The odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
A coin toss is used to determine which team will receive the ball at the beginning of a football game.
The Cougars always choose tails in the toss.
There will total of 8 cases and in 8 cases there will be three cases in which exactly two heads will come so,
3:8
The cases = {TTT, TTH, THT, HTT, HHT, HTH, HHT, HHH}
Thus, the odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.
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The Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per min.
Draw this Ferris Wheel, labeling the radius, height, and center. Supposing the minimum height of the Ferris Wheel occurs when t=0, write the sinusoidal function for the height as a function of time. Last graph on a coordinate plane, label the key points.
The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter
As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.
The general form of the cosine function representing the displacement of the rider is:
f(t) = a cos(bt+c) + d, where:
amplitude = |a| which is the distance that travels above and below the midpoint
period = 2 π/|b| which is the time period i.e. time required to complete one cycle
-c/b is the phase shift.
d = vertical displacement of the function
Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.
So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.
The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.
The rider starts from the bottom position, so there will be no phase shift, so c=0
Given that the center of the wheel is 19 m above the ground, so d=19m
Therefore the equation will be
height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter
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What is The Value Of X
Answer:
X = 92 degrees
Step-by-step explanation:
the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88
180-88= 92 so X = 92
Find the range of values of x for which
[tex]2{x}^{2} \geqslant 9x + 5[/tex]
See attached images for work.
been having this question for a while and this app wont help
Answer:
b
Step-by-step explanation:
eq y=x+4 is for x>=2 inclusive
how many sets of 5 students can be selected out of 30 students?
Answer:
142 506
Step-by-step explanation:
here the order does not matter
Then
we the number of sets is equal to the number of combinations.
Using the formula :
the number of sets is 30C5
[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]
[tex]=142506[/tex]
There are 142506 ways in which 5 students can be selected out of 30 students.
How can a certain number of individuals be selected using a combination?The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.
By using the formula:
[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]
where;
n = total number of individual in the set = 30r = number of chosing individuals to be selected = 5[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]
[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]
[tex]\mathbf{^nC_r = 142506}[/tex]
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let g(x) be a vertical shift of f(x)=-x up 4 units followed by a vertical stretch by a factor of 3. Write the rule for g(x).
A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,
Vertical Shift by 4 units,
f(x)+4
Vertical stretch by a factor of 3
g(x) = 3(f(x) + 4)
g(x) = -3x + 12
Hence, the function g(x) can be written as g(x) = -3x + 12.
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tôi là người Việt Nam ai giúp giải bài này nha bài 2 ạ
The geometric sequence graphed shows the number of mold spores in a Petri dish per day (please help!)
Answer:
f(1) = 2
f(n) = 2 × f(n - 1) , n ≥ 2
Step-by-step explanation:
the point of coordinates (1 , 2) is on the graph
Then
f(1) = 2
…………………………
We notice that :
f(2) = 4
f(3) = 8
f(4) = 16
16/8 = 8/4 = 4/2 = 2/1 = 2
________________________
This means the common ratio
of the geo sequence = 2
Hence ,
f(n) = 2 × f(n - 1)
Answer: f(n) = 2 × f(n - 1) , n ≥ 2
Step-by-step explanation:
Which equation is equivalent to y−3=4(x−5)?
y=4x−2y is equal to 4 x minus 2
y=−4x−23y is equal to negative 4 x minus 23
y=4x−17y is equal to 4 x minus 17
y=−17x+4
Answer:
y = 4x - 17
Step-by-step explanation:
y - 3 = 4(x - 5) ← distribute parenthesis by 4
y - 3 = 4x - 20 ( add 3 to both sides )
y = 4x - 17
For what value of x is line m parallel to line n?
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
Here, we can use an angle rule.
We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.
This means we can use the rule:
Corresponding angles are equal.
This means that:
[tex]8x + 50 = 130[/tex]
We can now use this equation we have formed to solve for [tex]x[/tex]:
[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]
Therefore, our final answer is [tex]x=10[/tex].
What is halfway between 4 /5 and − 2 /3 ?
please help asap!!!
Rewrite the following equation as a function of x.
Answer:
B
Step-by-step explanation:
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f(x)= 9280 - 20x [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y - 29 = 0[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y = 29[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{20 x+ y}{320} = 29[/tex]
[tex]\qquad \tt \rightarrow \: 20x + y = 29 \sdot320[/tex]
[tex]\qquad \tt \rightarrow \: y = 9280 - 20x[/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 9280 - 20x[/tex]
[tex] \textsf{Correct option - A } [/tex]Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Find the value of x in each case:
x = 90°
2x = 180°
Step-by-step explanation:
angle VTS= angle TSR (alternate angle)
now in ∆TRS,
2x + x + x = 360° (angle sum property of ∆)
4x = 360°
x = 90°
Example 1.29 Initially, a box contains three white and five red balls. Balls
are drawn at random from the box. Whenever a red ball is drawn, it is placed
back into the box together with one extra red ball. Whenever a white ball is
drawn, it is placed back into the box together with two extra white balls. What
is the probability that the first three balls are drawn out of the box alternated
in colour?
Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:
[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].
0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
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13 7in 7in 7in volume and surface area pyramid
The Volume and Surface Area of Prism is 294 in² and 114.33 in³.
What is pyramid?A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.
Surface rea of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 7*7 + 7*7+ 7*7)
= 2 ( 49+49+49)
= 2*3*49
= 294 in²
Now, Volume,
= bhl/3
= 7*7*7/3
= 114.33 in³
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Suppose f(x) = x² and g(x)= (1/5x)^2
Which statement best compares the graph of g(x) with the graph of f(x)?
A. The graph of g(x) is the graph of f(x) shifted units left.
B. The graph of g(x) is the graph of f(x) vertically stretched by a
factor of 5.
OC. The graph of g(x) is the graph of f(x) horizontally stretched by a
factor of 5.
D. The graph of g(x) is the graph of f(x) horizontally compressed by a
factor of 5.
Answer:
B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.
What trigonometric ratio would you use to find the distance from the base of the tower of your keys ? Identify your choice, then calculate the distance
The choice trigonometric ratio is tangent and the distance is 3. 98 meters.
How to determine the trigonometric ratioThe given angle is 86
The opposite side is given as 57 meters
The distance is in the adjacent
Thus, trigonometric ratio to use is the tangent
Tangent = opposite/ adjacent
We have,
tan 86 = 57/x
14. 300 = 57/x
x = 57/ 14. 300
x = 3.i 98 meters
Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.
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If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?
5(4 + 4) – 6
5(5(4) – 6) – 6
54 – 6 + 54 – 6
5(4) – 6 + 5(4) – 6
What's your annual income if you're unemployed?
Answer:
$46,819 is the average unemployed salary
What is the length of the line?
Choose 1 answer: A. 7 B. The square root of 10 C. Square root of 29 D.Square root of 21
Answer:
C
Step-by-step explanation:
= The square root of (5^2+2^2)= The square root of 29 ---> C
find area of shape below to 1 dp
The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
The figure is divided into two parts one is a rectangle and the second is a semicircle.
Area of figure = Area of rectangle + Area of a semicircle
Area of figure = L × B + (πr²/2)
A = 10 cm × 15 cm + (3.14 ×(5)^2/2)
A= 189.25 cm²
Hence the area of the shape will be 189.25 cm²
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Answer the following questions
A. 10 -4 ×5=?
B. 3+8×4=?
C. (3+8)×4=?
Answer:
A=30
B=35
C=44
Step-by-step explanation:
Find the average rate of change of f(x) = -3x² + 1 over each of the following intervals.
(a) From 2 to 4
(b) From -2 to 0
(c) From 2 to 5
The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38
How to find the average rate of change?We are given the function;
f(x) = -3x² + 1
(a) From 2 to 4;
f(2) = -3(2)² + 1
f(2) = -12 + 1
f(2) = -11 (2, -11)
f(4) = -3(4)² + 1
f(4) = -47 (4, -47)
Slope = (-47 - (-11))/(4 - 2)
Slope = -36/2
Slope = -18
(B) From -2 to 0;
f(-2) = -3(-2)² + 1
f(2) = -12 + 1
f(2) = -11 (-2, -11)
f(4) = -3(0)² + 1
f(4) = 1 (0, 1)
Slope = (1 - (-11))/(0 - (-2))
Slope = 12/2
Slope = 6
(C) From 2 to 5;
f(2) = -3(2)² + 1
f(2) = -12 + 1
f(2) = -11 (2, -11)
f(5) = -3(5)² + 1
f(5) = -74 (0, -74)
Slope = ((-74) - 2)/(0 - 2)
Slope = -76/-2
Slope = 38
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Circle Q is shown. Line segments P Q and R Q are radii. The length of R Q is 6. Angle P Q R is 45 degrees. Sector P Q R is shaded.
Which statements are true about circle Q? Select three options.
The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
The statements that are true about circle Q are:
The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.The area of the shaded sector depends on the length of the radius.The area of the shaded sector depends on the area of the circle.How to explain the circle?The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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Answer:
1,3,4
Step-by-step explanation:
which numbers belong to the solution set of the equation?
22x=902
Answer:
D. 41
Step-by-step explanation:
To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:
The only solution for 22x=901 is 41
Answer: x=41
Step-by-step explanation:
Hii!
Do you need to know the solution set of 22x=902? No problem! (:
We just need to divide both sides by 22 to solve for "x".
x=41; this equation has one solution only
--
Hope that this helped! Best wishes.
--
What is the line that has a slope of -2/3 and passes through point -3,-1?
Answer:
y = (- 2/3)x - 3
Step-by-step explanation:
y = mx + c
y = (- 2/3)x + c
Now let's substitute the values (-3,-1)- 1 = (- 2/3)(-3) + c
-1 = 2 + c
c = - 3
Therefore,
y = (-2/3)x - 3
Answer:
y = -2/3x - 3
Step-by-step explanation:
y = mx + b
y = y coordinate → given: - 1
m = slope → given: - 2/3
x = x coordinate → given: - 3
b = y intercept → need to find
y = -2/3x + b → -1 = -2/3(-3) + b
-1 = 2 + b
subtract 2 from both sides
-1 - 2 = 2 - 2 + b
-3 = b
y = -2/3x - 3
5 positive integers that have a mode of 2, a median of 5, a mean of 6 and a range of 10.
2,2,5,9,12
The numbers should be 2, 2, 5, 9 and 12.
What is mean, mode and median?
The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.
Let us take numbers 2, 2, 5, 9 and 12.
Mean = 192+2+5+9+12)/5mean = 30/5
mean= 6
mode = 2median = 5range = 12-2range = 10.
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URGENTTT...A survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose. This table shows the results:
The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.
The probability of a person that is a student:
P(student) = (75+15)/110 = 0.83
The probability:
P(student|pirate) = 75/80 = 0.93
The probability of both events is different.
Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.
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The graph of which function has an axis of symmetry at x = 3?
f(x) = x2 + 3x + 1
On a coordinate plane, a parabola opens up. It goes through (negative 4, 5), has a vertex at (negative 1.75, 6.75), and goes through (1, 5).
f(x) = x2 – 3x – 3
On a coordinate plane, a parabola opens up. It goes through (negative 2, 7), has a vertex at (1.75, 5), and goes through (5, 7).
The graph of the function has an axis of symmetry at x = 3 will be D. f(x) = x² - 6x - 1. On a coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
What is axis of symmetry?It should be noted that the axis of symettry is the line that divides an object into two equal halves.
Here, the graph of the function has an axis of symmetry at x = 3 is option D. On the coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).
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Answer: D. f(x) = x² - 6x - 1
Right on Edge 2023 :)
Find y.
Help me please:))
Answer:
y = 47
Step-by-step explanation:
All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: y=47 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y[/tex]
[tex]\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0[/tex]
[tex]\qquad \tt \rightarrow \:2y - 3y + 47 = 0[/tex]
[tex]\qquad \tt \rightarrow \: - y = - 47[/tex]
[tex]\qquad \tt \rightarrow \:y = 47 \degree[/tex]
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