find the area inside the loop of the limacon given by r=7−14sinθ
Answers
The area inside the loop of the limacon given by r=7−14sinθ is 49π square units.
How to find area ?To find the area inside the loop of the limacon given by the polar equation r=7−14sinθ, we can use the following steps:
Find the points where the curve intersects the x-axis by setting r=0:
0 = 7 - 14sinθ
sinθ = 1/2
θ = π/6 or 11π/6
Find the limits of integration for θ by noting that the loop starts at θ=0 and ends at θ=2π:
θ limits: 0 ≤ θ ≤ 2π
Use the formula for the area of a polar region:
A = 1/2 ∫[a,b] r(θ)² dθ
where r(θ) is the polar equation and a and b are the limits of integration.
Rewrite the polar equation in terms of sinθ and cosθ:
r(θ) = 7 - 14sinθ
r(θ)² = (7 - 14sinθ)² = 49 - 196sinθ + 196sin²(θ)
= 196cos²(θ) - 196cos(θ) + 49
Substitute the limits of integration and evaluate the integral:
A = 1/2 ∫[0,2π] (196cos²(θ) - 196cos(θ) + 49) dθ
= 1/2 (98π)
Simplify the result to get the final answer:
A = 49π
Therefore, the area inside the loop of the limacon given by r=7−14sinθ is 49π square units.
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Related Questions
Now that you’ve calculated all the missing values, complete the table.
Answers
Missing Blank for:
Raul and his friends: (3/4) / (1/20) = 15
Items: 15
Cars: (7/8) / 2 = 7/16
Weight per item: 7/16
Baby elephants: (3/4) / (3/8) = 2
Items: 2
Goats: (1/2) / 4 = 1/8
Weight per item: 1/8
Desks: (3/8) / (1/32) = 12
Items: 12
In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices
Answers
In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance statistic is computed.
What is Analysis of variance ?
With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.What are some instances where ANOVA has been applied?
An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.Learn more about Analysis of variance
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I need help asap!! will give crown
Answers
Answer:
A. Rectangle
Step-by-step explanation:
Shown in the attachment are the four points graphed on a coordinate plane.
We can see that the opposite sides are parallel to each other and have the same length.
The answer cannot be B. Square because the side lengths of this quadrilateral are not all equal to each other.
The answer cannot be C. Rhombus because of the same reason as above.
The answer cannot be D. Trapezoid because the bases of the quadrilateral are not of different lengths.
Therefore, the answer must be A. Rectangle since the angles are 90° angles, and the opposite sides are parallel and equal.
the radius of the cylinder is 6 m and the height is 10 m what's the volume?
Answers
in an examination 60% exam in failed in maths 55% failed in English and 25 failed in both subjects if none of the exam in past in the both subject find the number of exam in who passed in mathematics only
Answers
Answer:
60% x 25
55 % x 25
10 in english
25 is total and rest will be math
so 25-10 = 15
15 students failed math
what is the binomial expansion of (x+1)^5
Answers
Answer: "A"
somewhat of a trick question
use pascals triangle (or binomial expansion)
0-1
1-1,1
21,2,1
3- 1,3,3,1
4- 1,4,6,4,1
5- 1,5,10,10,5,1
NOTICE THAT "A" has the 1,5,10,10,5,1 in the 5th row
Step-by-step explanation:
which statistic (mean, median, or mode) is most appropriate in each of the following situations? tables in the dining hall are numbered 1 through 12 for students who eat there. the principal calls out a number for the table that will go through the buffet line first. the other tables follow in order of the table numbers. one student is sure the principal calls certain tables more often. she keeps track of which numbers are called over a 21-day period. mean median mode the offensive line of a football team is larger than in previous years. the program will list a statistic to show this fact. mean median mode a reporter is doing a story on the falling prices of homes in a large neighborhood. the reporter wants to demonstrate how the prices have fallen for the typical home, not just the most expensive houses. mean median mode
Answers
Mode is the most appropriate statistic in the given situation.
What are mean, mode, and median?A data set's mean (average) is calculated by adding all of the numbers in the set and then dividing by the number of values in the set. When a data set is ordered from least to greatest, the median is the middle value. The mode is the number that appears the most frequently in a data set.
The statistical method that gives the value of an entity that occurs the greatest number of times in a set of data values is defined as mode. For example, if the test scores of five students are 35, 45, 35, 35, and 50, the mode of the given set of data is 35 because it occurs the most frequently.
The student is certain that the principal will frequently call out the names of a certain number of tables. She keeps track of the tables over the course of 21 days, and as the table number is called out the most number of times in that time period, the value of the table number is determined by the Mode of the data.
Thus, the most suitable method is Mode.
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Jen and Jude are trying to save money over the next two months to buy a new scooter they need a total of $103 Jen saves $21.25 each month how much does Jude need to save each month so they have enough money
Answers
Answer:
30.25.
Step-by-step explanation:
multiply the 21.25 by 2 months. then subtract that by the 103, and then divide that by 2 to get the 30.25.
please rate and mark as brainlest
Please explain steps and formulas used.
Trader Bubba Industries must choose between solar and an electric-powered forklift truck for moving materials in its factory. Because both forklifts perform the same function, the firm will choose only one. (They are mutually exclusive investments.) The solar truck will cost more, but it will be less expensive to operate; it will cost $30,000, whereas the electric-powered truck will cost $20,000. The life for both types of truck is estimated to be 8 years, during which time the net cash flows for the solar-powered truck will be $8,000 per year and those for the electric-powered truck will be $5,000 per year. Trader Bubba Industries' assets are $400 million, financed through bank loans, bonds, preferred stocks, and common stocks. The amounts are as follows: Bank loans: $50 million borrowed at 3% Bonds: $200 million, paying 4% coupon with semi-annual payments, and maturity of 10 years. Trader Bubba sold its $1,000 par-value bonds for $1020 and had to incur $20 flotation cost per bond. Preferred Stocks: $100 million, paying $15 dividends per share. Trader Bubba sold its preferred shares for $220 and had to incur $20 per share flotation cost. Common Stocks: $50 million, beta is 2, the risk-free rate is 2percent, and the market rate is 6%. Tax rate: 40 percent Please answer the following questions using the information above. Don't forget to show all your work. a) What is the after-tax cost of the loans? b) What is the after-tax cost of the bonds? c) What is the after-tax cost of the preferred stocks? d) What is the after-tax cost of the common stocks? e) Calculate the weighted average cost of capital (WACC). Please show your work precisely by indicating each component and weight. f) Calculate the NPV and IRR for each type of truck and decide which to recommend. (Use the cost of capital you found in "e" when calculating the NPV and IRR)
Answers
Trader Bubba Industries should recommend buying the solar truck as it has a higher NPV than the electric-powered truck.
a) After-tax cost of the loans
The cost of the loan is given as $50 million borrowed at 3%. The tax rate is 40%.
Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate)
After-tax cost of the loan = 3% * (1 - 0.4) = 1.8%
b) After-tax cost of the bonds
The cost of the bonds is given as $200 million, paying 4% coupon with semi-annual payments, and maturity of 10 years. Trader Bubba sold its $1,000 par-value bonds for $1020 and had to incur $20 flotation cost per bond. The tax rate is 40%.
Formula to calculate the after-tax cost of debt: After-tax cost of debt = cost of debt * (1 - tax rate) * (1 - flotation cost) / (1 - tax rate)
After-tax cost of bonds = 4% * (1 - 0.4) * (1 - 0.02) / (1 - 0.4) = 2.424%
c) After-tax cost of the preferred stocks
The cost of preferred stocks is given as $100 million, paying $15 dividends per share. Trader Bubba sold its preferred shares for $220 and had to incur $20 per share flotation cost. The tax rate is 40%.
Formula to calculate the after-tax cost of preferred stocks: After-tax cost of preferred stocks = cost of preferred stocks * (1 - flotation cost / market price) / (1 - tax rate)
After-tax cost of preferred stocks = $15 * (1 - 20 / 220) / (1 - 0.4) = 9.75%
d) After-tax cost of the common stocks
The beta of common stocks is given as 2, the risk-free rate is 2%, and the market rate is 6%. The tax rate is 40%.
Formula to calculate the after-tax cost of common stocks: After-tax cost of common stocks = risk-free rate + beta * (market rate - risk-free rate) * (1 - tax rate)
After-tax cost of common stocks = 2% + 2 * (6% - 2%) * (1 - 0.4) = 5.2%
e) Weighted average cost of capital (WACC)
WACC = w1r1 + w2r2 + w3r3 + w4r4
Where w = weight,
r = cost of capital.
W1 = $50 million / $400 million = 0.125 or 12.5% (weight of loans)
W2 = $200 million / $400 million = 0.5 or 50% (weight of bonds)
W3 = $100 million / $400 million = 0.25 or 25% (weight of preferred stocks)
W4 = $50 million / $400 million = 0.125 or 12.5% (weight of common stocks)
WACC = 0.125 * 1.8% + 0.5 * 2.424% + 0.25 * 9.75% + 0.125 * 5.2% = 3.874%
f) Net Present Value (NPV) and Internal Rate of Return (IRR) for both types of trucks
Formula to calculate NPV: NPV = -Initial Investment + ∑(Net Cash Flows / (1 + r)t)
Where Initial Investment is the cost of the truck,
Net Cash Flows are the cash flows of each year,
r is the discount rate, and
t is the year.
For the solar truck,Initial investment = $30,000
Net Cash Flows per year = $8,000
Discount rate = WACC
NPV = -$30,000 + $8,000 / (1 + 3.874%) + $8,000 / (1 + 3.874%)2 + ... + $8,000 / (1 + 3.874%)8 = $28,845.80IRR = 12.23%
For the electric-powered truck,Initial investment = $20,000
Net Cash Flows per year = $5,000
Discount rate = WACC
NPV = -$20,000 + $5,000 / (1 + 3.874%) + $5,000 / (1 + 3.874%)2 + ... + $5,000 / (1 + 3.874%)8 = $17,716.80IRR = 13.15%
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A car insurance company is interested in modeling losses from claims coming from a certain class of policy holders for the purposes of pricing and reserving. The policy has a deductible of $500 per claim, up to which the policy holder must pay all costs, and after which the insurance company will pay all additional costs associated with the claim. The insurance company also purchases reinsurance to assist in paying out large claims, which will pay any costs to the insurance company in excess of $15,000. To help with interpreting this policy, some examples of how different-sized claims would be payed out are shown below. Assume the losses for claims on this policy follow an exponential distribution with a mean of $3000 (note: this corresponds with a rate parameter A=1/3000). Example claims: i) A claim carries a loss of $353 dollars. The policy holder must pay the entire $353 associated with the claim, since the cost is less than the deductible for the policy. ii) A claim carries a loss of $2567 dollars. The policy holder pays the deductible of $500, and the insurance company pays the remaining $2067. iii) A claim carries a loss of $32,000 dollars. The policy holder pays the deductible of $500, the insurance company pays $15,000, then reinsurance covers the remaining $16,500. find the probability that the insurance company needs to pay on a claim they receive (i.e. find the probability that the cost of a claim exceeds the deductible of $500)
Answers
The probability that the insurance company needs to pay on a claim they receive, i.e., the cost of a claim exceeds the deductible of $500, is approximately 83.33%.
In this scenario, the losses from claims on the policy are assumed to follow an exponential distribution with a mean of $3000. The exponential distribution is commonly used to model continuous random variables with a constant hazard rate. In this case, the hazard rate is determined by the mean of $3000.
To find the probability that the cost of a claim exceeds the $500 deductible, we need to calculate the cumulative probability of the exponential distribution beyond the deductible amount. Since the exponential distribution is memoryless, we can consider the deductible as a starting point and calculate the probability of the claim exceeding that amount.
Using the exponential distribution's probability density function (PDF), we can determine the probability of a claim exceeding the deductible. The PDF for an exponential distribution with rate parameter A is given by f(x) = A * exp(-A * x), where x is the claim amount.
Integrating the PDF from the deductible amount ($500) to infinity will give us the probability that the cost of a claim exceeds the deductible. However, in this case, we can simplify the calculation since we know the mean of the exponential distribution is $3000. The probability of a claim exceeding the deductible can be approximated as the ratio of the mean loss exceeding the deductible to the mean loss overall, which is (3000 - 500) / 3000 = 0.8333 or 83.33%.
Therefore, the probability that the insurance company needs to pay on a claim they receive, i.e., the cost of a claim exceeds the deductible of $500, is approximately 83.33%.
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Which of these strategies would eliminate a variable in the system of equations? { 2 � + 3 � = − 5 2 � − 3 � = 10 ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 2x+3y=−5 2x−3y=10 Choose all answers that apply: Choose all answers that apply: (Choice A) Subtract the bottom equation from the top equation. A Subtract the bottom equation from the top equation. (Choice B) Add the equations. B Add the equations. (Choice C) Multiply the top equation by 2 22, then add the equations. C Multiply the top equation by 2 22, then add the equations
Answers
The solution to the system of equations is (x,y) = (1.25, -2.5) and the solution to the system of equations is (x,y) = (0, -5/3).
How to eliminating variables in a system of equations requires using one of the algebraic methods?Let's try these strategies on the given system of equations:
2x+3y=−5
2x−3y=10
A. Subtract the following formula from the above formula:
(2x + 3y) - (2x - 3y) = (-5) - 10
6 years = -15
y = -2.5
Substituting y = -2.5 into one of the equations gives:
2x + 3(-2.5) = -5
2x - 7.5 = -5
2x = 2.5
x = 1.25
So the solution to the system of equations is (x,y) = (1.25, -2.5).
This strategy eliminates the x variable, but not the y variable. B. Add equations.
(2x + 3y) + (2x - 3y) = (-5) + 10
4x = 5
x = 1.25
Substituting x = 1.25 into one of the equations gives:
2(1.25) + 3 years = -5
3 years = -7.5
y = -2.5
So the solution of the system of equations is (x,y) = (1.25, -2.5).
This strategy removes the variable y but not the variable x.
C. Multiply the above formula by 2, then sum these formulas. 2(2x + 3y) + (2x - 3y) = 2(-5) + 10
4x = 0
x = 0
Substituting x = 0 into one of the equations gives:
2(0) + 3 years = -5
y = -5/3
So the solution to the system of equations is (x,y) = (0, -5/3).
This strategy eliminates the x variable, but not the y variable.
Therefore, there is no way to completely eliminate variables in the system of equations.
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And 7/8 hours Greg reads 2/3 chapters what’s the unit rate in chapters per hour?
Answers
The unit rate in chapters per hour is 21/16 hours
How to calculate the unit rate?Greg read 7/8 hours in 2/3 chapter
The unit rate can be calculated as follows
7/8= 2/3
1= x
cross multiply both sides
2/3x= 7/8
x= 7/8 ÷ 2/3
x= 7/8 × 3/2
x= 21/16
Hence 21/16 chapters is read in one hour
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teacher: how can we change the base of a logarithm? student:
Answers
We can change the base formula by:
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
The change of base formula is used to change the base of a logarithm. We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.
The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.
Base Formula: -
The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.
Change of base formula
logₐ b = logₓ a /logₓ b
OR
logₓ a, logₓ b = logₓ a
Change of Base Formula
Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:
logₐ b = [logₐ x] / [logₐ y]
In this formula,
The argument of the logarithm in the numerator is the same as the argument of the original logarithm.The argument of the logarithm in the denominator is the same as the base of the original logarithm.The bases of both logarithms of numerator and denominator should be the same and this base can be any positive number other than 1.Change of Base Formula Derivation
Change of base formula derivation can be understood from the following steps. Let us assume that
log ₐ b = p, logₙ a = q, and logₙ b = r.
By converting each of these into exponential form, we get,
a = \(b^{p}\), a = \(x^{q}\), and b = \(n^{r}\)
From the first two equations,
\(x^{q}\) = \(n^{r}\)
Substituting b = \(n^{r}\) (which is from third equation) here,
(\(n^{r}\))\(^{p}\) = \(x^{q}\)
\(n^{r}\))\(^{p}\) = \(x^{q}\)(Using a property of exponents)
p r = q
p = q / r
Substituting the values, we get,
logₐ b = [logₐ x] / [logₐ y]
For Example:
Evaluate the value of log₆₄ 8 using the change of base formula.
Solution:
We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.
log₆₄ 8 = [log 8] / [log 64]
= [log 8] / [log 82]
= [log 8] / [2 log 8] [∵ log am = m log a]
= 1 / 2
Answer: log₆₄ 8 = 1 / 2
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Hey lol pls help meim rlly bad at math
Answers
Answer:
x=24 ,y=156 ,z=24
Step-by-step explanation:
using linear pair 180 degrees
Which expression is not equivalent to the other three?
Answers
Answer:
second option,
4 + 7x - 2
Step-by-step explanation:
all expressions equal '7x-6' except for the second option:
4 + 7x - 2 = 7x + 2
A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit in the coordinate plane represents 1 ft. What is the approximate area of the baseball diamond?
Answers
The area of the baseball diamond is 8192 sq. units.
We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).
The side of the square can be computed using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).
Thus, the side of the square,
a = √((x₂ - x₁)² + (y₂ - y₁)²),
or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,
or, a = √(64² + (-64)²),
or, a = √(4096 + 4096),
or, a = 64√2 units.
Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.
Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.
Thus, the area of the baseball diamond is 8192 sq. units.
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Osgood missed 8 out of 30 problems on a math test, what percent of the problems did he get correct?
Answers
Circle O has a center of (-1,5) and passes through the point (2,9) write the equation in center radius form and standard form
Answers
Firstly, calculate the radius r of the circle using distance between two points
\(\begin{gathered} r\text{ = }\sqrt[]{(2-(-1))2+(9-5)^2} \\ r=\text{ }\sqrt[]{(2+1)^2+(4)^2} \\ r=\sqrt[]{3^2+4^2} \\ r=\sqrt[]{9+16} \\ r=\sqrt[]{25} \\ r=\text{ 5} \end{gathered}\)Then use the radius r=5 and the center (-1 , 5) to find the equation of the circle
\(\begin{gathered} r^2=(x-h)^2+(y-k)^2 \\ 5^2=(x-(-1))^2+(y-5)^2 \\ 5^2=(x+1)^2+(y-5)^2 \end{gathered}\)The center radius form is
\(5^2=(x+1)^2+(y-5)^2\)The standard form is
\(\text{ 25}^{}=(x+1)^2+(y-5)^2\)
Claire rides her bicycle five miles each day for four days and two miles each day for the remaining three days of the week.
Which of the following shows the number of miles she cycles in a week?
Answers
Answer:B.(5 x 4)+(2x3)
пожалуйстаааа помогитее, у меня мало баллов но прошу
Answers
Answer:
Я не вижу достаточно, чтобы прочитать весь вопрос, но я надеюсь, что это поможет.
и как человек с английским в качестве основного языка и изучающий русский, я с удовольствием использую эти навыки.
Work out the percentage change to 2 decimal places when a price of £189 is decreased to £150.
Answers
Answer:
The percentage change is -21%
Step-by-step explanation:
The percentage change can be expressed by the formula;
(new price -old price)/old price * 100%
New price = £150
old price = £189
Inputing these values in the formula, we have;
(150-189)/189 * 100%
-39/189 * 100%
= -20.63% and that is approximately -21%
Kevin earns 2.4% interest each year on the money in his savings account. He kept $157.00 in his savings account for an entire year. How much money did Kevin earn in interest?
Answers
Answer:
That is the solution
Step-by-step explanation:
157,00.102,4%=
..........
..........
160,768
find the area of the circle. use 3.14 for π. do not round answer
Answers
Radius = 14 : 2 = 7 in.
Area = 7 x 7 x 3.14 = 153.86 (in2)
Answer:
153.86 in²
Step-by-step explanation:
Before finding the area of the circle, first, let us find the radius.
d = 2r14 = 2r
Divide both sides by 2.
7 in = r
And now let us find the area of the circle.
Area = π r²= 3.14 × 7 × 7
= 21.98 × 7
= 153.86 in²
Please help with need an answer
Answers
2x+3=3x+7
-3 -3
-----------------
2x=3x+4
-3x -3x
--------------
-x=4
divide both sides by -1
answer is
x=-4
if ur confused about any steps tell me and ill explain
After my salary was increased by $16\%,$ it was $\$52{,}200$. What was my salary before the increase
Answers
%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.
What is percentage?A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.
Considering the query
It was $52,200 after a 16% raise in my pay.
In light of the conditions stated, come up with
\($=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$\)
= $45000
Before the raise, I was making $45,000.
Therefore, the answer is $45,000.
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HELP ASAP WILL GIVE BRAINLIEST!! What is the value of 8.25p + 3.99c, when p=12 and c=8.
Answers
Answer:
130.92
Step-by-step explanation:
8.25(12)+3.99(8)
99+31.92
130.92
an object is traveling at a velocity of 9 ft/s and an acceleration of 2 ft/s2. estimate the change in position in the next 4 seconds.""
Answers
The estimated change in position of the object in the next 4 seconds is 52 ft.
How to find change in position?To estimate the change in position of the object in the next 4 seconds, we can use the kinematic equation:
d = vt + (1/2)at^2
where d is the change in position, v is the initial velocity, a is the acceleration, and t is the time interval.
Substituting the given values, we get:
d = (9 ft/s)(4 s) + (1/2)(2 ft/s^2)(4 s)^2
= 36 ft + 16 ft
= 52 ft
Therefore, the estimated change in position of the object in the next 4 seconds is 52 ft.
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Please help me with this problem. Best answer will get brainliest!
Answers
Answer:
c=20 e=114 d=46 dec=180
Step-by-step explanation:
y=5
Answer:
m∠C = 32°
m∠D = 82°
m∠DEC = 66°
Step-by-step explanation:
Exterior Angle Theorem says that the degree measure that with an angle forms a straight line (Ex. Angle DEF in the picture) is equal to the sum of the two other angles in the triangle. This means that the measure of angle DEF is equal to the measure of angle DCE plus the measure of angle CDE. This would mean that 9y + 1 + 3y + 5 = 114, meaning that 12y + 6 = 114, which means that 12y = 108, which means that y = 9. If we plug 9 in for all of these values, we get that angle D is 9 * 9 + 1, which is 82 and that angle C is 3 * 9 + 5, which is 32. Next, we know that the sum of angles in a triangle is 180, so we subtract 32 and 82 from 180 to find the measure of angle DEC, and this is 66 degrees.
My question is on the pic Find the equation of the line
Answers
ANSWER
D. y = -5x + 3
EXPLANATION
The equation of a line in slope-intercept form is,
\(y=mx+b\)Where m is the slope and b is the y-intercept.
In this graph, we can see that the y-intercept - which is the value of y where the line intersects the y-axis, is 3,
To find the slope, we will use the second point shown in the graph above. The formula to find the slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
\(m=\frac{y_1-y_2}{x_1-x_2}\)Using the points (0, 3) and (1, -2),
\(m=\frac{3-(-2)}{0-1}=\frac{3+2}{-1}=-5\)Hence, the equation of the line is y = -5x + 3.
calculus grades (1.6) the dotplot shows final exam scores for mr. miller’s 25 calculus students. a. find the median exam score.b. Without doing any calculations, would you estimate that the mean is about the same as the median, higher than the median, or lower than the median?
Answers
a. To find the median exam score, we need to arrange the scores in order from least to greatest. Then we find the middle score. In this case, the dotplot is not available, so I cannot provide the exact median score. However, once the scores are arranged in order, we can identify the middle score as the median.
b. Without doing any calculations, it is difficult to estimate whether the mean is about the same as the median, higher than the median, or lower than the median. However, if the distribution is roughly symmetric, we can expect the mean to be about the same as the median. If the distribution is skewed, then the mean will be pulled towards the tail of the distribution, and may be higher or lower than the median depending on the direction of the skew. Without additional information about the shape of the distribution, it is difficult to make an accurate estimate.
a. To find the median exam score, follow these steps:
1. Arrange the final exam scores from the dot plot in ascending order.
2. Since there are 25 students (an odd number), the median is the middle value. It is the 13th value in the ordered list.
b. Without doing any calculations, we can estimate if the mean is about the same as the median, higher, or lower based on the distribution of the scores. If the dot plot shows a symmetric distribution, the mean and median would be approximately equal. If the distribution is skewed to the right (with a few high scores pulling the average up), the mean would be higher than the median. If the distribution is skewed to the left (with a few low scores pulling the average down), the mean would be lower than the median. if the distribution is roughly symmetric, we can expect the mean to be about the same as the median.
To know more about the mean and the median. Click on the link.
https://brainly.com/question/30891252
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