If the amount of jen's monthly phone bill is normally distributed with a mean of $86 and standard deviation of $9, Between the values of $77 and $95 inclusive, 68.26% of Jen's phone bills are expected to fall.
To find the values between which 68.26% of Jen's phone bills lie, we need to use the properties of the normal distribution and the empirical rule.
The empirical rule states that for a normal distribution, approximately 68% of the data lie within one standard deviation of the mean. Therefore, we can find the values between which 68.26% of Jen's phone bills lie by calculating the range of values that are one standard deviation away from the mean.
Using the given population mean of $86 and population standard deviation of $9, we can calculate one standard deviation as follows:
One standard deviation = population standard deviation = $9
To find the lower and upper bounds for 68.26% of Jen's phone bills, we can subtract and add one standard deviation from the mean, respectively:
Lower bound = population mean - one standard deviation = $86 - $9 = $77
Upper bound = population mean + one standard deviation = $86 + $9 = $95
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A,B and c lie on a straight line segment A , E and d lie on a straight line segment AB = 5cm AC= 30cm and EB = 4cm work out the length of dDC
The length of dDC is 16 cm. We can use the similarity of triangles ACD and ABE to find the length of DC.
We know A,B and c lie on a straight line segment A , E and d lie on a straight line segment
AC/AB = AD/AESubstituting the given values, we get:
30/5 = AD/(AD+4)Simplifying the equation, we get:
AD = 20
Now, we can use the similarity of triangles ACD and ABE again, to find the length of DC.
CD/BE = AD/AE
Substituting the values, we get:
CD/4 = 20/(20+5)
Simplifying the equation, we get:
CD = 16
Therefore, the length of dDC is 16 cm.
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what is the probability i put at least 7 pieces of bread into my cheap toaster before it destroys itself?
The probability of being able to toast at least 7 pieces of bread before the toaster catches on fire and destroys itself is approximately 0.0128
We can approach this problem using the negative binomial distribution, which models the number of successful trials (toasting without the toaster catching on fire) before a specified number of failures (the toaster catching on fire and destroying itself) occur.
Let X be the number of successful toasting trials before the toaster catches on fire and destroys itself. We want to find P(X ≥ 7), the probability that at least 7 pieces of bread can be toasted before the toaster is destroyed.
The negative binomial distribution can be expressed as
P(X = k) = (k+r-1)C(r-1) × p^r × (1-p)^k
where r is the number of failures (the toaster catching on fire and destroying itself), p is the probability of success (toasting without the toaster catching on fire), and (k+r-1)C(r-1) is a combination factor that represents the number of ways to arrange k successes and r-1 failures in a sequence.
In this case, r = 1 (we want to know the probability of the first failure occurring after at least 7 successes), p = 0.75 (the probability of successfully toasting a piece of bread), and we want to find P(X ≥ 7).
P(X ≥ 7) = 1 - P(X < 7)
= 1 - Σ[k=0 to 6] (k+1) × p × (1-p)^k
≈ 0.0128
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The given question is incomplete, the complete question is:
I bought a cheap toaster. Every time I use it there is a chance that it will catch on fire with
probability p = 0.25, burn my toast, and destroy itself. But with probability (1 − p) it makes
perfect toast!
What is the probability I put at least 7 pieces of bread into my cheap toaster before it
destroys itself?
a ferris wheel has five cars, each containing four seats in a row. there are 20 people ready for a ride. in how many ways can the ride begin? what if a certain two people want to sit in different cars?\
There are 5 possible ways for the ride to begin.
The ferris wheel has 5 cars with 4 seats in each car, making a total of 20 seats. If there are 20 people ready for the ride, then each car can have 4 people. Therefore, there are 5 possible ways for the ride to begin.
If two certain people want to sit in different cars, then there are 4^2 (4x4) combinations of cars for these two people. This gives us 16 possible ways for the ride to begin.
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which numbers will round to 19 when they are rounded to the nearest whole number? select each correct answer. responses 19.46 19.46 18.48 18.48 19.91 19.91 18.82 18.82 19.33 19.33 1, fully attempted. 2, fully attempted. 3, fully attempted. 4, fully attempted. 5, fully attempted. 6, fully attempted. 7, unattempted. 8, unattempted.
The numbers that will round to 19 when rounded to the nearest whole number are 19.46 and 19.91.
To round a number to the nearest whole number, we look at the decimal part of the number. If it is less than 0.5, we round down to the nearest integer. If it is greater than or equal to 0.5, we round up to the nearest integer.
For the given set of numbers, we can round them to the nearest whole number and check which ones round to 19:
19.46 rounds up to 19
18.48 rounds down to 18
19.91 rounds up to 20
18.82 rounds up to 19
19.33 rounds up to 19
Therefore, the numbers that round to 19 when rounded to the nearest whole number are 19.46 and 19.33.
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Answer
D =
E =
Please help
Answer:
d = 3.75
e = 8/3
Step-by-step explanation:
8/6 = 5/d = e/2
4/3 = 5/d
4d = 3 × 5
d = 3.75
4/3 = e/2
3e = 4 × 2
e = 8/3
what is the difference of (4m^2-5) -(5m-20)
Answer:
4m^2+15-5m
Step-by-step explanation:
Remove parentheses.
4m^2-5-5m+20
Collect like terms.
4m^2+(-5+20)-5m
Simplify
4m^2+15-5m
Center of Triangles I please help
The value of angle CI is equal to 40 for the triangle.
What is geometry?
Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that I is the incenter of the triangle AI = 3x+7, BI = 5x-11, and CI = 52-2x.
The value of BI will be calculated as,
AI = BI
3x + 7 = 5x - 11
2x = 18
x = 6
Now for the value of angle CI:
CI = 52 - 2x
CI = 52 - 2 x 6
CI = 52 - 12
CI = 40
Therefore, the value of angle CI is equal to 40 for the triangle.
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Tiana drew a scale drawing of a picnic area near the river. She used the scale 1 inch : 7 yards. If the picnic area is 7 inches wide in the drawing, how wide is the actual picnic area?
The measures of the angles of a triangle are shown in the figure be
45°
106⁰
C
Search
(2x-9)°
PLS HURRY !!
I need help on this asap!
In linear equation, 0.75x + 2y ≤ 16 , 2x + 4y ≤ 40 are the solution represent .
What is the most effective way to explain linear equations?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.
if the small pair is x, the large pair is y.
45 minutes = 0.75 hour
120 minutes = 2 hour
so, 0.75x + 2y ≤ 16
2x + 4y ≤ 40
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i have a deck of cards, and i deal all of the cards to players, with each player getting cards. if is at least and is at least , then how many possible values of are there?
Answer:
4
Step-by-step explanation:
We want xy=54=2*3^3 such that x is at least 2 and y is at least 5. Thus, the possible combinations (x,y) are (2,27), (3,18), (6,9), and (9,6). There are 4 such combinations.
a die is thorn four times. what is the probability that each number thrown is at least as high as all of the numbers that were thrown earlier?
Answer:
Step-by-step explanation:
The first roll can be any number from 1 to 6, since there are no earlier rolls to compare it to.
For the second roll, the probability of rolling a number greater than the first roll is 1/2, since there are only three numbers left on the die that are greater than the first roll.
Similarly, the probability of rolling a number greater than the first two rolls on the third roll is 1/3, and the probability of rolling a number greater than the first three rolls on the fourth roll is 1/4.
Therefore, the probability of rolling four numbers that are at least as high as the previous rolls is:
1 x 1/2 x 1/3 x 1/4 = 1/24
So the probability of rolling four numbers that are at least as high as the previous rolls is 1/24.
The probability of rolling each number higher than the previous number when a die is thrown four times is 1/3.
To calculate this probability, we must first understand the concept of a combination. A combination is a way of selecting items from a set, such that the order of selection does not matter. In this case, the set is the numbers 1-6.
The probability of rolling each number higher than the previous number is equal to the probability of selecting four numbers from a set of six without repeating any of them.
We can calculate this probability by dividing the number of desired combinations by the total number of possible combinations.
The number of desired combinations is equal to the number of ways we can choose the first number from the set (6 choices), multiplied by the number of ways we can choose the second number from the remaining five (5 choices), and so on.
Therefore, the number of desired combinations is 6*5*4*3, which is 360.
The total number of possible combinations is equal to the number of ways we can choose four numbers from a set of six, which is 6*5*4*3*2*1, or 720.
Therefore, the probability of rolling each number higher than the previous number when a die is thrown four times is 360/720, which is equal to 1/3.
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at the end of 2024, marin co. has accounts receivable of $673,200 and an allowance for doubtful accounts of $24,010. on january 24. 2025, it is learned that the company's receivable from madonna inc. is not collectible and therefore management authorizes a write- off of $4.147.
The write-off of the receivable from Madonna Inc. is a necessary adjustment to ensure the accuracy of Marin Co.'s financial statements. Without it, the company's accounts receivable would be overstated and their financial statements would not provide an accurate portrayal of the company's financial position.
At the end of 2024, Marin Co. had accounts receivable of $673,200 and an allowance for doubtful accounts of $24,010. On January 24th, 2025, it was determined that the company's receivable from Madonna Inc. was not collectible and management authorized a write-off of $4,147. This action reduces the accounts receivable balance by $4,147, and reduces the allowance for doubtful accounts by the same amount. The net effect on the balance sheet is a reduction of $4,147 in both accounts receivable and allowance for doubtful accounts.
The impact of the write-off on the company's financial statements is a decrease in net income for the period. This is because a write-off is recognized as an expense, which reduces the amount of net income reported in the period. The amount of the write-off is recorded as an expense on the income statement. In this case, the amount of the write-off is $4,147.
The journal entry to record the write-off would be: Accounts Receivable 4,147; Allowance for Doubtful Accounts 4,147. This entry reduces the accounts receivable and allowance for doubtful accounts by $4,147. The write-off of $4,147 is recorded as an expense on the income statement, and this reduces the net income reported for the period.
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complaints about an internet brokerage firm occur at a rate of 3 per day. the number of complaints appears to be poisson distributed. a. find the probability that the firm receives 2 or more complaints in a day. probability
The probability that the firm receives 2 or more complaints in a day is 0.33.
This can be calculated using the Poisson distribution formula. The Poisson distribution is a probability distribution used to calculate the probability of an event occurring a given number of times in a fixed interval of time or space.
It is based on the assumption that the rate of occurrence of an event is constant.
In this case, we are looking at the probability of the firm receiving 2 or more complaints in a day. Let x = 2, where x is the number of complaints in a day. Then, the Poisson distribution formula is: P(x) = (e-λ λx) / x!
Where e = 2.71828 and λ = 3 (the rate of complaints per day).
Plugging in the values, we get: P(2) = (2.71828-3 * 32) / 2! = 0.33. Therefore, the probability that the firm receives 2 or more complaints in a day is 0.33.
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If you add two positive numbers together, which of the following is true about the result?
Answer:
If you add two positive numbers together you will get a positive.
Step-by-step explanation:
a square has side length of 7.3 in . if the area is multiplied by 19 , what happens to the perimeter?
The new perimeter is 127.2 inches if it is multiplied by 19.
What do you mean by the are and perimeter of the square ?
The area of a square is calculated by squaring the length of one of its sides. If the area of a square is multiplied by a factor, the length of the sides will be multiplied by the square root of that factor. One way to express the concept of perimeter for a square is to state that it is the total distance around the outer boundary of the shape, which is equal to the sum of the lengths of all four sides.
Determining the the value of perimeter :
The area of the square is [tex]7.3 \times 7.3 = 53.29[/tex] square inches.
If this area is multiplied by 19, the new area will be 1012.51 square inches.
To find the new side length of the square, we take the square root of the new area:
[tex]\sqrt{1012.51} = 31.8[/tex] (rounded to one decimal place)
Therefore, the new side length of the square is 31.8 inches.
To find the new perimeter, we multiply the new side length by 4:
[tex]31.8 \times 4 = 127.2[/tex]inches
So the new perimeter is 127.2 inches.
To summarize, when the area of the square with side length 7.3 inches is multiplied by 19, the perimeter is multiplied by the square root of 19, which is approximately 4.36. The new perimeter is 127.2 inches.
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Find the value of X in the isosceles trapezoid
In an isosceles trapezoid, the diagonals are congruent, so the value of X is 7.
What is isosceles trapezoid?In an isosceles trapezoid, the two angles formed by each leg and a base are congruent, and the diagonals that connect opposite vertices are congruent as well.
According to question:An isosceles trapezoid is a four-sided polygon with two parallel sides that are of equal length and two non-parallel sides that are also of equal length. The non-parallel sides are often referred to as the legs of the trapezoid, and the parallel sides are called the bases.
In an isosceles trapezoid, the diagonals are congruent, so we can set KM and JL equal to each other and solve for x:
KM = JL
2x+10 = 5x-11
Subtracting 2x and adding 11 to both sides, we get:
21 = 3x
x = 7
Therefore, the value of x in the isosceles trapezoid is 7.
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It is the year 3000. Noah’s descendants are still racing around the park, but thanks to incredible technological advances, now with much more powerful gadgets at their disposal. How might their newfound access to teleportation and time-travel devices alter the graph of stories of their daily adventures?
Ultimately, teleportation and time travel would certainly have both positive and negative effects on the graph of the lives of Noah's descendants, presenting both new chances and difficulties.
what is graph ?A graph shows the relationship between variables or values by visualising data or information. It comprises of a coordinate system with an x-axis and y-axis, and data points or lines plotted on it. In a variety of disciplines, including mathematics, physics, economics, and social sciences, graphs are used to convey and interpret data. They can be employed to display patterns, trends, comparisons, and connections between different data points. Bar graphs, line graphs, scatter plots, pie charts, and histograms are examples of common graph types.
given
Having the capacity to teleport and go through time could potentially present new difficulties and complexities for writers.
Plotlines could get more complicated and sophisticated if characters travel between several eras or parallel realities.
Also, being able to travel across great distances quickly can make the globe seem smaller and less mysterious, which could make it more difficult to convey a sense of awe and discovery through storytelling.
Ultimately, teleportation and time travel would certainly have both positive and negative effects on the graph of the lives of Noah's descendants, presenting both new chances and difficulties.
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Which is the most accurate way to estimate 48% of 39?
Answer:
18.72
Step-by-step explanation:
48% is 0.48 as a decimal
0.48*39=18.72
20 POINTS!!DUE TODAY NEED HELP NOW!!!!!!!!
Use this information to answer questions 3, 2, and 5. Other than (1, 0), (0, 1), (-1, 0), and (0, -1), the coordinates used in the previous question involved approximations. The point (0.8, 0.6), however, lies exactly on the unit circle.
What relationships or patterns do you notice in the coordinates?
3. Explain why this must be true.
5. What are the approximate angle measures needed to intersect at (0.8, 0.6) and each of these new points?
4. List all other points on the unit circle that also like exactly at the intersection of two grid lines.
This is true because coordinates (0.8, 0.6) satisfy the equation x² + y² = 1.
The approximate angle measures needed to intersect at (0.8, 0.6) and each of these new points is 38.66 degrees.
Other points on the unit circle are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6).
How to determine coordinates on a unit circle?The coordinates (0.8, 0.6) lie exactly on the unit circle because they satisfy the equation x² + y² = 1, which defines the unit circle. Plugging in x = 0.8 and y = 0.6 gives 0.8² + 0.6² = 1, which is true.
To find the angle measure needed to intersect at (0.8, 0.6) and each of the new points, we can use the inverse tangent function. If we let theta be the angle between the positive x-axis and the line connecting the origin and the point of intersection, then we can use the equation tan(theta) = y/x to find the angle. For example, to find the angle needed to intersect at (0.8, 0.6) and (1, 1), we have tan(theta) = 0.6/0.8, which simplifies to theta = arctan(0.6/0.8) ≈ 38.66 degrees.
The other points on the unit circle that also lie exactly at the intersection of two grid lines are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6). These points can be obtained by reflecting (0.8, 0.6) across the x-axis, y-axis, or both.
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sam survey, a statistician at mathmagic land university wants to construct a 95% confidence interval with no more than 3% margin of error for the proportion of students who own their own car. what is the least number of students he would have to sample? (assume that this way you know that the sample is large enough.)
Sam would have to sample at least 1068 students.
Sam, a statistician at Mathmagic Land University wants to construct a 95% confidence interval with no more than 3% margin of error for the proportion of students who own their own car.
Let us calculate the least number of students he would have to sample. What is the least number of students Sam would have to sample?
Given that the confidence interval is 95% with a margin of error no more than 3%.The margin of error formula is given by Margin of error = Z-value * Standard error.
We know that Z-value for a 95% confidence interval is 1.96. This corresponds to 0.03 of the confidence interval. Hence, we can calculate the standard error as follows:
Standard error = Margin of error / Z-value= 0.03 / 1.96 = 0.0153We know that the standard error formula is given byStandard error = √p(1-p)/n.
Here, we need to find the minimum sample size required to get the least number of students who own their own car, hence the proportion can be assumed to be 0.5 (which will be the maximum value of p).0.0153 = √(0.5 × (1-0.5) )/n
On simplification, we get, n = 1067.55. Hence, Sam would have to sample at least 1068 students to construct a 95% confidence interval with no more than 3% margin of error for the proportion of students who own their own car.
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8x 2 + [ 3x3-8] = with explanation pls and its due in six minutes
Answer: 16x+3x^3−8
Please mark me brainliest :)
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
8 is subtracted from the cube of a number.
Answer: ChatGPT is acting weird
Step-by-step explanation:
The cube of a number x is represented as x^3, and 8 is subtracted from it.
So, the algebraic expression is:
x^3 - 8
I need help with this please
Answer: The second cooper weighed 7 pounds. He weighed more by 5 ounces
Step-by-step explanation:
Answer:
Cooper weighs more and here's why
Step-by-step explanation:
6 pounds and 11 ounces is equal to 6.6875 pounds
112 ounces is equal to 7 pounds.
That's why Cooper weighs more.
0.3125 pounds, or 5 ounces is the weight difference, so approximately 0.31 pounds is how much more Cooper weighs than Cane
The players of a travel volleyball team have no more than a combined total of 385
shirts and hats to sell for a fundraiser to fund a trip. The shirts sell for $12
each, and the hats sell for $25
each. The players must make a combined total of at least $7,450
from the fundraiser. If s
represents the number of shirts sold during the fundraiser, and h
represents the number of hats sold during the fundraiser, which system of inequalities represents the scenario?
system of inequalities represents the scenario: The differences are 12s + 25h 7450 and s + h 385.
When expressions or values do not have an equal relationship to one another, this relationship is referred to in mathematics as an inequality. Inequality is the product of an unbalanced system. The symbol "=" denotes equality between two quantities, and the symbol denotes inequality between them.
The maximum count of hats and shirts sold in this case is 385 if s stands for the quantity of shirts sold during in the fundraiser and h for the amount of hats sold during in the campaign.
=> s +h 385
And the players must make a combined total of at least $7, 450 from the fundraiser, then shirts sell for $12 each, and the hats sell for $25 each then,
=> 12*s+25*h 7450
=> 12s + 25h 7450
Hence the inequalities are, s +h 385 and 12s + 25h 7450.
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consider the differential equation given by[math equation]the goal of this problem is to solve this differential equation numerically, analytically and compare the solutions. find the exact solution (i.e. the analytical solution) use euler's method to solve the differential equation with a step size h=0,001; (this is the numerical solution)
The number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
Step-by-step explanation:
The differential equation is missing in your question. However, I will give a general overview of how to solve a differential equation numerically using Euler's method and how to find an analytical solution.
Numerical Solution using Euler's Method:
Suppose we have a first-order differential equation of the form y' = f(x, y), where y' represents the derivative of y with respect to x. To solve this numerically using Euler's method, we need to start with an initial condition y(x0) = y0, and we want to find the value of y at some other point x1 = x0 + h.
The Euler's method involves approximating the derivative y' by the difference quotient (y1 - y0) / h, where y1 is the value of y at x1. Rearranging this equation, we get:
y1 = y0 + h * f(x0, y0)
Using this equation, we can iteratively compute the value of y at different points by using the previous value of y. For example, to find y2, we can use the equation:
y2 = y1 + h * f(x1, y1)
We continue this process until we reach the desired endpoint.
Analytical Solution:
An analytical solution to a differential equation is an explicit expression for y(x) that satisfies the differential equation for all values of x. To find an analytical solution, we may use techniques such as separation of variables, integrating factors, or other methods specific to the type of differential equation.
For example, if we have a differential equation of the form y' = k * y, where k is a constant, we can use separation of variables to obtain:
dy / y = k * dx
Integrating both sides, we get:
ln|y| = k * x + C
where C is an arbitrary constant of integration. Solving for y, we get:
y = Ce^(kx)
where C = ±e^C is a constant determined by the initial condition.
Comparison of Solutions:
Once we have the numerical and analytical solutions, we can compare them by plotting the graphs of y(x) for each method. If the numerical solution was computed with a small enough step size, it should converge to the analytical solution as the number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.
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Use the Figure below to Answer this question
In linear pair, Value of x is 133° .
What is linear pair in math?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.
A pair of neighboring angles created by the intersection of two lines is referred to as a linear pair. A linear pair is formed in the illustration by the numbers 1 and 2. The same goes for pairs 2 and 3, 3 and 4, and 1 and 4. In a linear pair, the two angles are always supplementary, which implies that their sum total is 180 degrees.
47° + x° = 180°
x° = 180° - 47°
= 133°
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the value of a boat is 21 200. it loses 6 of its value every year. find the approximate monthly percent decrease in value.
The approximate monthly percent decrease in value of the boat is 0.5%.
The given value of a boat is 21 200, and it loses 6% of its value every year. We are to find the approximate monthly percent decrease in value.
The given information is as follows: The value of a boat = $21,200The percentage decrease in value = 6%We are to find the approximate monthly percent decrease in value. Annual decrease in value of a boat is 6% of $21,200= $1,272Monthly decrease in value of a boat will be 1/12 of the annual decrease = $1,272/12≈ $106Thus, the approximate monthly percent decrease in value of the boat will be
[tex]$\frac{106}{21,200}*100\%=0.5\%$[/tex]
Therefore, the approximate monthly percent decrease in value of the boat is 0.5%.
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Your question is incomplete, but probably the complete question is :
The value of a boat is $21,200. It loses 6% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.
Please use the information below for an arithmetic sequence to do the following:
a. sub 1 equals 3 d equals 4
A) List the first 6 terms of the sequence
B) Write the terms of this sequence as a series.
C) Provide a graph of the aritmetic sequence.
D) List the first 6 partial sums of the series.
SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!
Answer:
See below, please.
Step-by-step explanation:
A) The first term of the sequence is given as sub 1 = 3 and the common difference is given as d = 4. Therefore, the first 6 terms of the sequence are
sub 1 = 3
sub 2 = sub 1 + d = 3 + 4 = 7
sub 3 = sub 2 + d = 7 + 4 = 11
sub 4 = sub 3 + d = 11 + 4 = 15
sub 5 = sub 4 + d = 15 + 4 = 19
sub 6 = sub 5 + d = 19 + 4 = 23
B) The terms of this sequence can be written as a series as
3 + 7 + 11 + 15 + 19 + 23 + ...
C) The graph of the arithmetic sequence is a straight line with a positive slope, as each term of the sequence is obtained by adding a constant (d = 4) to the previous term.
D) The first 6 partial sums of the series can be calculated as
S1 = 3
S2 = 3 + 7 = 10
S3 = 3 + 7 + 11 = 21
S4 = 3 + 7 + 11 + 15 = 36
S5 = 3 + 7 + 11 + 15 + 19 = 55
S6 = 3 + 7 + 11 + 15 + 19 + 23 = 78
Therefore, the first 6 terms of the sequence are 3, 7, 11, 15, 19, and 23. The terms of the sequence can be written as a series as 3 + 7 + 11 + 15 + 19 + 23 + ..., and the graph of the sequence is a straight line with a positive slope. The first 6 partial sums of the series are 3, 10, 21, 36, 55, and 78.
Which of the following shows that the two composite figures cover the same area?
-7
5
y
7
X
The option that correctly shows the area of the composite figures is:
B: For both figures, A = 6 + 4 + 2 + 2 + 1 = 15 units²
How to find the area of a composite figure?The area of a triangle is given by the formula:
A = ¹/₂ * base * height
Area of rectangle = Length * Width
Area of shape on left = (4 * 2) + (2 * 2) + (¹/₂ * 2 * 1) + (¹/₂ * 2 * 2)
Area of shape on left = 8 + 4 + 1 + 2
Area of shape on left = 15 units²
Area of shape on the right = (¹/₂ * 6 * 3) + (¹/₂ * 4 * 3)
Area of shape on the right = 9 + 6
Area of shape on the right = = 15 units²
Thus, option B is the correct option showing the area of the composite figures.
Read more about Area of Composite Figure at: https://brainly.com/question/29710027
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