The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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The y-intercept of the graph of y=-7x+140y is located at (0, c) What is the value of c ?
The y-intercept of the graph is located at (0, 0). So, the value of c is 0.
What is graph?
A graph is a visual representation of data that displays the relationship between two or more variables. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. The vertices represent the variables, while the edges represent the relationship between them.
To find the y-intercept of the graph of y = -7x + 140y, we need to substitute x = 0 into the equation and solve for y. This will give us the y-coordinate of the point where the graph intersects the y-axis.
Substituting x = 0, we get:
y = -7(0) + 140y
y = 140y
Simplifying the equation, we get:
139y = 0
Dividing both sides by 139, we get:
y = 0
Therefore, the y-intercept of the graph is located at (0, 0). So, the value of c is 0.
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What is the slope of 8,2 & 8,4
Answer:
infinity
Step-by-step explanation:
No fr it is that i even double checked by looking it up
two vectors are linearly dependent if and only if they are collinear.
true
false
Find the value of x and EF. A and B are midpoints.
Answer:
x = 5.5
EF = 14
Step-by-step explanation:
We can use ratios to solve
AG 7
----------- = -----------------
EG 2x+3
We know that EG is 2 times AG since A is the midpoint
AG 7
----------- = -----------------
2 AG 2x+3
Canceling like terms
1 7
----------- = -----------------
2 2x+3
Using cross products
1 (2x+3) = 2*7
2x+3 = 14
Subtract 3 from each side
2x+3-3 = 14-3
2x =11
Divide by 2
x = 11/2
x = 5.5
EF = 2x+3 = 2*5.5+3 = 14
Use the binomial series to find the Maclaurin series for the function.
f(x) = 1/((1+x)^4)
The Maclaurin series for the function f(x) = 1/((1+x)^4) using the binomial series is: f(x) = ∑(n=0 to infinity) (-1)^n * (n+3) * x^n / 4!
To find the Maclaurin series for the function f(x), we can use the binomial series, which states that:
(1+x)^r = ∑(n=0 to infinity) (r choose n) * x^n (where (r choose n) = r! / (n! * (r-n)!).)
In this case, we have:
f(x) = 1/((1+x)^4)
We can rewrite this as:
f(x) = (1+x)^(-4)
Using the binomial series, we get:
(1+x)^(-4) = ∑(n=0 to infinity) (-1)^n * (-4 choose n) * x^n
Simplifying the expression for (-4 choose n), we get:
(-4 choose n) = (-4)! / (n! * (-4-n)!) = (-1)^n * (n+3)! / (4!)
Substituting this back into the binomial series, we get:
(1+x)^(-4) = ∑(n=0 to infinity) (-1)^n * (n+3)! / (4! * n!) * x^n
Simplifying the expression for (n+3)! / (4! * n!), we get:
(n+3)! / (4! * n!) = (n+3)(n+2)(n+1)/24
Substituting this back into the expression for f(x), we get:
f(x) = ∑(n=0 to infinity) (-1)^n * (n+3)(n+2)(n+1)/24 * x^n
Simplifying the expression for (n+3)(n+2)(n+1)/24, we get:
(n+3)(n+2)(n+1)/24 = (1/4!) * (n^3 + 6n^2 + 11n + 6)
Substituting this back into the expression for f(x), we get:
f(x) = ∑(n=0 to infinity) (-1)^n * (n^3 + 6n^2 + 11n + 6) / 4! * x^n
Simplifying the expression for (-1)^n * (n^3 + 6n^2 + 11n + 6), we get:
(-1)^n * (n^3 + 6n^2 + 11n + 6) = (-1)^n * (n+1)(n+2)(n+3)
Substituting this back into the expression for f(x), we get:
f(x) = ∑(n=0 to infinity) (-1)^n * (n+1)(n+2)(n+3) / 4! * x^n
This is the Maclaurin series for the function f(x).
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A researcher wants to determine if the number of calories burned during an hour is the same for running and walking. What type of data would be measured?
Group of answer choices
scale
nominal
independent t test
ANOVA
The researcher wants to determine if the number of calories burned during an hour is the same for running and walking. To conduct this investigation, the researcher would measure continuous scale data.
Continuous scale data is quantitative data that can take any numerical value within a certain range.
In this case, the researcher would measure the number of calories burned, which is a continuous variable that can have various values within a specific range (e.g., 0, 100, 200, etc.).
By measuring the calories burned for both running and walking, the researcher can compare and analyze the numerical data to determine if there is a significant difference between the two activities.
It is important to note that the type of statistical analysis required to evaluate the data would depend on the specific research design and the number of groups involved.
If the researcher is comparing only two groups (running and walking), an independent t-test may be appropriate.
On the other hand, if there are more than two groups or additional factors being considered, an analysis of variance (ANOVA) might be more suitable.
The choice of statistical analysis method would depend on the specific research question and study design.
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How do you find the domain and range of a sequence?
A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers.
The domain basically can be defined a set of all possible inputs for the function.
The range is basically the difference between the highest and the lowest numbers of a sequence.
To find the range, first put all the numbers in order. Then subtract the lowest number from the highest. The difference gives you the range of the list.
The domain of a sequence consists of the natural (counting) numbers 1, 2, 3, 4, ...Whereas the range of a sequence consists of the terms of the sequence.
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Two curves are orthogonal if their tangent lines are perpendicular at each point of intersection. Are the given families of curves orthogonal trajectories of each other? That is, is every curve in one family orthogonal to every curve in the other family? x^2 + y^2 = ax
x^2 + y^2 = by
Yes, the given curves are orthogonal.
What is orthogonal trajectory?In mathematics, an orthogonal trajectory is a curve, which intersects any curve of a given pencil of (planar) curves orthogonally.
Given equation is,
x²+y²=ax
Differentiating,
2x+2yy'=a
y' = (a-2x)/2y = m1
Again,
x²+y²=by
Differentiating,
2x+2yy'=by'
y' = -2x/(2y-b) = m2
For both curves are orthogonal, we have
m1*m2 = -1
(a-2x)/2y*-2x/(2y-b) = -1
-2ax+4x² = -4y²+2yb
4(x²+y²) = 2ax+2yb
Since, ax = (x²+y²)
by = (x²+y²)
Then,
4(x²+y²) = 2(x²+y²) +2(x²+y²)
4(x²+y²) = 4(x²+y²) (true)
Hence, the above response is appropriate.
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Using the same facts as #16, how long would it take to pay off 60% of the a. About 45 months b. About 50 months c. About 55 months d. About 37 months
To calculate how long it would take to pay off 60% of the debt,
we can use the same facts as in problem #16. Let's go through the steps:
1. Determine the total amount of debt: Find the original debt amount given in problem #16.
2. Calculate 60% of the debt: Multiply the total debt by 0.6 to find the amount that represents 60% of the debt.
3. Divide the amount obtained in step 2 by the monthly payment: This will give us the number of months it will take to pay off 60% of the debt.
Now, let's apply these steps to the options provided:
a. About 45 months: To determine if this is the correct answer, we need to perform the calculations outlined above using the original debt amount and the monthly payment given in problem #16.
b. About 50 months: Same as option a, perform the calculations using the original debt amount and the monthly payment.
c. About 55 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
d. About 37 months: Perform the calculations outlined above using the original debt amount and the monthly payment.
After performing the calculations for each option, compare the results with the options provided to find the correct answer.
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Answer with explaination every steps
Answer:
y = - 35
Step-by-step explanation:
Expressing as a fraction , that is
\(\frac{y}{-7}\) = 5 ( multiply both sides by - 7 to clear the fraction )
y = - 35
Which two lengths for a ratio of 1:2
Answer:
D. AI. EF
HERE AI is radius of circle while EF is diameter of the circle hence the ratio would be 1:2
indicate the answer choice that best completes the statement or answers the question. 1. how many different samples of size 3 (without replacement) can be taken from a finite population of size 10? a. 30 b. 1,000 c. 720 d. 120
The correct option is option (d).
Using Combination,
Total 120, different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Population size: The population is the entire group of guesses. A sample is a specific group for which you collect data. It is denoted by N.
Sample Size: The sample size is always smaller than the total size of the population. A sample is a subset of the population set. It is denoted by n.
we have given that , n = 3 and N = 10
Using the following formula for calculating the possible number of different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Number of possible different samples of size n from Population size N = NCn = N!/n! (N-n)!
then we have, 10C3 = 10!/3! × 7!
=> 10×9×8/3×2 = 15×8 = 120
Hence, 120 different samples of size 3 (without replacement) is possible from Population of size 10.
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A company sells two different safes. The safes have different dimensions, but the same volume. What is the height of Safe B?
Safe A is a rectangular prism with a length of 18 inches, a width of 15 inches, and a height of 24 inches. Safe B is a rectangular prism with a length of 18 inches, a width of 18 inches, and a height of h inches
Answer:
125/6
Step-by-step explanation:
So if these two have the same volume it is just the sense of plugging number in. Let’s first find the whole volume of cube a
Cube A : L x W x H
18 x 15 x 25
270 x 25
6750 inches cubed
now let’s find what we know of cube b
Cube B: L x W x H
18 x 18 x h
324 x h
Now we know that in order for the volumes to be the same, we have to find a number that when multiplied by 324 would give us 6750. We can do this by dividing the two numbers
6750 / 324
125/6
when we multiply
18 x 18 x (125 / 6)
We get a volume of 6750
lmk if this helps
The height of safe B is 20 inches.
How do you determine the volume of a rectangular prism?The volume of a rectangular prism is the product of all its dimensions.
∴ The volume of a rectangular prism = height*width*length
How do we solve the given question?We are given dimensions of two safes A and B, in the shape rectangular prism.
Denoting safe A with subscript 1, and the safe B with subscript, we get:
l₁ = 18 inches, w₁ = 15 inches, h₁ = 24 inches.
l₂ = 18 inches, w₂ = 18 inches, h₂ = h inches.
We are told that the volumes of the safe A and B are equal, so
The volume of safe A = The volume of safe B
or, 18*15*24 = 18*18*h
or, h = (18*15*24)/(18*18) = 20
∴ The height of safe B is 20 inches.
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In a class of 147 students, 95 are taking math (M), 73 are taking science (S), and 52 are taking both math and science. What is the theoretical probability of randomly choosing a student who is taking math? Round your answer to the nearest tenth.
Answer:
The correct answer is 64.6%
Step-by-step explanation:
95 student total are taking a math class out of 147 kids. 95/147 = 0.646, carry the decible and you get your percentage which is 64.6%
Which answer choice shows two hundred two and two thousandths?
OA) 200.02
B) 200.202
OC) 202.02
OD) 202.002
Answer: D
Step-by-step explanation:
Two hundred two =202
The thousands place is the third place=.002
Answer:
D
Step-by-step explanation:
pls help
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
the answer is 12 yd if you are talking about the question mark.
Step-by-step explanation:
Well, if you split this figure into two rectangles, then the 16 yd length becomes 12 yd because the one congruent to it is 4 yd. Both sides are congruent so you'd get 12 yd.
Answer:
BRAINLIEST
Step-by-step explanation:
A marrathon is 26.6 miles long. There is a water station every 1 31/100 miles along the race route which expression represents the total number of water stations
Answer:
We are told that a marathon is 26.2 miles long. There is a water station every 1 and 3/100 miles along the race route. We are supposed to write an expression that represents the total number of water stations.
Let x be the total number of water stations.
First of all, we will convert our mixed fraction into an improper fraction.
1 3/100 = 103/100
The total number of water station in the marathon of 26.2 miles will be,
103/100 * x = 26.2
x = 26.2 * 100/103
Therefore, x = 26.2 * 100/103 will represent the total number of water stations.
Have a nice day and stay safe.
: )
Find the perimeter of the triangle.
Answer:
P
=
a
+
b
+
c
Step-by-step explanation:
What is the slope of the line RS that contains the points R(-2, -3), S(3, -5)
HELP ASAP
Answer:
\(slope = \dfrac{-2}{5}\)
Step-by-step explanation:
The slope of a line passing through points , \( (x_1,y_1) \) and \( (x_2,y_2) \) is ,
\(\implies slope = \dfrac{y_2-y_1}{x_2-x_1}\)
Using this we have ,\(\implies slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\\implies slope = \dfrac{-5+3}{3+2}\\\\\implies \boxed{\boxed{slope = \dfrac{-2}{5}}}\)
which is the better buy chord charts A 13:10 B 18:15
Step-by-step explanation:
is there more to the question?
how much 550 ml to cups
550 ml was found to be equivalent to approximately 2.324 cups using conversion factor method.
To convert 550 ml (milliliters) to cups, you can use the following conversion factor:
1 cup = 236.588 ml
Dividing 550 ml by 236.588 ml/cup, we get:
550 ml / 236.588 ml/cup = 2.324 cups (rounded to three decimal places)
Therefore, 550 ml is equivalent to approximately 2.324 cups
A conversion factor is a mathematical ratio used to convert a quantity from one unit of measurement to another. The conversion factor is usually derived from the relationship between the two units of measurement.
For example, if you want to convert a length measurement from feet to meters, you can use the conversion factor 1 ft = 0.3048 m.
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12x5 what is the answer
Answer:
60
Step-by-step explanation:
Answer:
Step-by-step explanation:
it's 60 5+5+5+5+5+5+5+5+5+5+5+5
Can you please answer these questions?
1. Enzo is distributing the snacks at snack-time at a day-care. There are 11 kids attending today. Enzo has 63 carrot sticks, which the kids love. (They call them orange hard candy!)
Wanting to make sure every kid gets at least 5 carrot sticks, how many ways could Enzo hand them out?
2. How many 3-digit numbers must you have to be sure there are 2 summing to exactly 1002?
3. Find the co-efficient of x^6 in (x−2)^9?
The coefficient of x^6 is given by the term C(9, 6) * x^3 * (-2)^6.
Therefore, the coefficient of x^6 in (x - 2)^9 is 84.
To distribute the carrot sticks in a way that ensures every kid gets at least 5 carrot sticks, we can use the stars and bars combinatorial technique. Let's represent the carrot sticks as stars (*) and use bars (|) to separate the groups for each kid.
We have 63 carrot sticks to distribute among 11 kids, ensuring each kid gets at least 5. We can imagine that each kid is assigned 5 carrot sticks initially, which leaves us with 63 - (11 * 5) = 8 carrot sticks remaining.
Now, we need to distribute these remaining 8 carrot sticks among the 11 kids. Using stars and bars, we have 8 stars and 10 bars (representing the divisions between the kids). We can arrange these stars and bars in (8+10) choose 10 = 18 choose 10 ways.
Therefore, there are 18 choose 10 = 43758 ways for Enzo to hand out the carrot sticks while ensuring each kid gets at least 5.
To find the number of 3-digit numbers needed to ensure that there are 2 numbers summing to exactly 1002, we can approach this problem using the Pigeonhole Principle.
The largest 3-digit number is 999, and the smallest 3-digit number is 100. To achieve a sum of 1002, we need the smallest number to be 999 (since it's the largest) and the other number to be 3.
Now, we can start with the smallest number (100) and add 3 to it repeatedly until we reach 999. Each time we add 3, the sum increases by 3. The total number of times we need to add 3 can be calculated as:
(Number of times to add 3) * (3) = 999 - 100
Simplifying this equation:
(Number of times to add 3) = (999 - 100) / 3
= 299
Therefore, we need to have at least 299 three-digit numbers to ensure there are 2 numbers summing to exactly 1002.
To find the coefficient of x^6 in the expansion of (x - 2)^9, we can use the Binomial Theorem. According to the theorem, the coefficient of x^k in the expansion of (a + b)^n is given by the binomial coefficient C(n, k), where
C(n, k) = n! / (k! * (n - k)!).
In this case, we have (x - 2)^9. Expanding this using the Binomial Theorem, we get:
(x - 2)^9 = C(9, 0) * x^9 * (-2)^0 + C(9, 1) * x^8 * (-2)^1 + C(9, 2) * x^7 * (-2)^2 + ... + C(9, 6) * x^3 * (-2)^6 + ...
The coefficient of x^6 is given by the term C(9, 6) * x^3 * (-2)^6. Calculating this term:
C(9, 6) = 9! / (6! * (9 - 6)!)
= 84
Therefore, the coefficient of x^6 in (x - 2)^9 is 84.
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find x: 3x-14+6-4-2x=12
Answer:
x=24
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
G.SRT.B.5 Worksheet #2
What do the coordinates of an undefined slope have in common?
The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.
Elion has three more quarters than dimes in his pocket, for a total of 2.50 write an equation that could be used to determine the number of dimes, d, in his pocket
pls show work
The equation that could be used to determine the number of dimes, d, in his pocket is: 0.35d + 0.75 =2.50.
How to find the equation?Let the number of dimes be d
Let number of quarters be q
Hence,
d + q = 2.50
q = d+3
1 dimes = $0.10
1 quarters = $0.25
0.10d +0.25q = 2.50
Substitute value of q into 0.10d +0.25q = 2.50
0.10d +0.25 (d+3) = 2.50
0.10d +0.25d +0.75 = 2.50
0.35d + 0.75 =2.50
Hence, the equation is : 0.35d + 0.75 =2.50.
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what would be examined by determining how many students met the cutoff score and how many did not meet the cutoff score for a test on day 1 and again on day 2?
The appropriate test statistic for comparing the number of students who met or did not meet a cutoff score on two different days would be the McNamar's test.
McNamar's test is a statistical test used to compare paired proportions or counts of dichotomous data.
In this case, the paired proportions would be the number of students who met or did not meet the cutoff score on day 1 and day 2.
The test statistic for McNamar's test is the chi-square statistic, calculated using the following formula,
X² = ((b-c)²) / (b + c)
where b is the number of students who met the cutoff score on day 1 but not day 2,
And c is the number of students who did not meet the cutoff score on day 1 but did meet the cutoff score on day 2.
The chi-square statistic follows a chi-square distribution with 1 degree of freedom.
A p-value can be calculated based on this distribution to determine if there is a statistically significant difference between the paired proportions.
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The above question is incomplete, the complete question is:
What test statistic would be examined by determining how many students met the cutoff score and how many did not meet the cutoff score for a test on day 1 and again on day 2?
A rectangular prism has a length of 16in, a height of 15in, and a width of 6in. What is its volume, in cubic in?
Answer:
9in
Step-by-step explanation:
a p e x
Answer:
Step-by-step explanation:
my electric bills for june, july, and august last summer were $75, $75, and $150, respectively. what was the mean amount for the three bills?
The mean amount for the three bills is $100 .
In the question ,
it is given that
the electricity bill for June is = $75
the electricity bill for July is = $75
the electricity bill for August is = $150
Sum of the electricity for three months = 75 + 75 + 150 = 300
number of months = 3
The mean of the three months can be calculated using the formula ,
mean = (sum of bill for three months )/( number of months)
Substituting , the values
we get
mean = 300/3
= 100
Therefore , the mean amount is $100 .
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