line in point slope form is y = -1/4x + 17/2.
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the teacher orders tights for the dance class. She buys as many tights as there are students. What equation can solve the amount of tights needed.
The equation that can be solve to know the amount of tights needed is c = 20p.
What equation can solve the amount of tights needed?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the teacher orders 20 tights for the dance class and she buys as many as p tights as there are students.
The equation will be illustrated thus:
Let total amount be c
c = 20 × p
c = 20p
The equation is c = 20p.
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Complete question
A teacher orders 20 tights for the dance class. She buys as many as p tights as there are students. What equation can solve the amount of tights needed?
Solve each inequality. Use the number line provided to test intervals.
Thank you!! :)
Answer:
[-2, 2/5] ∪ [2, ∞)
Step-by-step explanation:
You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.
FactorsThe inequality can be rewritten to a comparison with zero by subtracting the right-side expression.
7x³ -20x +11 -(2x³ +2x² +3) ≥ 0
5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify
x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms
(x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor
(x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares
IntervalsThe values of x that make this product equal to zero are
x -2 = 0 ⇒ x = 2
5x -2 = 0 ⇒ x = 2/5
x +2 = 0 ⇒ x = -2
These x-intercepts divide the domain into 4 intervals where we need to check the sign.
From left to right:
(-∞, -2)
Using x = -3, we find the product to be ...
(-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0
[-2, 2/5]
Using x = 0, we find the product to be ...
(0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution
(2/5, 2)
Using x = 1, we find the product to be ...
(1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0
[2, ∞)
Using x = 3, we find the product to be ...
(3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution
The solution to the inequality is [-2, 2/5] ∪ [2, ∞).
__
Additional comment
The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.
The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.
if someone tossed a fair coin in the air three times and it came up heads all three times, what is the likelihood that it will come up heads on the fourth try?
The probability that the coin will come up heads on the fourth try is 1/2.
Given,
If a fair coin were tossed three times and each time it landed on its head.
We have to find the probability that it will come up heads on the fourth try;
Here,
Coming up short in the first three of four attempts.
The probability will not depend on the first three occurrences in the fourth try.
Consequently, the likelihood of winning the fourth time will be as follows:
Desired outputs as a percentage of overall output
=> 1 / 2
Hence,
The probability of the coming head in the fourth time is 1/2 because the coming head in the fourth time is independent of the coming head in the first three times.
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Multiply the following polynomials. Write the simplified answer in descending order. Use the ^ (shift + 6) to indicate exponents.
DO NOT add spaces between any numbers or characters. For example: (x+2)(x+3) = x^2+5x+6.
(3xy - 1)(4xy + 2)
Answer:
12x^2.y^2 + 2xy - 2
Step-by-step explanation:
I put the dot so you don't get confused thinking it is 2y. Tell me if I misinterpreted the question
Solve for d -9a-12=12-d
Answer:
d= 24 + 9a
Step-by-step explanation:
– 9a – 12 = 12 – d
by collecting like terms
–9a +d = 12 +12
–9a +d = 24
d= 24 + 9a
Answer:
Step-by-step explanation:
-9a-12=12-d
d=9a+24
every fifth adult entering an airport is checked for extra security screening. what sampling technique is used?
It belongs to isometric sampling or systematic sampling in every fifth adult entering an airport is checked for extra security screening.
What is systematic sampling?
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.
Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening.
After that person, they choose every 50th person who passes through for extra screening as well
By the topic
The sampling interval is 50, which is periodic.
It belongs to isometric sampling or systematic sampling.
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Help solve the proportion
Answer: 9
Step-by-step explanation:
in preparation, you identify all possible outcomes and the probability of each outcome. which approach to negotiation are you using? game theory individual differences cognitive approach situational characteristics
By identifying all possible outcomes and the probability of each outcome the negotiation used here is Game theory.
The study of mathematical models of strategic interactions between rational beings is known as game theory and it has uses in computer science, logic, systems science, and all branches of social science.
The most well-known application of game theory is The Prisoner's Dilemma for instance take two offenders who were detained following an arrest as an example. The prosecution lacks concrete proof to prove their guilt. Officials, however, take the inmates out of their isolation cells and question each one separately in order to extract a confession.
The area of mathematics known as "game theory" is concerned with the analysis of such games. Classical game theory and combinatorial game theory are the two primary subfields of game theory. Traditional game theory examines games where participants can move, wager, or strategize all at once.
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If I buy a new video game set that is originally $40, how much will I save if they are 40% off?
Answer: $16 dollars
Step-by-step explanation: 40% of 40 is 16 so you save $16. Game would now cost $24.
What is the circumference in terms of pi for a circle with a area 81?
Answer:
C≈31.9
Step-by-step explanation:
Surface Area =
A. 52 in2
B. 78 in2
C. 45 in2
Answer:
78 in² (Choice B)
Step-by-step explanation:
Since they have exploded the 3-D cuboid into 2-D, it is easier to compute
Looking at the 2-D version you can see 4 rectangles each 3" x 5"
At the bottom on each side are 2 squares each 3" x 3"
Area of a rectangle = l x w
In this case, area of each rectangle = 3 x 5 = 15
Since there are 4 rectangles, total area of these four = 4 x 15 = 60 in²
Each square is area 3" x 3" = 9"
Since there are 2 such squares, total area of these two = 9 x 2 = 18in²
Total area of the 2-D blowup which is the same as the Surface Area of the prism = 60 in² + 18in² = 78 in²