The value of n(AxB) is mathematically given as
n(A x B) = 18
What is the magnitude of the sample?Generally, It is possible to extend the formula for calculating the magnitude of a vector to any number of dimensions. For instance, the magnitude of a four-dimensional vector denoted by
a=(a1,a2,a3,a4) may be calculated using the following formula: a=a21+a22+a23+a24.
The question "how much of a quantity" is what's meant to be answered when one asks about magnitude.
For instance, the magnitude may be used to provide an explanation for why the speeds of a vehicle and a bicycle cannot be compared directly to one another. It is also possible to use it to describe the distance traveled by an item or the quantity of an object in terms of its magnitude. Both of these applications need the usage of magnitude.
n(A x B) = |A| x |B|
= 6 x 3
n(A x B) = 18
Where
|A| is the number of elements in set A (in this case, 6) and |B| is the number of elements in set B (in this case, 3).The product of these two values is the total number of ordered pairs that can be formed from the elements of A and B, which is 18.
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NO LINKS!!
Use a diagram at right to answer the following questions. Parts a-f only
Part (a)
You are correct.Line p can be named as "line RV" or "line AV" since these points are on line p. The order of the lettering doesn't matter.
==============================================
Part (b)
Pick any three non-collinear points in plane W. In other words, we pick three points in the plane that do not fall on the same line.
The following points are located in this plane: S, R, Q, T, Z
Here are some possible names:
Plane STRPlane SZQPlane QTZSomething like "Plane SRQ" isn't valid since those three points are on the same line. Infinitely many planes pass through these three points.
The ordering of the letters doesn't matter. For instance, "plane STR" is the same as "plane RTS".
==============================================
Part (c)
You are correct.As mentioned in part (b) earlier, these points fall on the same straight line. Hence they are considered collinear.
==============================================
Part (d)
Pick any four points that reside in plane W.
You have this list to choose from: S, R, Q, T, Z
Let's say we pick the first four to write S, R, Q, T as the answer
These points are coplanar because they reside in the same plane. The non-coplanar points are A and V since they are outside the plane W.
==============================================
Part (e)
Technically there aren't any line segments shown. Instead the diagram shows lines. But we can focus on a subset of a particular line to form a segment.
For instance, line p has points A and V on it. Therefore we can form segment AV
The symbolic notation for this would be to write [tex]\overline{\text{AV}}[/tex]
==============================================
Part (f)
Answer: Ray RA and Ray RVReason:
A line is composed of opposite rays. For instance, a vertical line consists of a ray pointing north and a ray pointing south. The two rays are glued together at the endpoints.
For line p, we can glue together ray RA and ray RV to form this line. Unlike the other naming conventions, the order does matter. Something like "ray RV" is not the same as "ray VR". The first letter tells us the endpoint that doesn't go on forever.
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A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.
P(3 whites)
A: 6/43
B: 2/39
C: 5/41
D: 1/36
Answer:1/30 is the correct answer
Step-by-step explanation:
first, calculate the total number of chips: 4+5+1=10
since we know that chips are not replaced.
probability of finding the first white chip: 4/10 (4 white chips,10 total)
after removing 1 white chip remaining white chips=3, total chips=9
probability of finding the second white chip:3/9 (3 white chips,9 total)
after removing 1 white chip remaining white chips=2, total chips=8
probability of finding the third white chip 2/8 (2 white chips,8 total)
after removing 1 white chip remaining white chips=1, total chips=7
Now the probability of finding 3 white chips is:
probability=(4/10) * (3/9) * (2/8)=1/30
A train was scheduled to reach the Mumbai Central railway station
1435 hours. It reached the station at 8:15 pm. How late was the train
Answer:
5 hours and 40 minutes late
Step-by-step explanation:
I am assuming by 1435 hours you meant 14:35 -- 2:35 pm.
Hence you subtract 8:15 by 2:35 as the two times you're subtracting should always be the same time format (12 or 24-hour) which is 12 hours in this case.
08:15
- 02:35
Since the minutes of the time above (:15) is higher than 35, we need to add 60 to 15 minutes and at the same time, reduce 8 hours by 1 hour to 7 hours since we are adding 60 minutes (1 hour) to :15:
07:75 (15+60)
- 02:35
and answer will be 5 hours and 40 minutes
Seats for Sale
State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?
Answer:
a. To determine how many seats should be reserved for premium ticket holders, Frank can use revenue management techniques. One common method is to use the expected revenue per seat, which is calculated by multiplying the number of seats by the expected price per seat and then multiplying that by the probability of that number of seats being sold. Frank can then compare the expected revenues for different numbers of premium seats and choose the number of seats that maximizes the expected revenue.
b. If the number of premium seats is 1,000, then the expected revenue is:
(1,000 x $200 x 0.10) + (75,000 - 1,000) x $40 x 1 = $200,000 + $3,000,000 = $3,200,000
If the number of premium seats is 5,000, then the expected revenue is:
(5,000 x $200 x 0.30) + (75,000 - 5,000) x $40 x 0.7 = $3,000,000 + $2,330,000 = $5,330,000
If the number of premium seats is 10,000, then the expected revenue is:
(10,000 x $200 x 0.24) + (75,000 - 10,000) x $40 x 0.76 = $4,800,000 + $3,768,000 = $8,568,000
and so on for the rest of the numbers.
From the above calculations, we see that the expected revenue is maximized at 10,000 premium seats, which is expected to generate $8,568,000.
c. Using the expected value of the number of premium seats would be calculated by multiplying the number of seats by its probability. The expected value of the number of premium seats is:
1,000 x 0.10 + 5,000 x 0.30 + 10,000 x 0.24 + 15,000 x 0.15 + 20,000 x 0.10 + 25,000 x 0.06 + 30,000 x 0.05 = 10,000.
Comparing this with the number of seats obtained by maximizing the expected revenue (10,000), we see that both approaches yield the same number of premium seats. This means that both approaches would yield the same potential revenue.
A rainstorm in Portland, Oregon, has wiped out the electricity in about 10% of the households in the city. A management team in Portland has a big meeting tomorrow, and all 6 members of the team are hard at work in their separate households, preparing their presentations. What is the probability that none of them has lost electricity in his/her household? Assume that their locations are spread out so that loss of electricity is independent among their households.
Answer:
The probability that a given household has lost electricity is 10%, or 0.1. So the probability that a given household has not lost electricity is 1 - 0.1 = 0.9.
Since the loss of electricity is independent among the households of the management team, we can find the probability that none of them has lost electricity by multiplying the probability of no loss in any one household (0.9) by itself 6 times, since there are 6 members of the team:
0.9 * 0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.54
So the probability that none of the management team members has lost electricity in his or her household is 54%.
How many square feet of outdoor carpet will we need for this hole?
Answer:30
Step-by-step explanation:2*5 + 2*4 + 2*2 + 2*4
=10+8+8+4
=30
Write the equation of the line in fully simplified slope-intercept form.
-12-11-10-9-8-7-6-5
-3-2
12
n1098 65432
11
-2
-9
-10
-12
2 3 4 5 6 7 8 9 10 11 12
The equation of the line in slope intercept form is y = - 1 / 2 x - 8.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptLet's find the slope of the line before we can find the equation of the line.
The slope is the change in the dependent variable with respect to the change in the independent variable.
Hence,
m = y₂ - y₁ / x₂ - x₁
Therefore,
(0, -8)(-2, -7)
Hence,
slope = m = -7 + 8 / -2 - 0
m = 1 / -2
m = - 1 / 2
The y-intercept is -8.
Therefore, the equation of the line is y = - 1 / 2 x - 8.
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which function decays the fastest
100(.2661)^t
or
100(.1593)^t
The second function 100(.1593)^t decays faster than the first function 100(.2661)^t.
How to determine the function that decay fastestTo find which function decays the fastest, we need to compare the decay rates of the two functions.
The decay rate of a function is determined by the exponent in the function. In this case, the exponent is t.
The smaller the exponent, the faster the decay rate.
So, in the first function 100(.2661)^t, the exponent is t.
In the second function 100(.1593)^t, the exponent is also t.
We can compare the decay rates of the two functions by comparing the values of the bases, .2661 and .1593.
The base of a function represents the rate of decay, the smaller the base the faster the decay rate.
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Find the area of the triangle shown to the
nearest tenth of a square inch.
Note: This isn't a right triangle!
14 in.
6.5 in.
32°
The area of the Triangle is 24.11 inch².
What is area of Triangle?The area of any triangle can be calculated using the lengths of two of its sides and the sine of their included angle.
The trigonometric formula for the area of triangles is
area sin C= 1/2 , where and are the lengths of two sides and is the measure of the included angle.
Given:
a= 14 inch
b= 6.5 inch
and, angle = 32 degree
Now, The area of Triangle
= ab sin [tex]\theta[/tex] /2
= 14 x 6.5 x sin 32 /2
= 7x 6.5 x sin 32
= 7 x 6.5 x 0.5299
= 24.11 inch²
hence, the area is 24.11 inch²
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19. The speed, s, in feet per second, of an object dropped from a
height, h, in feet, is given by the formula s (h) = √64h. Evaluate
the function for heights of 0 feet to 25 feet by calculating points
every 5 feet.
The plotted graph is shown below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
s (h) = √64h
now, when h=0
s(0) = √64h = 0
and, when h= 5
s(5) = √64h
= √64 x 5
= 8 x 2.25
= 17.88
and, when h= 10
s(25) = √64h
= √64 x 10
= 8 x 3.162
= 25.29
and, when h= 15
s(25) = √64h
= √64 x 15
= 30.98
and, when h= 20
s(25) = √64h
= √64 x 20
= 35.77
and, when h= 25
s(25) = √64h
= √64 x 25
= 8 x 5
= 40
The plotted graph is shown below.
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Tell whether b = 12 is a solution of b - 7 = 5
Answer:
Yeah, [tex] \sf b = 12 [/tex]
Step-by-step explanation:
Given equation,
→ b - 7 = 5
Now the value of b will be,
→ b - 7 = 5
→ b = 7 + 5
→ [ b = 12 ]
Hence, the value of b is 12.
Answer: Yes
Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.
Try solving 12-7. It is 5.
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Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis.
y=x2, y=5−4x, x=0 for x≥0
The volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis is 8.90 unit³.
How do you find the volume of a solid?Since the region is the one for then the intersection we are interested on is x=1 as it can also be seen in the graph.
Where h(x) is the height of the shell which here is the distance between the parabola and the line, so (since the line is on the top we subtract from it the parabola
Notice the limits of the integral are the x-axis (x=0) and the intersection of the parabola and the line that we found before (x=1)
We want the volume generated when the area bounded by the curves :
v = x2 v = 8 —7x , and
x = 0 for x > 0 is revolved about the y axis using the cylindrical shell method .
The intersection of y = x2 and y = 8 —7x is :
y= x2 = 8 — 7x x2 + 7x —8 = 0
(x + 8)(x — 1) = 0 x = —8 or
x = 1 .
We thus have for x > 0 the two curves intersect at x = 1 and y = 12 = 1 .
The limits for integration are --- 0 <x < 1 .
The upper curve is --- y2 = 8 —7x ,
and the lower curve is --- yi = x2 .
The height of the shell is --- h = y2 -yi = 8 —7x — x2 •
The radius of the shell is --- R = x •
[tex]$$The surface area of the shell is :$$A=2 \pi \mathrm{Rh}=2 \pi x\left(8-7 x-x^2\right)=2 \pi\left(8 x-7 x^2-x^3\right) .$$The differential of volume which is the cylindrical shell is :$$\mathrm{dv}=\mathrm{Adx}=2 \pi\left(8 x-7 x^2-x^3\right) \mathrm{dx}$$[/tex]
[tex]$$We then have the volume of revolution is :$$\begin{aligned}v & =2 \pi \int_0^1\left(8 x-7 x^2-x^3\right) \mathrm{d} x \\& =2 \pi\left(4 x^2-\frac{7}{3} x^3-\frac{1}{4} x^4\right)_0^1 \\& =2 \pi\left[4\left(1^2-0^2\right)-\frac{7}{3}\left(1^3-0^3\right)-\frac{1}{4}\left(1^4-0^4\right)\right] \\& =2 \pi\left(4-\frac{7}{3}-\frac{1}{4}\right) \\& =2 \pi\left(\frac{48-28-3}{12}\right) \\& =2 \pi\left(\frac{17}{12}\right) ; \text { or, we have : } \\v & =\frac{17 \pi}{6} .\end{aligned}$$[/tex]
17π/6 = 8.90 unit³
Thus, The volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis is 8.90 unit³.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2 Mark this and return
The following equations which are equivalent are:
2 + x = 5 x + 1 = 4 Negative 5 + x = negative 2How to determine equivalent equation?2 + x = 5
collect like terms
x = 5 - 2
x = 3
x + 1 = 4
Subtract 1 from both sides
x = 4 - 1
x = 3
9 + x = 6
Subtract 9 from both sides
x = 6 - 9
x = -3
x + (negative 4) = 7
x +(-4) = 7
Open parenthesis
x - 4 = 7
x = 7 + 4
x = 11
Negative 5 + x = negative 2
-5 + x = - 2
x = -2 + 5
x = 3
Therefore, 2 + x = 5; x + 1 = 4; Negative 5 + x = negative 2 are equivalent to each other.
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Tom makes 298.50 $ in 6 days. How much does he make in 3 days?
Answer:
in 3 days Tom made $149.25
Step-by-step explanation:
If Tom made 298.50 in 6 days, you can find the amount made in 3 days by dividing that number in half.
298.5 / 2 = 149.25
Use what you know about zeros of a function and end behavior of a graph to choose the graph that matches the function f(x) = (x − 2)(x − 1)(x − 4). The graph starts at the top left, continues down through the x axis at 1 to a minimum around y equals negative one half, goes back up through the x axis at 2 to a maximum around y equals 2, and goes back down through the x axis at negative 4. The graph starts at the bottom left, continues up through the x axis at negative 4 to a maximum at y equals 2, goes back down through the x axis at negative 2 to a minimum around y equals one half, and goes back up through the x axis at negative 1. The graph starts at the top left, continues down through the x axis at negative 4 to a minimum around y equals negative 2, goes back up through the x axis at negative 2 to a maximum around y equals one half, and goes back down through the x axis at negative 1. The graph starts at the bottom left, continues up through the x axis at 1 to a maximum around y equals one half, goes back down through the x axis at 2 to a minimum at y equals negative 2, and goes back up through the x axis at 4.
The correct statement regarding the graph of the function f(x) = (x - 2)(x - 1)(x - 4) is given as follows:
The graph starts at the bottom left, continues up through the x axis at 1 to a maximum around y equals one half, goes back down through the x axis at 2 to a minimum at y equals negative 2, and goes back up through the x axis at 4.
How to obtain the graph of the function?The function is defined as follows:
f(x) = (x - 2)(x - 1)(x - 4).
Considering the linear factors of the function, the values of x through which the function intercepts the x-axis are given as follows:
x - 2 = 0 -> x = 2.x - 1 = 0 -> x = 1.x - 4 = 0 -> x = 4.The end behavior of a function is given by the limit of the function is the input x goes to either negative infinity or positive infinity.
As the function has three zeros with multiplicity one, it is a cube function, hence:
The graph starts at the bottom left, when x -> -∞, as (-∞)³ = -∞.The graph ends at the top right, when x -> ∞, as (∞)³ = ∞.More can be learned about the end behavior of a function at brainly.com/question/1365136
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find the present value of 2400 due in 4months at 4.5% simple interest
Answer:
Step-by-step explanation:
Interest per annum - 4.5
Interest per 1/3 of an annum - 4.5 x 1/3 = 1.5%
Use the S.I formula,
2400 x (100 + interest)/100
= 2400 x (100 + 1.5)/100
= 24 x 101.5
= 12 x 203
= 2436.
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Factorise the following
a. x square - 16
b. 8m square - 50n square.
Answer:
(i) (x+4)(x-4)
Step-by-step explanation:
(ii)64m² - 800mn +2500n²
Please help thank you!
HELP
IMMAGE ATTACHED
Answer:
[tex]\frac{y-7}{y+8}[/tex]
y cannot equal -8
Step-by-step explanation:
[tex]\frac{(y-7)(y-5)}{(y+8)(y-5)}[/tex] y-5 cancel out
[tex]\frac{y-7}{y+8}[/tex]
Question 2
For this problem, let's assume the Earth is a perfect sphere of radius 6371 km. Calculate the
volume of the Earth in cubic kilometers (km³). Which of these comes closest to your answer?
Hint: the volume of a sphere is given by (4/3) π R³, where R is the radius. If you specify the radius
in km, the volume will come out in km³. You can use the approximate value π = 3.14.
A 6371
B 27,000
C 170 million
D 1 trilion
Volume of earth in shape of a sphere is 1 Trillion km^3 i.e. D.
What is a sphere?
A sphere is a three-dimensional object that is round in shape. The sphere is defined in three axes, i.e., x-axis, y-axis and z-axis. This is the main difference between circle and sphere. A sphere does not have any edges or vertices, like other 3D shapes.
The points on the surface of the sphere are equidistant from the center. Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere. Examples of spheres are a ball, a globe, the planets, etc.
Volume of sphere=4/3πr^3. where r=radius.
Surface area=4πr^2.
Now,
Given radius for earth=6371 km
so, Volume of earth=4/3*3.14*6371^3≈1Trillion km^3.
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Please please look at the picture and answer the question thank you so much
Answer:
t = I/(Pr)
Step-by-step explanation:
We divide P*r on both sides to isolate t and we get t=I/(P*r)
Add one-fourth of two subtracted from thrice a number to twice the same number.
The expression in the mathematical form will be (1/4)( 2 - 3x ) / ( 2x ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The word form of the expression is given as adding one-fourth of two subtracted from thrice a number to twice the same number.
The expression can be written as,
E = (1/4)( 2 - 3x ) / ( 2x ).
Hence, the expression will be (1/4)( 2 - 3x ) / ( 2x ).
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Help with question please
Answer:
b.
Step-by-step explanation:
the result is created :
first result row first result element =
= first A row × first B column
first result row second result element =
= first A row × second B column
...
third result row second result element =
= third A row × second B column
third result row third result element =
= third A row × third B column
the multiplication of a row and a column is done by :
left row element × top column element +
middle row element × middle column element +
right row element × bottom column element
AB =
-4×3 + -3×-5 + 5×-1 -4×-4 + -3×-5 + 5×-3 -4×-1 + -3×1 + 5×2
-5×3 + -4×-5 + -2×-1 -5×-4 + -4×-5 + -2×-3 -5×-1 + -4×1 + -2×2
-1×3 + -2×-5 + -4×-1 -1×-4 + -2×-5 + -4×-3 -1×-1 + -2×1 + -4×2
=
-2 16 11
7 46 -3
11 26 -9
so, b is correct.
How much is 9.6 KB kilobytes
9.6 KB kilobytes is equal to 0.0096 MB
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
1kB=1000 bytes
1MB=1000 KB
1kB=1/1000MB=0.001 MB
9.6 KB is nothing but 9600 bytes
9.6 KB in MB we have to convert
Now multiply 9.6 with 0.001
9.6×0.001
0.0096 MB
Hence, 9.6 KB kilobytes is equal to 0.0096 MB
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Answer both questions please
The number of tiles in figure 70 and figure 93 are 142 and 188.
How many tiles are in figure 70?Figure 2 = 6
Figure 3 = 8
The common difference = 8 - 6
= 2
figure 2 = a + (n - 1)d
Where,
a = first term
figure 2 = a + (n - 1)d
6 = a + (2 - 1)2
6 = a + (1)2
6 = a + 2
6 - 2 = a
a = 4
Figure 70 = a + (n -1)d
= 4 + (70-1)2
= 4 + (69)2
= 4 + 138
Figure 70 = 142
Figure 93 = a + (n -1)d
= 4 + (93 - 1)2
= 4 + (92)2
= 4 + 184
Figure 93 = 188
Therefore, figure 70 and 93 have 142 and 188 tiles respectively.
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Please help me with this question!
Measure of ∠CEA = 91°
What is arc?The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle.
Given,
In figure
chord AB and chord CD intersect at E
m(arc CA) = 140°
m(arc DB) = 42°
∠CEA intercepts arc CA and has it vertex inside the circle
Thus,
∠CEA = (m(arc CA) + m(arc DB))/2
∠CEA = (140° + 42°)/2
∠CEA = 182°/2
∠CEA = 91°
∠CEA measures 91°
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happy paws charges 21.00 plus 3.50 per hour to keep a dog during the day. Woof watchers charges 10.00 plus 4.75 per hour. Complete the equation and solve it to find for how many hours the total cost of services is equal. Use the variable h to represent the number of hours
Answer: 8.8 hours
Step-by-step explanation:
To start off, we’ll make an equation that “connects” both companies:
10 + 4.75h = 21 + 3.5h (we put h to represent the number of hours)
Move all similar terms to one side:
4.75h - 3.5h = 21 - 10
Simplify:
1.25h = 11
h = 8.8
I hope this helps!
Find the perimeter of triangle ABC. Round your answer to two decimal places.
(9,-2) (5,1) (9,-3)
Answer: To find the perimeter of a triangle, we need to add the length of all three sides of the triangle.
To find the length of each side, we can use the distance formula which is the square root of (x2-x1)^2 + (y2-y1)^2.
The distance between point A (9,-2) and point B (5,1) is: √((9-5)^2 + (-2-1)^2) = √16 + 9 = √25 = 5.
The distance between point B (5,1) and point C (9,-3) is: √((9-5)^2 + (-3-1)^2) = √16 + 16 = √32 = 5.66.
The distance between point C (9,-3) and point A (9,-2) is: √((9-9)^2 + (-3- -2)^2) = √1 + 1 = √2 = 1.41
The perimeter is the sum of the length of all three sides:
Perimeter = 5 + 5.66 + 1.41 = 12.07
Round the answer to two decimal places, the perimeter of the triangle is 12.07.
Step-by-step explanation:
Find the equation of a line in slope-intercept form if the slope is 0
and the point is (-3, -2). Is this line vertical or horizontal?
HINT: You can find the equation of the line in slope-intercept form by:
1. Use point-slope form, then solve for y.
OR
2. Use y=mx+b: Plug in your point and your slope to find b; then write in
slope-intercept form.
So, The line is a horizontal one, and the equation is y = -2 of a line in slope-intercept form if the slope is 0 and the point is (-3, -2).
Define slope.In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
Define line's steepness and direction.Positive slope lines lean to the right, and they become steeper as the slope increases. A line with a negative slope slopes left, and the slope's magnitude determines how steep the line is. Since there is no slope on a horizontal line, it has a slope of zero.
The slope of the line is 0, which means the line is horizontal.
The point-slope form of the equation of a line is: y - y1 = m(x - x1)
With the point (-3, -2) and the slope of 0, we have:
y - (-2) = 0(x - (-3))
y = -2
The slope-intercept form of the equation of a line is: y = mx + b
The y-intercept of the line is -2, so the equation of the line in slope-intercept form is: y = 0x + (-2)
The line is a horizontal one and it's equation is y = -2
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By selling a stool for Rs. 67.50, a carpenter loses 10 %. How much percent would he gain by selling it for Rs 82.50?
Answer:
Rs. 7.50
or a gain of 10%
Step-by-step explanation:
Let x be the price of the stool
10% = 10/100 = 0.10
Loss = 0.1x
Selling price at 10% loss = x - 0.1x = 0.x
We are given this sale price is 67.50
So
0.9x = 67.50
x = 67.50/0.9 = 75
If he sells it at 82.50, the profit would be 82.50 - 75 = 7.5
This would represent a gain of 7.5/75 x 100 percent
= 10%
Answer:
The carpenter would gain 10% profit.
Step-by-step explanation:
67.5 is 90% of 75.
82.50 is 110% of 75.
