Answer:
P(2, then 2) = [tex]\frac{1}{36}[/tex]
P(3, then 5) = [tex]\frac{1}{36}[/tex]
P(4, then odd) = [tex]\frac{1}{12}[/tex]
Step-by-step explanation:
Given: A fair number cube is rolled
To find: P(2, then 2) , P(3, then 5) , P(4, then odd)
Solution:
Probability refers to chances of occurrence of some event.
Probability = Number of favourable outcomes/Total number of outcomes
Sample space = [tex]\left \{ 1,2,3,4,5,6 \right \}[/tex]
Total number of outcomes = 6
P(2, then 2) = P(2)P(2) = [tex]\frac{1}{6}(\frac{1}{6})=\frac{1}{36}[/tex]
P(3, then 5) = P(3)P(5) = [tex]\frac{1}{6}(\frac{1}{6})=\frac{1}{36}[/tex]
Odd numbers out of the sample space = [tex]\left \{ 1,3,5 \right \}[/tex]
P(4, then odd) = P(4)P(odd) = [tex](\frac{1}{6})(\frac{3}{6} )=\frac{1}{12}[/tex]
To calculate the probability of rolling specific numbers on a fair, six-sided die, multiply the probabilities for each individual roll. P(2, then 2) and P(3, then 5) are both 1/36. P(4, then odd) is calculated as P(4) multiplied by the combined probability of rolling an odd number, resulting in 1/12.
Understanding Probability with a Fair Number Cube:
When rolling a fair, six-sided die, each outcome has an equal probability of occurring. Specifically, the probability (P) of any one number, such as a 2 or a 3, is 1/6 since it is a fair die. When considering sequential rolls, we have to calculate the probability of each event happening one after another, which involves multiplying the probabilities of the individual events.
P(2, then 2) = P(2) * P(2) = (1/6) * (1/6) = 1/36.P(3, then 5) = P(3) * P(5) = (1/6) * (1/6) = 1/36.P(4, then odd) involves the probability of rolling a 4 first, and then an odd number, which could be a 1, 3, or 5. The probability for each odd number is 1/6, and since there are three odd numbers, the combined probability of rolling an odd number is 3/6 or 1/2. Therefore, P(4, then odd) = P(4) * P(odd) = (1/6) * (1/2) = 1/12.Thus, to find the probability of rolling specific numbers or combinations on a number cube, you can calculate each probability separately and then combine them as needed using multiplication.
A 10-foot ladder leans against the side of a house with its base 2.2 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth. The ladder reaches feet high.
Answer:
Ladder reaches 9.76 high.
Step-by-step explanation:
From the figure attached,
Ac is the ladder which reaches at the point A when leans against the side of a house.
Length of the ladder = 10 feet
Distance of the ladder form the base of a house = 2.2 ft
By Pythagoras theorem,
AC² = AB² + BC²
(10)² = h² + (2.2)²
h² = 100 - 4.84
h = √95.16
h = 9.755 feet
≈ 9.76 feet
Therefore, the ladder reaches the 9.76 high.
The answer is 9.7 feet
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
Answer:
[Tex]A(t)=5000(0.7)^t[/tex]
Step-by-step explanation:
The problem presented is one in which the population of the bacteria depreciates by a decay factor r every year.
Since it is a decay problem, we use the model:
[Tex]A(t)=P(1-r)^t[/tex]
Initial Population, P=5000
Decay Rate,r=30%=0.3
t=time interval
Therefore, the equation that represents this situation is:
[Tex]A(t)=5000(1-0.3)^t[/tex]
[Tex]A(t)=5000(0.7)^t[/tex]
The equation that represents this situation is y = 5000(0.7)ˣ
An exponential decay is given by:
y = abˣ
where a is the initial value of y, b is the rate of decay and y, x are variables.
Since the culture begins with 5000 cells, hence a = 5000. The cells die by 30% each year, hence b = 100% - 30% = 0.7
The equation is: y = 5000(0.7)ˣ
Therefore the equation that represents this situation is y = 5000(0.7)ˣ
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[tex]f(x)=\sqrt x+2[/tex]
What is the inverse?
Answer:
[tex](x-2)^2[/tex]
Step-by-step explanation:
To find the inverse of this function, you need to replace the location of the x and the y.
You start with [tex]y=\sqrt{x}+2[/tex]. Now, replace the x and the y, and try to isolate the y.
[tex]x=\sqrt{y}+2\\x-2=\sqrt{y}\\y=(x-2)^2[/tex]
Hope this helps!
PARA HORNEAR UN PASTEL DE UN KILO SE NECESITA ENTRE OTROS INGREDIENTES UN TERCIO DE HARINA Y 3 CUCHARADAS DE VAINILLA CUANTA VAINILLA ES NECESARIA 3 KILOS Y MEDIO
Answer: 10 + 1/2 spoons of vanilla.
Step-by-step explanation:
This question says:
For 1kg of cake, we need 1/3 kg of flour and 3 spoons of vanilla.
How much vanilla do we need if we want to make a cake of 3 + 1/2 kg?
Ok, if for 1kg we need 3 spoons, then for (3 + 1/2)kg we need (3 + 1/2) times 3 spoons, this is:
(3 + 1/2)*3 spoons
=3*3 + 3/2 = 9 + 3/2 = 9 + 2/2 + 1/2 = 10 + 1/2
We need 10 + 1/2 spoons of vanilla.
A golfer is standing on a tee with a green in a valley below. If the tee is 43 yards higher
than the green and the direct distance from the green to the hole is 177 yards, find the
angle of depression from the tee to the green.
Answer:
[tex]13.65^0.[/tex]
Step-by-step explanation:
Given,
Height of tee, H = 43 yard
Direct distance of the hole is, D = 177 yards
Now, Angle of depression of tee
[tex]\tan \theta = \dfrac{H}{D}[/tex]
[tex]\tan \theta = \dfrac{43}{177}[/tex]
[tex]\tan \theta =0.2429[/tex]
[tex]\theta = 13.65^\circ[/tex]
Hence, angle of depression from tee to the green is [tex]13.65^0.[/tex]
if a=2, b= -1, c= -3 and d= -2 find :
1/2bc-6ac+2ab
1/4(ac)² +1/6ac
Answer:
34
8
Step-by-step explanation:
1/2bc - 6ac + 2ab
(1/2)(-1)(-3) - (6)(2)(-3) + (2)(2)(-1)
(1/2)(4) - (-36) + (-4)
2 + 36 - 4
34
1/4(ac)² + 1/6ac
(1/4)[(2)(-3)]² + (1/6)(2)(-3)
(1/4)(-6)² + (1/6)(-6)
(1/4)(36) + (-1)
9 - 1
8
If you toss a coin 4 times, what is the probability of landing heads, heads, tails, heads and then heads?
Answer: 0%
Step-by-step explanation:
if you toss a coin 4 times you cant get 5 results.
What percent is 18 out of 20
Answer:
it's 90%
Step-by-step explanation:
1. Divide 18 by 20 and you will get a decimal form answer
2. Then you multiple it by 100 and you will get your answer which is 90.00%
18 out of 20 is 90 percent.
What percent is 18 out of 20?To find the percentage of 18 out of 20, you can follow these steps:
1. Divide the given number (18) by the total number (20).
18 ÷ 20 = 0.9
2. Multiply the result by 100 to get the percentage.
0.9 × 100 = 90
Therefore, 18 out of 20 is 90 percent.
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Which of the following is equal to the rational expression when x*-2 or 3?
X^2 +5x+6/X^2-X-6
Answer:
i am very sorry but i am trying to solve it so wait a few minutes please
Step-by-step explanation:
Answer: D
x+3/x-3
Step-by-step explanation:
What is the inverse of f(x)= 1/5 x
Is it an inverse function?
The inverse of the function f(x) = 1/5x is found by switching the roles of y and x, then solving for y. This results in the inverse function f^-1(x) = 5x, which undoes the effect of the original function.
Explanation:The inverse of a function, in this case f(x) = 1/5x, is the function that will reverse the effect of the original function. In this case, to find the inverse function of f(x), you swap the roles of y and x in the original function and solve for y.
So, f(x) = 1/5x becomes x = 1/5y. Multiply both sides by 5 to get rid of the denominator on the y-side, which results in 5x = y. Thus, the inverse function is f^-1(x) = 5x.
It's indeed an inverse function as it reverses the effect of the initial function f(x).
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HELP ASAP GIVING BRAINLIST AND A LOT OF POINTS!!!!!
Tara starts with $20, in which she buys 2 items for d amount. Subtract 2d from the total for your answer.
1) 20 - 2d
To find the average distance, add all the numbers together, and divide by the amount of numbers there are:
3) (t + w)/2
~
If the circumference of a circle measures 3π cm, what is the area of the circle in terms of π?
Answer:
the area of the circle is [tex]2.25\pi\ cm^2[/tex].
Step-by-step explanation:
We have,
Circumference of a circle is 3π cm
Formula of circumference of a circle is given by :
[tex]C=2\pi r[/tex]
r is radius of circle
[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{3\pi }{2\pi}\\\\r=1.5\ cm[/tex]
Area of a circle is given by :
[tex]A=\pi r^2\\\\A=\pi (1.5)^2\\\\A=2.25\pi\ cm^2[/tex]
So, the area of the circle is [tex]2.25\pi\ cm^2[/tex].
11. The measure of an angle formed by two tangents to a circle is 90. If the radius of the circle
is 8 centimeters, how far is the vertex of the angle from the center of the circle?
Vertex of the angle is 11.31 cm far from the center of the circle.
Given in the question,
Measure of angle formed by two tangents of the circle (∠PVQ) = 90°Measure of the radius (OP)= 8 cmIn ΔOPV and ΔOQV,
OP ≅ OQ (Radii of the circle)
PV ≅ QV (Tangents from a point outside the circle)
OV ≅ OV (Reflexive property)
ΔOPV ≅ ΔOQV (SSS property of congruence)
Therefore, m∠PVO = m∠QVO = 45°
By triangle sum theorem,
m∠POV + m∠PVO + m∠OPV = 180°
m∠POV + 45° + 90° = 180°
m∠POV = 45°
Hence, ΔOPV is an isosceles triangle.
OP = PV = 8 cm
By applying Pythagoras theorem in ΔOPV.
OV² = OP² + PV²
OV² = 8² + 8²
OV = √128
OV = 11.31 cm
Therefore, vertex V is 11.31 cm from the center of the circle.
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The distance from the vertex of the angle to the center of the circle is 0 centimeters.
Explanation:In this problem, we have two tangents to a circle, and we are given that the angle between them is 90 degrees. We need to find the distance from the vertex of the angle to the center of the circle.
Since the angle between the tangents is 90 degrees, the tangents are perpendicular to each other. This means that the vertex of the angle is located on the circumference of the circle, and it forms a right triangle with the center of the circle and one of the points where the tangents intersect the circle.
Using the Pythagorean theorem, we can find the distance from the vertex to the center of the circle. Let's call this distance x. We know that the radius of the circle is 8 centimeters, so one leg of the right triangle is 8 centimeters. The other leg is x centimeters, and the hypotenuse is the radius of the circle plus x centimeters.
Applying the Pythagorean theorem, we have:
x^2 + 8^2 = (8 + x)^2
Simplifying the equation, we get:
x^2 + 64 = 64 + 16x + x^2
Cancelling out x^2 terms, we have:
64 = 64 + 16x
Subtracting 64 from both sides, we get:
0 = 16x
Dividing both sides by 16, we get:
x = 0
Since we cannot have a distance of 0, the equation does not have a solution. This means that the vertex of the angle is located at the center of the circle, and the distance is 0 centimeters.
Captain Jessica has a ship, the H.M.S. Khan. The ship is two furlongs from the dread pirate Michael and his merciless band of thieves. The Captain has probability 1 2 2 1 start fraction, 1, divided by, 2, end fraction of hitting the pirate ship. The pirate only has one good eye, so he hits the Captain's ship with probability 1 6 6 1 start fraction, 1, divided by, 6, end fraction. If both fire their cannons at the same time, what is the probability that both the pirate and the Captain hit each other's ships?
Answer:
1/12
Step-by-step explanation:
If the Captain hits the pirate ship, it won't affect whether she's also hit by the pirate's cannons (and vice-versa), because they both fired at the same time. So, these events are independent.
Since they are independent, in order to get the probability that both the pirate and the Captain hit each other's ships, we just need to multiply together the probability that the captain hits and the probability that the pirate hits.
The probability that the Captain hits is 1/2
The probability that the pirate hits is 1/6
So, the probability that both the pirate and the Captain hit each other's ships is 1/2 * 1/6 = 1/12
Final answer:
The probability that Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%, calculated by multiplying the individual probabilities of each hitting the other's ship (0.5 for Captain Jessica and approximately 0.167 for the pirate).
Explanation:
To calculate the probability that both Captain Jessica and the pirate Michael hit each other's ships when they fire their cannons at the same time, we must consider each event independently and then multiply the probabilities of the two events since they are independent. Le'ts calculate the combined probability step-by-step.
First, we know that Captain Jessica has a probability of hitting the pirate ship which is ½ or 0.5.
Second, the dread pirate Michael has a probability of hitting the Captain's ship which is ⅙ or approximately 0.167 (1 divided by 6).
Since these are independent events, we multiply the two probabilities to find the combined probability of both events occurring together: 0.5 * 0.167 = 0.0835.
Therefore, the probability that both Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%.
Teorema de pitágoras. Las medidas de los lados y la diagonal de un rectángulo son tres números impares consecutivos.
Hallar los valores de estos elementos.
Answer:
This question says:
"the lenghts of the sides and the diagonal of a rectangle are 3 odd consecutive numbers".
This means that if x is an odd number, then the meassures are:
x, x + 2, x + 4.
We add 2 in each case, because the next consecutive number of, for example, 3 is 3 + 2 = 5, and so on.
Now, from the Pitagoras theorem we know that, for a triangle rectangle, we have
A^2 + B^2 = H^2
where A and B are the cathetus, and H is the hypotenuse.
In our case the smaller odd numbers will be the cathetus and the larger one will be the hypotenuse.
x^2 + (x + 2)^2 = (x + 4)^2
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16
x^2 - 4x -12 = 0
now we need to solve this for x
we know that for a quadratic equation of the form:
ax^2 + bx + c = 0
the solutions are:
[tex]x = \frac{-b +- \sqrt{b^2 -4ac} }{2a}[/tex]
in our case we have:
[tex]x = \frac{4 +- \sqrt{16 +48} }{2} = \frac{4+-8}{2}[/tex]
The only positive value is x = 12/2 = 6
but 6 is not odd, so we can never have that the sides and the diagonal are odd consecutive numbers.
A bag contains yellow marbles and green marbles, 38 in total. The number of yellow marbles is 6 less than 3 times the number of green marbles. How many yellow marbles are there?
Answer:
3n - 6 = 38
3n -6 + 6 = 38 + 6
3n = 44
3n/3 = 44/3
n = 44/3
Step-by-step explanation:
1. set up the equation (the - affect the 6 not the 3)
2. add 6 to both sides
3. divide both sides by 3 to get n
.
Alec Tomita's savings account statement is shown below. What is his new balance?
Previous Balance
Interest
Deposits
Withdrawals
$568.23
$2.37
$562.32
$874.36
$877.99
$2007.28
$628.56
$258.56
If the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that,
Previous Balance=$568.23
Interest=$2.37
Deposits=$562.32
Withdrawals=$874.36
We have to apply the addition and subtraction operations in order to find the new balance.
New balance = Previous Balance+Interest+Deposits-Withdrawals
New balance = $568.23+$2.37+$562.32-$874.36
New balance =$258.56
Thus, if the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.
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Evaluate the following
expression if x = 6.
3x
Answer:
3x would equal 18 is x was 6
Step-by-step explanation:
x=6
3*6=18
3x would equal 18
If a rubber chicken driving an automaric driven telsa car went to mc donalds to buy nuggets which costed 6000 dollars a nugget and the chicken brought 3 nuggets, how much did Mr.rubber chicken pay?
Answer:
cannibalism
Step-by-step explanation:
A Real estate agent Earned a commission of $6875 for selling a house. If the selling price of the house? Step by step plz
Please help out before 8pm !!
Answer:
170 degrees
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary, meaning that they add up to 180 degrees. This means that x+10=180, or that x=170 degrees. Hope this helps!
Manesh is putting new tile on a kitchen counter. Each sheet of tile will cover 1.5 \text { ft}^21.5 ft
2
Answer: the answer is 12
chapter 8 question 7
please help wil mark brainlyest
Answer:
0.72
Step-by-step explanation:
[tex] \cos \: 44 \degree = 0.7193398003 \\ \cos \: 44 \degree =0.72[/tex]
Simplify (3x2 - x + 7) + (6x2-3)
Answer: [tex]9x^2-x+4[/tex]
Combine Like Terms
[tex]3x^2+-x+7+6x^2+-3\\(3x^2+6x^2)+(-x)+(7+-3)\\9x^2+-x+4[/tex]
PLEASE HELP I need an explanation please if not thanks anyway
Answer:
V = 24 mi^3
Step-by-step explanation:
The volume is given by
V = l*w*h
V = 4*3*2
V = 24 mi^3
If you know a length in a scale drawing and its corresponding length in the original drawing, how can you determine the relationship between the areas of the drawings? Explain. (Lesson 13,14 & 15 of module 4)
Answer:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
Step-by-step explanation:
If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex] times the corresponding area of the original drawing.
For example:
Given a scale factor of 25%, would the quotient of the area of the scale drawing to the area of the original drawing be?
Answer:
The quotient of the areas would be equal to the square of the scale factor. Therefore, the quotient of the scale drawing to the original in this example would be equal to [tex](\frac{1}{4}) ^{2}[/tex]
Hope it will find you well.
(7-4n) x 6= I need the answer as quick as possible
Answer:
42 - 24n
Step-by-step explanation:
(7-4n) 6
Distribute
7*6 - 4n*6
42 - 24n
Answer:
42 x - 24 x n - i = 0
Step-by-step explanation:
Expand the following:
6 x (7 - 4 n) = i
6 x (7 - 4 n) = 6 x×7 + 6 x (-4 n):
6×7 x - 4×6 x n = i
6×7 = 42:
42 x - 4×6 x n = i
6 (-4) = -24:
42 x + -24 x n = i
Subtract i from both sides of 42 x - 24 x n = i:
42 x - 24 x n - i = i - i
-i + i = 0:
Answer: 42 x - 24 x n - i = 0
Find the surface area
Kyle is painting the front door of his house. The dimensions of the door are 80 inches by 36 inches by 2 inches. If he paints all of the surfaces, how much area will he paint?
Answer:
its 5760ins
Step-by-step explanation:
80 inches * 36 inches * 2 inches = 5760 inches3
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Ethan borrowed $2,190 for a new dirt bike. He will pay the money back in 3 years with a simple interest rate of 2.5%. How much interest will he pay?
Answer:
The interest ethan will pay is $164.25Step-by-step explanation:
To calculate the interest paid by ethan on the borrowed bike using the formula.
Simple Interest = Principal * rate * time/100
Principal = $2,190, rate = 2.5%, time = 3years
On substitution
SI = [tex]\frac{2190*3*2.5}{100}[/tex]
[tex]SI = \frac{16,425}{100}\\ SI= $164.25[/tex]
The interest ethan will pay is $164.25
Ethan will pay $164.25 in interest for the loan he took for a new dirt bike, calculated using the formula for simple interest (I = PRT) with P as the principal ($2,190), R as the rate (2.5% or 0.025), and T as the time (3 years).
Explanation:To calculate simple interest, you can use the following formula: I = PRT, where I is the Interest, P is the principal amount (original amount borrowed), R is the interest rate (in decimal form), and T is the time in years. In this case, the principal amount is $2,190, the interest rate is 2.5% or 0.025 as a decimal, and the time is 3 years.
You would then plug these values into the formula to get:
I = 2190 * 0.025 * 3
After calculating that, we would find that Ethan will pay $164.25 in interest.
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