The cosine of angle ABM is sqrt(2) / 4.Let's consider the regular tetrahedron ABCD with M being the midpoint of CD. We can use the properties of equilateral triangles to determine the cosine of angle ABM.
First, we can find the length of AM by considering the right triangle ABM. Since AB and BM are equal edges of the equilateral triangle ABM, we can use the Pythagorean theorem to find AM:
AM = sqrt(AB^2 - BM^2)
Next, we can find the length of AB by considering the equilateral triangle ABC. Since all sides of an equilateral triangle are equal, we have:
AB = BC = CD = DA
Now, we can use the dot product formula to find the cosine of angle ABM:
cos(ABM) = (AB . AM) / (|AB| |AM|)
where AB . AM is the dot product of vectors AB and AM, and |AB| and |AM| are the magnitudes of these vectors.Substituting the values we have found, we get:
cos(ABM) = [(AB^2 - BM^2) / 2AB] / [sqrt(AB^2 - BM^2) AB]
Simplifying this expression gives:
cos(ABM) = (1 - (BM/AB)^2) / (2 sqrt(1 - (BM/AB)^2))
Since the tetrahedron is regular, we know that AB = BC = CD = DA, and therefore BM = AD/2. Substituting these values, we get:
cos(ABM) = (1 - (1/4)^2) / (2 sqrt(1 - (1/4)^2))
Simplifying this expression gives:
cos(ABM) = sqrt(2) / 4.
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The cosine of angle ABM is square (2)/4. Consider the tetrahedron ABCD where M is the center of CD. We can use the product of equilateral triangles to determine the cosine of angle ABM.
First, we can find the length of AM from triangle ABM. Since AB and BM are equilateral triangles ABM, we can use the Pythagorean theorem to find AM:
AM = sqrt(AB^2 - BM^2)
which is the resolution.
Equilateral triangle ABC.
Since all sides of the triangle are equal:
AB = BC = CD = DA
Now, we can find the cosine of angle ABM using the dot property:
cos (ABM) = (AB .AM ) / (AB AM )
EU. AM is the product of the vectors AB and AM, AB and
AM is the magnitude of the vectors. Substituting the value we found, we get:
cos(ABM) = [(AB^2 - BM^2) / 2AB] / [sqrt(AB^2 - BM^2) AB], simplifying this expression to give:
cos(ABM) = (1 - (BM/AB)^2) / (2 sqrt(1 - (BM/AB)^2))
Since the tetrahedron is regular, we know AB = BC = CD = DA, BM = AD/2. Substituting these values, we get:
cos(ABM) = (1 - (1/4)^2) / (2 sqrt(1 - (1/4)^2))
Simplifies this expression to give:
cosine(ABM) = square root(2)/4.
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heloo need help with this integration
Use the given function to find the [tex]y[/tex]-coordinate of [tex]A[/tex].
[tex]x=2 \implies y = 10+8\cdot2+2^2-2^3 = 22[/tex]
Find the equation of the line through the origin and [tex]A[/tex]. This line has slope
[tex]\mathrm{slope} = \dfrac{22-0}{2-0} = 11[/tex]
and passes through (0, 0), so its equation is
[tex]y - 0 = 11 (x-0) \implies y = 11x[/tex]
Then the area of the shaded region is given by the definite integral
[tex]\displaystyle \int_0^2 (y - 11x) \, dx = \int_0^2 (10 + 7x + x^2 - x^3) \, dx \\\\ ~~~~~~~~ = \left(10x + \frac72 x^2 + \frac13 x^3 - \frac14 x^4\right)\bigg|_0^2 \\\\ ~~~~~~~~ = 10\cdot2+\frac72\cdot2^2+\frac13\cdot2^3-\frac14\cdot2^4 = \boxed{\frac{98}3}[/tex]
How many pairwise comparisons must you make for a case with 15 statistically independent scenarios?
There are 105 comparisons made with 15 statistically independent scenarios.
According to the statement
we have given value of n is 15.
Then r = 2. so,
we use the formula NcR then
Substitute the values in it then
15c2
we open it according to ncr formula
In this formula we arrange the terms according to the following
NcR formula = n! /r! * (n-r)!
then the terms will arrange in this way.
So,
ncr = 15! / 2! * 13!
After solving the statement some terms will be cancel with each other and remaining terms are
ncr = 15*14/2
ncr = 210/2
ncr = 105
here the value becomes 105.
So, There are 105 comparisons made with 15 statistically independent scenarios.
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The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The quarterly rate of growth is 0.03 or 3%. The growth rate is 1.03. 920(1.03) is the number of cars multiplied by 1.03. Base arrowRight Coefficient arrowRight Exponent arrowRight Rate
The number of compounding per year is[tex]N = 920(1+0.03)^4t[/tex]
How can the number of compounding per year be calculated?This can be calculated by making use of the formular; 920(1.03)^4t and use the compound interest equation which is N=P( 1+r/n)^nt
We know that 12% was given as the rate per year, then to get the quarter rate we divide by factor of 4, which is 12/4= 3%
The compounding for t years = n*t = 4t where n=4.
and the Initial number of cars serviced=920
Then we can substitute the values into the above equation, we have Thus [tex]N = 920(1+0.03)^4t[/tex]
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CHECK THE COMPLETE QUESTION BELOW:
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. 920(1.03) is the number of cars multiplied by 1.03. The quarterly rate of growth is 0.03 or 3%. The compound periods multiplied by the number of years is 4t. The initial number of cars serviced is 920. The growth factor is represented by 1.03. The growth rate is 1.03. Exponent arrowRight Base arrowRight Coefficient arrowRight Rate arrowRight
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: no, it's not similar because we cannot multiply it by any factor that the ratio will be the
Step-by-step explanation:
The product of donnies age and 6 is 72. use variable d to represent donnies age
Answer: D times 6 = 72
D= 12
Step-by-step explanation:
The term product means multiplication. Donnie's age is represented by the letter d, so if the product of d and 6 is 72, or in other words, d times 6 is 72, then d would equal 12
A rectangular park is 70 meters wide and 120 meters long. Give the length and width of another rectangular park that has the same perimeter but a smaller area.
Answer:
1 m by 189 m
Step-by-step explanation:
The perimeter is 2(70+120)=380.
The area is (70)(120)=8400.
If we let the park have a width of 1 meter and a length of 189 meters, then the area will be 189 square meters, which is smaller than 8400 square meters, as required.
Select the correct answer. if 6 cards are drawn at random from a standard deck of 52 cards, what is the probability that exactly 2 of the cards are spades? a. 0.038 b. 0.200 c. 0.315 d. 0.465 e. 0.747
Answer:
0.315
Step-by-step explanation:
sutopa has 3/4 the money maneet has. maneet has $18 less than Kim. together, they have $286.40. How much money does each of them have?
The amount of money Kim, maneet and Sutopa have is $115.6, $97.6 and $73.2 respectively.
EquationKim = xManeet = x - 18Sutopa = 3/4(x-18)Total = $286.40x + (x - 18) + 3/4(x-18) = 286.40
x + x - 18 + 3/4x - 13.5 = 286.40
2 3/4x = 286.40 + 13.5 + 18
11/4x = 317.9
x = 317.9 ÷ 11/4
= 317.9 × 4 / 11
= 1,271.6 / 11
x = $115.6
So,
Kim = x
= $115.6
Maneet = x - 18
= 115.6 -18
= $97.6
Sutopa = 3/4(x-18)
= 3/4(97.6)
= $73.2
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What is the length of the apothem, rounded to the nearest inch? recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon. 4 in. 5 in. 9 in. 11 in.
Answer:
Step-by-step explanation:
What is the length of the apothem, rounded to the nearest inch? recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon. 4 in. 5 in. 9 in. 11 in.
Answer:
9
Step-by-step explanation:
apothem (AB)
1/2 of the length (10) is 5
AB^2 + 5^2 = 10^
AB^2 = 100-25
Square root of AB^2 = square root of 75
AB = 8.66
8.66 is about 9
In a bag there are 3 red 4 white, and 5 blue marbles. once a marble is selected it is not required. find: p(white, red) find: p(blue, white, red.)
Answer:
Below in bold.
Step-by-step explanation:
Total number of marbles = 3+4+5 = 12
P(white, red) = 4/12 * 3/11
= 12/132
= 1/11,
P(blue, white, red) = 5/12 * 4/11* 3/10
= 60/1320
= 6/132
= 1/22.
Select the correct answer. what is this expression in simplified form? v12 . 4v3 options a.7 b.4v15 c.6 d.24
Answer:
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
a cube with volume 343 cubic inches is inscribed in a sphere so that each vertex of the cub touches the sphere. what is the lenght of the radius in inches of the sphere
The length of the radius of the sphere is 9.26 inches.
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is denoted by the letter r, and the specified point represents its center.
Volume of cube=343 cubic inches
Side of cube=[tex]\sqrt[3]{343}[/tex] = 7 inches
The radius of the sphere is equal to half the diagonal length of the cube since the cube is inscribed inside the sphere, whose diameter is the cube's diagonal length. Utilizing the distance formula, we can determine the cube's diagonal length.
[tex]d=\sqrt{7^{2}+7^{2}+7^{2} } \\=\sqrt{7*7^{2} } \\=7\sqrt{7}[/tex]
To determine the radius of the sphere, divide the value by two.
Radius of sphere=[tex]\frac{7\sqrt{7} }{2}[/tex] = 9.26 inches
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An isosceles triangle has two equal sides. If two of the sides are 5 inches and 2 inches, what is the perimeter of the triangle
Step-by-step explanation:
12 inches
djaikfnshaidifb
Find the value of a°,b°,x°,y° from the given figure
Answer:
Hope it helps u, any questions u may ask me
x=70 [alternate interior angles]
y=60 [alternate interior angles]
a=110 [By linear pair]
b=120 [By linear pair]
Which of the following is a simpler way to write StartFraction cosine theta Over sine theta EndFraction
The correct option is (d) cotФ.
As, cosineФ/sineФ = cotФ.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
The basic trigonometric identities are-
Sine, (Sin) Cosine, (cos)Tangent, (tan)Secant, (sec)Cosecant (cosec)Cotangent (cot)Solution for the given trigonometric function; (cosineФ/sineФ)
Use formula of tanФ
tanФ = sineФ/cosineФ
Also, from basic trigonometric ratios.
tanФ = 1/cotФ
Substitute sineФ/cosineФ to get the result
1/cotФ = sineФ/cosineФ
Further simplify,
cotФ = cosineФ/sineФ
Therefore, the value of cosineФ/sineФ = cotФ
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Which of the following is a simpler way to write StartFraction cosine theta Over sine theta EndFraction-
(a) tanФ
(b) secФ
(c) cosecФ
(d) cotФ
Answer: D, cot o
Step-by-step explanation:
edge :-]
The triangle below is being reduced by a scale factor of two-thirds. What is the base of the new drawing? 15 m
Answer:
10
Step-by-step explanation:
A scale factor of 2/3 means multiplying all side lengths by 2/3
15*2/3=10
The vertices of a quadrilateral are A(-1,6),B(-2,4),C(2,2), and D(3,4). Write a paragraph proof to determine whether quadrilateral ABCD is a rectangle. 15px
Determining the slopes of each side, we get the slope of [tex]\overline{AB}[/tex] is [tex]2[/tex], the slope of [tex]\overline{BC}[/tex] is -1/2, the slope of [tex]\overline{CD}[/tex] is 2, and the slope of [tex]\overline{AD}[/tex] is -1/2. Since the slopes of sides AB and CD and BC and AD are equal, it follows that [tex]\overline{AB} \parallel \overline{CD}[/tex] and [tex]\overline{BC} \parallel \overline{AD}[/tex]. Thus, ABCD is a parallelogram because it is a quadrilateral with two pairs of opposite congruent sides. However, we can also note that the slope of side AB is the negative reciprocal of that of sides BC, and thus [tex]\overline{AB} \perp \overline{BC}[/tex]. Using the fact that perpendicular lines form right angles, we can conclude that [tex]\angle ABC[/tex] is a right angle, and since ABCD is thus a parallelogram with a right angle, it must also be a rectangle.
Answer:
Answers will vary based on the method used, but the final slope-intercept form of the equation of AB↔ will be the same.Let the equation of AB↔ in slope-intercept form be y=mx+d, where m is the slope and d is the y-intercept.The coordinates of points A and B are (1, 1) and (5, 3), respectively, so the slope of AB↔ is m=yB−yAxB−xA=24=0.5.Substitute the value of m back in the equation:y = 0.5x + d.Substitute the coordinate of point A (1, 1) in the equation above, and solve for d: 1 = 0.5 + dd = 0.5.Therefore, the equation of AB↔ is y = 0.5x + 0.5. To check whether C lies on AB↔ substitute the x-coordinate of C into the right side of the equation: 0.5 (2.6) + 0.5 = 1.8.The result is equal to the y-coordinate of C. Thus, C satisfies the equation of AB↔ which means that C lies on AB↔.
Step-by-step explanation:
I did it
Each of the following is an example of quantitative data, except Group of answer choices weight in ounces income in dollars political affiliation age in years
The correct option is C. political affiliation.
An example of quantitative data are-
weight in ouncesage in yearsincome in dollarsWhat is quantitative data?Data that expresses a definite quantity, amount, or range is known as quantitative data. In most cases, the data is accompanied with measuring units, such as metres in the case of a person's height. Setting boundaries for such data makes sense, and performing mathematical operations on the data has significance.
Types of Quantitative Data are-
Counter: A measure of entities. For instance, the quantity of users who have downloaded a specific app from the App Store.Measurement of physical objects: Calculating the dimensions of any physical object is called measurement. The HR executive, for instance, meticulously measures the size of each cubicle given to the new hires.Sensory calculation: Mechanism to automatically "sense" the parameters being monitored in order to generate a continuous source of data. A digital camera, for instance, transforms electromagnetic signals into a string of numerical data.Data projection: Algorithms and other mathematical analysis techniques can be used to project future data. For instance, after conducting a thorough investigation, a marketer will forecast a rise in sales following the introduction of a new product.To know more about quantitative data, here
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The complete question is-
8. Each of the following is an example of quantitative data, except ______.
A. weight in ounces
B. income in dollars
C. political affiliation
D. age in years
If (x + 1)(x-3) = 5, then which of the following statements is true?
Ox+1=0 orx-3=0
Ox+1=5 orx-3=5
Ox-4-0 orx+2=0
Answer:
(x-4)=0 or (x+2)=0 is correct
Step-by-step explanation:
(x+1)(x-3)=5
x^2 -3x +x -3=5
x^2-2x-8=0
x^24x+2x-8=0
(x+2)(x-4)=0
so,
(x-4)=0 or (x+2)=0
The solutions to the expression are:
x - 4 = 0 or x + 2 = 0.
Option C is the correct answer.
We have,
To determine which of the following statements is true:
(x + 1) = 0 or (x - 3) = 0
(x + 1) = 5 or (x - 3) = 5
(x - 4) = 0 or (x + 2) = 0
We can solve the given equation (x + 1)(x - 3) = 5 by expanding the equation and setting it equal to 0:
(x + 1)(x - 3) - 5 = 0
Expanding the equation:
x² - 3x + x - 3 - 5 = 0
x² - 2x - 8 = 0
Now we can factor the quadratic equation:
(x - 4)(x + 2) = 0
From this factorization, we find two possible solutions:
x - 4 = 0 --> x = 4
x + 2 = 0 --> x = -2
Therefore,
The correct statement is:
(x - 4) = 0 or (x + 2) = 0
i.e
x - 4 = 0 or x + 2 = 0.
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Can someone help me with these problems and show work
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Find equation of the line passing through the point (-1,0) and parallel to the line y=-1/2x + 3/7
Answer:
Step-by-step explanation:
A parallel line will have the same slope, m, as the reference line given by the form y=mx+b. b is the y-intercept, the value of y when x=0.
The reference line of y = -(1/2)x + (3/7) has a slope of -(1/2).
The parallel line will have the same slope, so we can write:
y - -(1/2)x + b
We need a value of b that forces the line to go through point (-1,0). Enter that point in the equation and solve for b:
y - -(1/2)x + b
0 - -(1/2)(-1) + b
b = -(1/2)
The equation of the line parallel to y = -(1/2)x + (3/7) and going through (-1,0) is
y=-(1/2)x - (1/2)
Which theorem correctly justifies why the lines m and n are parallel when cut by a transversal k
The theorem which justifies that two lines are parallel when cut by a transversal k is converse of the alternate interior angles theorem.
Given that two lines m and n are parallel.
We have to find the theorem which justifies that the lines m and n are parallel when cut by a transversal k.
Parallel lines are those lines which do not meet each other at any point on the surface.
If we know that the alternte interior angles are equal,then m and n become parallel to each other.
So the converse of the alternate interior angles theorem correctly justifies that the lines are parallel if cut by a transversal k.
Hence to justify that two lines are parallel if they are cut by a transversal k, we have to use converse of the alternate interior angles theorem.
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Question is incomplete as it should include the following options:
1) converse of the corresponding angles theorem,
2) converse of the alternate interior angles theorem.
3) converse of the same side interior angles theorem,
4) converse of the alternate exterior angles theorem.
Which two factors are needed to calculate the velocity of an object?
A. Speed
B. Direction
C. Mass
D. Acceleration
A binomial has two terms.
O True
O False
Answer: True.
Step-by-step explanation:
The prefix "bi-" shows that there are two terms in a binomial expression. Therefore, this statement is True.
I hope this helps! :)
Answer:
A. True.
Step-by-step explanation:
A binomial has two terms.
Think of it this way. Any object's name that starts with 'bi' has two of something. For example, a bicycle, bicycles have 2 wheels.
Hope this helps!
I really need help with this question. I have attached two screenshots, the first is the question and the second one is the options that I have as the answer. I would really appreciate an answer!!!
Using proportions, it is found that the coordinates of point B are given as follows:
A. (1.6, 0).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Point B is 3/4 of the way from AB to AC, hence:
[tex]B - A = \frac{3}{4}(C - A)[/tex]
The points are:
A(-2,-3).B(x,y).C(3,1).
Then, to find the x-coordinate:
[tex]x + 2 = \frac{3}{4}(3 + 2)[/tex]
x + 2 = 3.6.
x = 1.6.
For the y-coordinate:
[tex]y + 3 = \frac{3}{4}(1 + 3)[/tex]
y + 3 = 3
y = 0.
Hence option A is correct.
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15. Juan has a fair six-sided die, if Juan rolls the die
twice in a row, what is the probability that the die
will show a 3 both times?
Answer:
1/36
Step-by-step explanation:
The probability for showing a three the first time is 1/6, and then again is another 1/6, multiply and you get 1/36
What is the range of possible sizes for side x?
The range of the values are 8.3<x< 8.38
How to determine the range of valuesThe given figure is an isosceles triangle, with none of its side equal.
Using the Pythagorean theorem, we have
[tex] {x}^{2} = \sqrt{ {8}^{2} } + \sqrt{ {2.5}^{2} } [/tex]
[tex] x = \sqrt{70.25} [/tex]
[tex]x = 8.38[/tex]
Thus, the range of the values are 8.3<x< 8.38
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A motorcycle's wheel has 30 spokes on it. what is the angle between each of the spokes?
Answer:
The circle is a round shape that has a total angle of 360 degrees. If a circle is divided into 6 equal parts, the measure of the angles between spokes is 12 degrees.
Step-by-step explanation:
to find the angle
360/30=12
the angle is 12 degrees
I hope this helps and have a good day!
Annette the shoe salesperson has two job offers. The Comfort over Style Shoe Emporium has offered her a $52,000 salary plus $3.25 for every pair of shoes she sells. The Heels for Fashion Slaves Boutique has offered a $37,000 salary plus $4.75 for every pair of shoes she sells. Over what range of shoe sales will Annette make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job?
Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:
C(x) = 52000 + 3.25xH(x) = 37000 + 4.75xHe will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:
C(x) > H(x)
52000 + 3.25x > 37000 + 4.75x
1.5x < 15000
x < 15000/1.5
x < 10000
The range is x < 10000.
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The sides of a triangle are 3 1 2 cm , 4 2 5 cm and 5 1 4 cm respectively. what is its perimeter?
Answer:
1251 cm
Step-by-step explanation:
Perimeter is just adding the side lengths together.