a. 3 students read comics and novel only.
b. 1 student read textbook and novel only.
c. 31 students read none of the three categories.
Here's a Venn diagram that shows the information given:
_________
/ \
/ \
/ \
/ \
/ A \
/ \
/__________\
| | |
| | |
| C | B |
| | |
|__________|__________|
\ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
|
|
|
D
The three circles represent the three categories: novel, comics, and textbook.
The overlap between the circles represents the number of students who read more than one category.
The letters A, B, C, and D represent the following regions:
A: Only comics and novel (not textbook)
B: Only textbook and novel (not comics)
C: Only textbook and comics (not novel)
D: All three categories
To answer the questions:
a. To find the number of students who read comics and novel only (region A), we need to add up the number of students who read both comics and novel (5) and subtract from it the number of students who also read textbook (2).
So, the number of students who read comics and novel only is 5 - 2 = 3.
b. To find the number of students who read textbook and novel only (region B), we follow the same process.
We add up the number of students who read both textbook and novel (3) and subtract from it the number of students who also read comics (2).
So, the number of students who read textbook and novel only is 3 - 2 = 1.
c. To find the number of students who read none of the three categories, we start with the total number of students (50) and subtract from it the number of students who read at least one category.
To find the latter number, we add up the number of students who read only novel (3), only comics (9), only textbook (2), and all three (5), which gives us 19. So, the number of students who read none of the three categories is 50 - 19 = 31.
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4.) What is the area of the sector with a central angle of 60° and a radius of 2m?
Round your answer to the nearest tenth or leave in terms of .
area =
A
2 60
B
2/3
m²
Work:
The "area" of sector which is having "central-angle" of 60° and the radius of 2m is 2.094 m².
The "Sector" of circle is defined as region bounded by "two-radii" of circle and arc intercepted between them. The two radii that bound the sector are called the "sides" of the sector.
The center of the circle is called as vertex of the sector. The area of a sector can be found using the formula : A = (θ/360)πr², where θ is = angle of sector;
The measure of "central-angle" is = 60°, and radius of circle is = 2m,
So, Area is = (60/360)π(2)²,
⇒ Area is = 4π/6 ≈ 2.094 m²,
Therefore, area of sector is 2.094 m².
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The given question is incomplete, the complete question is
What is the area of the sector with a central angle of 60° and a radius of 2m?
The circumference of a circle is 20 � π cm. Find its radius, in centimeters.
The required radius of the circle is 10 cm.
The formula for the circumference C of a circle in terms of its radius r is given by:
C = 2πr
We are given that the circumference of the circle is 20π cm. So we can set this expression equal to 20π and solve for r:
20π = 2πr
Dividing both sides by 2π, we get:
r = 10
Therefore, the radius of the circle is 10 cm.
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For the following vectors, (a) find the dot product v•w ; (b) find the angle between v and w , (c) state whether the vectors are parallel, octagonal, or neither. V=-3i-4j, w=6i+8j
A- v•w
B-the angle between v and w is theta ^•?
C- the vectors v and w are?
an experienced bungee jumper leaps from a tall bridge and falls towards the water. The bridge is 241 feet above the water and the bungee cord is 149 feet long unstretched. When will the cord begin to strech? The gravity formula is as follows: h(t)= -16t + [tex]v_{0}[/tex]t + [tex]h_{0}[/tex]
The cord will begin to stretch after approximately 1.46 seconds.
How to solve for when the stretch startsh(t) = -16t^2 + V0t + h0
149 = h0 - h(t)
Substituting h0 = 241 and h(t) = -16t^2 + V0t into this equation, we get:
149 = 241 - (-16t^2 + V0t)
we get:
16t^2 - V0t - 92 = 0
4(16)(-92) / (2(16)
t = sqrt(1856) / 32
Using a calculator, we get:
t ≈ 1.46 seconds
Therefore, the cord will begin to stretch after approximately 1.46 seconds.
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According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6
Let x represent the months and y represent the average maximum monthly temperature.
Plot the data on a scatterplot. Choose the plot that best represents the data.
a.
On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6).
b.
On a coordinate plane, points are around (5, 85), (6, 90), (7, 80), (8, 70), (9, 60), (10, 50), (48, 1), (50, 3), (62, 4), (66, 4), (76, 5), (82, 8).
c.
On a coordinate plane, points are around (0, 49), (1, 52), (2, 62), (3, 68), (4, 78), (5, 85), (50, 12), (60, 10), (70, 10), (80, 9), (88, 8), (87, 9), (89, 9).
d.
On a coordinate plane, points are around (0, 48), (2, 52), (13, 50).
Please select the best answer from the choices provided
a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6) best represents the data.
This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.
Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.
Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.
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Given a triangle with coordinates X(2, -1), Y(-5, -4), and Z (-2, 3), what type of triangle is it?
Answer:
Step-by-step explanation:
Distance between 2Points XY=Distance between 2 points YZ=7.615
Distance between 2 points ZX=5.6568
Hence it is an isosceles triangle
Today, you want to sell a R1 000 par value zero coupon bond you own. The bond matures in five years. How much will you receive for your bond, if the market yield to maturity is currently 5,33%? 10
With a market yield to maturity of 5.33%, the amount that would be received for a R 1,000 par value zero coupon bond that matures in five years, but sold today will be R747.26.
Price calculation for coupon bondsTo calculate the price you will receive for your zero coupon bond, we can use the formula:
P = F / (1 + r)^n
where:
P is the priceF is the par value (face value) of the bondr is the yield to maturity as a decimaln is the number of years to maturity.In this case, the par value is R1,000, the yield to maturity is 5.33%, or 0.0533 as a decimal, and the number of years to maturity is 5.
P = 1000 / (1 + 0.0533)^5P ≈ R747.26Therefore, you can expect to receive approximately R747.26 for your R1,000 par value zero coupon bond when the market yield to maturity is 5.33%.
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Which expression is equivalent to 3w-4-w-93w−4−w−9?
A 2w-13
b 4w - 13
c 2w + 5
d -w - 13
Answer: A
Step-by-step explanation:
To simplify 3w-4-w-9, we need to combine the like terms (terms that have the same variable and exponent).
3w - w = 2w
-4 - (-9) = -4 + 9 = 5
So,
3w - 4 - w - 9 = 2w - 13
Therefore, the expression 3w-4-w-9 is equivalent to 2w-13, which is option A.
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for for the value of the home. The model will have the form V(t) = V0e^kt. Let t be years since 2011 and V (t) be the value of the home.
a. The home's value is increasing at a rate of approximately 1.55% per year.
b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex]
c. The predicted value of the home in 2022 is approximately $123,240.
d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
To find the growth rate k, we can use the formula [tex]V(t) = V0e^{(kt)}[/tex]. We have two data points: V(0) = 95000 and V(7) = 105000 (since 2018 is 7 years after 2011). Inputting these values into the formula yields:
V(0) =[tex]V0e^{(0k)}[/tex] = V0
V(7) = [tex]V0e^{(7k)}[/tex]= 105000
When the second equation is divided by the first, the result is:
V(7)/V(0) = [tex]e^{(7k)}[/tex] = 105000/95000 = 1.1053
Taking the natural logarithm of both sides and calculating k yields:
ln(1.1053) = 7k
k ≈ 0.0155
This means that the home's value is increasing at a rate of approximately 1.55% per year.
b. The exponential model is V(t) = [tex]95000e^{(0.0155t)}[/tex].
c. The predicted value of the home in 2022 is approximately $123,240.
To predict the home's value in 2022, we need to find the value of V(t) when t = 11 (since 2022 is 11 years after 2011). Substituting into the exponential model gives:
V(11) = [tex]95000e^{(0.0155*11)}[/tex] ≈ $123,239.62
So the predicted value of the home in 2022 is approximately $123,240.
d. The home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
We need to solve for t in equation V(t) = 130,000.
130,000 = [tex]95,000e^{(0.0155t)}[/tex]
Dividing both sides by 95,000 and taking the natural logarithm of both sides, we get:
ln(130,000/95,000) = 0.0155t
Simplifying, we get:
t = (ln(130,000/95,000))/0.0155
t = (ln(1.368)/0.0155
t = 0.313 / 0.0155
t ≈ 20.23
Therefore, the home's value reached $130,000 approximately 20 years after 2011, which is in the year 2031.
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Complete question:
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form V(t) = V0e^(kt) . Let t be years since 2011 and v (t) be the value of the home.
a. What is the growth rate k for the model? What does that number mean?
b. What is the exponential model?
c. Predict the value of the home in 2022.
d. During what year did the value of the home reach $130,000?
ABC~ DEF. What sequence of transformations will move ABC onto DEF?
A. A dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
B. A dilation by a scale factor of 1/2, centered at the origin, followed by the translation (x,y)-> (x+7,y)
C. The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin.
D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x,y)-> (x+7,y)
Note that the sequence of transformations that will move ABC onto DEF is; "The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin." *Option C)
What is transformation?A transformation is a mathematical function that repositions points in one-, two-, three-, or any other n-dimensional space.
A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.
Note that translation takes B(0,0) to B'(7, 0),
Takes A(0, 4) to A'(7, 0) and C (3, 0) to C' (10, 0)
when you multiply the new points by the scale factor of 2, you'd get the new figure when the coordinates are graphed.
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Answer:
D. Dilation by 2, translation right by 7.
Step-by-step explanation:
You want to know the sequence of transformations that maps ∆ABC to ∆DEF.
Scale factorSegment DE is 8 units long, and located at x=7. Segment AB is 4 units long and located at x=0.
The scale factor is the ratio of segment lengths:
DE/AB = 8/4 = 2
Triangle DEF is dilated by a factor of 2 (eliminates B).
TranslationTriangle DEF is oriented the same way as triangle ABC, so there is no reflection involved (eliminates A). As we noted, segment DE is 7 units to the right of segment AB, so a translation of x ⇒ x+7 is involved.
SequenceThe translation must occur after the dilation about the origin (eliminates C). If it were to occur first, the translation would be multiplied by the scale factor, so that DE would end up at x=14.
The required sequence of transformations is ...
D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) ⇒ (x+7, y).
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3.) Given the regular polygon. Find the measure of each numbered angle.
m<1 = 30
m<2 = 15
m<3 =
75
Work/expanation:
The b. m<angle1 = 45°,
mangle2 = 67.5°
How to solveAn octagon has 8 sides.
Sum of interior angles = 180° x (n-2) = 180° x (8-2) = 180° x 6 = 1,080°
1,080° ÷ 8 sides = 135° interior angle.
Angle 2 = 135° / 2 = 67.50°
Angle 1 = 180° - 135° = 45°
If these were the choices given:
a. mangle1 = 45°, mangle2 = 135°
b. mangle1 = 45°, mangle2 = 67.5° ⇔ THIS IS THE CORRECT ANSWER.
c. mangle1 = mangle2 = 60°
d. mangle1 = 22.5°, mangle2 = 78.75°
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Write an explicit formula for an, the nth term of the sequence 25,30,35,....
Answer:
[tex]a_{n}[/tex] = 5n + 20
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
30 - 25 = 35 - 30 = 5
this indicates the sequence is arithmetic with explicit formula
[tex]a_{n}[/tex] = a₁ + d(n - 1)
where a₁ is the first term and d the common difference
here a₁ = 25 and d = 5 , then
[tex]a_{n}[/tex] = 25 + 5(n - 1) = 25 + 5n - 5 = 5n + 20
1.6 Solve the following equation using
7x-8y+5z=5
-4x+5y-3z=-3
x-y+z = 0
a. Crammer's rule
b. Inverse Method
[10]
[10]
Answer:
Step-by-step explanation:
a. Using Cramer's Rule:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The determinant of the coefficients matrix is:scssCopy code| 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = 7(5)(1) + (-8)(-3)(1) + 5(-4)(-1) - 1(-3)(7) - 1(5)(-8) - (-1)(-3)(5) = 70To find x, we replace the x-coefficients with the constants and solve for x:scssCopy code| 5 -8 5 | | -3 5 -3 | | 0 -1 1 | x = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (5(5)(1) + (-8)(-3)(1) + 5(-3)(-1) - 1(-3)(5) - 1(5)(-8) - 0(-1)(-4))/70 = 9/14To find y, we replace the y-coefficients with the constants and solve for y:scssCopy code| 7 5 5 | | -4 -3 -3 | | 1 0 1 | y = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (7(-3)(1) + (-8)(-3)(1) + 5(0)(-1) - 1(5)(-3) - 0(-8)(-4) - 1(-1)(-4))/70 = -1/14To find z, we replace the z-coefficients with the constants and solve for z:scssCopy code| 7 -8 5 | | -4 5 -3 | | 5 -1 0 | z = | 7 -8 5 | | -4 5 -3 | | 1 -1 1 | = (7(5)(0) + (-8)(-3)(1) + 5(-1)(-1) - (-1)(5)(5) - 1(5)(-8) - 0(-1)(-4))/70 = -12/35Therefore, the solution to the system of equations is x = 9/14, y = -1/14, z = -12/35.b. Using Inverse Method:The system of equations can be written in matrix form as:Copy code| 7 -8 5 | | x | | 5 | | -4 5 -3 | x | y | = |-3 | | 1 -1 1 | | z | | 0 |The coefficients matrix is:Copy code| 7 -8 5 | | -4 5 -3 | | 1 -1 1
One kind of transformation we'll explore is a translation.
The thin gray parabola is `y=x^{2}`.
Select the graph that best shows `y=x^{2}` translated `2` units down.
The graph that best shows `y=x^2` translated `2` units down is graph d
Selecting the graph that best shows `y=x^2` translated `2` units down.From the question, we have the following parameters that can be used in our computation:
y = x^2
When the function y=x^2` is translated `2` units down, we do the following
We subtract 2 from the function equation
So, we have
y = x^2 - 2
This means that the translated function is 2 units below the function y = x^2
From the list of options, this is represented with graph (d)
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Select the correct answer. A company manufactures computers. Function N represents the number of components that a new employee can assemble per day. Function E represents the number of components that an experienced employee can assemble per day. In both functions, t represents the number of hours worked in one day. Which function describes the difference of the number of components assembled per day by the experienced and new employees? A. B. C. D. Reset Next
The function that describes the difference of the number of components assembled per day by the experienced and new employees is:
E(t) - N(t)
This is because E(t) represents the number of components assembled by an experienced employee in t hours, and N(t) represents the number of components assembled by a new employee in t hours. Therefore, the difference between the two functions will give us the difference in the number of components assembled per day by the two types of employees.
Out of the given options, option A represents the correct answer:
E(t) - N(t) = (5t) - (3t) = 2t
Therefore, the correct answer is A.
Place value of 4 in 265 473
Answer:
The place value of 4 in 265 473 is 40,000
Answer:
Step-by-step explanation:
Order:
3 is in the ones place and has a value of 3
7 is in the tens place and has a value of 70
4 is in the hundreds place and has a value of 400
5 is in the thousands place and has a value of 5000
6 is in the ten thousands place and has a value of 60,000
2 is in the hundred thousands place and has a value of 200,000
freddy drew a plan for a rectangular piece of material that he will use for a blanket. the three of the vertices are (-2, -3), (-2.3,1.6), (4.6,1.6). what are the coordinates of the fourth vortex?
The coordinates of the fourth vortex of the rectangular piece of material drawn by Freddy would be (4. 6, - 3 ).
How to find the fourth vortex ?Rectangles are quadrilaterals which have two sets of parallel lines. This means that two sets of sides are equal which are the opposite ones. This means that when plotted on a coordinate plane, of the four points, the x - values should repeat twice and the y - values should repeat twice as well.
They would do so by alternating with each other. This means that in a rectangle with (-2, -3), (- 2 . 3, 1 . 6), ( 4 . 6 , 1. 6 ), the fourth vertex would be the two x and y values that are yet to repeat which would be:
( 4. 6, - 3 ).
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Find the solution(s) of the quadratic equation x 2 squared + 2x - 15=0
Answer: -5, 3
Step-by-step explanation:
Equation:
x² + 2x -15 = 0 The equation is already set =0 so you will factor.
To factor, find 2 numbers that multiply to the last term (-15) but add up to the middle term (+2). Be careful with signs, signs matter
+5 and -3 multiply to -15 but add up to the +2 so these are your factored numbers
put it in factored form
(x+5)(x-3)=0 set each parenthesis =0 to solve for x
x+5 = 0 x-3=0
x= -5 and x=3
. In ΔABC, m < B = 14°, m < C = 42° and a = 34. Find the length of b to the nearest tenth.
i Got u Bro!
Obtuse scalene triangle.
Sides: a = 34 b = 9.922 c = 27.442
Area: T = 112.86
Perimeter: p = 71.364
Semiperimeter: s = 35.682
Angle ∠ A = α = 124° = 2.164 rad
Angle ∠ B = β = 14° = 0.244 rad
Angle ∠ C = γ = 42° = 0.733 rad
Height: ha = 6.639
Height: hb = 22.75
Height: hc = 8.225
Median: ma = 11.694
Median: mb = 30.495
Median: mc = 20.951
Inradius: r = 3.163
Circumradius: R = 20.506
Vertex coordinates: A[27.442; 0] B[0; 0] C[32.99; 8.225]
Centroid: CG[20.144; 2.742]
Coordinates of the circumscribed circle: U[13.721; 15.239]
Coordinates of the inscribed circle: I[25.76; 3.163]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 56° = 2.164 rad
∠ B' = β' = 166° = 0.244 rad
∠ C' = γ' = 138° = 0.733 rad
Find the measure of each angle indicated.
P
U
160°
W
95° ?
V
Answer:
? = 65°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PUV is an exterior angle of the triangle , then
? + 95° = 160° ( subtract 95° from both sides )
? = 65°
a. Express each of the following as a function of 15°
6. tan165°
7. sin285°
Expressing each as a function of 15°, we have 6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°
Expressing each as a functionFrom the question, we have the following trigonometry function that can be used in our computation:
6. tan165°
7. sin285°
The above expressions are tangent and sine functions of 165 and 285 degrees
By mathematical expression, we have
165° = 150 + 15
285° = 270 + 15
This means that we can replace the expressions with 150 + 15 and 270 + 15
So in terms of 15 degrees, we have
6. tan165° = tan(150 + 15)° and 7. sin285° = sin(270 + 15)°
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A software developer's current annual gross wage is $93,400. For retirement, the developer wants to have enough saved to live off 80% of the current annual gross wage and draw 4% the
first year. What is the total amount the developer will need in retirement savings to meet their retirement income goal?
O$1,868,000
O$1,688,000
O$1,088,600
O $1,068,800
Answer:
c
Step-by-step explanation:
What is the value of x?
X
30°
24
Express your answer in radical form.
Enter your answer in the box.
Answer:
x = 12
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin30° = [tex]\frac{1}{2}[/tex] , then
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{24}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 24 ( divide both sides by 2 )
x = 12
In which quadrant would an angle x lie if sinx is negative and tanx is negative?
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Step-by-step explanation:
If sin is neg AND tan is neg then cos is positive
(because tan = sin/cos)
this occurs in Q IV
Which set of data could be reasonably modeled by a quadratic function?
The quadratic function is represented by option A. both graph.
From the set of data representing in the graph ,
A quadratic function is a second-degree polynomial of the form f(x) = ax² + bx + c, where a, b, and c are constants.
It represents a parabolic curve when plotted on a graph.
Generally, a quadratic function is suitable for modeling data that shows a U-shaped or inverted U-shaped pattern.
Representation of x-axis and y-axis is not clearly specified in the graph .
We assume different conditions.
Projectile motion,
The trajectory of a ball thrown into the air or a projectile fired from a cannon can be modeled by a quadratic function.
Falling objects,
The distance a dropped object falls over time can be modeled by a quadratic function.
Profit vs. production,
The relationship between a company's profit and the level of production can be modeled by a quadratic function.
The profit generally increases with production but eventually reaches a maximum point before declining.
Trajectory of a car,
The distance traveled by a car accelerating from a stationary position can be modeled by a quadratic function.
Height vs. time,
The height of an object thrown upwards, such as a bouncing ball, can be modeled by a quadratic function.
The height increases, reaches a maximum point, and then decreases.
Here both the graphs represents the quadratic function.
Therefore, the set of the data clearly modelled the quadratic function is present by option A. Both graph.
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Write an explicit formula for an, the n^th term of the sequence
2,−8,32,....
Answer:
36
Step-by-step explanation
6x6
Help! I dont know the answe and Ive been stuck for a minute..
Dm on ig: 1.rockkyy I have more questions!
Answer:
a³ = -357911/5832.
Step-by-step explanation:
We can use the given equation to find the value of n, and then use it to find the value of a³.
a¹ = 13 and a = ⁿ⁻¹ - 4
Substituting the value of a in terms of n in the first equation, we get:
ⁿ⁻¹ - 4 = 13
ⁿ⁻¹ = 13 + 4
ⁿ⁻¹ = 17
ⁿ = 18
Now, substituting the value of n in the equation a = ⁿ⁻¹ - 4, we get:
a = 18⁻¹ - 4
a = 1/18 - 4
a = -71/18
Finally, to find a³, we can cube the value of a:
a³ = (-71/18)³
a³ = -357911/5832
Therefore, a³ = -357911/5832.
ILL GIVE 20 POINTS !!!! PLSS HELP ASAP
Answer: 10/40 or 1/4
Step-by-step explanation:
Add up all the amount of rolls, so 10+6+4+8+6+6=40
then add the probability of rolling a 3 or 6 = 10
divide that quantity out of the whole
answer is 10/40 and simplified is 1/4
hope it helps
Need Help!!!! A pre-image has coordinates J(3, -6) and K(-1, -2). The image has coordinates J'(6, 3) and K'(2, -1). Describe the clockwise rotational path of the line segment.
After considering the given data we conclude that the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
We have to evaluate the center and angle of rotation to explain the clockwise rotation of the line segment.
So in the first step, we can evaluate the midpoint of the line segment JK and the midpoint of the line segment J'K'. we can calculate the vector connecting the midpoint of JK to the midpoint of J'K'. This vector is (4-1, 1-(-4) = (3,5)
The center of rotation is the point that is equidistant from the midpoints of JK and J'K'. We can evaluate this point by finding the perpendicular bisector of the line segment connecting the midpoints.
The slope of this line is the negative reciprocal of the slope of the vector we just found, which is -3/5. We can apply the midpoint formula and the point-slope formula to evaluate the equation of the perpendicular bisector:
Midpoint of JK: (1, -4)
Midpoint of J'K': (4, 1)
The slope of the vector: 3/5
(x₁ + x₂)/2, (y₁ + y₂) /2
Point-slope formula: y - y₁ = m(x - x₁)
Perpendicular bisector: y - (-4) = (- 3/5)(x - 1)
Applying simplification , we get: y = (- 3/5)x - 1.2
To evaluate the center of rotation, we need to find the intersection point of the perpendicular bisector and the line passing through the midpoints of JK and J'K'. This line has slope ( 3 - (4)) /(4 - 1) = 7/3 and passes through the point (4, 1). Applying the point-slope formula, we can evaluate its equation:
y - 1 = (7/3)( x - 4)
Apply simplification , we get: y = (7/3)x - 17/3
To evaluate the intersection point, we can solve the system of equations:
y =(- 3/5)x - 1.2 = (7/3)x - 17/3
Evaluating for x and y, we get x = -6 and y = -1.
Therefore, the center of rotation is (-6, -1).
√( 4 - 1)² + ( 1 - ( - 4))²) = 5√(2)
Distance between image points and center of rotation
√( ( 6 - (-6))² + ( 3 - (-1))² = 13
The ratio of these distances gives us the scale factor of the transformation, which is 13/√2).
The angle of rotation is negative as the image moves clockwise direction. We can apply the inverse tangent function to find the angle of the vector connecting the midpoint of JK to the midpoint of J'K':
Angle of vector: arctan(5/3) = 59.04 degrees
Therefore, the clockwise rotational path of the line segment is a rotation of -59.04 degrees about the point (-6, -1).
To learn more about midpoint formula
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10. A pizza with a diameter of 5 inches is divided into 8 sectors
of equal area.
What is the approximate area of each pizza slice? Round
your answer to the nearest hundredth.
O
O
The approximate area of each pizza slice is 2.45 sq inches
What is the approximate area of each pizza slice?From the question, we have the following parameters that can be used in our computation:
Diameter = 5 inches
This means that
Radius, r = 5/2 inches
Evaluate
Radius, r = 2.5 inches
The approximate area of each pizza slice is calculated as
Area = Circle area/number of sectors
So, we have
Area = 3.14 * 2.5^2/8
Evaluate
Area = 2.45 sq inches
Hence, the approximate area of each pizza slice is 2.45 sq inches
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