If the APR on Mario's credit card is 26.99%, Mario's new balance, including interest will be B. $3,269.10.
What is the APR?Annual percentage rate (APR) is the annual finance charge applied to a credit balance.
The APR includes interest and other fees for borrowing credit.
Current credit card balance = $2,673.19
Minimum payment within the month = (102.00)
Purchase payments 626.00
Finance Charge $71.91 ($3,197.19 x 26.99% x 1/12)
Ending credit card balance = $3,269.10 ($3,197.19 + $71.91)
Annual percentage rate = 26.99%
Monthly percentage rate = 2.25% (26.99% ÷ 12)
Thus, Mario will end up with a credit card balance of $3,269.10 after one month with APR of 26.99%.
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The greater of two numbers is twice the lesser. If the greater is x, what is the lesser.
Answer:
1/2x
Step-by-step explanation:
Answer:
The lesser is x/2.---------------------------------------------------
Let the numbers be x and y, where x is greater and y is lesser.
Given that x = 2y.
Find y:
x = 2y Divide both sides by 2x/2 = yy = x/2Marsha deposited $10,000 into a savings account five years ago. The simple interest rate is 4%. How much money did Marsha earn interest
The interest that Marsha will earn is $2000.
What will be the interest earned?Simply multiplying the daily interest rate by the principal and the number of days between payments yields simple interest. Consumers who pay their loans on time or early each month benefit from simple interest. Auto loans and short-term personal loans are typically interest-only loans.
In this case, Marsha deposited $10,000 into a savings account five years ago. The simple interest rate is 4%.
The interest will be:
= PRT
P = Principal = $10000
R = Rate = 4%
T = Time = 5
Interest = PRT
= $10000 × 4% × 5
= $2000
The interest is $2000.
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Write a polynomial of least degree with roots 0, 4, and 9
Answer:
Your Polynomial: [tex]x^3-13x^2+36x=0[/tex]
Step-by-step explanation:
Given information: 0 , 4 , 9
0 -> x = 0 -> (x - 0) = 0
4 -> x = 4 -> (x - 4) = 0
9 -> x = 9 -> (x - 9) = 0
(x - 0)(x - 4)(x - 9) = 0
x * (x - 4) * (x - 9) = 0
(x^2 - 4x) * (x - 9) = 0
x^3 - 9x^2 - 4x^2 + 36x = 0
Given that f is increasing, f is increasing, and that the range of g is included in f what can be said about f o g?
H(x) is a decreasing function too. fog will be decreasing function.
An easy definition of a function?
As a set of inputs with one output for each, a function is defined as a relationship between them.
In plain English, a function is an association between inputs in which each input is connected to precisely one output.
Let h(x) = f(g(x))
Hence,
h'(x) = f'(g(x) ) . g(x)
h'(x) = f'g(x)) . g(x)
Now g(x) is a strictly decreasing function.
Then
g'(x) < 0 for all real x.
Hence
h'(x) < 0
since h'(X) = f'(g(X)) . g'(X) and g'(x) < 0
Therefor h(x) is a decreasing function too.
Hence fog will be decreasing function.
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Which of the following is two dimensional and infinitely large? A.a solid
B.a sphere
C.space
D.a plane
The height of a triangle is 8 em shorter than its base. If the area of the triangle is 24 cm2, find the height of the triangle a) 07cm b) O12 cm c) O 13 cm d) O 3cm e) O4 cmf) O None of the above
When the area is 24 cm², the height of the triangle is 4 cm.
What is area?The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.
Here,
area=1/2(bh)
h=b-8
24=1/2(b(b-8))
48=b²-8b
b²-8b-48=0
b²-12b+4b-48=0
b(b-12)+4(b-12)=0
b=-4,12
b=12 cm
h=12-8
h=4 cm
The height of triangle is 4 cm when area is 24 cm².
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whats the midpoint of (2,9) and (10,-8)
Answer:
(6, 0.5)
Step-by-step explanation:
midpoint = x1+x2/2 , y1+y2/2
midpoint = 2+10/2 , 9+(-8)/2
midpoint = 12/2, 1/2
midpoint = 6, 0.5
Please help! Question in attachment.
1) Using the common factors of the new area of 12,000 m², the new dimensions of the larger rectangle (lot) are:
Length 100 mWidth 120 m.2) The percent increase for the length and width are:
Length 25%Width 20%.How are the new dimensions determined?The new dimensions of the larger lot are determined as follows:
Length of smaller lot = 80 m
Width of smaller lot = 100 m
Area of smaller lot = 8,000 m² (80 x 100)
The increase in the area of the larger lot = 4,000 m²
The total area of the larger lot = 12,000 m² (8,000 + 4,000)
Remember that area is length x width.
The factors that can result in 12,000 m² when multiplied are 100 m and 120 m, they also meet the requirement for increasing the dimensions by the same amount (20 m).
Length of larger lot = 100 m (80 + 20)
Width of larger lot = 120 m (100 + 20)
Percentage increases:Length = 25% (100 - 80)/80 x 100)
Width = 20% (120 - 100)/100 x 100)
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In the accompanying diagram of right triangle ABC,
altitude BD is drawn to hypotenuse AC.
Which statement must always be true?
1) AD/AB = BC/AC
2) AD/AB = AB/AC
3) BD/BC = AB/AD
4) AB/BC = BD/AC
The ratio of the length of the altitude to the length of one side of the triangle is equal to the ratio of the length of the hypotenuse to the length of the other side.1) AD/AB = BC/AC is true
In the accompanying diagram of right triangle ABC, altitude BD is drawn to hypotenuse AC. This means that the length of BD is equal to the length of the altitude from the vertex of the right angle to the hypotenuse. This also means that the length of BD is a right triangle's altitude. In a right triangle, the altitude of a right triangle is the line segment connecting one vertex of the right angle to the hypotenuse, and is perpendicular to the hypotenuse. This also means that the ratio of the length of the altitude to the length of one side of the triangle (AD/AB) is equal to the ratio of the length of the hypotenuse to the length of the other side (BC/AC). This statement must always be true, regardless of the size of the triangle or its specific shape. This is because the ratio of the length of the altitude to the length of one side of the triangle is always equal to the ratio of the length of the hypotenuse to the length of the other side.
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help math. Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The linear function is y = 5x + 12 and the number of customers after 3 and 4 hours are 27 and 41 respectively.
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line.
m = slopeb = y-interceptUsing the data in the table, we can write can a linear function to represent it.
Taking two points;
A = (0, 12)B = (1, 17)The slope of the line is calculated as;
m = y₂ - y₁ / x₂ - x₁
m = 17 - 12 / 1 - 0
m = 5 / 1
m = 5
Using the value of the slope to calculate the y - intercept.
y = mx + b
17 = 5(1) + b
17 = 5 + b
b = 17 - 5
b = 12
The linear function is written as y = 5x + 12
a) The number of customers in the store after 3 hours is
y = 5x + 12
y = 5(3) + 12
y = 15 + 12
y = 27
b) The number of customers in store after 4 hours is
y = 5x + 12
y = 5(4) + 12
y = 20 + 12
y = 41
The linear function to model the table is y = 5x + 12
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A basketball manufacturer selects a random sample of its basketballs each week to ensure a consistent air pressure within them is maintained. In Week 1, the sample had a mean air pressure of 8.2 psi (pounds per square inch) and a margin of error of 0.1 psi. In Week 2, the sample had a mean air pressure of 7.7 psi and a margin of error of 0.3 psi. Based on these results, which of the following is a reasonable conclusion? A) Most of the basketballs produced in Week 1 had an air pressure under 8.2 psl, whereas most of the basketballs produced in Week 2 had an air pressure under 7.7 psi. B) The mean air pressure of all the basketballs produced in Week I was 0.5 psi more than the mean air pressure of all the basketballs produced in Week 2 C) The number of basketballs in the Week 1 sample was more than the number of basketballs in the Week 2 sample. D) It is very likely that the mean air pressure of all the basketballs produced in Week 1 was less than the mean air pressure of all the basketballs produced in Week 2.
B) The mean air pressure of all the basketballs produced in Week I was 0.5 psi more than the mean air pressure of all the basketballs produced in Week 2
What is manufacturer?
A manufacturer is a person or business that turns raw materials into completed products using a variety of tools, machinery, and procedures, and then sells those products to customers, wholesalers, distributors, retailers, or other manufacturers who can use them to make more complicated products.
A basketball manufacturer selects a random sample of its basketballs each week to ensure a consistent air pressure within them is maintained. In Week 1, the sample had a mean air pressure of 8.2 psi (pounds per square inch) and a margin of error of 0.1 psi. In Week 2, the sample had a mean air pressure of 7.7 psi and a margin of error of 0.3 psi. Based on these results, Option B, which states that the average air pressure of all basketballs created during week one was 0.5 psi higher than that of all basketballs produced during week two, is the right response.
Option C is not discussed in any detail.
Factually, Option D is inaccurate.
Because the margin of error would have been 0, Option A is wrong.
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Given the function:
f(x) = 1/2 (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answer: C
Step-by-step explanation:
It's easy! Don't worry!
f(x) = 1/2(3x+7)
f(9) = 1/2(3(9)+7)
f(9) = 1/2(27+7)
f(9) = 1/2(34)
f(9) = 17
Trust me when you finish algebra this stuff is cake not going to lie. I did it under a minute. ;)
Also, gl passing algebra!
at the beginning of her senior year maria received a $5,000 subsidized loan and a $4,500 unsubsidized loan with an apr of 5.05%. if maria begins making payments on her loans 6 months after graduation, how much interest will she owe to the nearest dollar?
Answer:
$114
Step-by-step explanation:
You want to know the interest due on student loans of $5000 (subsidized) and $4500 (unsubsidized) with an APR of 5.05% when Maria starts making payments 6 months after graduation.
SubsidizedThe government pays the interest for the first 6 months after graduation, so Maria owes no interest on her subsidized loan.
UnsubsidizedThe interest is figured beginning at graduation. The formula is ...
I = Prt . . . . . . P is the principal amount, r is the interest rate, and t is years
I = $4500(0.0505)(1/2) = $113.625 ≈ $114
Maria will owe $114 in interest on her loans 6 months after graduation.
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researchers wanted to check if carpeted rooms in hospitals contained more bacteria than uncarpeted rooms. to determine the amount of bacteria in a room, researchers pumped the air from the room over a petri dish for eight carpeted and eight uncarpeted rooms. colonies of bacteria were allowed to form in the 16 petri dishes. the results are presented in the table. (measured as bacteria per cubic foot) carpeted: 11.8, 10.8, 8.2, 10.1, 7.1, 14.6, 13.0, 14.0 uncarpeted: 12.1, 12.0, 8.3, 11.1, 3.8, 10.1, 7.2, 13.7 do carpeted rooms have more bacteria than uncarpeted rooms at a
No , the carpeted rooms does not have more bacteria than uncarpeted rooms .
Given ,
α=0.05
n1=8
n2 = 8
mean = ∑x / n
x1 = 11.8+10.8+7.1+14.6+8.2+10.1+13.0+14.0 / 8 = 11.2
and
x2 =12.1+12.0+3.8+10.1+8.3+11.1+7.2+13.7 /8 = 9.78
Variance ,
s1 =2.6
s2 = 3.2
HYPOTHESES
H0 : μ 1 =μ 2
H1 : μ 1 ≠μ 2
Either the alternative hypothesis or the null hypothesis applies to the claim. The equality must be present in the null hypothesis. The alternative hypothesis declares the opposite of the null hypothesis if the claim is the null hypothesis.
On calculating we get the test statistic t as,
t = 1.771
The null hypothesis is rejected if the test statistic's value falls within the rejection zone.
0.956<1.771,
therefore , fail to reject H .
Therefore , there is no support for the null hypothesis , so we accept the alternate hypothesis as true.
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A marketing company wanted to test what makes people purchase more cereal and they varied box size and flashy/simple graphics. Which of the following would be the main effects tested in this study? a. the results comparing each box size and comparing flashy vs Simple graphics b. behavior of purchasing cereal c. the results comparing each box size only d. the results comparing flashy vs. simple graphics only
Option A is correct that is the results comparing each box size and comparing flashy vs simple graphics.
Given this, a marketing firm tested several package variations, including size, complexity, and simplicity, to determine which would encourage customers to buy more cereal.
Which of the following would be the key conclusions of the study?
We are aware of this since we are comparing various box and graphic sizes.
When contrasting the sizes of each box and the flashy vs. simple images, the influence of the research can be noticed.
The comparison of the sizes of each box and the effectiveness of flashy vs. straightforward images shows that Option A is the best choice.
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A chain restaurant hires a new vice president with vast experience in the industry. The new vice president claims that based on his observations in the industry that if the company offers a rewards program to its diners then sales will increase by an average of at least $600 per restaurant per week. The executive management team decides to pilot a rewards program in a few areas and evaluate the impact after one year. Below are the sales changes (sales for the week compared to the same week the previous year) for a sample of restaurants. You can copy the data into Excel to complete this problem. There are 35 observations; be sure to copy all of them. a) To conduct a test of the vice president's claim the appropriate null hypothesis is the population mean does not equal 600. b) The point estimate for the mean change in sales is Select) c) The standard deviation for the change in sales is (Select) d) The estimated standard error for this problem is [Select] e) The appropriate test statistic for this problem is Select) f) The appropriate p-value for this hypothesis test is g) Based on your results and using a 0.05 level of significance for your test you [Select] the null hypothesis.
Previous question
On solving the provided question, we can say that - h1: μ < $600 and mean - 1/35 X 20307 = 580.2
What is null hypothesis ?According to a well-known statistical theory known as the null hypothesis, there is no statistically significant association between any two sets of observable data and measurable events.
By putting X = sales change in $
Null hypothesis -
h0= μ ≥ $600
alternative hypothesis is
h1: μ < $600
where μ is population mean change in sales per week
point estimate of mean change in sales is
mean - 1/35 X 20307 = 580.2
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1. 7h25min to min= ?
2. 3h25min to min= ?
3. 35600sec to hminsec= ?
please help me with the answer. thank you.
7h25min to min= 445min
3h25min to min= 205min
35600sec to hminsec= 9h53min20sec
Extra Explanation:
To convert hours to minutes, we can multiply the number of hours by the number of minutes in an hour. For example, 7 hours is equal to 7 * 60 = 420 minutes. Similarly, 3 hours is equal to 3 * 60 = 180 minutes.
To convert seconds to hours, minutes, and seconds, we can first convert the total number of seconds to minutes by dividing by the number of seconds in a minute (60). For example, 35600 seconds is equal to 35600 / 60 = 600 minutes. We can then convert the total number of minutes to hours by dividing by the number of minutes in an hour (60). For example, 600 minutes is equal to 600 / 60 = 10 hours. Finally, we can find the remaining minutes and seconds by taking the remainder when the total number of minutes is divided by 60. For example, the remainder when 600 is divided by 60 is 53 minutes. The remaining seconds can be found in a similar manner.
Answer:
7h25mins =445 mins
3h25mins = 205 mins
35600s =9 h 53mins and 20 sec
Step-by-step explanation:
a min equals 60 sec
an hour equals 60 mins
for example 7h equals 60mins ×7
so 420 then add 25 min which then becomes 445 mins
Please help! (Attached image) remainder Theorem
The remainder when the polynomial is divided by x - 5 is given as follows:
B. 24.
The remainder when the polynomial is divided by x - 8 is given as follows:
B. 87.
What is the Remainder Theorem?The Remainder Theorem states that when a polynomial y = f(x) is divided by a binomial given by x - a, the remainder is given by f(a).
The polynomial for this problem is given as follows:
f(x) = 2x² - 5x - 1.
Hence the remainder when the polynomial is divided by x - 5 is calculated as follows:
f(5) = 2(5)² - 5(5) - 1 = 24. (option B).
(x - 5 = 0 -> x = 5 is the value at which the numeric value has to be calculated to obtain the remainder).
Hence the remainder when the polynomial is divided by x - 8 is calculated as follows:
f(8) = 2(8)² - 5(8) - 1 = 87. (option B).
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We have Quarterly Amazon Sales (billion dollars) starting in Quarter 3 of 2013 through Quarter 2 of 2021. In Quarter 2 of 2021 the Amazon Sales was 96.1 billion dollars. Use the output provided below to report the updated forecast for the Amazon Sales for Quarter 3 of 2021. The variable time period is coded in the following way: Start with t = 1 for Quarter 3 of 2013, t = 2 for Quarter 4 of 2013. The value of t will increase by 1 for each subsequent quarter. In this example we have created indicator variables for Quarters 1, 2 and 3. Quarter 4 is the baselevel. Using the output here for the model accounting for trend and seasonality as well as the output for the AR(1) model report the updated forecast for Amazon Sales in Quarter 3 of 2021. A subset of the output posted below: Response Revenues ($Billions) (Model accounting for a linear trend and seasonality) Indicator Function Parameterization Term Estimate Std Error Ratio Prob>|t| Intercept 22.67 2.170013 8.15 <0001* Time period 2.538 0.114582 19.54 <.0001* Quarter[1] - 10.44 2.376946 -4.39 0.0003* Quarter[2] -11.156 2.385217 -4.68 0.0001* Quarter[3] -8.773 2.290687 -3.83 0.0010* Bivariate Fit of Residual Revenues ($Billions) 2 By Lag residuals (AR(1) Model output) Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.0856 0.479018 -0.18 0.8598 Lag residuals 0.762 0.132836 5.74 <.0001 The Updated forecast for the Amazon Sales accounting for Trend, Seasonality and Adjusted for the Serial Correlation using the AR(1) model is: _________ billion dollars. If the answer is 75.2432 billion dollars just type 75.2432 Record your answer with at least 4 decimal places.
The AR(1) model was used to create an updated forecast for Amazon sales that account for trend, seasonality, and serial correlation is 97.6510
Accounting and revenue
Accounting is the recording of financial transactions along with storing, sorting, retrieving, summarizing, and presenting the results in various reports and analyses.Revenue in accounting refers to the entire amount of money made through selling products and services from a company's core operations. Revenue is another term for a company's earnings, also known as sales or turnover.Given that:
Equation of regression
Revenue = 22.67 + 2.538*t - 10.44*Q1 + 11.156*Q2- 8.77*Q3
t = 1 for the third quarter of 2013.
t = 33 for the third quarter of 2021
Revenue = 22.67 + 2.538*33 - 8.77 = 97.6510 billion dollars.
Therefore, Revenue = 97.6510 billion dollars
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initial investment $ 415,000 $ 230,000 $ 720,000 $ 945,000 present value of future cash flows 765,000 415,000 1,200,000 1,560,000
Is Shaylee able to invest in all of these projects simultaneously is no. Since the company has limited excess of money i.e. 2 Million to invest.
What is probability index?
The present value of benefits for each dollar of investment is calculated using the profitability index approach. In other words, it involves the ratio that is produced by comparing the ratio of the initial investment to the present value of future cash flows from a project.
A solid investment is one with a profitability index of greater than 1.0, with higher values indicating more alluring enterprises.
The ratio between the initial investment and the present value of future cash flows is measured by the profitability index (PI). The index can be used to rate investment projects and display the value produced per investment dollar.
Profitability Index = Present Value of Cash INflows / Present Value of Cash Outflows
Project : Profitability Index
A : 1.8434 (765,000 / 415,000)
B : 1.8043 (415,000 / 230,000)
C : 1.6667 (1200,000 / 720,000)
D : 1.6508 (1560,000 / 945,000)
Order of Preference
Project - Order of Preference
A - First Preference
B - Second Preference
C - Third Preference
D - Fourth Preference
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coordinate geometry find the coodinates of the centroid of each triangle with the given vertices geometry answers
The Coordinates of the centroid of a triangle with the given vertices are (0, 4), (8, 10) and (6, 1) is (14/3, 5) and Centroid of triangle with vertices (1,5),(3,8),(0,2) is (4/3, 5).
What is Centroid of a triangle?The centroid of a triangle is one of the point where all three medians of the triangle intersect. The median is a line segment drawn from one vertex to the midpoint on the opposite side. Triangle centroid divides each median into individual words in a 2:1 ratio. The centroid is usually at 2/3 of the median.
If the three vertices of a triangle are A(x₁,y₁) B(x₂,y₂), C(x₃,y₃), the centroid of the triangle is given by the formula :
G(x₁+x₂+x₃/3, y₁+y₂+y₃/3 ).
We have , two triangles with vertices,
a) triangle whose vertices are A(0, 4), B(8, 10) and C(6, 0). So, the coordinates of the centroid of a triangle whose vertices are (0, 4), (8, 10) and (6 , 1) are ( (0+8+6)/3 , (4+10+1)/3 ) or (14/3, 5).
b) triangle whose vertices are P(1, 5), Q(3,8) and R(0, 2). So, the coordinates of the centroid of a ∆PQR are ( (1+3+0)/3 , (5+8+2)/3 ) or (4/3, 5).
Hence, the required coordinates of Centroid are (14/3, 5), (4/3, 5).
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Complete question:
Coordinate geometry find the coodinates of the centroid of each triangle with the given vertices are a) (0, 4), (8, 10) and (6, 1)
b) (1,5),(3,8),(0,2)
Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.
The total time taken by Amy to complete her assignments is 19/20 hours.
What is addition?Addition is one of the four basic operations of arithmetic, Addition in maths is a process of combining two or more numbers.
Given that, Amy finished her chemistry assignment in 1/5 hours. Then she completed her history assignment in 3/4 hours.
Total time taken by Amy = Time taken for chemistry assignment + Time taken for history assignment
= 1/5+3/4 = (15+4)/20
= 19/20
Hence, The total time taken by Amy to complete her assignments is 19/20 hours.
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the usher at a wedding asked each of the 808080 guests whether they were a friend of the bride or of the groom. here are the results
The probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.
Given that, at a wedding each guest asked the 80 guests whether they were a friend of the bride or of the groom.
What is the probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Total Number of Guests which forms the Sample Space, n(S)=80
Let the event (a friend of the bride) =A
Let the event (a friend of the groom) =B
n(A) =59
n(B)=50
Friends of both bride and groom,
So,
n(A∪B)=n(A)+n(B)-n(A∩B)
n(A∪B)=59+50-30
n(A∪B)=79
The number of Guests who was a friend of the bride OR of the groom = 79
Thus,
P(A∪B)=n(A∩B)/n(S)
= 79/80
= 0.9875
Hence, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.
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Identifying subgroups of the overall marketplace based on factors such as age or income level is considered:
Demographic segmentation is considered for identifying subgroups of the overall marketplace based on factors such as age or income level.
A precise method of identifying an audience is known as demographic segmentation. It is based on information such as age, gender, marital status, family size, income, education, race, occupation, nationality, and/or religion. It is one of the four primary categories of marketing segmentation and is possibly the most used approach.
By concentrating on specific qualities that may represent relevant markets for a firm, demographic segmentation joins consumers and potential customers together. The five primary demographic subgroups are :
Agegenderoccupationcultural background family statusDemographic segmentation is the process of dividing a market into subgroups based on factors such as age, gender, income level, education level, and geographic location. This is a common way for businesses to identify and target specific groups of consumers who are likely to be interested in their products or services. By understanding the characteristics of different demographic segments, businesses can tailor their marketing efforts and products to better meet the needs and preferences of these groups. This can help businesses to effectively reach and engage their target audience, and ultimately increase sales and profits.
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6. Writing When you add a
one-digit number to a
decade number, what do you
notice about the ones place
digit of the sum?
When one adds a one digit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added.
What is a decade number?It's important to bite that a decade number simply means the numbers that are counted when counting numbers by tens to 100.
In this situation, when one adds a one diigit number to a decade number, the thing that one notice about the ones place digit of the sum is that it is the exact value that you added. Any example will be:
= 10 + 2
= 12
In this case, the 2 is in the units value of the number
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After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.6+4 /(t+4)^3 feet per year, where t is the time (in years).
(a) Find the number of feet that the tree will grow in the second year.
(b) Find the number of feet the tree will grow in the third year.
a.) 0.5367 feet
b.) 0.5223 feet'
Given the rate at which an eucalyptus tree will grow modelled by the equation 0.5+6/(t+4)³ feet per year, where t is the time (in years).
The amount of growth can be gotten by integrating the given rate equation as shown:
[tex]\int\limits {0.5} \, + \frac{6}{(t+4)^{3} } dt[/tex]
[tex]=\int\limits {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx[/tex]
[tex]=0.5t+\int\limits6u^{-3} du \, \,where \,u=t +4 \, and \, du=dt[/tex]
[tex]=0.5t+6*\frac{u^{-3} }{-2} + C[/tex]
[tex]=0.5t-3u^{-2}+C[/tex]
[tex]=0.5t-3(t+4)^{-2} +C[/tex]
a) The number of feet that the tree will grow in the second year can be gotten by taking the limit of the integral from t =1 to t = 2
[tex]\int\limits^2_1 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \, =[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[0.5(2)-3(2+4)^{-2} ]-[0.5-3(5)^{-2} ][/tex]
[tex]=\frac{11}{12}-\frac{1}{2}-\frac{3}{25}[/tex]
[tex]=0.9167-0.5+0.12[/tex]
[tex]=0.5367[/tex]
b) The number of feet that the tree will grow in the third year can be gotten by taking the limit of the integral from t =2 to t = 3
[tex]\int\limits^3_2 {0.5} \,dt + \int\limits\frac{6}{(t+4)^{3} } dx \,[/tex]
[tex]=[0.5t-3(t+4)^{-2} ][/tex]
[tex]=[1.5-\frac{3}{49} ]-[1-\frac{1}{12} ][/tex]
=1.439-0.9167
=0.5223 feet
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fill in the missing words what are congruent triangles? triangles with the exactly the same and . this means that all (angles and sides) are congruent.
Congruent triangles are two triangles with the exact same shape and size.
This means that all of their angles and side lengths are congruent, or equal. In order to determine if two triangles are congruent, we must first make sure that the angles of both triangles are the same.
We can do this by using the Angle-Angle (AA) theorem, which states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are congruent. The next step is to check that all three side lengths of both triangles are equal.
We can use the Side-Side-Side (SSS) theorem to do this, which states that if all three side lengths of one triangle are equal to the three side lengths of another triangle, then the two triangles are congruent.
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The following series are geometric series. Determine whether each series converges or not. For the convergent series, enter the sum of the series. For the divergent series, enter DIV. Also for each series, enter the first term a and the common ratio r. Determine whether the following series is convergent or divergent. If convergent find the sum, and if divergent enter DIV: 4 - 4/2+ 4/4 - 4/8 +... =
The given series is convergent and the first term is 4 and the common ratio is -0.5 and the sum of the series is 8/3 .
The given series is 4 - 4/2+ 4/4 - 4/8 +...
We can see that the first term of the geometric series is 4
Hence a = 4
The second term is -4/2 and the third term is 4/4
Hence r = 4 ÷ (-4/2) = -4/2 ÷ 4/4 = - 1/2 or -0.5
Since the common ratio is less than 1 we can say that the series is convergent.
Now for a convergent series we know that the sum of the terms of the series is equal to
S = a / (1-r)
or, S = 4 / (1-(-0.5))
or, S = 4 / 1.5
or, S = 8/3
Hence the sum of the convergent series is 8/3 .
Both the ratio test and the root test are based on a comparison with a geometric series and hence function in comparable scenarios.
In fact, if the ratio test works (that is, if the limit exists and is not equal to 1), then so does the root test; the contrary is not true. The root test is thus more broad, although in practise, determining the limit for regularly encountered kinds of series is frequently challenging.
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Can someone help me with this please
it's either S or R according to me
According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 5x³-7x+11?
0 +1.1.1.5
O
11
0 + 3.1.1.5,
45, +11
5
0 0 ±, ±3. 1. ±1, , 25, ±11
Answer:
1/5
-1/5
11/5
-11/5
1
-1
11
-11
Step-by-step explanation:
The Rational Root Theorem states that if a polynomial equation with integer coefficients has a rational root, then that root must be of the form p/q, where p is a factor of the constant term (in this case, 11) and q is a factor of the leading coefficient (in this case, 5).
Using this information, we can determine that the potential rational roots of the polynomial f(x) = 5x³-7x+11 are all of the following:
1/5
-1/5
11/5
-11/5
1
-1
11
-11
Note that this list includes all possible rational roots of the polynomial, but not all of these roots will necessarily be actual roots. To determine which of these potential rational roots are actual roots, we would need to test them by plugging them into the polynomial and solving for x.