Answer:Answer and Explanation: An algebraic expression for the phrase '6 more than the product of 8 and n' is '8n + 6.
Step-by-step explanation:
A regular pentagon has an apothem of
3 cm and a side length of 4.4 cm, find
its area.
The area of the polygon is 33cm²
What is area of polygon?A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross.
The area of a polygon is expressed as;
A = 1/2 × p × a
where p is the perimeter of the polygon and a is the apothem.A pentagon is a 5 sides polygon.
Therefore;
Perimeter = 5 × 4.4
= 22cm
apothem = 3cm
area = 1/2 × 22 × 3
= 11× 3
= 33 cm²
therefore the area of the Pentagon in is 33cm²
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A researcher is analyzing bacteria on a door handle after cleaning it with antibacterial disinfectant. Initially there were 15 bacteria, but the researcher noticed that the number of bacteria quadruples every hour,t. Write a function B(t) to represent the number of bacteria t hours after the initial measurement. Write a exponential function
The exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
The function B(t) can be represented by an exponential function of the form:
B(t) = a[tex]b^t[/tex]
where 'a' is the initial number of bacteria and 'b' is the growth factor or rate at which the number of bacteria quadruples.
Given that the initial number of bacteria is 15 and the number of bacteria quadruples every hour, we can express 'b' as:
b = 4¹ = 4
Substituting the values of 'a' and 'b' in the general form of exponential function, we get:
B(t) = 15 (4[tex])^t[/tex]
Therefore, the exponential function representing the number of bacteria t hours after the initial measurement is B(t) = 15 (4[tex])^t[/tex].
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Solve the system of equations.
y=4x2+3x−5y=2x2+x+7
What is the sum of the y-coordinates of the solutions to the system?
Enter your answer in the box.
Answer:
37
Step-by-step explanation:
We are given the system of equations:
y = 4x^2 + 3x - 5
y = 2x^2 + x + 7
We can set the two equations equal to each other to get:
4x^2 + 3x - 5 = 2x^2 + x + 7
Simplifying, we get:
2x^2 + 2x - 12 = 0
Dividing both sides by 2, we get:
x^2 + x - 6 = 0
Factoring the left-hand side, we get:
(x + 3)(x - 2) = 0
Therefore, the solutions are x = -3 and x = 2.
To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:
y = 4(-3)^2 + 3(-3) - 5 = 16
and
y = 4(2)^2 + 3(2) - 5 = 21
Therefore, the sum of the y-coordinates of the solutions is:
16 + 21 = 37
Answer: 37.
A car and a bus left Sunrise Village for Sunset Village of the same time, travelling along the
same route. After travelling for 4 h, the car reached Sunset Village, but the bus had only
completed 5/8 of the journey. The bus travelled at a speed which was 30 Km/h slower than the car
a) Find the distance between the two villages.
b) Find the average speed of the bus.
Answer:
a) 192Km
b) 50
Step-by-step explanation:
<
1
0.964
8.92
-0.982 increasing decreasing strong
z, hours
y.gallons
Generate a linear regression equation and a correlation coefficient for these data.
1
9.2
2
The linear regression equation is y =
This means there is a ¦
8.4
The correlation coefficient is
O
The number of of gallons is
3
7.7
4
6.1
weak -1.17 10.69
O+O
5
4.5
correlation between the gallons and hours.
as the hours are increasing.
-0.82
Please help bro. Im struggling.
1. The linear regression equation is y = -1.17x+ 10.69
2. The correlation coefficient is -0.982.
3. This means there is a strong negative correlation between the gallons and hours.
4. The number of gallons is decreasing as the hours are increasing.
How do we calculate for the linear regression equation and correlation coefficient?Step 1: find slope.
Formula for slope m = (n × Σ(xy) - Σx × Σy) / (n × Σ(x²) - (Σx)²)
Σx = 1 + 2 + 3 + 4 + 5 = 15
Σy = 9.2 + 8.4 + 7.7 + 6.1 + 4.5 = 35.9
Σ(xy) = (1 × 9.2) + (2 × 8.4) + (3 × 7.7) + (4 × 6.1) + (5 × 4.5) = 96
Σ(x²) = 1 + 4 + 9 + 16 + 25 = 55
n = 5
Therefore ∴
m = (5 × 96 - 15 × 35.9) / (5 × 55 - 15²) = -1.17
y-intercept b = (Σy - m × Σx) / n
b = (35.9 - (-1.17) × 15) / 5 = (53.15) / 5 = 10.63
Therefore the linear regression equation is y = -1.17x + 10.63
correlation coefficient (r): (n × Σ(xy) - Σx × Σy) / sqrt((n × Σ(x²) - (Σx)²) × (n × Σ(y²) - (Σy)²))
r = (5 × 96 - 15 × 35.9) / sqrt((5 × 55 - 15²) × (5 × 271.95 - 35.9²)) = -0.982
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A recent study of high school students shows the percentage of females and males who took advanced math courses. A simple random sample of high school students was interviewed. The students were asked whether they had taken an advanced math course. Of the 150 females, 53 answered yes, as did 89 of the 275 males.
Part A: Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses. Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (8 points)
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain. (2 points)
Construct and interpret a 98% confidence interval for the difference in population proportions of females and males who took advanced math courses.
The parameter of interest is the difference in population proportions of females and males who took advanced math courses. We can denote this parameter by p₁ - p₂, where p₁ is the population proportion of females who took advanced math courses, and p₂ is the population proportion of males who took advanced math courses.
To construct a confidence interval for the difference in population proportions, we need to check the following conditions,
The sample of high school students should be a simple random sample.
The sample of high school students should be independent of each other.
Both groups of females and males who took advanced math courses should have at least 10 successes and 10 failures.
The sample proportions of females and males who took advanced math courses can be calculated as follows,
p₁ = 53/150 = 0.353
p₂ = 89/275 = 0.324
The sample size of females and males can also be calculated as follows,
n₁ = 150
n₂ = 275
The standard error of the difference in sample proportions can be calculated as follows,
SE = √[(p₁(1 - p₁))/n₁ + (p₂(1 - p₂))/n₂]
= √[(0.353(1 - 0.353))/150 + (0.324(1 - 0.324))/275] ≈ 0.048
Using a t-distribution with (n₁ + n₂ - 2) degrees of freedom and a 98% confidence level, we can construct a confidence interval for the difference in population proportions as follows:
(p₁ - p₂) ± t*SE
where t is the t-score corresponding to a 98% confidence level and (n₁ + n₂ - 2) degrees of freedom. Using a t-table, we can find that t ≈ 2.33.
Substituting the values into the formula, we get,
(0.353 - 0.324) ± 2.33*0.048
0.029 ± 0.112
True difference in population proportions of females and males who took advanced math courses lies between 0.029 and 0.147.
Part B: Does your interval from part A give convincing evidence of a difference between the population proportions? Explain.
Yes, our interval from part A gives convincing evidence of a difference between the population proportions because it does not contain zero. The interval (0.029, 0.147) is entirely positive, which means that the proportion of females who took advanced math courses is higher than the proportion of males who took advanced math courses. Additionally, the interval does not contain the value of one, which means that the difference in population proportions is not due to chance. Therefore, we can conclude that there is a significant difference in the population proportions of females and males who took advanced math courses.
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Helpppppp pleaseeeee
The resulting matrix from an elementary row operation to get a 1, in row 1 column 1 is:
R₁ = [1 4 -8] and R₂ = [2 4 7]
What is the row of a matrixA rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.
The row operation R₁ - 4 — R₁ will be carried out as follows:
5 - 4 = 1 {row 1 column 1}
9 - 4 = 5 {row column 2}
-4 - 4 = -8 {row column 3}
Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:
R₁ = [1 4 -8] and R₂ = [2 4 7]
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Another Statistics question pls help me
Answer:
55
Step-by-step explanation:
0* .4
28*.5
410*.1
on the first day of training Zari runs 2 miles north, the 4 miles east and then back home via shortest route. Taye runs 2 miles west then 4 miles south, and then back home again via the shortest route. a. draw their routes on the coordinate plane above, use a straightedge for accuracy. b. create a proof that demonstrates that the two triangles formed by their routes are congruent. proof needs three pairs of congruent properties of the triangles followed by a triangle congruency statement. show if congruent by ASA, SAS, or SSS.
By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle DEF.
Instructions to draw the routes:
Draw the x-axis and y-axis to create a coordinate plane.
Mark the starting point of Zari's run as (0,0) on the coordinate plane.
From (0,0), move 2 units north to reach (0,2).
From (0,2), move 4 units east to reach (4,2).
From (4,2), move directly back to the starting point (0,0) using the shortest route.
Mark the starting point of Taye's run as (0,0) on the coordinate plane.
From (0,0), move 2 units west to reach (-2,0).
From (-2,0), move 4 units south to reach (-2,-4).
From (-2,-4), move directly back to the starting point (0,0) using the shortest route.
Instructions to prove that the two triangles are congruent using ASA:
Label the vertices of Zari's triangle as A (0,0), B (4,2), and C (0,0).
Label the vertices of Taye's triangle as D (0,0), E (-2,-4), and F (0,0).
Show that angle A and angle D are congruent because they are both right angles (90 degrees).
Show that segment AB and segment DE are congruent because they both have a length of 4 units.
Show that segment AC and segment DF are congruent because they both have a length of 2 units.
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find x
find x
find x
Solve for x.
A
Set up the proportion.
XI7
The solution for the variable x is x = 8.4
How to determine the solution for the variable xfrom the question, we have the following parameters that can be used in our computation:
The right triangle
Using the proportion of similar triagles, we have
x/7 = 10/x
This gives
x * x = 7 * 10
So, we have
x² = 70
Next, we have
x = √70
Evaluate
x = 8.4
Hence, the solution for the variable x is x = 8.4
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 8.2 mg and a standard deviation of 1.45 mg. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 42 cigarettes with a mean nicotine amount of 7.73 mg.
Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 42 cigarettes with a mean of 7.73 mg or less.
P(M < 7.73 mg) = ???
The probability of randomly selecting 42 cigarettes with a mean of 7.73 mg or less is: 0.0179
How to find the p-value from z-score?The formula to find the z-score of the given normal distribution is:
z = (x' - μ)/(σ/√n)
where:
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given:
x' = 7.73 mg
μ = 8.2 mg
σ = 1.45 mg
n = 42
Thus:
z = (7.73 - 8.2)/(1.45/√42))
z = -2.1
From online p-value from z-score calculator, we have:
p = 0.0179
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please help! I don't understand this at all
The equation that represents the consecutive odd numbers whose product is 63 is; (x + 9) (x + 7) = 0
What are odd numbers?Odd numbers have special properties and relationships to other numbers, which make them important in mathematics. For instance, the sum of two odd numbers and the difference between two odd numbers both always equal one.
We can see that we can solve the double brackets by equation them to zero so we have that;
(x + 9) (x + 7) = 0
x = -9
x = -7
Thus;
(-9) (-7) = 63
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Can someone please help me with this
Answer:
cot(65 deg)
Step-by-step explanation:
cot(x) is the complimentary func. of tan(x) with the relation:
tan x = cot (90 - x) and
cot x = tan (90 - x)
Set up the integral (or integrals) needed to compute the area between the curves. Use the smallest possible number of integrals. x= -5 x= 3 y= 9x y=x^2-10
The area between the curves is 61.5 square units.
How did we arrive at this value?To compute the area between the curves y = 9x and y = x^2 - 10, find the points of intersection between the curves.
Setting the two equations equal to each other:
x^2 - 10 = 9x
Move all to one side:
x^2 - 9x - 10 = 0
Factor the quadratics:
(x - 10)(x + 1) = 0
So, the points of intersection are x = -1 and x = 10.
Now, determine which curve is above the other in the interval between -5 and 3. Evaluating the y-coordinates of each curve at a point in this interval, say x = 0.
y = 9x, y = 0 at x = 0, so the curve passes across the origin.
y = x^2 - 10, y = -10 at x = 0.
Therefore, the curve y = 9x is above y = x^2 - 10 in the interval [-5, 3].
To compute the area between the curves, take the integral of the top curve minus the integral of the bottom curve over the interval of intersection:
∫(-1 to 3) [9x - (x^2 - 10)] dx
Simplify:
∫(-1 to 3) [ -x^2 + 9x + 10] dx
Then, integrate each term of the polynomial:
[ (-1/3) x^3 + (9/2) x^2 + 10x ] evaluated from x = -1 to x = 3
Plug into the limits of integration and then simplify:
= [ (81/2) - (19/3) ] - [ (-1/3) - (17/2) ]
= 61.5
Therefore, the area between the curves is 61.5 square units.
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According to the graph, what is the maximum number of passengers he can transport What is the maximum amount he can collect? Use the graph to determine the amount he charges a single passenger.
I can't see the chart...
A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. The following is the setup for this hypothesis test: H0:p=0.12 Ha:p≠0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. The following table can be utilized which provides areas under the Standard Normal Curve:
The p-value from the hypothesis is 0.0583 which is not significant at p<0.05
What is the p-valueTo determine the p-value of the hypothesis, we need to use the formula;
z = (x - a) / √(a(1 - a)/n)
a = hypothesized proportionx = sample proportionn = sample sizex = 93 / 900 = 31/300 = 0.103
a = 12% = 12/100 = 0.12
n = 900
Substituting the values into the formula;
z = (0.103 - 0.12)/√(0.12(1 - 0.12)/900)
z = -0.017 / √0.0001173
z = -1.569
Using a standard normal distribution table;
p-value = 0.058324
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Madison tossed a paper cup and records wether it lands on its side. In 20 trails the cup lands on its side 19 times. In 90 trials the cup lands on its side 81 times
Answer:90% probability
Step-by-step explanation:
To calculate the experimental probability of the cup landing on its side, we can use the formula:
experimental probability = number of times the cup landed on its side / total number of trials
For the first set of trials, the experimental probability is:
experimental probability = 19/20 = 0.95
For the second set of trials, the experimental probability is:
experimental probability = 81/90 = 0.9
So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.
y = 25 - 2x need input x and output y 21 and 19
If we substitute x = 21 into the equation Y = 25 - 2x, we get:
Y = 25 - 2(21)
Y = 25 - 42
Y = -17
Therefore, if x = 21, then Y = -17.
If we substitute x = 19 into the equation Y = 25 - 2x, we get:
Y = 25 - 2(19)
Y = 25 - 38
Y = -13
Therefore, if x = 19, then Y = -13.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The result of the logarithm function is equal to 9. (Correct choice: D)
How to determine the missing component in a logarithm
The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:
aᵇ = n ↔ ㏒ₐ n = b
Where:
a - Baseb - Exponentn - ResultIf we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:
n = 9
3² = 9
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Factor out the Greatest Common Factor (GCF): 64d³ - 24d²
The factored form of 64d³ - 24d² is 8d²(8d³ - 3).
Define greatest common factorThe greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.
The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:
64d³/8d² - 24d²/8d²
Simplifying the fractions:
8d³ - 3
Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).
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A science class measured the mass of an amount of sand.about how many grains of sand are there in 7 grams of sand
Therefore , the solution of the given problem of expressions comes out to be there are roughly 7,000 grains of sand in 7 grammes of sand.
What exactly is an expression?Instead of using random estimates, it is preferable to use shifting numbers that may also prove increasing, reducing, variable or blocking. They could only help one another by trading tools, information, or solutions to issues. The justifications, components, or quantitative comments for tactics like further disagreement, production, and blending may be included in the assertion of truth equation.
Here,
A kilogramme (1000 grammes) of sand is thought to contain around 1 million grains of sand. This indicates that 1 gramme of sand contains roughly 1000 grains of sand.
Using this calculation, we can determine how many sand grains there are in 7 grammes roughly as follows:
=> Number of sand grains in 7 grammes = (# of sand grains in 1 gramme) x (7 grams)
=> 1000 x 7 = the number of sand grains in 7 grammes.
=> 7,000 sand grains are included in 7 grammes.
In accordance with this calculation, there are roughly 7,000 grains of sand in 7 grammes of sand.
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In a coordinate plane, what is the distance between the points (6,−10)
and (6,−7)
?
The distance between the points (6,−10) and (6,−7) is 3 units
What is the distance between the points (6,−10) and (6,−7)?From the question, we have the following parameters that can be used in our computation:
Points (6,−10) and (6,−7)
Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates
Using the above as a guide, we have the following:
Distance = -7 - -10
Evaluate
Distance = 3
Hence, the distance between the points (6,−10) and (6,−7) is 3 units
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A bank charges a monthly fee of 0.5% for a checking account. Lily’s account has $325 in it. Which function models the balance B of Lily’s account in dollars, as a function of time in months?
A. B(t) = 325(1 − 0.005)t
B. B(t) = 325(1 + 0.0005)t
C. B(t) = 0.05(1 − 3.25)t
D. B(t) = 325 + 12(1 + 0.0005)t
The correct function that models the balance B of Lily’s account as a function of time in months is option A, which is B(t) = 325(1 − 0.005)ᵗ.
To see why, we can start with the initial balance of $325 and note that each month, the bank charges a monthly fee of 0.5%, which is equivalent to a monthly interest rate of 0.005. This means that after one month, the balance will be reduced by 0.5% or 0.005 times the original balance, giving:
B(1) = 325 - 0.005(325)
Similarly, after two months, the balance will be reduced by another 0.5% of the new balance, giving:
B(2) = (325 - 0.005(325)) - 0.005(325 - 0.005(325))
We can simplify this expression by factoring out the common factor of 325(1 - 0.005) after each term, giving:
B(2) = 325(1 - 0.005)²
Generalizing this pattern, we can see that after t months, the balance will be:
B(t) = 325(1 - 0.005)ᵗ
Therefore, option A is the correct function that models the balance of Lily’s account.
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Express each of the following as (i)Percentage (ii)Decimal :
a) 3¾ (b) 6½/50
Can someone please answer these 2 questions asap and please show me the breakdown of it so I learn a better way of doing it.
Answer:
x = 5√2, x = 3√2
Step-by-step explanation:
Question 1:
Using the 30-60-90 triangle properties, YX = WX /√3.
YX = 5√3 /√3 = 5.
Using the 45-45-90 triangle properties, x = YX *√2.
x = 5 *√2 = 5√2.
Question 2:
Using the 45-45-90 triangle properties, BC = AB *√2.
BC = 6 *√2 = 6√2.
Using the 30-60-90 triangle properties, x = BC / 2.
x = 6√2 / 2 = 3√2.
Please help !!!!!
!!!!!
Answer: 10w + 3 + 4.5w = 90
Step-by-step explanation:
a right angle is 90 degrees, so 10w + 3 and 4.5w have to add up to 90 degrees
Select the expression that is less than 10 2/3.
A. 10 2/3 x 9/10
B. 1 x 10 2/3
C. 10 2/3 x 2 1/3
D. 2 1/8 x 10 2/3
Answer:
A
Step-by-step explanation:
1. A sample of 250 high-school students in a city results in an average number of text messages sent per month of 172.6, with a margin of error of + 4.8. If there are 3000 high-school students in the city, what is the estimated number of text messages sent in a month? between______ and____text messages
Answer:
Step-by-step explanation:
1) Find the upper bound of the confidence interval:
Upper bound = sample mean + margin of error
= 172.6 + 4.8
= 177.4
2) Find the lower bound of the confidence interval:
Lower bound = sample mean - margin of error
= 172.6 - 4.8
= 167.8
3) Estimate the total number of text messages sent in a month:
Total number of text messages sent = (number of students in the population / number of students in the sample) x sample mean
= (3000 / 250) x 172.6
= 2071.2
Therefore, the estimated number of text messages sent in a month is 2071.2, with a 95% confidence interval between 167.8 and 177.4 text messages.
Answer:
Between 503400 and 532200 text messages----------------------------
Determine the average number of text messages sent per student within the margin of errorFind lower bound:
172.6 - 4.8 = 167.8 text messagesFind upper bound:
172.6 + 4.8 = 177.4 text messages Estimate the total number of text messages for all 3000 studentsLower bound:
167.8 text messages × 3000 students = 503400 text messagesUpper bound:
177.4 text messages × 3000 students = 532200 text messagesThe estimated number of text messages sent in a month for all 3000 high-school students in the city is:
Between 503400 and 532200 text messagesAlexia is cutting construction paper into rectangles for a projects. She needs to cut one rectangle that is a 9 inches x 14 1/3 inches. she needs to cut another that is 10 1/4 inches by 10 1/3 inches. How many total square inches of construction paper does Alexia need for her project?
Answer:
234.8525 square inches
Step-by-step explanation:
To find the total area of construction paper needed for the project, we need to find the area of each rectangle and add them together.
For the first rectangle, the dimensions are:
Length = 9 inches
Width = 14 1/3 inches
Area of the first rectangle = Length x Width
Area of the first rectangle = 9 inches x (43/3) inches
Area of the first rectangle = 9 inches x 14.33 inches
Area of the first rectangle = 128.97 square inches (rounded to two decimal places)
For the second rectangle, the dimensions are:
Length = 10 1/4 inches
Width = 10 1/3 inches
Area of the second rectangle = Length x Width
Area of the second rectangle = (41/4) inches x (31/3) inches
Area of the second rectangle = 10.25 inches x 10.33 inches
Area of the second rectangle = 105.8825 square inches (rounded to four decimal places)
Therefore, the total area of construction paper needed for the project is:
Total area = Area of first rectangle + Area of second rectangle
Total area = 128.97 square inches + 105.8825 square inches
Total area = 234.8525 square inches (rounded to four decimal places)
Therefore, Alexia needs a total of approximately 234.8525 square inches of construction paper for her project.
