In the figure below, which term best describes point L?
A. Circumcenter
B. Incenter
C. Orthocenter
D. Centroid
Answers
The term that best describes the point L is (d) the centroid
How to determine the point L?From the figure, we can see that:
The three lines drawn from point L divide the sides of the triangles into equal segments.
Also, the lines from point L are perpendicular to the sides.
The above description represents the definition of a centroid
Hence, the term that best describes the point L is (d) the centroid
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Related Questions
If you are extremely good at slopes, pls look at the screenshot below and help me!
Answers
Answer:
B.) y= 6x+10 y=6x+8 and no solution
Step-by-step explanation:
n − 10 + 9n − 3 4) −4x − 10x
Answers
Answer:
9n−14x−44
Step-by-step explanation:
Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________. 0.50 0.075 0.75 1.00
Answers
The probability of x taking on a value between 75 to 90 is 0.25.
Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.
The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.
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which expressions is equivalent to 4(2x+3y)
Answers
Answer: 8x+12y
Step-by-step explanation:
Assuming this is a problem in a unit on distributive property, and thus, due to the apparent lack of options, will solve it as such:
The distributive property dictates that a(b+c) = ab+ac.
Thus,
4(2x+3y)
8x+12y
Hope it helps :)
Answer:
8x+12y
Step-by-step explanation:
Multiply both numbers times the number is outside the parenthesis
. This is the Monty Hall Paradox problem, stated in the lecture note 1. a) There are three empty boxes. I will put $100 in a box and close them. Now you will select a box containing money. b) First, you will select one of boxes. c) Then, I will open one box that does not contain the bill (I already know which box has the money). d) Now, there are two closed boxes, and one of them will have the money. e) You will be asked to change your mind if you want. If you have a chance to switch your selection, do you want to switch? Or keep your first selection? What is your decision? Why?
Answers
I would switch my selection. The reason is that switching provides a higher probability of winning the money. This is known as the Monty Hall Paradox.
Initially, when we choose one box out of three, the probability of selecting the box with the money is 1/3. The remaining two boxes have a combined probability of 2/3 of containing the money.
When the host opens one of the empty boxes, it doesn't change the fact that the initial probability of our selected box having the money is still 1/3. However, the information revealed by the host's action increases the probability of the other unopened box containing the money to 2/3.
By switching our selection, we essentially transfer our initial 1/3 probability to the other unopened box, which now has a probability of 2/3 of containing the money. Thus, switching increases our chances of winning to 2/3, while sticking with our initial selection keeps the probability at 1/3.
Therefore, to maximize our chances of winning, it is advantageous to switch our selection.
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Complete question:
This is the Monty Hall Paradox problem, stated in the lecture note
1. a) There are three empty boxes. I will put $100 in a box and close them. Now you will select a box containing money.
b) First, you will select one of boxes.
c) Then, I will open one box that does not contain the bill (I already know which box has the money).
d) Now, there are two closed boxes, and one of them will have the money.
e) You will be asked to change your mind if you want.
If you have a chance to switch your selection, do you want to switch? Or keep your first selection? What is your decision? Why?
Matthew makes a series of payments at the beginning of each year for 20 years. The first payment is 100. Each subsequent payment through the tenth year increases by 5% from the previous payment. After the tenth payment, each payment decreases by 5% from the previous payment. Calculate the present value of these payments at the time the first payment is made using an annual effective rate of 7%.
Answers
The total present value of these payments at the time the first payment is made is 1,735.85 (747.26 + 988.59).
To calculate the present value of these payments, we need to use the formula for the present value of an annuity:
\(PV = (P/i) x [1 - (1+i)^-n]\)
Where:
P = payment amount
i = annual effective rate
n = number of payments
Using this formula, we can calculate the present value of the first 10 payments:
\(PV = (100/0.07) x [1 - (1+0.07)^-10] = 747.26\)
To calculate the present value of the remaining 10 payments, we need to first calculate the payment amounts. To do
this, we can use the following formula:
\(Pn = P1 x (1 + g)^n\)
Where:
Pn = payment in year n
P1 = first payment amount
g = growth rate
n = number of years since first payment
For the 11th payment:
\(P11 = 105 x (1 + 0.05)^1 = 110.25\)
For the 12th payment:
\(P12 = 110.25 x (1 + 0.05)^1 = 115.76\)
And so on, until the 20th payment:
\(P20 = 163.32 x (1 - 0.05)^8 = 79.24\)
Now we can calculate the present value of these payments:
PV = \((110.25/0.07) x [1 - (1+0.07)^-10] + (115.76/0.07) x [1 - (1+0.07)^-9] + ... + (79.24/0.07) x [1 - (1+0.07)^-1]\)
PV = 988.59
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Points D and E are aligned with a ruler. Point D is at the mark of 4.5 cm, and the distance between points D and E is 3.4 cm. At which, two marks on the ruler could point E be located?
Answers
Answer:
E could be located at 7.9cm.
Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them?
Answers
Answer:
Jim + June + Alex = 82 (x+9) x + (x-8) = 82 3x +1 = 82 3x = 82 - 1 = 81 x = 81/3 = 27. ANSWER. June is 27 years old; Jim is 27+9 = 36 years old; Alex is 27-8 = 19 years old.
Zellie is taking the stairs in her building from her floor to the top of the building. After 2 minutes, she was 100 steps from the bottom floor. After 5 minutes she was 196 steps from the bottom floor.
Answers
Answer:
The question seems to be incomplete, so i will think that this is a linear equation, where we can find the velocity at which she moves, and also her initial position.
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case we have two points:
"After 2 minutes, she was 100 steps from the bottom floor."
this can be represented with the point: (2min, 100 steps)
" After 5 minutes she was 196 steps from the bottom floor"
This can be represented with the point (5min, 196 steps)
With this, we can find the slope of this equation:
a = (196 steps - 100 steps)/(5min - 2min) = 96steps/3min = 32 steps/min
This means that she does 32 steps in one minute.
Then we can write her positon equation as:
y = (32steps/min)*x + b
where x represents the time, and b is her initial position.
If we replace x by 2 min, and y for 100 steps, we get:
100steps = (32steps/min)*2min + b
100 steps = 64 steps + b
100 steps - 64 steps = b = 36 steps.
This means that she started to take the stairs 36 steps from the bottom floor.
A study of parents of kindergarteners included 349 parents who were chosen at
random. Of these parents, 47% said they sent their children to pre-kindergarten. School
records show that only 31% of parents of kindergarteners sent their children to pre-
kindergarten. Identify the statistic and the parameter.
Three hundred forty-nine is the parameter and 47% is the statistic.
Three hundred forty-nine is the statistic and 47% is the parameter.
Three hundred forty-nine is the parameter and 31% is the statistic
Forty-seven percent is the parameter and 31% is the statistic
Forty-seven percent is the statistic and 31% is the parameter
Answers
Answer:
Forty-seven percent is the statistic and 31% is the parameter
Step-by-step explanation:
Various terms are used in mathematics when it comes to carrying out particular studies in statistics.
A) Parameter
A parameter when is comes to statistical studies can be defined as the term that tells us more about a group or population of people.
B) Statistic
Statistic is a measure that tells us about is a characteristic of a sample or part of a given population.
In the above question, we are told that: a study of parents of kindergarteners included 349 parents who were chosen at random. Of these parents, 47% said they sent their children to pre-kindergarten. School records show that only 31% of parents of kindergarteners sent their children to pre- kindergarten.
According to the definition of Parameter and Statistic that I explained above,
A) The Parameter is 31% . This is
because it tell us about percentage ( a sample) of parents whose children are in kindergarten that sent their children to prekindergarten first.
B) The Statistic is 47% . This is because, it tell us about the percentage of parents that sent their children to prekindergarten.
ASAP PLS HELP ME WILL MARK U AS BRAINLIST
Answers
The measure of angle ABC is 132°.
The total measure of ABC and BCD is 180° because it is a straight angle.
If BCD is 48°, they ABC is 132°. You get this because you subtract 180° by 48°.
It is a fact that every integer n ≥ 1 can be written in the
form
cr·^3r+ cr−1 ·3^r−1 +· · ·+c2 ·3^2 + c1 ·3 + c0,
where cr= 1 or 2 and ci= 0, 1, or 2 for all integers i =
0, 1, 2, . . . , r − 1. Sketch a proof of this fact.
Answers
Every integer n ≥ 1 can be written in the form
\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0\), where
cr = 1 or 2 and
ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1.
To prove that every integer n ≥ 1 can be written in the form:
\(n = cr · 3^r + cr-1 · 3^(r-1) + ... + c2 · 3^2 + c1 · 3 + c0,\)
where cr = 1 or 2 and ci = 0, 1, or 2 for all integers i = 0, 1, 2, ..., r - 1, we can use a constructive proof.
Start with the base case: For n = 1, we have n = 1 = 1 · 3^0, which satisfies the given form.
Assume the statement holds for all positive integers up to k.
Consider the integer k + 1.
Divide k + 1 by 3: If k + 1 is divisible by 3, then set cr = 1 and use the remaining quotient (k + 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.
If k + 1 is not divisible by 3, set cr = 2 and use the remaining quotient (k + 1 - 1) / 3 as the next value for k in the assumption. Repeat this process until the quotient becomes 1.
At each step, we update the values of cr, and the resulting expression follows the given form.
By repeatedly applying this process, we eventually reach 1, and the final expression satisfies the specified form.
Therefore, by induction, every integer n ≥ 1 can be written in the specified form.
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A farm has 8 cows, 28 chickens, 4 pigs, and 12 goats. which ratio is the
greatest?
a. number of pigs to number of chickens
b. number of goats to number of chickens
c. number of cows to number of goats
od. number of pigs to number of cows
Answers
Answer:
C
Step-by-step explanation:
ratio of pigs to chickens = 4/28, which simplifies to 1/12
ratio of goats to chickens = 12/28, which simplifies to 3/7
ratio of cows to goats = 8/12, which simplifies to 2/3
ratio of pigs to cows = 4/8, which simplifies to 1/2
since 2/3 is the largest, the answer is C
Which of the following subsets of R^3×3 are subspaces of R^3×3
A. The invertible 3 × 3 matrices B. The 3 × 3 matrices with all zeros in the third row C. The 3 × 3 matrices in reduced row-echelon form D. The diagonal 3 × 3 matrices E. The 3 × 3 matrices with trace (the trace of a matrix is the sum of its diagonal entries)
F. The 3 x 3 matrices of
Answers
The subspaces of R^3x3 are: B. The invertible 3x3 matrices, C. The 3x3 matrices with all zeros in the third row, D. The diagonal 3x3 matrices, and F. The 3x3 matrices of rank 1.
A subspace of R^3x3 is a subset that satisfies three conditions: it contains the zero matrix, it is closed under matrix addition, and it is closed under scalar multiplication.
B. The invertible 3x3 matrices form a subspace because the zero matrix is invertible and any linear combination or product of invertible matrices is also invertible.
C. The 3x3 matrices with all zeros in the third row form a subspace. Adding two matrices with all zeros in the third row results in a matrix with all zeros in the third row, and multiplying a matrix with all zeros in the third row by a scalar also yields a matrix with all zeros in the third row.
D. The diagonal 3x3 matrices form a subspace because the sum of two diagonal matrices is still a diagonal matrix, and scaling a diagonal matrix by a scalar preserves its diagonal structure.
E. The 3x3 matrices with a specific trace value do not form a subspace because the sum of two matrices with different trace values will generally not have the same trace.
F. The 3x3 matrices of rank 1 do form a subspace. The zero matrix is of rank 0, and any linear combination of rank 1 matrices will also have rank 1. Furthermore, scaling a rank 1 matrix by a scalar preserves its rank.
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PLEASE HELP
G(Ax)) may not be equal to HG(x)).
O A. True
O B. False
Answers
Answer:
A. True
・ᗜ・ ¯\_(ツ)_/¯
a line passes through both points (-2, 2) and (8, 9). what is the angle between the line and the x axis?
Answers
Step-by-step explanation:
To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:
m = (9 - 2) / (8 - (-2))
= 7 / 10
= 0.7
The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:
tan(θ) = 0.7
Taking the inverse tangent of both sides, we find:
θ = arctan(0.7)
Using a calculator, we can evaluate this to be approximately:
θ ≈ 35.87 degrees
Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.
-4 Choose a Taylor series and a center point a to approximate the following quantity with an error of 10 3√77 What Taylor series should be used to approximate the given quantity? O A. √x centered
Answers
To approximate the quantity 10√77 with an error of 10, a Taylor series centered at a specific point needs to be used.
Let's consider the function f(x) = √x and aim to approximate f(77) = √77. To do this, we can use a Taylor series expansion centered at a specific point. The general form of the Taylor series expansion for a function f(x) centered at a is:
f(x) ≈ f(a) + f'(a)(x - a) + (f''(a)(x - a)^2)/2! + (f'''(a)(x - a)^3)/3! + ...
To approximate f(77) with an error of 10, we need to find a suitable center point a and determine how many terms of the Taylor series are required to achieve the desired accuracy.
We can choose a = 100 as our center point, which is close to 77. The Taylor series expansion of √x centered at a = 100 can be written as:
√x ≈ √100 + (1/(2√100))(x - 100) - (1/(4√100^3))(x - 100)^2 + (3/(8√100^5))(x - 100)^3 - ...
Simplifying this expression, we can calculate the approximation of f(77) by plugging in x = 77 and retaining the desired number of terms to achieve an error of 10.
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the _____ of a trapezoid is a segment whose endpoints are the midpoints of its legs.
Answers
Answer:
The segment that connects the midpoints of the legs of a trapezoid is called the median of the trapezoid.
Step-by-step explanation:
Students are playing a game similar to blackjack (with a standard 52 card deck)- trying to get as close to 21 points without going over. The ace is only worth 1 point and each face card is worth 10 points, the remaining cards have face value. Player A draws a eight and a nine. Player B draws a four and a jack. If Player A next draws a two, what is the probability of Player B winning the round?
Answers
Use the following building blocks in the right column to assemble a direct proof that the product of two odd numbers is odd Not all blocks belong in the proof. Suppose that the product of two odd numbers is odd. Distributing we get nm-2(2kk)+1 Suppose that nm is odod. By multiplying these equations, we obtain nm = (2k + 1)(29 + 1). By definition of an odd integer, that means that nm is odd. Suppose that n and m are odd numbers. Then n = 2k + 1 for some integer k and m = 2q + 1 for some integer q. Then n 2k + 1 and m-2k + 1 for some integer k.
Answers
Using the following building blocks in the right column to assemble a direct proof that the product of two odd numbers is odd, we have:
Suppose that n \(\alpha\) m is oddThen n = 2k + 1, for some integers k, m = 2q + 1, for some integers qBy multiplying these equations, we obtain mn = (2k +1)(2q + 1)Distributing, we get: nm = 2(2kq + k + q) + 1By definition of odd integers, nm is oddWhat is a Mathematical Proof?A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.
The direct proof has been assembled above,
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Which of the four levels of measurement is most appropriate?
Answers
In the four levels of measurement : nominal, interval, ordinal, ratio: "ordinal," is most appropriate for the given for positions of the persons standing in a line
Explain the term levels of measurement?You may find out how accurately variables are recorded using levels of measurement, sometimes known as scales of measurement. A variable in scientific study is something that can have various values throughout your data collection (like height or test scores).Four degrees of measuring exist:
Nominal: The information is only classifiable.Ordinal: The information is classifiable and rankableIntervals: Data can be classified, rated, and spaced evenly between intervals.Ratio: The data is equally distributed, categorized, ranked, and contains a natural zero.Thus, in the four levels of measurement : nominal, interval, ordinal, ratio: "ordinal," is most appropriate.
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The complete question is-
determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for positions of persons in a line (extra?)
Tina, a single woman, earned wages of $70549, received $1287 in interest from a savings account, and contributed $2753 to a tax-deferred saving plan. She contributed $1505 to charity. Find Tina's federal tax. (More info in the attachment)
Answers
Answer:
\(\$14,733.25\)
Step-by-step explanation:
Taxable income refers to the income subject to taxes from government, including but not limited to federal tax.
Since taxable income is equal to $58,933, tax will be based off of this value. Because Tina is single and her income falls within the 25% range, her federal tax is equal to:
\(\$58,933\cdot 0.25=\boxed{\$14,733.25}\)
You deposit $1000 in an account that pays 6% interest compounded semiannually. After 3 years, the interest rate is increased to 6.48% compounded quarterly. What will be the value of the account after a total of 6 years?
Answers
Answer:
FV= $1,448.01
Step-by-step explanation:
To calculate the future value of the investment, we need to use the following formula using both interest rates:
FV= PV*(1+i)^n
Interest 6% compounded semmiannually:
i= 0,06/2= 0.03
n= 2*3= 6 semesters
FV= 1,000*(1.03^6)
FV= $1,194.05
Interest 6.48% compounded quarterly:
i= 0.0648/5= 0.0162
n= 3*4= 12 quarters
FV= 1,194.05*(1.0162^12)
FV= $1,448.01
Reggie plans to have a garden with 36 plants. He wants the ratio of tomato plants to cucumber plants to be 4:5. How many cucumber plants will be in Reggie's garden?
Answers
Answer:
20
Step-by-step explanation:
Total no of plants in a garden = 36
The ratio of tomato plants to cucumber plants to be 4:5.
Let tomato plants are 4x and cucumber plants is 5x.
ATQ,
4x+5x=36
9x = 36
x = 4
For cucumber plant, 5x = 5(4) = 20
So, there are 20 cucumber plants will be in Reggie's garden
Aaron had $22 to spend on 4 beakers for his science class. After buying them, Aaron had $2 left. How much did each of the beakers cost?
Answers
Answer:4
Step-by-step explanation:22-4=18-4=14-4=10-4=6=2
Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?
A. 2w^2 + 5w, where w is the width
B. 2w^2 + 5, where w is the width
C. 2w^2, where w is the width
D. 10w^2 + 5 w, where w is the width
Answers
The expression 5w + 2w² represents the area, in square feet, for each cabin size
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.
Area of a rectangle = length * width = l*w
length is equal to 5 feet more than twice the width.
=> l= 5+2w
So, area = ( 5+2w ) *w
= 5w + 2w²
Thus, the expression 5w + 2w² represents the area, in square feet, for each cabin size
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Rocky thinks of an odd integer and adds the next two consecutive integer to it
Answers
Answer:
3 is an odd integer
next two consecutive integers are 4 and 5
then 3+4+5=12
like this u can take other integers
5+6+7=18
9+10+11=30..........
Step-by-step explanation:
hope this helps
Compare √180 and 105/8 using<, >, or =.
Answers
Answer:
√180 > 105 / 8
Step-by-step explanation:
105 / 8 = 13.125
√169 = 13
√196 = 14
we now know that √180 is about 13 to 14
using a calculator the value of √180 is about 13.4
so √180 must be greater than 105/8
the boxplot shows the fuel economy ratings for 67 subcompact cars with the same model year. some summary statistics are also provided. the extreme outlier is an electric car whose electricity usage is equivalent to 112 miles per gallon. if that electric car is removed from the data set, how will the standard deviation be affected? the iqr?
Answers
Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.
The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.
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A circle with radius of 2 cm sits inside a 11 cm x12 cm rectangle What is the area of the shaded region?
Answers
Answer:
119.4 cm^2
Step-by-step explanation:
Area of a circle is \(\pi\) x radius^2, and the area of a rectangle is length * width. 11 cm x 12 cm = 132 cm^2 (rectangle's area). The circle's area would be \(\pi\) x 2^2 which would equal 12.56637061 cm^2 (left unrounded until the end). Then subtract 12.56637061 from 132 cm^2 and that would equal 119.4 cm^2 rounded to the tenth.