Answers
[tex]\textit{Pythagorean Identities} \\\\ \sin^2(\theta)+\cos^2(\theta)=1\implies \sin^2(\theta)=1-\cos^2(\theta)\\\\\\ 1+\cot^2(\theta)=\csc^2(\theta) \\\\[-0.35em] ~\dotfill\\\\ \boxed{1+cot^2(x)}-cos^2(x)-cos^2(x)cot^2(x) \\\\\\ \boxed{csc^2(x)}-cos^2(x)-cos^2(x)cot^2(x)\implies csc^2(x)-cos^2(x)[1+cot^2(x)] \\\\\\ csc^2(x)-cos^2(x)[csc^2(x)]\implies csc^2(x)[1-cos^2(x)]\implies csc^2(x)sin^2(x) \\\\\\ \cfrac{1}{sin^2(x)}\cdot sin^2(x)\implies \text{\LARGE 1}[/tex]
Related Questions
A rider must be 80 inches tall to ride the Flaming Fun roller coaster. If Sancho was 5 inches shorter, he would be
able to say that 2.5 times his height is the minimum height to ride the Flaming Fun roller coaster.
How tall is Sancho?
Ps. Do that equation and solve it show the work
Answers
Answer:
37 Inches
Step-by-step explanation:
80 / 2.5 = 32
32 + 5 = 37
Which inequality shows a correct comparison?
A. -115 < -27
B. -78 > 47
C. -85 > -65
D. 126 < -218
Answers
The inequality which shows a correct comparison among the given answer choices as required is; Choice A; -115 < -27.
Which answer choice represents a correct comparison?As evident in the task content; the answer choice (inequality) which represents a correct comparison is to be determined.
Recall, on the number line, given a number, x; any number to the left of x on the number line is said to be less than x.
On this note, since -115 is to the left of -27, the correct comparison is; Choice A; -115 < -27.
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he contents of a sample of 26 cans of apple Juice showed a standard deviation of 0.06 ounces. we are interested in testing to determine whether the variance of the population is significantly more than 0.003. The alternative hypothesis is a. S 0.003 b. S 0.003 c. ?,0.003 d. ?2 0.003
Answers
The alternative hypothesis for this problem is that the population variance is significantly more than 0.003, represented as [tex]H1: S2 > 0.003.[/tex]
To test this hypothesis, we can use a chi-square test of variance. This test is calculated as [tex]X2 = (n-1) * (s2/σ2)\\[/tex], where n is the sample size, s2 is the sample variance, and σ2 is the hypothesized population variance.
In this case, the sample size is 26, so n = 26. The sample variance is 0.06, so s2 = 0.06. The hypothesized population variance is 0.003, so σ2 = 0.003. Plugging these values into the formula above gives us [tex]X2 = (26-1) * (0.06/0.003) = 75.[/tex]
Since this value is greater than the critical value of the chi-square distribution at α = 0.05, the null hypothesis can be rejected and it can be concluded that the population variance is significantly more than 0.003.
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80% of a number is x. What is 100% of the number? Assume x>0
Answers
The 100 percent of the asked number is 5x/4
What is percent?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
Given that, 80% of a number is x, we need to find 100% of the number,
Let the number be y,
Therefore,
80% of y = x
y = 5x/4
Therefore, the number is 5x/4
100% of 5x/4 = 5x/4
Hence, the 100 percent of the asked number is 5x/4
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Please help me I don't understand this.
Answers
The height of the plane to the nearest meter is, 1023. So option A is correct
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
To find the height of the plane, we can use the following formula:
height = horizontal distance x tanα
Plugging in the given values, we have:
height = 4,812 × tan(12°)
= 4,812 × 0.21213
= 1,015.7 meters
Rounding to the nearest meter, the height of the plane is 1,016 meters.
So the answer is 1,016 meters
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7. Find all of the subgroups in A4. What is the order of each subgroup?
Answers
The subgroups of A4 and their orders are.
Subgroups of order 2 = {(), (1 2), (1 3), (1 4), (2 3), (2 4), (3 4)}, each of order 2
Subgroups of order 3= {(), (1 2 3), (1 3 2)}, each of order 3
Subgroup of order 4= {(), (1 2 4 3), (1 4)(2 3), (1 3)(2 4)}, of order 4
Full group A4: {all even permutations, order 12}
What is a subgroup?A subgroup is a subset of a group that is itself a group under the same group operation.
We have,
Group A4 is the group of even permutations of four elements.
It has order 12.
i.e
4! = 24 total permutations of four elements, but half of them are odd and thus not in A4.
To find all the subgroups of A4.
We can use the fact that the order of a subgroup must divide the order of the group.
Thus, the possible orders of subgroups are 1, 2, 3, 4, 6, and 12.
And,
We also know that there is a subgroup of order 1 (the trivial subgroup, consisting of just the identity permutation) and a subgroup of order 12 (the full group A4).
To find the other subgroups,
We can look for elements that generate subgroups of different orders.
One useful element to consider is the 3-cycle (1 2 3), which generates a subgroup of order 3.
This subgroup consists of the identity, the 3-cycle (1 2 3), and the 3-cycle (1 3 2).
There are two such subgroups in A4, corresponding to the three possible choices of which element to leave out of the 3-cycle.
Another useful element is the 2-cycle (1 2), which generates a subgroup of order 2.
This subgroup consists of the identity and the 2-cycle (1 2).
There are three such subgroups in A4, corresponding to the three possible pairs of elements to include in the 2-cycle.
Now,
We can consider the product of the 3-cycle (1 2 3) and the 2-cycle (1 2), which is the 4-cycle (1 2 4 3).
This generates a subgroup of order 4, consisting of the identity, the 4-cycle (1 2 4 3), and the two 2-cycles (1 4) and (2 3).
Thus,
The subgroups of A4 and their orders are.
Subgroups of order 2 = {(), (1 2), (1 3), (1 4), (2 3), (2 4), (3 4)}, each of order 2
Subgroups of order 3= {(), (1 2 3), (1 3 2)}, each of order 3
Subgroup of order 4= {(), (1 2 4 3), (1 4)(2 3), (1 3)(2 4)}, of order 4
Full group A4: {all even permutations, order 12}
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The complete question.
Find all of the subgroups in A4 that have order 12.
What is the order of each subgroup using 3-cycle and 2-cycle?
suppose that 4 j of work is needed to stretch a spring from its natural length of 36 cm to a length of 49 cm. (a) how much work is needed to stretch the spring from 40 cm to 44 cm? (round your answer to two decimal places.) j (b) how far beyond its natural length will a force of 50 n keep the spring stretched? (round your answer one decimal place.) in cmfor part a I tried .3 and .28 but both were wrong and b I got 156.5 but was also wrong
Answers
(a) The work required to stretch the spring from 36 cm to 49 cm is 4 j. (b) A force of 50 N will keep the spring stretched by 13 cm beyond its natural length, or to a total length of 49 cm + 13 cm = 62 cm.
(a) The work required to stretch the spring from 36 cm to 49 cm is 4 j.
Let x be the additional length needed to stretch the spring from 40 cm to 49 cm.
Then, the work required to stretch the spring from 40 cm to 49 cm is (4 j / 13) * x, since it takes 4 j to stretch the spring by 13 cm.
We have x = 9 cm - 4 cm = 5 cm. Therefore, the work required to stretch the spring from 40 cm to 49 cm is (4 j / 13) * 5 = 20 j / 13, or approximately 1.54 j when rounded to two decimal places.
(b) Let k be the force constant of the spring. We can use Hooke's law, which states that F = kx, where F is the force applied, x is the displacement from the natural length, and k is the force constant.
We know that a force of 50 N is required to stretch the spring from 36 cm to 49 cm, which is a displacement of 13 cm.
Therefore, we have 50 N = k * 13 cm, or k = 50 N / 13 cm.
Let y be the displacement from the natural length when a force of 50 N is applied to the spring.
Then, we have 50 N = k * y, or y = 50 N / k. Substituting k = 50 N / 13 cm, we get y = (50 N / (50 N / 13 cm)) = 13 cm.
Therefore, a force of 50 N will keep the spring stretched by 13 cm beyond its natural length, or to a total length of 49 cm + 13 cm = 62 cm. When rounded to one decimal place, this is 62.0 cm.
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What are the coordinates of R′ for the dilation centered at P with scale factor 0.5?
Answers
The coordinates of R′ for the dilation centered at P with scale factor 0.5 is (2, 2.5).
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
Given:
Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.
The coordinate of the R' after the dilation is (-1,-0.5)
Given:
The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).
The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,
Q' = Q- P
Q' = (-3 -(-3), 2- (-3))
Q' = (0, 5)
Similarly for R' = R- P
R' = (1 -(-3), 2- (-3))
R' = (4, 5)
and, after dilation by scale factor 0.5 then
R" = 0.5 x (4, 5)
R" = (2, 2.5)
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A credit card with an APR of 28% has a balance of $1000 on it. You make a $400 payment that posts on the 11th day of a 31-day month. How much interest will you be charged for the month?
Answers
To calculate the interest charged for the month on a credit card with a balance of $1000 and an APR of 28% after making a $400 payment on the 11th day of a 31-day month, we need to first calculate the average daily balance for the month.
The average daily balance is calculated as follows:
(Previous balance × number of days in billing cycle) + (New charges × number of days since posting of new charges) - (Payments and credits × number of days since payment/credit) / Number of days in billing cycle
In this case, the previous balance is $1000, the number of days in the billing cycle is 31, the new charges are 0, the number of days since posting of new charges is 20 (since the payment posted on the 11th day of the month), the payment/credit is $400, and the number of days since payment/credit is 21. Plugging in these values, we get:
($1000 × 31) + (0 × 20) - ($400 × 21) / 31 = $727.10
Therefore, the average daily balance for the month is $727.10.
To calculate the interest charged for the month, we multiply the average daily balance by the daily periodic rate, which is the APR divided by 365 (since there are 365 days in a year):
$727.10 × (0.28 / 365) × 31 = $19.97
Therefore, the interest charged for the month is $19.97.
Select which option is most appropriate for describing the number line below.
A number line is divided into twelfths with each twelfth labeled. A dashed arrow is shown starting at ten-twelfths and ending at, as well as pointing to, seven-twelfths. Another dashed arrow is shown starting at seven-twelfths and ending at, as well as pointing to, three-twelfths.
A.
4
12
+
3
12
−
3
12
=
10
12
B.
10
12
−
3
12
−
3
12
=
4
12
C.
10
12
−
3
12
−
4
12
=
3
12
D.
10
12
−
4
12
−
3
12
=
4
12
Answers
The option which is most appropriate for describing the number line below is option C. [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]
What is Number Line?A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.
Given a number line, where it is divided into twelfths, with each twelfth labeled.
So the labeled numbers are [tex]\frac{1}{12}[/tex], [tex]\frac{2}{12}[/tex], ..............[tex]\frac{10}{12}[/tex], [tex]\frac{11}{12}[/tex], [tex]\frac{12}{12}[/tex].
A dashed arrow is shown starting at ten-twelfths and ending at, as well as pointing to, seven-twelfths.
Arrow starts at [tex]\frac{10}{12}[/tex] and ends at [tex]\frac{7}{12}[/tex].
There is a distance of [tex]\frac{10}{12}[/tex] - [tex]\frac{7}{12}[/tex] = [tex]\frac{3}{12}[/tex].
So the first form of expression is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] in order to get [tex]\frac{7}{12}[/tex].
Then the dashed arrow starts from [tex]\frac{7}{12}[/tex] and ends at [tex]\frac{3}{12}[/tex].
There is a distance of [tex]\frac{7}{12}[/tex] - [tex]\frac{3}{12}[/tex] = [tex]\frac{4}{12}[/tex].
So the second form is [tex]\frac{7}{12}[/tex] - [tex]\frac{4}{12}[/tex] in order to get [tex]\frac{3}{12}[/tex].
So the complete description of the number line is,
[tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]
Hence the correct option is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex].
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Please help !! I can’t figure this question out
Answers
Answer: also too tiny
Step-by-step explanation:
show a closer picture
¿Qué ecuación de suma se puede usar para
comprobar el resultado de 456-342 = 114?
Dibuja un diagrama de barras para mostrar
cómo se relacionan los números
del problema.
Answers
The addition equation that can be used to check the result of 456 - 342 = 114 is:
456 + (-342) = 114
Here's how you can draw a bar chart to represent the problem:
The Bar Chart+
456|
- |
342|
---|
114|
Each bar represents a number in the equation and the height of the bar shows the magnitude of the number.
In this bar chart, 456 and 342 are represented by positive bars and the subtraction symbol is represented by the height of the bar being reduced by the magnitude of 342.
The result, 114, is represented by the height of the final bar.
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The question in English is: "Which addition equation can be used to
check the result of 456-342 = 114?
Draw a bar chart to show
how the numbers are related
of the problem."
Please help asap! For a test (25 points)
The diameter of a circle is 4 m. Find its area in terms of π.
Answers
Answer: 4[tex]\pi[/tex] m^2
Step-by-step explanation:
The formula to calculate the area of a circle:
[tex]\pi r^{2}[/tex]
Given that the diameter of a circle is 4, we can work out that r (the radius) is 2.
(The radius is half of the diameter)
Therefore we can plug in our values:
[tex]\pi 2^{2}[/tex]
[tex]2^{2}[/tex] = 4
Therefore your answer is:
[tex]4\pi[/tex] [tex]m^{2}[/tex]
(Remember your units!)
Answer: A=12.566
Step-by-step explanation:
A=πr^2
R=2
π*4=12.566
I don't know how you want the answer rounded so I just rounded it to the nearest thousandths
Math help! Get back to me in 30 minutes or less please! :)
Please solve for the variable indicated.
I= Prt, solve for t
If you could break it down step by step that would be super helpful! I’m very confused. Thank you!
Answers
Answer: thanks for 14 points
Step-by-step explanation:lol
coordinate plane with triangle efg with e at 0 comma 5, f at 1 comma 1, and g at negative 2 comma 1. point h at 1 comma 1 is on segment gf, and points e and h are connected with a segment.triangle efg is dilated by a scale factor of 3 centered at (0, 1) to create triangle e'f'g'. which statement is true about the dilation? (1 point)
Answers
Option A. segment EH and segment E prime H prime both pass through the centre of dilation is true.
Given triangle EFG:
E(0, 5), F(1, 1), G(-2, 1)
Center of dilation is H(0, 1)
The scale factor is k = 3
The rule for this dilation is:
(x, y) → (k(x - a) + a, k(y - b) + b)
(x, y) → (3x, 3(y - 1) + 1) = (3x, 3y - 2)
The coordinates of E'F'G' are:
E → E' = (0, 5) → (0, 13)
F → F' = (1, 1) → (3, 1)
G → G' = (-2, 1) → (-6, 1)
Points H and H overlap as the centre of dilation at (0, 1)
a. Segment EH and segment E prime H prime both pass through the centre of dilation.
True
b. The slope of segment EF is similar to the slope of segment E prime H prime.
False
c. Segment EG will overlap Segment E prime G prime.
False
d. The Segment EH ≅ to segment E prime H prime.
False
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The correct question is:
Coordinate plane with triangle EFG with E at 0 commas 5, F at 1 comma 1, and G at negative 2 commas 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.
Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the dilation?
a. segment EH and segment E prime H prime both pass through the center of dilation.
b. The slope of segment EF is the same as the slope of segment E prime H prime.
c. segment E prime G prime will overlap segment EG.
d. segment EH ≅ segment E prime H prime.
recall from example 3 in section 1.3 that the set of diagonal matrices in m2x2(f) is a subspace. find a linearly independent set that generates this subspace.
Answers
A linearly independent set that generates the subspace of diagonal matrix in M2x2(F) is {[1,0;0,0], [0,0;0,1]}.
A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a, b∈F.
A linearly independent set of vectors that generate this subspace is {[1,0;0,0], [0,0;0,1]}. Any diagonal matrix can be written as a linear combination of these two vectors.
A subspace of M2x2(F) is a set of all diagonal matrices, which are matrices of the form [a,0;0,b] with a,b∈F. This means that all the diagonal entries in the matrix must be non-zero. To find a linearly independent set that generates this subspace, we can start by considering the simplest form of a diagonal matrix, which is [1,0;0,0]. This vector is linearly independent, as it cannot be expressed as a linear combination of any other vector in the space. Similarly, [0,0;0,1] is also linearly independent, as it can't be expressed as a linear combination of any other vector.
These two vectors form a linearly independent set that generates the subspace of diagonal matrices in M2x2(F). Any diagonal matrix can be written as a linear combination of these two vectors. For example, the matrix [2,0;0,3] can be expressed as 2[1,0;0,0]+3[0,0;0,1]. Thus, this set of vectors is sufficient to generate the entire subspace.
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The diameter of a circle is 12 millimeters. What is the circle's circumference?
Answers
Answer:
37.7 mm
Step-by-step explanation:
The line plot represent the wait time in line for a ride at the local fare which of the following best describes the shape of the data and why
Answers
The data is skewed and might mean that the wait times were higher for that day because the fair was busy that day.
The correct option is B.
What is skewed data?In other words, data with a lower bound are frequently skewed right, and data with an upper bound are typically biased left.
Start-up effects can also cause skewness.
Given:
The line plot represents the wait time in line for a ride at the local fare.
In the data set form,
10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 14, 15, 16.
The mean of the data set,
= {(10 x 4) + (11 x 4) + (12 x 2) + (13 x 2) + 14 + 15 + 16}/15
= 179/15
= 11.93
The median of the data set = 11.
The mean value is greater than the median value.
So, the data is skewed right.
Therefore, the data is skewed right.
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solve for z. 2z+2=10 z=
Answers
Answer:
z = 4
Step-by-step explanation:
2z+2=10
To solve for z, subtract 2 from each side.
2z+2-2=10-2
2z=8
Divide each side by 2
2z/2 = 8/2
z = 4
Order these numbers from least to greatest.
12
50
Note that for this question you can use your mouse to drag the numbers into their positions.
(please help meee) :(
Answers
The given numbers, when ordered from least to greatest, are :
- 6. 44, - √ 40, 0. 2 bar, 12 / 50How to order the numbers ?To order the numbers, you need to convert the numbers to the same standard. In this case, we can convert the numbers to whole numbers and decimals.
- √ 40 is :
= - 6. 32
0. 2 bar is 0. 22222222...
- 6. 44 is already in the appropriate form
12 / 50 :
= 12 ÷ 50
= 0. 24
The order from least to greatest is therefore:
- 6. 44, - √ 40, 0. 2 bar, 12 / 50
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Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 4 cos-(x), а 3D 0 4, 82 3 32 4 512 90
Answers
The first four nonzero terms of the Taylor series for f(x) = 4 cos(x), centered at a = 3π/4, are: 4 cos(3π/4), -4 sin(3π/4), -4 cos(3π/4), 4 sin(3π/4)
The Taylor series for a function f(x) centered at a value "a" is given by:
f(x) = f(a) + f'(a)(x - a) + (f''(a))/2! (x - a)^2 + (f'''(a))/3! (x - a)^3 + ...
To find the first four nonzero terms of the Taylor series for f(x) = 4 cos(x), centered at a = 3π/4, we need to evaluate the function and its derivatives at x = 3π/4:
f(3π/4) = 4 cos(3π/4)
f'(3π/4) = -4 sin(3π/4)
f''(3π/4) = -4 cos(3π/4)
f'''(3π/4) = 4 sin(3π/4)
Now we can plug these values into the Taylor series to get:
f(x) = 4 cos(3π/4) - 4 sin(3π/4)(x - 3π/4) - 4 cos(3π/4) (x - 3π/4)^2 + 4 sin(3π/4) (x - 3π/4)^3 + ...
The first four nonzero terms of the series are:
f(x) = 4 cos(3π/4) - 4 sin(3π/4)(x - 3π/4) - 4 cos(3π/4) (x - 3π/4)^2 + 4 sin(3π/4) (x - 3π/4)^3
So, the first four nonzero terms of the Taylor series for f(x) = 4 cos(x), centered at a = 3π/4, are:
4 cos(3π/4), -4 sin(3π/4), -4 cos(3π/4), 4 sin(3π/4)
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Suppose angles 3 and 4 are complementary and ∠3 = 27°.
What is the measure (in degrees) of ∠4? (Do not include the degree symbol)
Answers
The measure (in degrees) of ∠4 would be 63 degree
What is complementary angles?If the total of the measurements of two angles equals 90 or 180 degrees, respectively, such angles are said to be complimentary and supplementary.
Complementary angles are the one whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.
A triangle's three angles add up to 180 degrees. The third angle is the result of 64 degrees being subtracted.
They have the same measurements, m 4 = 90.
A + 27 = 90
A = 63
Therefore, they are complimentary, their combined angles equal 90.
A = 63 degree
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Find the measure of the angle indicated
Answers
So that angle is 114
cumulative frequency distributions show the multiple choice question. accumulated counts up to and including the current bin as the bin limits increase. total count minus the current bin count. the number of observations in the each bin only. the number total number of observations in the bin and any bins with limits greater.
Answers
Cumulative frequency distributions show the accumulated counts up to and including the current bin as the bin limits increase. This means that for each bin, the cumulative frequency distribution includes the number of observations in that bin and any previous bins with lower limits.
If a data set is divided into five bins, and the number of observations falling into each bin are 10, 20, 30, 40, and 50, the cumulative frequency distribution for each bin would be 10, 30, 60, 100, and 150 respectively.
In other words, the cumulative frequency distribution is the total count of observations up to and including the current bin. This makes it easier to see the overall pattern of the data, and can be used to find the median, quartiles, and percentiles of a data set.
It is important to note that cumulative frequency distributions differ from frequency distributions, which only show the number of observations in each bin. Cumulative frequency distributions can also be used to calculate the total number of observations in any bin, including bins that have higher limits.
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The diagonals of a rhombus are perpendicular bisector of each other.
true or false
Answers
Answer:
true
Step-by-step explanation:
True, diagonals of a rhombus are perpendicular bisectors of each other.
I need help, what is 3 ¼ - 1 ½ =
Answers
Answer:
Step-by-step explanation:
7/4
3. Simplify the equation
Answers
Answer:
-tan(θ)
Step-by-step explanation:
We can use the following trigonometric identity to simplify tan(pi - theta):
tan(pi - theta) = -tan(theta)
Therefore, the simplified expression is:
tan(pi - theta) = -tan(theta)
Unit 6 similar triangles homework 5 parallel lines and proportional parts
Answers
Here's an explanation of similar triangles and how to use them to solve problems involving parallel lines and proportional parts:
Similar Triangles:Similar triangles are triangles that have the same shape but may have different sizes.
In other words, the corresponding angles of similar triangles are equal, and the corresponding sides are in proportion.
This means that if we know the ratio of the sides of one triangle, we can find the corresponding sides of the other triangle.
Parallel Lines and Proportional Parts:
When two parallel lines are intersected by a third line, the corresponding angles formed by the third line are equal.
This leads to several important proportional relationships that we can use to solve problems.
Some of them are:
"alternate interior angles" theorem "corresponding angles" theorem, etc
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Zeke and Erin were playing a game with a number cube and a spinner divided into equal ports red.
yellow, and blue. Zeke wins if the number cube is a factor of and the spinner lands on red Erin
wins if she rolls a 5 or 6 and the spinner lands on yellow or blue.
1 Create a probability table or free to show all outcomes of rolling a number cube and spinning the
spinner,
R₁
≤18
y₁
B3
2. What is the probability of Zeke winning? What is the probability of Erin winning?
Answers
The probabilities of winning are 1/6 and 2/9
How to determine the probability tableFrom the question, we have the following parameters that can be used in our computation:
Devices = Number cube and spinner
Using the above as a guide, we have the following sample space:
S = {(1, Red), (2, Red), (3, Red), (4, Red), (5, Red), (6, Red), (1, Yellow), (2, Yellow), (3, Yellow), (4, Yellow), (5, Yellow), (6, Yellow), , (1, Blue), (2, Blue), (3, Blue), (4, Blue), (5, Blue), (6, Blue)}
The probability of winningFor Zeke, we have: Factor of 2 and Red
From the sample space, we have
P(Zeke) = 3/18
P(Zeke) = 1/6
For Erin, we have: 5 or 6 and Yellow or Blue
From the sample space, we have
P(Erin) = 4/18
P(Erin) = 2/9
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(Multiplying and Dividing with Scientific Notation MC)
How many times smaller is 5 x 10−7 than 8.5 x 10^
−4? HELP ASAP
Answers
The scientific notation of 5 x 10−7 is 5 x 10 to the power of negative 7.
What is notation?Notation is a set of symbols and instructions used to represent numbers, equations, and other mathematical expressions. Notation is used to explain rules and procedures, as well as make complex mathematical concepts easier to read and understand. Notations can range from simple abbreviations to complex mathematical symbols. In mathematics, notation can help to simplify complex problems and provide a way for mathematicians to communicate their ideas.
This means that it is 5 times as small as 1. The scientific notation of 8.5 x 10^−4 is 8.5 x 10 to the power of negative 4. This means that it is 8.5 times as small as 1. Therefore, 5 x 10−7 is 8.5 times smaller than 8.5 x 10^−4. By dividing the two numbers, we get 8.5/5 = 1.7. This means that 5 x 10−7 is 1.7 times smaller than 8.5 x 10^−4.
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