The probability that the colour changes, while she is watching, is 1/7
Concept: Event probability = number of favorite results /Total number of results
It is given that the traffic light runs repeatedly in the following time cycle: green for 30 seconds, then yellow at 3 seconds, and then red for 30 seconds.
This means that the traffic light passes through 63 seconds to complete one-time cycle.
It is also given that Leah chooses a random 3 second time interval to watch the light.
We should find the probability that the color changes while Leah is looking.
The green light will change after 30 seconds and after three seconds it will change to yellow light, that is at 33 second it is yellow and after another 30 seconds it will change to red light.
Now let time t=0
The light changes at three different times: t=30,t = 33 and t = 63
This means that the light will change if Leah watches at intervals [27,30]
, [30,33] or [60,63]
Since each interval is 3 seconds and there are 3 intervals, Leah will have a chance of 9 seconds.
That makes a total of 9 seconds out of 63
⇒Probability that Leah watches the color change=Number of seconds she watches/Total seconds
=9/63=17
∴ The probability that Leah observes the color change is 1/7
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What is the area of this triangle? Enter your answer in the box. units²
Answer:
10u²
Step-by-step explanation:
The formula for area of a triangle is b*h/2. When you plug in the numbers, you get 10. Hope this helps!
Solve for x.
2x² +21x-61 = (x+7)²
Please
Answer:
[tex]x = \frac{-7 +\sqrt{489} }{2}[/tex]
[tex]x = \frac{-7 - \sqrt{489} }{2}[/tex]
Step-by-step explanation:
2x² +21x-61 = (x+7)²
expand
2x² + 21x - 61 = x² + 14x +49
move everything to one side
x² + 7x - 12 = 0
use quadratic formula
[tex]x = \frac{-b +- \sqrt{b^{2}-4ac } }{2a}[/tex]
plug in the values
[tex]x = \frac{-7 +- \sqrt{7^{2}-4(1)(-110) } }{2(1)}[/tex]
solve
[tex]x = \frac{-7 +- \sqrt{49-4(1)(-110) } }{2}[/tex]
[tex]x = \frac{-7 +- \sqrt{49 + 440 } }{2}[/tex]
[tex]x = \frac{-7 +- \sqrt{489} }{2}[/tex]
please helpppp!!!!!!!
(3(1) + 9)² - 64
(3 + 9)² - 64
(12)² - 64
= 144 - 64
= 80
Which irrational number can be multiplied by –StartRoot 41 EndRoot to get a product that equals 1?
StartRoot StartFraction 1 Over 41 EndFraction EndRoot
Negative StartRoot 41 EndRoot
Negative StartRoot StartFraction 1 Over 41 EndFraction EndRoot
StartRoot 41 EndRoot
The irrational number that can be multiplied to produce 1 is - √41/41
Irrational numbersLet the following expression
-√41 x = 1
We are to find the value of x that will make the expression true
√41 x = -1
Divide both sides by √41
√41 x/ √41 = -1/ √41
x = - √41/41
Hence the irrational number that can be multiplied to produce 1 is - √41/41
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(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Going by the rules of the game to pick a random card and then multiply it by a roll of a number cube, we can find that:
The probability a person wins a game is 3/8 or 37.5%.For a participant to win 25% of the time, they needs to get 32 or higher. The probability of a score of 36 or higher in 4 consecutive attempts is 1/1,1296.Teacher should tell people that just as the lower numbers could be picked, the products that are 32 or higher can be picked as well.What sample space represents the data?If the die is rolled, it will land on a number between 1 and 6 while there are only four cards that can be picked.
The sample space is:
Dice Card Product
1 5 5
1 6 6
1 7 7
1 8 8
2 5 10
2 6 12
2 7 14
2 8 16
3 5 15
3 6 18
3 7 21
3 8 24
4 5 20
4 6 24
4 7 28
4 8 32
5 5 25
5 6 30
5 7 35
5 8 40
6 5 30
6 6 36
6 7 42
6 8 48
Based on the products, we can come up with the following frequency table:
Frequency table
Product Frequency
5 1
6 1
7 1
8 1
10 1
12 1
14 1
16 1
15 1
18 1
21 1
24 2
20 1
28 1
30 2
32 1
25 1
35 1
40 1
36 1
42 1
48 1
Total 24
The frequency table shows that to get 28 or more, a person will have a relative frequency of:
= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1
= 9
Probability is:
= 9 / 24
= 3/8
= 37.5%
How can a person win only 25% of the time?The number of products required to win 25% of the time is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
What is the probability that a player wins a large prize?The probability of getting 36 or higher is:
= ∑(Probabability of picking 36 and above numbers)
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 consecutive times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
= 0.0007716
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please help me I'm in a rush
Answer:
78 m²
Step-by-step explanation:
V = bh
V = 13 m × 6 m
V = 78 m²
the sum of perimeter of two similar polygons is 24cm,and the ratio of their corresponding sides is 1:3, find the perimeter of the larger polygon
Answer:
18
Step-by-step explanation:
Polygon A : Polygon B = x : 3x
4A = 24
A = 6
B = 18
B is the larger polygon so the perimeter is 18.
Elizabeth, Frank, Gary, and Helen are getting in line to buy lunch in the cafeteria. How many different ways could they line up so that Helen is first in line?
Stan guessed on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices. What is the probability that he got at least 2 questions correct
The probability that he got at least 2 questions correct is 0.756.
Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.
Basic Probability Rules
For any event A, 0 ≤ P(A) ≤ 1The sum of the probabilities of all possible outcomes is 1The Complement RuleProbabilities Involving Multiple Events.Addition Rule for Disjoint EventsLearn more about probability here https://brainly.com/question/24756209
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Please include what axioms and theorems were used as well.
Part (i)
1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)
2. AB = AB (reflexive property)
3. Triangles ABD and BAC are congruent (SAS)
Part (ii)
4. BD=AC (corresponding sides of congruent triangles are equal)
Part (iii)
5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)
Answer:
Hey!
In △ABD and△BAC,
AD = BC (it's given)
∠DAB = ∠CBA (it's given)
AB = BA (Common)
By SAS congruence rule,
∴△ABD≅△BAC
=> BD = AC (By C.P.C.T) (ii)
And, ∠ABD = ∠BAC (By C.P.C.T) (iii)
Hope it helps, any confusions you may ask.
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people.
Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Will the town's tax status change within the next 3 years?
Using an exponential function, the inequality is given as follows:
[tex]9400(0.857)^t < 6000[/tex]
The solution is t > 2.9, hence the tax status will change within the next 3 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 9400, r = 0.143.
The population after t years is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 9400(1 - 0.143)^t[/tex]
[tex]A(t) = 9400(0.857)^t[/tex]
The tax status will change when:
[tex]A(t) < 6000[/tex]
Hence the inequality is:
[tex]9400(0.857)^t < 6000[/tex]
Then:
[tex](0.857)^t < \frac{6000}{9400}[/tex]
[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]
[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]
Since both logs are negative:
[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]
t > 2.9.
The solution is t > 2.9, hence the tax status will change within the next 3 years.
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Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12
Answer:
obtuse because 6^2+10^2<10^2
Step-by-step explanation:
The given triangle whoe sides are 6cm, 10cm, and 12cm is an obtuse triangle and it can be determine by using pythagorian theorem, i.e. 6^2 + 10^2 < 12^2.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a^2 + b^2 = c^2.
here, we have,
Given :
The side lengths of a triangle are: 6cm, 10cm, and 12cm.
Pythagorian theorem can be used to find out that the triangles are acute or obtuse. According to pythagorian theorem, the sum of square of shorter side is equal to the square of the third side of the right angle triangle.
According to pythagorian theorem:.
That is, H^2 = P^2 + B^2.
There are some rules to find the triangle is obtuse or acute:
If H^2 > P^2 + B^2, than the triangle is obtuse.
If H^2 < P^2 + B^2, than the triangle is acute.
Now, applying pythagorian theorem:
we get,
6^2 + 10^2 = 12^2
136 = 144
Here, it is clearly observe that 136 < 144, i.e. 6^2 + 10^2 < 12^2 therefore, the triangle is obtuse.
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Will give brainliest.
Answer:
Its a right isosceles triangle
Answer:
right isosceles
Step-by-step explanation:
it has the right at the top
A square-based pyramid has a base of area 16 cm² and a volume of 16 cm³. Calculate:
a. The perpendicular height of the pyramid.
b. The height and area of the base of a similar pyramid with a volume of 1024 cm³.
Answer:
3
Step-by-step explanation:
V=⅓b²h
16=⅓*16*h
16=16h/3
h=3cm
Susan saw birds and mice eating seeds on the ground. She counted 14 heads. 40 legs in total. how many birds and mice are on the ground
Answer:
Birds = 8
Mice = 6
Step-by-step explanation:
Conditions
Let the birds = x
Let the mice = y
Equations
x + y = 14
2x + 4y = 40
Solution
Using the top equation solve for x
x = 14 - y
Use this result to substitue for x
2(14 - y) + 4y = 40
Remove the brackets
28 - 2y + 4y = 40
Combine
28 + 2y = 40
Subtract 28 from both sides
28 - 28 + 2y = 40 - 28
2y = 12
Divide by 2 on both sides
2y/2 = 12/2
y = 6
Solve for x
x + y = 14
x + 6 = 14
Subtract 6 from both sides
x + 6 - 6 = 14 - 6
x = 8
Answer:
7 mice and 7 birds
Step-by-step explanation:
14 heads would mean there are 14 animals in total, as each animal has one head.
Birds have two legs, and mice have four.
2+4=6
40/6=6.67 (recurring)
6.67*2=13.3 (recurring)
6.67*4=26.67 (recurring)
Animal legs can't be in decimal numbers, so we can round the numbers.
13.3 becomes 13, 26.67 becomes 27.
13+27=40
Now we can see that there are 13 bird legs and 27 mice legs.
Divide the bird legs by 2 to get 6.5
Divide the mice legs by 4 to get 6.75
Again, we can't have a decimal of an animal, so we can round.
6.5 becomes 7, and 6.75 also becomes 7.
Therefore, there is 7 of each type of animal.
The oven temperature was at 325325325 degrees because my mom just finished baking a pie. i increased the temperature 757575 degrees so i could bake a pizza. after the pizza was cooked, i turned off the oven. the oven cooled to the room temperature of 686868 degrees.
The amount of the temperature decrease will be 332 °C.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The oven temperature was at 325 degrees because my mom just finished baking a pie.
I increased the temperature, 75 degrees, so I could bake a pizza.
Then the temperature will be
⇒ 325 °C + 75 °C
⇒ 400 °C
After the pizza was cooked, I turned off the oven.
The oven cooled to the room temperature of 68 degrees.
Then the amount of the temperature decrease will be
⇒ 400 °C – 68 °C
⇒ 332 °C
The remaining question is given below.
How much did the temperature decrease?
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Select the correct answer
Answer:
option b is the answer
Step-by-step explanation:
7. Which transformation of (x, y) is a dilation? (TEKS G.3.A)
F (3x, y)
G (-y, x)
H (3x, 3y)
J (x + 3, y + 3)
Answer:
H (3x,3y)
Step-by-step explanation:
Dilation is a transformation when figure is enlarged or reduced by scale factor. During dilation, every point of preimage is dilated by scale factor, so it means each coordinate of that point must be multiplied by scale factor.
Hence, H(3x,3y) can be the result of dilation with scale factor of 3.
One factor of f (x ) = 4 x cubed minus 4 x squared minus 16 x + 16 is (x – 2). What are all the roots of the function? Use the Remainder Theorem.
[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]
[tex]divide \: by \: x - 2[/tex]
[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]
[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]
[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]
[tex]z(x) = - 8x + 16[/tex]
[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]
[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]
[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]
[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]
[tex]x = 2[/tex]
[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]
Answer: B
Step-by-step explanation:
Edge 2023
Is anyone able to solve this?
The value of ? and X are 24 and 32 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
X = 20 +x
X= 32
Hence the value of ? and X are 24 and 32 respectively
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2. Simplify the expression. (x3)(x7)²
1
x18
x14
x126
Step-by-step explanation:
[tex] = ( {x}^{3} ) { ({x}^{7} )}^{2} [/tex]
[tex] = {x}^{3} \times {x}^{7 \times 2} [/tex]
[tex] = {x}^{3} \times {x}^{14} [/tex]
[tex] = {x}^{3 + 14} [/tex]
[tex] = {x}^{17} [/tex]
Which of the following is equivalent to
60 1/2
Answer:
30 or 120 /4
Step-by-step explanation:
a^p/q here p denotes power raised and q denotes inverse power or root. So, 60^1/2 denotes square root of 60 raised to power 1.
prove that: (1 +tantheta)^2 + (1 - tantheta)^2 = Sec^2 theta pls answer and God will bless u
Answer:
Step-by-step explanation:
[tex]=(1 +tan\theta)^2 + (1 - tan\theta)^2\\=(1+2tan\theta+tan^2\theta)+(1-2tan\theta+tan^2\theta)\\=2(1+tan^2\theta)\\=2sec^2\theta.\\[/tex]
a number is chosen ar random from 1 to 50. find the probaility of selecting multiplies of 3
Answer:
16/50 or 32% chance of getting a multiple of 3
Step-by-step explanation:
Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48
Attached is a chart for reference!
So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)
step by step explanation:
(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48
probability (multiples of 3)= nó of required outcome/ nó of possible outcome
16 /50 = 8/25 ( you get this after dividing 16/50)
in percentage 8/ 25 would give you 32%
Find the missing side lengths.
AB=
BC=
Answer:
Step-by-step explanation:
There are four people in the Hayden family.each person always eats 3/4 of a cheese pizza. How whole many pizzas should they order? Solve and draw a picture to match this problem
The family consumes 3 whole pizzas in total. They should order 3 whole pizzas to have enough for everyone.
How did we arrive at the value?To find out how many whole pizzas the Hayden family should order, we can calculate the total number of pizzas they need.
Since each person always eats 3/4 of a pizza, the total amount they eat can be calculated as follows:
3/4 + 3/4 + 3/4 + 3/4 = 4 × (3/4) = 3
So, the family consumes 3 whole pizzas in total. Therefore, they should order 3 whole pizzas to have enough for everyone.
As for the picture, imagine a circle representing a whole pizza. Divide it into four equal parts to represent each person's portion (3/4). Repeat this division three times to represent the three pizzas needed.
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The formula used to convert degrees Celsius to degrees Fahrenheit is
F=C+32.
Convert 59°F to degrees Celsius. Solve the formula for C, and then use it to
convert the temperature.
Which is the correct formula and conversion?
OA. C=F-32; conversion: 59°F = 135°C
OB. C= (F-32); conversion: 59°F = 15°C
OC. C= (F-32); conversion: 59°F = 106°C
OD. C=F-32; conversion: 59°F = 15°C
The formula to convert degrees Fahrenheit to Celsius is:
[tex]\bf{^{\circ}C=\dfrac{5}{9}(^{\circ}F-32) \ \ \to \ \ \ Formula }[/tex]
Convert 59°F to degrees Celsius.
Add the number 59 in the formula, and solve.
[tex]\bf{=\dfrac{5}{9}(59-32) }[/tex]
Subtract 32 from 59.
[tex]\bf{=\dfrac{5}{9}(27) }[/tex]
Multiply 5 x 9 = 135, then divide 135/9 = 15.
[tex]\bf{=15 \ ^{\circ}C}[/tex]
Therefore 59 °F = 15 °C. The correct option is "D".
{ Pisces04 }The figure below shows one of the steps used in inscribing a square in a circle.
Answer:
Step-by-step explanation:
given the equation P=S1t-S2t which equation is solved for t A. t=p(s1-s2) B. t=p-S1+S2 C. t=p/S1+S2
Answer:
C
Step-by-step explanation:
P = S1t - S2t ← factor out t from each term on the right side
P = t(S1 - S2) ← isolate t by dividing both sides by S1-S2
[tex]\frac{P}{S1-S2}[/tex] = t
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) =____
f(x) = x² 5
-5
-5
O A. g(x) = (x + 2)²
OB. g(x)=(x-2)²
O c. g(x)²2-2.
OD. g(x)=x² +21
X
g(x) = ?
5
Answer:
B
Step-by-step explanation:
given f(x) then f(x ± a ) is a horizontal translation of f(x)
• if + a , then a shift left of a units
• if - a then a shift right of a units
here g(x) is the graph of f(x) moved 2 units right , then
g(x) = (x - 2)²