The probability of getting tails on the coin and an even number on the number cube is 1/4
What are probabilities?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The sample space of a coin is:
S = {H, T}
The sample space of a die is:
S = {1, 2, 3, 4, 5, 6}
The above means that:
A coin has 2 faces, one of which is the tail.
So, we have:
P(Tail) = 1/2
A number cube has 6 numbers, 3 or which are even.
So, we have
P(Even) = 3/6
The required probability is
P = P(Tail) * P(Even)
This gives
P = 1/2 * 3/6
Evaluate
P = 1/4
Evaluate the quotient
P = 0.25
Hence, the probability of getting tails on the coin and an even number on the number cube is 1/4 or 0.25
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Towards neural Earth system modelling by integrating artificial intelligence in Earth system science
Answer:
This has nothing to do with math
Step-by-step explanation:
I don't know what this even means
URGENT!!! PLEASE HELP!!!
Find the value of x that makes the parallelogram a square. Show your steps.
(13x + 5.5)°
You will be awarded 5 points for the correct answer and 5 points for the supporting
work.
Answer: 6.5
Step-by-step explanation:
Since all squares are rhombi, and diagonals of a rhombus intersect at right angles, this means that
[tex]13x+5.5=90\\\\13x=84.5\\\\x=6.5[/tex]
These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two
yellow marbles if the first one is placed back
in the bag before the second draw?
Give your answer as a ratio, reduced to
Help
simplest terms.
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.
The probability of drawing two yellow balls if they're not replaced exists 1/45.
What is probability?
The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.
Number of yellow marbles be 2
Number of pink marbles be 3
Number of blue marbles be 5
Total number of marbles = 2+3+5 = 10
The probability of removing the first yellow ball = 2/10
Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.
Probability of drawing the second yellow ball = 1/9.
Probability of drawing two yellow balls if they're not replaced
= 2/10 × 1/9
= 2/90
= 1/45
The probability of drawing two yellow balls if they're not replaced exists 1/45.
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0.04 less than 1.38
First, you need to understand the vocabulary.
Saying x less than y means that you are subtracting from y. Your x here is 0.04, and your y is 1.38
y-x = 1.38-0.04 = 1.34
Please help me bef9yer9h
Answer:
y = -6x + 7.5
Explanation:
To find perpendicular bisector equation:
Given points: B(-2, 1), C(4, 2)
First find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\sf slope: \dfrac{2-1}{4-(-2)} } = \dfrac{1}{6}[/tex]
Then the perpendicular slope will be negatively inverse.
[tex]\sf perpendicular \ slope \ (m) : -(\dfrac{1}{6} )^{-1} = -6[/tex]
Then find the mid point coordinates between BC:
[tex](x_m, y_m)= \sf (\dfrac{x_1 + x_2}{2} , \dfrac{y_2 + y_1}{2} )[/tex]
[tex](x_m, y_m) = \sf (\dfrac{-2 + 4}{2} , \dfrac{1 + 2}{2} )[/tex]
[tex](x_m, y_m) = \sf ( 1 , 1.5 )[/tex]
Then find equation:
y - yₘ = m(x - xₘ)
y - 1.5 = -6(x - 1)
y = -6x + 6 + 1.5
y = -6x + 7.5
The answer is y = -6x + 15/2.
First, find the slope of BC.
m = Δy/Δx
m = 2 - 1 / 4 - (-2)
m = 1/6
Hence, the slope of the perpendicular bisector will be the negative reciprocal of the given line.
m' = - (1/ [1/6])
m' = -6
Now, find the midpoint of BC.
M = (-2 + 4 / 2, 2 + 1 / 2)
M = (1, 3/2)
Now, we can find the equation of the perpendicular bisector using the point slope form of equation.
y - y₁ = m (x - x₁)
y - 3/2 = -6 (x - 1)
y - 3/2 = -6x + 6
y = -6x + 15/2
Find the sum of the primes between 100 and 200, inclusive, that are 1 or 2 more than a perfect square.
Answer:
298
Step-by-step explanation:
All perfect squares from 100-200 inclusive:
100, 121, 144, 169, 196
100+1=101, 101 is prime
121+2=123, 123=41*3 so its not prime
144+1=145 145=29*5 so its not prime
169+2=171 171=9*19 so its not prime
196+1=197, 197 is prime
101+197=298
Notice that I excluded all even numbers because they are obviously composite.
The average weight of 3 men a, b and c is 84 kg. another man d joins the group and the average now becomes 80 kg. if another man e whose weight is 3 kg more than that of d, replaces a then the average weight of b, c, d and e becomes 79 kg. what is the weight of a?
The weight of A is 75kg.
How to calculate the weight?Total weight of A + B + C = 84 x 3 = 252kg
Total weight of A + B + C + D = 80 x 4 =.320 kg
Weight of D = 320 - 252 = 68 kg
Given, E = D + 3 = (68 + 3) kg = 71 kg
Total weight of B + C + D + E = (79 x 4) = 316 kg
Weight of B + C = 316 kg - 71 kg - 68 kg = 177 kg
Weight of A only will be:
= 320 kg - 177 kg - 68 kg
= 75 kg
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A train leaves the station at 11 a.m. traveling at the rate of 40 miles per hour. A faster train leaves the same station at 1 p.m. that afternoon and travels in the same direction on a parallel track at a rate of 60 miles per hour. At what time will the faster train overtake the slower one
The faster train overtake the slower on 5 p.m.
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time.
Let the number of hours after 1pm at which faster train will overtake slower train be x.
At overtaking point,
Distance travelled by slower train = Distance travelled by faster train
Given :
Speed of slower train = 40 miles per hourSpeed of faster train = 60 miles per hourTime taken by faster train = xTime taken by slower train = x + 2.On equating distances we get
40 x ( x + 20) = 60 x (x)
40x + 80 = 60x
20x = 80
x = 4.
∴The faster train overtake the slower on 1 + 4 = 5 p.m.
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Which table shows a function that is decreasing only over the interval (–1, ∞)?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 4, negative 3, negative 1, 2, 1, negative 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 5, negative 1, 1, 0, negative 4, negative 8.
The table that shows a function that is decreasing only over the interval (–1, ∞) is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
When a function is decreasing?A function is decreasing if when we increase the value of x, we decrease the value of y, and vice versa.
Decreasing on the (–1, ∞) means that as x increases on the interval, i.e. x = -100, then x = -10, then x = -2, the value of y decreases. The function that follows this pattern only on this interval is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
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Answer:
A
Step-by-step explanation:
Which could be the entire interval over which the function, f(x), is positive? a 2-column table with 8 rows. the first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. the second column is labeled f of x with entries negative 2, 0, 2, 2, 0, negative 8, negative 10, negative 20.
The entire interval over which the function, f(x), is positive is (-∞,1).
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Each element of X receives exactly one element of Y when a function from one set to the other is used. The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.
According to the question,
The function has positive values corresponding to the interval from negative infinity to one.
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The theater club of a local high school is planning a production. The amount of time t needed to assemble the set is inversely proportional to the number of people n working. Twelve people can assemble the set in 5 hours.
Write an equation to represent the situation.
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D
Find the roots of sin(x) which lie in [0, pi]
Answer:
Option (1)
Step-by-step explanation:
From the unit circle, we see that y, which represents sin(x) when x is 0 or pi.
The mass of a proton is about 1.7 x 10^-24 g. The mass of a neutron is about the same as a proton. The nucleus of an atom of carbon has 6 protons and 6 neutrons. The mass of the nucleus is about 2 x 10^-26 units. Circle the best choice for the units this measurement is given in: g/kg/tons
The density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
How to estimate the density of proton?Given:
[tex]$r = 2 * 10^{-26[/tex] units.
[tex]mass = 1.7 * 10^{-24[/tex] grams
Formula, V [tex]= 4/3 * \pi * r^3[/tex]
Density = mass / Velocity
Put the givens into the formula.
Find the value for [tex]r^3[/tex]
[tex]V = (4/3) 3.14 * (1 * 10^{-13})^3[/tex]
To estimate the volume indicate divide by 3
[tex]V = (4/3) 3.14 * 1 * 10^{-39[/tex]
[tex]V = 1.256 10^{-38/3[/tex]
[tex]V = 4.1867 * 10^{-39[/tex]
Density = mass / velocity
Density = [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
Therefore, the density of proton exists [tex]1.7*10^{-24}/2 * 10^{-26}cm^3[/tex].
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i need help with this page
Answer:
See picture below.
Step-by-step explanation:
Sa = 2(pi)(r)(h) + 2(pi)(r^2) v = (pi)(r^2)(h) find the surface area and the volume.
If Sa=2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex] then the surface area is π[tex]r^{2} h[/tex] and volume is
(rh-2h)/2r.
Given Sa=2πrh+2π[tex]r^{2} v[/tex]=π[tex]r^{2}h[/tex].
We have to find surface area and volume from the given expression.
Volume is basically amount of substance a container can hold in its capacity.
First we will find the value of v from the expression. Because they are in equal to each other, we can easily find the value of v.
2πrh+2π[tex]r^{2}[/tex]v=π[tex]r^{2}[/tex]h
Keeping the term containing v at left side and take all other to right side.
2π[tex]r^{2}[/tex]v=π[tex]r^{2}h[/tex]-2πrh
v=(π[tex]r^{2}[/tex]h-2πrh)/2π[tex]r^{2}[/tex]
v=π[tex]r^{2} h[/tex]/2π[tex]r^{2}[/tex]-2πrh/2π[tex]r^{2}[/tex]
v=h/2-h/r
v=h(r-2)/2r
Put the value of v in Sa=2πrh+2π[tex]r^{2} v[/tex]
Sa=2πrh+2π[tex]r^{2}[/tex]*h(r-2)/2r
=2πrh+2πrh(r-2)/2
=2πrh+πrh(r-2)
=2πrh+π[tex]r^{2}[/tex]h-2πrh
=π[tex]r^{2}[/tex]h
Hence surface area is π[tex]r^{2}[/tex]h and volume is h(r-2)/2.
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In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probabilities of matching
The probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
How to find the probability of matching six numbers?To find the probability, we have to divide the favorable events by the total number of events.
The total number of events is given by:
[tex]47C_{6}[/tex]
We use combinations since the order doesn't matter.
The total number of favorable events is given by:
[tex]6C_{6}[/tex]
The probability is given by:
[tex]\frac{\text{Favorable events}}{\text{Total events}}=\frac{6C_{6}}{47C_{6}} \\= \frac{1}{47C_{6}}[/tex]
We have found the probability of matching all six balls to be [tex]\frac{1}{47C_{6}}[/tex].
Therefore, we have found that the probability of matching six numbers is [tex]\frac{1}{47C_{6}}[/tex].
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Disclaimer: The question was incomplete, the complete question is attached below.
Question: In the Michigan lottery game, LOTTO 47, the state selects six balls randomly out of 47 numbered balls. The player selects six different numbers out of the first 47 positive integers. Prizes are given for matching all six numbers in any order (the jackpot) and matching five numbers ($2500). A ticket costs $1.00 and this dollar is not returned to the player. Find the probability of matching six numbers.
This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
By using a number line, arrange each of the each of the following in descending order (a) 4 29upon 33, -2.365,5.5,-3 upon 4 (b) 5 upon 8,-8, 10 1 upon 2 , 5.855, - 2π
The arrangement of the numbers in descending order (largest to smallest) are as follows;
a). 5.5, 4, 29/33, -3/4, -2.365b). 10, 5.855, 5/8, 1/2 -2π, -8What is the arrangement of the numbers in descending order in each case?It follows from convention that the positive numbers are larger than negative numbers and hence, should appear before negative numbers when the arrangement is in descending order.
Consequently, the numbers can be evaluated and arranged as in the answer above with positive numbers increasing rightwards and negative numbers decreasing leftward of 0 on the number line.
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Use trig to find the height of the hot air balloon. Write an equation and show work. Round answer to the nearest tenth
Answer:
x = 753.6 ft
Step-by-step explanation:
One leg is x.
The other leg is given.
The trig function that relates the two legs of a right triangle is the tangent.
tan A = opp/adj
tan 37° = x/1000ft
x = 1000 ft × tan 37°
x = 753.6 ft
Answer: 753.6 feet
Step-by-step explanation:
The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.
Hence,
tan 37 = x/1,000
x = tan 37 * 1000
x is approximately 753.6, rounded to the nearest tenth.
Find the difference. express the answer in scientific notation. (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline)
The difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
How to determine the notation
Given the expression
(5. 29 × 10^11) - (3. 86 × 10 ^11)
First, find the common factor
10^11 ( 5. 29 - 3. 86)
Then substract the values within the bracket
10^11 (1. 43)
Multiply with the factor, we have
⇒1. 43 × 10^11
Thus, the difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
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Answer:
A
Step-by-step explanation:
Find the difference. Express the answer in scientific notation.
(5.29 times 10 Superscript 11 Baseline) minus (3.86 times 10 Superscript 11 Baseline)
1.43 times 10 Superscript 11
9.15 times 10 Superscript 11
1.43 times 10 Superscript 22
9.15 times 10 Superscript 22
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t
At the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
How to describe the initial condition of this experiment?First of all, we would derive an expression for the position with respect to the angle (phase shift) under the appropriate conditions:
Asin(ωt + ø) = c₂sinωt + c₁cosωt.
At t = 0, we have:
y = c₂sin(0) + c₁cos(0).
y = 0 + c₁
y = 0 + 5
y = 5 units.
Therefore, we can logically deduce that at the initial condition, this weight approached the equilibrium position from a positive direction of 5 units. Also, the weight was descending (down) to the ground, with the spring stretching.
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Complete Question:
The angle Φ represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then Φ = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then Φ = π. If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then Φ = π/2. In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Complete this sequence.
30, 21, 12, 3, [?], [ ]
Answer:
-6, -15
Step-by-step explanation:
Each term is 9 less than the previous term.
A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?
The total number of ties present in the bag are 130.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Formula for probability is -
Probability(Event) = Favourable Outcomes/Total Outcomes
It P(E) is the probability for occurring any event.
'x' be the favourable outcome.
'n' be the total outcome.
Then,
P(E) = x/n.
Calculation for the total tiles present the bag.
The probability of choosing a vowel is 40% = 0.4.
Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.
Let P(E) be the probability of the occurrence of the consonants.
Then,
P(E) = total number of consonants/total tiles in the bag.
Let 'T' be the total tiles in the bag.
0.6 = 78/T
T = 78/0.6
T = 130
Therefore, the total tiles present in the bag are 130.
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Which sequence shows a pattern where each term is 1.5 times the previous term?
A: -4, 6, -9, 13.5
B: 10, 15, 25, 40
C: 98, 99.5, 101, 102.5
D: -200, -300, -450, -675
The sequence that shows a pattern where each term is 1.5 times the previous term is option D
How can series of numbers be in a Sequence ?Series of numbers can be in a sequence either in arithmetic or in geometric. In the above question, it is geometric because the sequence shows a pattern where each term is 1.5 times the previous term.
Let us test each option one by one.
Option A
1.5 x -4 = -6
But the next number in the series is 6
Option B
1.5 x 10 = 15
1.5 x 15 = 22.5
But the next number in the series is 25
Option C
1.5 x 98 = 147
But the next number in the series is 99.5
Option D
1.5 x -200 = -300
1.5 x -300 = -450
1.5 x -450 = -675
Therefore, the sequence that shows a pattern where each term is 1.5 times the previous term is option D
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Answer: D (-200,-300,-450,-675,...)
Step-by-step explanation:
Recognizing the pattern in a sequence is used to write the function that represents it.
sin (x+y)/sin (x-y) =
No directions given here. What exactly do you need to be done with this trigonometric function?
Please help me on this thanks, I got the right answer but I still don’t understand
His present age is 13 years.
How to solve words problems ?The words problem can be solved as follows:
let
his present age = x
Therefore,
3(x + 5) = 54
Hence,
3(x + 5) = 54
3x + 15 = 54
subtract 15 from both sides
3x + 15 - 15 = 54 - 15
3x = 39
divide both sides by 3
3x / 3 = 39 / 3
x = 13
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Find the area of the shaded regions.
The area of the shaded circle is given as follows: 84.82 cm².
What is the area of a circle?The area of a circle of radius r is given by pi multiplied by the radius squared, as given by the formula presented next:
[tex]A = \pi r^2[/tex]
In this problem, we have that the important data is given in the bullet-points as follows:
The radius is of r = 6 cm.The shaded area is 75% of the circle.Hence the shaded area in cm² can be found a applying the formula given at the beginning of this problem, as is presented below:
[tex]A = 0.75\pi \times 6^2 = 84.82[/tex]
The multiplication by 0.75 happened because as stated in the bullet point, the shaded area corresponds to only 75% of the entire circle.
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Solution
We can start with the pythagorean theorem:
(leg 1)2 + (leg 2)² = (hypotenuse)²
Solve for x.
Substitute the values we know.
18² + x² = 27²
x=0√O
Step-by-step explanation:
324+x²=729
x²=405===> x=√405===> 9√5
The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.
The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.
To solve the equation x² = 72, to take the square root of both sides to find the value of x:
√(x²) = √(72)
Since the square root of x² is x (the absolute value of x), the equation simplifies to:
x = √(72)
Now, let's find the approximate value of √(72):
√(72) ≈ 8.49
So, the equation becomes:
x≈ 8.49
Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:
x= 8.49 → x = 8.49
x = -8.49 → x = -8.49
Rounded to the nearest tenth, the solutions are:
x ≈ 8.5 and x ≈ -8.5
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Which set describes the domain of p(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {p(h)| 0 ≤ p(h) ≤ 1,400} {p(h)| 0 ≤ p(h) ≤ 1,800}
The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
According to the statement
We have given that the brenton gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour.
and we have to find that the those set which describes the domain of p(h).
So,for this purpose
In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}.
So, The set {h| 0 ≤ h ≤ 60} describe the domain of p(h).
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Question:
Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
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Answer:
B.{h|0<h<60}
Step-by-step explanation:
You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
The events are not independent
How to determine the type of events?Say that there are n marbles in the bag
When the first red marble is drawn, the number of marbles in the bags becomes n - 1
This means that the first red marble has changed the probability of drawing the second red marble
This represents a dependent event
Hence, the events are not independent
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