Answer:
27 is a composite number. 27 = 1 x 27, or 3 x 9. Factors of 27: 1, 3, 9, 27. Prime factorization: 27 = 3 x 3 x 3, which can also be written 27 = 3³.
Answer:
3 x 3 x 3
Step-by-step explanation:
ok so 27 can be broken down to 3 and 9
3 x 9
and 3 x 9 can be broken down to 3 and 3 and 3
3 x 3 x 3
Given the right triangle shown below, prove cos2(θ) + sin2(θ) = 1.
A triangle with sides x, y, and hypotenuse r. Angle theta is opposite to side y.
By
, cos(θ) = StartFraction x Over r EndFraction, and by
, sin(θ) = StartFraction y Over r EndFraction.
Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ).
The
states that x2 + y2 = r2.
By
, we have [r cos(θ)]2 + [r sin(θ)]2 = r2.
Applying the
, the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2.
Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.
The blanks are filled by
Laws of Cosine,
Laws of Sine,
Pythagorean Theorem,
Substitution method,
Laws of Exponents
respectively.
What are the Laws of Cosine?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
[tex]cos(\theta)=\frac{\mbox{adjacent side}}{\mbox{hypotenuse}}=\frac{x}{r}[/tex]
What are the Laws of Sine?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
[tex]sin(\theta)=\frac{\mbox{opposite side}}{\mbox{hypotenuse}}[/tex]
What is Pythagorean Identity?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
Then the property
x²+y²=r²
is called the Pythagorean Identity.
How to fill the blanks?Given the right triangle shown below, prove cos²(θ) + sin²(θ) = 1.
A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
By Laws of Cosine
, cos(θ) = x/r, and
by Laws of Sine
, sin(θ) = y/r.
Multiplying both sides of the above equations by r, we get that
x = r cos(θ) and
y = r sin(θ).
The Pythagorean Theorem states that x² + y² = r².
By Substitution method , we have [r cos(θ)]² + [r sin(θ)]²= r².
Applying the Laws of Exponents, the equation can be written as r² cos²(θ) + r² sin²(θ) = r².
Dividing both sides of the equation by r² results in cos²(θ) + sin²(θ) = 1.
Hence, the blanks are filled by
Laws of Cosine,
Laws of Sine,
Pythagorean Theorem,
Substitution method,
Laws of Exponents
respectively.
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Answer:
the above is right
Step-by-step explanation:
Just took the test
5(m+4)=-2(-4-m)+3
help please
Answer:
m = -3
Step-by-step explanation:
5m + 20 = 8 + 2m +3
5m + 20 = 11 +2m
3m + 20 = 11
3m = -9
m = -3
17 - 5 x 4 divided by 2
Answer:
17-5×4 /2
12×4/2
48/2=24.
24 ans.
The answer is 24.
What is Division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
For example, for a sports event, if 30 students need to be divided into groups of 5 students, then how many total groups will be formed? Such problems can be solved easily using the division operation. Here we need to divide 30 by 5. The result will be 30 ÷ 5 = 6. So, there will be 6 groups of 5 students in each. You can verify this value by multiplying 6 and 5, which will give you the original number, 30.
The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.
Given:
17 - 5 x 4 / 2
= 12 * 4/2
=48/2
=24
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5. Susan receives a Federal Direct Subsidized Loan for $1,000 as a freshman in
college. If the interest rate is 5% per year compounded, how much will she owe upon
graduation?
A. $1,000 plus interest for four years
B. $1,000 plus interest for three years
C. $1,000
D. Nothing
Answer:
c 1,000
Step-by-step explanation:
The amount that Susan will pay upon graduation is; Option C: $1000
In the US, there are two major loans given by the United States department of education for eligible students.
They are;
Subsidized LoansUnsubsidized loansNow, subsidized and unsubsidized loans are federal loans that are given to eligible students to help cover the cost of their higher education at a four-year college or university.
Now, the major difference between both loans is that in subsidized loans, the US department of education usually pays the interest on the loans at maturity while the student pays the original sum alone. However in unsubsidized loans, the student is the one responsible for paying the interest on the loans as at when due in addition to the original amount.
Thus, since the student received a direct subsidized loan of $1000, it means the student will only pay back the $1000.
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What is the answer will mark brainliest
A
Hope it helps bye :)
Through(-5,-1), parallel to x=0
Answer:
x= -5
Step-by-step explanation:
. Suppose that the utility function is u(c, l) = log(c) - - l (a) Explain the intuition behind this utility function. Does the person likes consump- tion c? What about leisure l? (b) Find the equation of an indifference curve given a level of utility I. (c) Find the Marginal Rate of Substitution. (d) Show the optimal consumption-labor choice using a plot with c in the y-axis and in the x-axis. (e) Find the optimal amount of consumption and leisure assuming that h = 1 and π = T = 0.
(a) The utility function u(c, l) = log(c) - l represents a person's preferences for consumption (c) and leisure (l). The logarithmic term log(c) indicates that the person derives satisfaction or enjoyment from consumption. A higher value of c leads to greater utility, suggesting that the person likes consumption. On the other hand, the negative term -l represents disutility or a cost associated with engaging in labor or reducing leisure time. The person values leisure and would prefer to have more of it. Overall, the utility function balances the desire for higher consumption with the cost of reduced leisure.
(b) To find the equation of an indifference curve given a level of utility I, we set the utility function equal to I and solve for c in terms of l. The equation is:
I = log(c) - l
(c) The Marginal Rate of Substitution (MRS) represents the rate at which a person is willing to trade one good (leisure) for another (consumption) while maintaining the same level of utility. It is calculated by taking the derivative of the utility function with respect to leisure and dividing it by the derivative with respect to consumption:
MRS = ∂u/∂l / ∂u/∂c
For the given utility function, the MRS is constant and equal to 1. This implies that the person is willing to trade one unit of leisure for one unit of consumption, maintaining the same level of satisfaction.
(d) The optimal consumption-labor choice can be determined by maximizing utility subject to constraints, such as budget constraints or time constraints. Without additional information or constraints, it is not possible to precisely plot the optimal consumption-labor choice on a graph.
(e) To find the optimal amount of consumption and leisure, additional information or constraints are needed. The values of h (hours available for labor) and π (income or wage rate) would be necessary to consider the budget constraint. Similarly, the value of T (total time available) would be needed to account for the time constraint. Without these constraints, it is not possible to determine the optimal consumption and leisure levels.
Note: Please provide the missing values of h, π, and T to proceed with the calculation of the optimal consumption and leisure levels.
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all cell walls in all organisms are made of the same substance. 7th grade
Answer: false, only plants have a cell wall
Step-by-step explanation:
Answer:False
Hope This helps:)
Step-by-step explanation:
7. Consider a firm with the following production plan where {x,y,q} are outputs and {zi} are inputs. X=(x |-Z₁, Z2,-23, 24, 25, 26,-Z7) Y=(y,q |-Z₁, Z2, Z3, Z4,-25,-26,-Z7) Consider a Simple Production General Equilibrium Model where the representative agent has the following preferences where {ßi} is a real number less than 1 U(x, y) = P₁ log(x) + ß₂log(y) + ß3log (9) Is the market equilibrium in this economy Pareto optimal? A) No, since the production process to produce the good and also produces q which has a negative impact on utility. We can conclude that q is an externality, and the First Welfare Theorem requires that there be no market failures for it to hold. Since the First Welfare Theorem does not hold, the market equilibrium is not Pareto. B) Yes, since from the production plans it is possible to establish a frontier of production possibilities with the convexity properties necessary for equilibrium to exist. C) It is uncertain, it depends on whether there is a representative agent with convex preferences, otherwise the assumptions of the Second Welfare heorem would not hold. D) None of the above
A) No, since the production process to produce the good and also produces q which has a negative impact on utility.
We can conclude that q is an externality, and the First Welfare Theorem requires that there be no market failures for it to hold. Since the First Welfare Theorem does not hold, the market equilibrium is not Pareto.
Equilibrium is a scenario in which all relevant forces are in balance. When a market is in equilibrium, the price of a good or service is such that the quantity buyers are willing and able to buy is equal to the quantity sellers are willing and able to sell. The equilibrium price is the only one that can generate a stable market. Therefore, the equilibrium point where supply and demand meet is also known as market clearing.
However, when there is an externality, the market is not Pareto optimal because externalities occur when a production or consumption activity creates an impact on a third party that is not compensated for that cost.
A negative externality causes the social cost to exceed the private cost. This can lead to a Pareto inefficient outcome, resulting in market failure.
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When Molly adds all of her payments, how much will the car cost her?
Multiply the monthly payment by the number of months in the loan term to obtain the total loan repayment amount.
Molly's total car cost can be determined by adding up all her payments. However, without specific details about the payments, such as their frequency and duration, it is challenging to provide an exact answer. Nonetheless, I can provide a general approach to calculating the total cost.
Firstly, you need to gather information about Molly's car payment, including the purchase price, down payment (if any), interest rate, loan term, and any additional costs like taxes, fees, or insurance premiums. With these details, you can calculate the monthly loan payments using an amortization schedule formula or an online loan calculator.
An amortization schedule shows the payment amount, principal component, interest component, and remaining balance for every payment in the annuity. As the title suggests, it provides a complete understanding of where the money goes.
Multiply the monthly payment by the number of months in the loan term to obtain the total loan repayment amount. Add any additional costs to this total, such as taxes, fees, and insurance premiums.
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If point with coordinates (1, 4) is translated to point N', with coordinates (- 1, - 1) , which translation did Nu undergo?
Answer:
-1
Step-by-step explanation:
one in one five for three two one
Calculate the circumference of a circle with diameter 5 cm. Round to 2 d.p.
Answer:
15.71 cm
Step-by-step explanation:
Equation for the circumference of a circle: 2πr or dπ where r is the radius & d is the diameter.
5*π = 15.71
Answer:
15.71 cm
Step-by-step explanation:
Use the circumference formula, C = 2[tex]\pi[/tex]r
Since the radius of half of the diameter, the radius will be 2.5 cm
Plug in the radius into the formula and solve:
C = 2[tex]\pi[/tex]r
C = 2[tex]\pi[/tex](2.5)
C = 15.71
So, the circumference of the circle is approximately 15.71 cm
HELP ASAPP SHOW YOUR WORK i’ll mark brainliest!
Answer:
(x,y) (1, -4)
Step-by-step explanation:
3x-7= -4x
x=1
y= -4x1
y= -4
(x,y) (1, -4)
can i be brainliest
CAN SOMEONE PLEASE HELP ME OUT ANSWERING THESE QUESTIONS
Answer:
I need to see question #1 to answer the 2nd and 3rd one
Step-by-step explanation:
A scientist has developed a time-travel machine, but the machine is malfunctioning. At first he goes forward three years in time, then jumps forward two times the current year. Then, the machine takes him back 2000 years. He ends up in the year 2023. What year did he first operate the time-travel machine?
The scientist first operated the time-travel machine in the year 7.
To determine the year the scientist first operated the time-travel machine, we need to work backward from the given end point of 2023.
Since he ended up in 2023, we know that after going back 2000 years, the scientist was in the year 23. Going back even further, we subtract three years to account for the initial forward jump. This takes us to the year 20.
From there, we need to find the year when the scientist made the jump forward by two times the current year. To do this, we divide 20 by 2, resulting in 10. This means that the scientist made the jump forward in the year 10.
Finally, to determine the year when he first operated the time-travel machine, we subtract three more years from 10, which gives us the year 7.
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7) You borrow $30,000 to purchase a car, and will pay off the loan in 60 monthly payments with the first due in exactly one month. What are your monthly payments if the relevant interest rate is 6% per year =.5%=.005 per month? 8) Farmer Frank can sell his farm for a \$1,000,000 payment today. If he kept his farm would have eamed NET income (after all economic expenses, direct and indirect) of $20,000 at the end of each of the next 30 years with the first payment received in one year). At the end of 30 years the farm will be worth nothing. (Show calculations and provide a brief explanation) a) If the relevant annual interest rate over the next 30 years is 4% should Frank sell his farm? Why?
To calculate the monthly payments for the car loan, we can use the formula for the present value of an annuity. The loan amount is $30,000, the number of payments is 60, and the monthly interest rate is 0.5%. Plugging these values into the formula, we get:
Payment = Loan amount / Present value annuity factor
PV annuity factor = (1 - (1 + r)^(-n)) / r Where r is the monthly interest rate and n is the number of payments. Calculating the present value annuity factor: (1 - (1 + 0.005)^(-60)) / 0.005 = 49.3117 Monthly payment = $30,000 / 49.3117 ≈ $608.23 Therefore, the monthly payments for the car loan would be approximately $608.23. For Farmer Frank, if he keeps his farm, he would earn a net income of $20,000 at the end of each of the next 30 years. The future value of this income stream can be calculated using the formula for the future value of an ordinary annuity. The future value would be: Future Value = Payment * ((1 - (1 + r)^(-n)) / r) Where r is the annual interest rate and n is the number of periods. Future Value = $20,000 * ((1 - (1 + 0.04)^(-30)) / 0.04) ≈ $790,179.58 Comparing the future value of the income stream ($790,179.58) to the offer of $1,000,000 for selling the farm, it would be financially better for Frank to sell the farm. By selling the farm, he can receive a lump sum of $1,000,000 immediately, which is higher than the future value of the income stream. Therefore, Frank should sell his farm.
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find value of the following -100 + (-45) – ( -10) X (-4)
Eight students were asked to measure the correct length of a ruler in a laboratory. Here are their
observations in inches:
9.93, 9.96. 10.10, 10.02, 10.02, 9.90, 9.93, 9.92 Using this information, you would expect the likely size of the chance error to be about _inches or so. (round to three decimals)
The formula used to calculate the likely size of the chance error is SE = s/√n where SE is the standard error, s is the standard deviation, and n is the sample size. In this problem, there are eight students, so n = 8.
The standard deviation can be calculated using the formula σ = √(Σ(x - µ)² / n), where σ is the standard deviation, x is each data point, µ is the mean, and n is the sample size. Using the given data, the mean can be calculated as follows:
Mean = (9.93 + 9.96 + 10.10 + 10.02 + 10.02 + 9.90 + 9.93 + 9.92) / 8 = 9.985Next, calculate the sum of the squared deviations from the mean:Σ(x - µ)² = (9.93 - 9.985)² + (9.96 - 9.985)² + (10.10 - 9.985)² + (10.02 - 9.985)² + (10.02 - 9.985)² + (9.90 - 9.985)² + (9.93 - 9.985)² + (9.92 - 9.985)²Σ(x - µ)² = 0.0211.
Then, calculate the variance by dividing the sum of squared deviations by the sample size:
Variance = Σ(x - µ)² / n
Variance = 0.0211 / 8Variance = 0.00264Finally, calculate the standard deviation by taking the square root of the variance:
Standard deviation = √(Σ(x - µ)² / n)Standard deviation = √(0.00264)Standard deviation = 0.05134The standard error can now be calculated by dividing the standard deviation by the square root of the sample size:
Standard error = s/√nStandard error = 0.05134/√8Standard error = 0.01813
Given the measurements of eight students to determine the correct length of a ruler in a laboratory, we can calculate the size of the chance error using the formula SE = s/√n. This formula calculates the standard error, where s is the standard deviation and n is the sample size. To find the standard deviation, we use the formula σ = √(Σ(x - µ)² / n), where x is each data point, µ is the mean, and n is the sample size. Using the given measurements, the mean of the data is calculated to be 9.985. Using this mean, we can calculate the sum of the squared deviations from the mean, which is equal to 0.0211. Then, we can calculate the variance by dividing the sum of squared deviations by the sample size, which is equal to 0.00264. Finally, the standard deviation can be calculated by taking the square root of the variance, which is equal to 0.05134. By dividing the standard deviation by the square root of the sample size, we can find the standard error, which is equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.
Given the measurements of eight students, we used the formulas SE = s/√n and σ = √(Σ(x - µ)² / n) to calculate the size of the chance error. The mean of the data was found to be 9.985, and the sum of the squared deviations from the mean was equal to 0.0211. We used these values to calculate the variance, which was equal to 0.00264, and the standard deviation, which was equal to 0.05134. Finally, we found the standard error to be equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.
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Solve for m in the following equation:
x=7k(n + m)
Step-by-step explanation:
x=7k(n+m)
x/7k=n+m
x-n/7k=m
4. Find the value of x. Then find the measure of each labeled angle.
(3x - 10)
(x + 40)
The value of x is 25 and each angle measure is 65.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Angles are (3x - 10) and (x + 40)
Now, Equating both Angle
3x-10=x+40
3x-x=40+10
2x=50
x=25
Thus, the Angles are
3x-10 = 3(25)-10= 65
(x + 40)= 25+40=65
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The sum of three consecutive even integers is 72. What are the three numbers? List the numbers in order from least to greatest.
Answer:
22, 24, and 26
Step-by-step explanation:
hope this helps!
The taxi fare in a city is as follows: For the first kilometer, the
fare is Rs 9 and for the subsequent distance, it is Rs 6 per km.
Taking the distance covered as x km and total fare as Rs y, write
a linear equation for this information, and draw its graph.
Answer:
The linear equation is y = 6 x + 9
The graph is attached down
Step-by-step explanation:
The given information:
The cost of 1st km is 9 Rs
The cost of every kilometer after the first is 6 Rs
x represents the number of km
y represents the total cost of x km
The form of the linear equation is
y = m x + b, where
m is the slope of the line (rate of change)b is the y-intercept (initial value)From the given information above
m = 6 Rs/km
b = 9 Rs
Substitute them in the form of the equation
y = 6 x + 9
The graph:
Are the graphs of the lines x - 2y = 4 and y = 2x - 2 parallel, perpendicular, or neither? Explain your answer.
O A parallel; they both have slope 2.
O B. perpendicular, their slopes are opposite reciprocals.
O C. identical; they both have slope 2 and y-intercept -2.
O D. neither, their slopes are not the same and not opposite reciprocals.
Answer:
neither ; their slopes aren't the same and aren't reciprocals.
Step-by-step explanation:
neither ; their slopes aren't the same and aren't reciprocals.
I took the test, I got the question right.
O D. neither, their slopes are not the same and not opposite reciprocals.
Find the complementary angles of the following.
7. 12
A. 46
B. 78
C. 98
D. 31
E. 52
F. 64
Answer:
See below
Step-by-step explanation:
Complementary angles add up 90°
Complementary angles of following are:
A. 46 ° >> 90° - 46° = 44°B. 78 ° >> 90° - 78° = 12°C. 98 ° >> 180° - 98° = 82°D. 31 ° >> 90° - 31° = 59°E. 52 ° >> 90° - 52° = 38°F. 64° >> 90° - 64° = 26°How many pints are in 43 gallons
Answer:
344 liquid pints
Step-by-step explanation:
Answer:
5.375 Gallons
Step-by-step explanation:
43 Pints =
5.375 Gallons
plz mark as brainliest
What is the value of -4 + 91 + 72?
Answer:
159
Step-by-step explanation:
Answer:
159
Step-by-step explanation:
-4+91=87
87+72=159
A circle had a redius of 11 inches . What is the length of an arc subtended by a central angle of 5pi/12 radiant?
Round to the nearest tenth of an inch
Answer:
(5π/12)(11) = about 14.4 inches
The average distance of the Moon from Earth is about 384,400 kilometers. Write this number in scientific notation.
Answer:
[tex]3.844 * 10 ^ 5[/tex]
Step-by-step explanation:
Scientific notation is of the form [tex]N * 10^a[/tex]. Where N is a number [tex]1 \leq N < 10[/tex].
So in this case we need to move the decimal place to the left, in order to create such a number.
By moving the decimal place to the left we get: 3.84400
We moved the decimal to the left 5 times, so our value of [tex]a = 5[/tex] and [tex]N = 3.84400[/tex]
Therefore scientific notation is: [tex]3.844 * 10 ^ 5[/tex]
Solve For X. Giving Brainliest Explain!
Answer:
x = 6
Step-by-step explanation:
What we know:
* Values of angles 1 and 2, those being 54 and 83
* Sum of all angles of a triangle are = to 180
Process: Add 54 and 83
54 + 83 = 137
Subtract 137 from 180:
180 - 137 = 43
Solve for x:
7 x + 1 = 43
- 1 - 1
Subtract 1 from BOTH sides: 7x = 42
7x/7 = 42/7
Divide BOTH sides by 7 to isolate x variable: x = 6
Hope this helps and have a great rest of your day. Cheers!
The number of mosquitoes in brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by m(x)=-x(x-4)what is the maximum possible number of mosquitoes?
The maximum possible number of mosquitoes that can be found in Brooklyn is -4 million, which occurs when there is 2 centimeters of rainfall.
The given function of mosquitoes is m(x)=-x(x-4).
This is a quadratic function in which we can determine the maximum or minimum value using the formula for vertex.
The formula for the vertex of a quadratic function is as follows:
V = (-b/2a, f(-b/2a))
Where a, b, and c are the coefficients of the quadratic function f(x). Now, let's find the vertex of the given function.
Here a = -1, b = 4, and c = 0.
V = (-b/2a, f(-b/2a))
V = (-4/-2, f(2))
V = (2, -4)
Therefore, the vertex of the quadratic function m(x)=-x(x-4) is (2,-4).
The maximum possible number of mosquitoes that can be found in Brooklyn is -4 million, which occurs when there is 2 centimeters of rainfall. If there is no rainfall or if there is too much rainfall, there will be no mosquitoes. This makes sense because mosquitoes need a certain amount of water to breed, but too much water will wash away their breeding grounds.
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Answer:
4
Step-by-step explanation:
im smart
