Answer:
Most people found the probability of just stopping at the first light and the probability of just stopping at the second light and added them together. I'm just going to show another valid way to solve this problem. You can solve these kinds of problems whichever way you prefer.
There are three possibilities we need to consider:
Being stopped at both lights
Being stopped at neither light
Being stopped at exactly one light
The sum of the probabilities of all of the events has to be 1 because there is a 100% chance that one of these possibilities has to occur, so the probability of being stopped at exactly one light is 1 minus the probability of being stopped at both lights minus the probability of being stopped at neither.
Because the lights are independent, the probability of being stopped at both lights is just the probability of being stopped at the first light times the probability of being stopped at the second light. (0.4)(0.7) = 0.28
The probability of being stopped at neither is the probability of not being stopped at the first light, which is 1-0.4 or 0.6, times the probability of not being stopped at the second light, which is 1-0.7 or 0.3. (0.6)(0.3) = 0.18
The probability at being stopped at exactly one light is 1-0.18-0.28=.54 or 54%.
line m passes through the points
(-3, 5) and (1, -2) what's the slope of m?
Answer:
-7/4
Step-by-step explanation:
We can find the slope of a line passing through two points by using
m = (y2-y1)/(x2-x1)
= (-2 -5)/(1 - -3)
= -7/ (1+3)
= -7/4
what is the radius of a circle that has a circumference of 50.24 units
Answer:
r≈8
Step-by-step explanation:
Answer: 8 units
Step-by-step explanation:
C= 2*pi*r
50.24 = 2*3.14*r
50.24=6.28
50.24/6.28
8=r
sarah has 12 rubber band bracelets five of the bracelets are blue 1/6 of the bracelets are green the rest are red how many bracelets are red
Answer:
5
Step-by-step explanation:
First, get the number of green bracelets
Since they are 1/6, then this is equivalent to 1/6*12= 2 bracelets
Number of blue and green will be the sum of blue which is given as 5 and green already found to be 2
Blue and green=2+5=7
To get the number of red, we deduct the total blue and green feom the overal total
No. of red will be 12-7=5
Therefore, 5 bracelets are red
Choose a positive number. Using this number as the base, evaluate it when the exponent is 3, 0, and -2. Show all work.
Answer:
1= 8
2= 1
3= ¼
Step-by-step explanation:
Let me choose 2. 2 becomes my base.
When the exponent is 3
1. 2³ = 2 * 2 * 2
= 8
When the exponent is 0
2. 2^0.
From the laws of indices. Exponent zero to any number = 1.
Therefore, 2^0 = 1
When the exponent is = -2
3. 2 `² = ¹/2 * 2
= ¼
In Markov chains, if I was given a transition probability matrix with each of the probabilities specified, then how do I determine the following:1- Probability that state y is visited at least n times given that you start in state x. I know that I can solve it using Px(# of visits to state y ≥ n) = rhoxy(rhoyy)n−1 where rhoxy is the probability that starting at state x, I will be in state y in some positive time (i.e. rhoxy=Px(Ty<[infinity])). But I am not sure how to calculate rhoxy and I have spent so much time trying to figure it out!
Answer:
bbcs
Step-by-step explanation:
msade rekfflg.g
Which rectangular prism has a surface area of 56 square units? [Note: Art is not drawn to scale.]
A rectangular prism with a length of 5, width of 3, and height of 1.
A rectangular prism with a length of 2, width of 2, and height of 6.
A rectangular prism with a length of 5, width of 3, and height of 2.
A rectangular prism with a length of 6, width of 2, and height of 4.
Answer:
2
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
trust
A typical stop sign is in the shape of a regular octagon. The length of a side of a stop sign is 38.7 centimeters, and the radius is 50.6 centimeters. Calculate the area of the stop sign to the nearest square centimeter.
Answer:
7231cm^2
Step-by-step explanation:
Please kindly check the attached file for explanation.
Answer:
The area of the octagon stop sign to the nearest square centimetres is 187 cm²
Step-by-step explanation:
The stop sign is in the shape of a regular octagon, therefore, the area is given by the following relation;
Area of regular octagon = 2 × (Side Length)² × (1 + √2)
Where:
Side Length = 38.7 cm
Area of regular octagon = 2 × 38.7 × (1 + √2) = 186.86 cm²
The area of the octagon stop sign = 186.86 cm²
The area of the octagon stop sign to the nearest square centimetres = 187 cm².
Natalia is calculating the areas of parallelograms using the following formula: Area=bh, where b represents the base of the parallelogram and h represents the corresponding height. For her next parallelogram, b= 8 m and h = 4 m What is the area?
Natalia’s friend gives her the parallelogram shown below. Using her formula, Area=bh, what area can she calculate for this parallelogram?
h=10 in. b= 14 in.
Final answer:
The areas of the parallelograms are calculated by multiplying the base by the height. The first parallelogram's area is 32 m², and the second parallelogram's area is 140 in².
Explanation:
Natalia is calculating the areas of parallelograms using the formula Area = base × height. For the first parallelogram with a base (b) of 8 meters and a height (h) of 4 meters, the area will be:
Area = base × height = 8 m × 4 m = 32 m².
For the second parallelogram given by her friend, with a base (b) of 14 inches and a height (h) of 10 inches, the area will be:
Area = base × height = 14 in. × 10 in. = 140 in².
This formula is essential for understanding the relation between the dimensions of a parallelogram and its surface area.
please help asap ! What is the area of a circle with a radius of 6 inches?
9.7 in. ?
12 x in 2
36 in 2
81 in 2
Answer:
A = 36 pi in^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (6)^2
A = 36 pi in^2
Answer:
36pi in²
Step-by-step explanation:
Area = pi × r²
= pi × 6²
= 36pi
4. Find the value of x in the right triangle below.
60°
Answer:
12
Step-by-step explanation:
It is worthwhile memorizing the ratios of legs in a 30°–60°–90° triangle. Shortest to longest, the ratios are ...
1 : √3 : 2
Then the sides marked will have the ratio ...
6 : x = 1 : 2 = 6 : 12
x = 12
_____
You can also get there using trigonometry.
cos(60°) = 6/x
x = 60/cos(60° = 60/0.5
x = 12
how do u find the mean of a question
Answer:
you add all the number up and divide by how many numbers there are.
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Step-by-step explanation:
I hope this helps you out with your question! Can you plz consider marking me brainliest and thanks! Plz tell me how the answer was! It feel nice to be appreciated! Comment /free for a giveaway entry of 20 thanks and 2 brainliest. Have an awesome day! Let me know if you have any questions! -KaraYeaton18
Answer choices are:
CPCTC
If alternate interior angles are congruent, then lines are parallel
Congruent by SAS
Vertical lines are congruent
Answer:ABCD
Step-by-step explanation:
Alternate interior angles are congruent if two lines are parallel, leading to the similarity of triangles through the Angle Angle Angle theorem.
Alternate interior angles are congruent only if the two other lines are parallel. If the two other lines are not parallel, the angles will still be alternate interior angles but they will not have the same measure, that is, they will not be congruent. Two triangles are similar if all three corresponding angles are congruent, established by the Angle Angle Angle (AAA) theorem.
the perimeters of the square and the equilateral triangle are equal. Which equation represents this scenario? What is the value of x? What is the perimeter of the polygons?
Answer:
The perimeters of the square and the equilateral triangle are equal.
Which equation represents this scenario? ✔ 4(3x + 3) = 3(5x + 0.5)
What is the value of x? ✔ 3.5
What is the perimeter of the polygons?✔ 54 units
Step-by-step explanation:
Answer:
C,D, and C
Step-by-step explanation:
PLEASE HELP IM DESPERATE
Bobby likes to hike the trails near his house. On Saturday, he spent 4 hours hiking 8 miles. On Sunday, he plans to hike 12 miles.
If he hikes at the same rate, how many hours will he spend hiking on Sunday?
Answer: I believe it will take Bobby 2 more hours to hike 12 miles in total it’s 6 hours
Bobby will spend 6 hours hiking on Sunday.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that On Saturday, Bobby spent 4 hours hiking 8 miles. On Sunday, Bobby plans to hike 12 miles.
WE need to find the time he will spend hiking on Sunday.
Then 4 hours hiking = 8 miles.
12 miles = 4/8 x 12
= 1/2 x 12
= 6
Hence, it will take Bobby 2 more hours to hike 12 miles.
thus, he will spend 6 hours hiking on Sunday.
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Malia did push-ups and pull-ups in her physical education class. She did 24 push-ups and pull-ups combined, with each push-up taking her 2 seconds and each pull-up taking her 4 seconds. If she spent a total of 68 seconds doing the push-ups and pull-ups, how many pull-ups did she do?
A.2
B.4
C. 10
D.14
Answer:
10 pull
As 48 seconds + 20 seconds push = 68 seconds
Step-by-step explanation:
Because she did 10 push = 20 seconds = 2 seconds each
12 pull = 48 seconds = 4 seconds each
= 68 seconds combined.
Workings;
18 seconds found for the first set
We then find a divider of 68 and know that
6 x 3 = 18 seconds push
12 x 3 =36 seconds pull T= 54
14 left over = 1 x 12 seconds pull
+ 2 seconds push
= 10 push = 20 seconds combined.
= 12 pull = 48 seconds combined.
68/24 = 2.8- so 14 x 2 = 28 and 10 x 4 = 40 so the answer is 14 push and 10 pull
Answer:
It's 10.
Step-by-step explanation:
I just got it right on my unit test review.
Mika has $12 and spends $2 each day
Answer:
Mika will have 0 dollars after 6 days.
Just by looking at this question, I dont know what im supposed to solve. Im guessing we are just trying to find how many days until Mika runs out of money.
Mika has $12 and spends $2 each day.
If we turn this into an equation, we will get 12-2x=0
12-2x=0 subtract 12 from both sides
-2x=-12 multiply both sides by -1
2x=12 divide by 2
x=6
Mika will run out of money in 6 days
When 5 is subtracted from the square of a number, the result is 4 times the number. Find the negative solution.
The negative solution is - 1.
let
the number = x
When 5 is subtracted from the square of a number can be represented as follows;
x²-5The result is 4 times the number. The remaining part of the equation can be represented as follows:
x²-5 = 4xLets find the negative solution below
x²- 5 - 4x = 0
x² - 4x - 5 = 0
x² + x - 5x - 5 = 0
x(x + 1) -5(x + 1)
(x-5)(x + 1)
x = 5 or -1
Therefore, the negative solution is - 1.
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By solving the quadratic equation x^2 - 5 = 4x, we get two solutions: x = 5 and x = -1. The negative solution to this equation is x = -1.
Let's denote the unknown number as x. The problem statement translates to the equation x2 - 5 = 4x. To find the negative solution, we must solve this quadratic equation.
First, we move all terms to one side to get x2 - 4x - 5 = 0.
We then factor this quadratic if possible or use the quadratic formula. In this case,
(x - 5)(x + 1) = 0.
Setting each factor equal to zero gives us the solutions x = 5 and x = -1.
The question asks for the negative solution, so x = -1.
.1111111111111111111111... as a fraction
Answer:
11/100
Step-by-step explanation:
Is 5 m, 7 m, 11 m a right triangle
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
5 m, 7 m, and 11 m do not form a right triangle.
What is right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
To determine whether 5 m, 7 m, and 11 m form a right triangle, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. That is:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
So, let's check if the Pythagorean theorem holds true for the lengths of 5 m, 7 m, and 11 m:
11² = 5² + 7²
121 = 25 + 49
121 = 74
This is not true, so 5 m, 7 m, and 11 m do not form a right triangle.
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Dale works at a mattress store, and makes a salary plus commission. He has a $500 weekly salary and makes a 5% commission for sales over $3,000. Let ƒ(x) = .05x and g(x) = x − 3000. Write the composition (f o g)(x) and (g o f)(x). Which one represents Dale's commission?
Answer:
1. [tex]\( f\circ g(x)=0.05x-150[/tex]
2. [tex]\( g\circ f(x)=0.05x-3000[/tex]
3. The first one represents Dale's commission
Explanation:
1. The composition of the function
[tex]\( f\circ g(x)=f(g(x)) \)[/tex]
means that you first apply the function g(x) and then f(x) on the output of g(x).
That is:
f(x) = 0.05xg(x) = x - 3000[tex]f(g(x)=0.05(x - 3000)[/tex]
[tex]f(g(x))=0.05x-150[/tex]
2. The composition of the function
[tex]\( g\circ f(x)=g(f(x)) \)[/tex]
means that you first apply the function f(x) and then g(x) on the output of f(x).
That is:
[tex]g(f(x))=((0.05x)-3000)=0.05x-3000[/tex]
3. Which one represents Dale's commission
To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).
Therefore, you first use g(x).
Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.
Therefore, the composition that represents Dale's commission is the first one:
[tex]f(g(x)=0.05(x - 3000)[/tex]
[tex]f(g(x))=0.05x-150[/tex]
There are 850 toothpicks in a regular-sized box. If a jumbo box is made by doubling all the dimensions of the regular-sized box, how many toothpicks will the jumbo box hold?
Answer:
6800 toothpicks
Step-by-step explanation:
Capacity (how many can be held) is another word for volume.
The equation for volume is
V = lwh
And in the regular-sized box V = 850 toothpicks, so
850 = lwh
We need to double each dimension. Multiply length by 2, width by 2, and height by 2. 2*2*2 = 8, so multiply both sides by 8.
8* 850 = 8 * lwh
6800 = lwh
The jumbo box can hold 6800 toothpicks.
The jumbo box will hold 1700 toothpicks.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is that there are 850 toothpicks in a regular-sized box. A jumbo box is made by doubling all the dimensions of the regular-sized box.
The volume {V} cubic units of the box can hold 850 toothpicks.
The volume {1} cubic units of the box can hold (850/V) toothpicks.
The volume {2V} cubic units of the box can hold (850/V x 2V) toothpicks.
(850/V x 2V)
850 x 2
1700
Therefore, the jumbo box will hold 1700 toothpicks.
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The quality control team of a company checked 800 digital cameras for defects. The team found that 20 cameras had lens defects, 25 cameras had charging defects, and 6 cameras had both defects. What is the probability that a camera has a lens defect given that it has a charging defect?
Answer:
0.025
Step-by-step explanation:
-This is a conditional probability problem.
-Let L denote lens defect and C charging defect.
#We first calculate the probability of a camera having a lens defect;
[tex]P(lens)=\frac{Lens}{Total}\\\\=\frac{20}{800}\\\\=0.025[/tex]
#Calculate the probability of a camera having a charging defect:
[tex]P(Charging)=\frac{Charging}{Total}\\\\=\frac{25}{800}\\\\=0.03125[/tex]
The the probability that a camera has a lens defect given that it has a charging defect is calculated as:
[tex]P(L|C)=\frac{P(C)P(L)}{P(C)}\\\\=\frac{0.025\times 0.03125}{0.03125}\\\\=0.025[/tex]
Hence, the probability that a camera has a lens defect given that it has a charging defect is 0.025
The probability that a camera has a lens defect given that it has a charging defect is 6/25 or 0.24.
The question asks for the probability that a camera has a lens defect given that it has a charging defect. To find this probability, we use the concept of conditional probability. From the data given, 25 cameras have charging defects and 6 cameras have both defects. The probability that a camera has both a lens and charging defect among those with a charging defect is:
P(Lens defect | Charging defect) = P(Lens and Charging defect) / P(Charging defect)
Which translates to:
P(Lens defect | Charging defect) = Number of cameras with both defects / Number of cameras with charging defects
P(Lens defect | Charging defect) = 6 / 25
Therefore, the probability is 6/25 or 0.24.
Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air at an initial velocity of 7 feet per second. The equation h = -2t^(2) + 7t + 4 models the toy's height h in feet from the ground at t seconds after he threw it. a) How high is the toy after 0-4 seconds?
The toy's height after 0-4 seconds can be found by substituting different values of t into the given equation.
Explanation:The equation given to model the toy's height is h = -2t^2 + 7t + 4, where h is the height in feet and t is the time in seconds. To find the height of the toy after 0-4 seconds, we substitute different values of t into the equation.
For t = 0, h = -2(0)^2 + 7(0) + 4 = 4 feet.
For t = 1, h = -2(1)^2 + 7(1) + 4 = 9 feet.
For t = 2, h = -2(2)^2 + 7(2) + 4 = 12 feet.
For t = 3, h = -2(3)^2 + 7(3) + 4 = 11 feet.
For t = 4, h = -2(4)^2 + 7(4) + 4 = 4 feet.
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Can someone please please help me :(
Answer:i think its 15 because if you take the km numbers and subtract them
Step-by-step explanation:
Volunteers at Sam's school use some of the student council's savings for a special project. They buy 8 backpacks for $4 each and fill each backpack with paper and pens that cost $3. By how much did the student council's savings change because of this project?
Answer:
Student council's savings reduced by [tex]\$56[/tex]
Step-by-step explanation:
Given:
Volunteers buy 8 backpacks for $4 each and fill each backpack with paper and pens that cost $3
To find:
Change in student council's savings
Solution:
Cost of paper and pens in each backpack = [tex]\$3[/tex]
Total cost of paper and pens in 8 backpacks = [tex]\$8[/tex]× [tex]\$3[/tex] =[tex]\$24[/tex]
Cost of each backpack = [tex]\$4[/tex]
Total cost of 8 backpacks = [tex]8[/tex]×[tex]\$4[/tex] = [tex]\$32[/tex]
So, student council's savings reduced by [tex]\$32+\$24=\$56[/tex]
A box contains 3 black pens, 7 blue pens, and 5 red pens. She pulls a red pen, puts it back, pulls a blue pen, puts it back, and then pulls a black pen and uses it. P(red, then blue, then black)
Answer:
7/25
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome/total outcome
If the box contains 3 black pens, 7 blue pens, and 5 red pens, the total number of pens in the box is 3+7+5 = 15pens
Probability of pulling a red pen and replacing = 5/15 = 1/3
Probability of pulling a blue pen and replacing = 7/15
Probability of pulling a black pen and not replacing(using it) = 3/15
{Note that the total number of outcome used will still be 15 since the black pen was pulled out last even though it wasn't replaced.}
P(red, then blue, then black) = 1/3×7/15×3/15
= 63/225
= 7/25
I am a 7 digit even number the sum of my digits is 23 .My largest digit is in the hundreds place my smollest digit is in the tens place . My millions and tens thousands digits are the same the hundreds place is my only composit number .What number am i?
Answer:
There are two possibilities for the number. They are 3531902 and 3135902
Step-by-step explanation:
(i) Given that the sum of the digits = 23
(ii) Largest digit is in the hundreds place (5th digit)
(iii) Smollest digit is in the tens place (6th digit)
(iv) Millions and tens thousands digits are the same, (1st and 3rd digit)
(v) Hundreds place is my only composit number(5th digit)
The composite numbers < 10 are 4, 6, 8, 9
(vi) Since the number is an even number, the 7th digit must be either 0,2,4,6,8.
It cannot be 4,6,8 due to case (v) and it cannot be 0 due to case (iii), hence 7th digit is 2 and the 6th digit has to be 0.
(vii) 5th digit has to be either 6,8 or 9, and by making it as 6 or 8, there are less options and it doesn't satisfy other conditions and so 9 is the 5th digit.
The 1 - 4 digits has to be filled by 1,3,5,7. By probability and case (i), there are 2 combinations, they are 3531902 and 3135902.
Sally had 8 pennies in her bank she spend 5 of her pennies how many pennies does she have now?
Answer:
3 Pennies
Step-by-step explanation:
8 - 5 = 3, sally would have 3 left
Answer:
3 pennies
Step-by-step explanation:
Basically since she only has 8 pennies, and she used 5 of them, you subtract.
8-5=3
She has 3 cents.
David bought a 5-gallon container of paint to paint his house. After he finished painting, he had 2 quarts of paint left over. How many quarts of paint did David use?
Answer:3 1/2
Step-by-step explanation: