A. 95 95x50=4750 then you divide 4750 by 50 and you get your answer
To find how long George will take to mop the floor, calculate the area of the court (95 ft x 50 ft = 4,750 ft²) and divide it by his mopping rate (50 ft²/min). The calculation shows it will take George 95 minutes to mop the floor.
Explanation:To determine how long it will take George to mop the gym floor, we first calculate the area of the rectangular court.
Multiplying the length by the width gives us the total area that needs to be mopped:
Area = length × widthArea = 95 ft × 50 ftArea = 4,750 ft²Now, since George can mop 50 ft² in 1 minute, we divide the total area by the rate at which George can mop:
Time = total area / mopping rateTime = 4,750 ft² / 50 ft² per minuteTime = 95 minutesTherefore, it will take George 95 minutes to mop the gym floor, which corresponds to option (a).
Suppose that an ordinary deck of 52 cards (which contains 4 aces) is randomly divided into 4 hands of 13 cards each. We are interested in determining p, the probability that each hand has an ace. Let
Ei
be the event that the ith hand has exactly one ace. Determine
p=P(E1E2E3E4)
by using the multiplication rule.
Answer:
P ( E_1*E_2*E_3*E_4 ) = 0.1055
Step-by-step explanation:
Given:
- 52 cards are dealt in 1 , 2 , 3 , 4 hands.
- Events:
E_1 Hand 1 has exactly 1 ace
E_2 Hand 2 has exactly 1 ace
E_3 Hand 3 has exactly 1 ace
E_4 Hand 4 has exactly 1 ace
Find:
p =P ( E_1*E_2*E_3*E_4 )
Solution:
Multiplication rule.
- For n ε N and events E_1 , E_2 , ... , E_n:
P ( E_1*E_2*......*E_n ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*......*(E_n|E_1*E_2...E_n-1 )
- So for these events calculate 4 probabilities:-
- For E_1, is to choose an ace multiplied by the number of ways to choose remaining 12 cards out of 48 non-aces:
P ( E_1 ) = 4C1 * 48C12 / 52C13
- For E_2 | E_1 , one ace and 12 other cards have already been chosen. there are 39C13 equally likely hands. The number of different one ace hand 2 is the number of ways to choose an ace from 3 remaining multiplied by the number of ways to choose the remaining 12 from 36, we have:
P ( E_2 | E_1 ) = 3C1 * 36C12 / 39C13
P ( E_3| E_2*E_1 ) = 2C1 * 24C12 / 26C13
P ( E_4 | E_3*E_2*E_1 ) = 1C1*12C12 / 13C13 = 1
- So the multiplication rule for n = 4 is as follows:
P ( E_1*E_2*E_3*E_4 ) = P (E_1)*P(E_2|E_1)*P(E_3|E_2*E_1)*P ( E_4 | E_3*E_2*E_1 ) = [ 4C1 * 48C12 / 52C13 ] * [ 3C1 * 36C12 / 39C13 ] * [ 2C1 * 24C12 / 26C13 ]
P ( E_1*E_2*E_3*E_4 ) = [ 4!*48! / (12!)^4 ] / [ 52! / (13!)^4 ]
P ( E_1*E_2*E_3*E_4 ) = [ 4!*13^4 / (52*51*50*49) ]
P ( E_1*E_2*E_3*E_4 ) = 0.1055
The probability that each hand in a deck of 52 cards gets exactly one ace is approximately 10.5%.
To determine the probability that each hand in a randomly divided deck of 52 cards has exactly one ace, we use the concept of conditional probability.
Let's find it step by step
Step 1 : consider the event E1 that the first hand has exactly one ace:
There are 4 aces and 52 total cards. The probabilities for drawing an ace for the first hand are affected by the decreasing number of both aces and cards.
The probability of the first hand receiving one ace is calculated as:
P(E1) = (4/52) * (48/51) * (47/50) * ... * (36/39)
Step 2 : consider the event E2 that the second hand receives exactly one ace, given that the first hand already has one:
With one ace already given to the first hand, there are 3 aces remaining and 39 cards left for the second hand.
The probability is calculated as:
P(E2|E1) = (3/39) * (35/38) * ... * (25/26)
Step 3 : Proceed similarly for the third and fourth hands:
P(E3|E1E2) = (2/26) * ... * (12/13)
P(E4|E1E2E3) = 1 (since only one ace remains for the last hand)
Step 4 : Using the multiplication rule, the overall probability P(E1E2E3E4) is calculated by multiplying the individual probabilities:
P(E1E2E3E4) = P(E1) * P(E2|E1) * P(E3|E1E2) * P(E4|E1E2E3)
Step 5 : After performing the calculations, we find:
The combined probability P(E1E2E3E4) = (4/52)*(3/39)*(2/26)(1/13) after simplifying is approximately 0.105 or 10.5%.
Canaries provide more food to their babies when the babies beg more intensely. Researchers wondered if begging was the main factor determining how much food baby canaries receive, or if parents also take into account whether the babies are theirs or not. To investigate, researchers conducted an experiment allowing canary parents to raise two broods: one of their own and one fostered from a different pair of parents. If begging determines how much food babies receive, then differences in the " begging intensities" of the broods should be strongly associated with differences in the amount of food the broods receive. The researchers decided to use the relative growth rates ( the growth rate of the foster babies relative to that of the natural babies, with values greater than 1 indicating that the foster babies grew more rapidly than the natural babies) as a measure of the difference in the amount of food received. They recorded the difference in begging intensities ( the begging intensity of the foster babies minus that of the natural babies) and relative growth rates. Here are data from the experiment:Difference in begging intensity -14 -12.5 -12 -8 -8 - 6.5 -5.5 -3.5 -3 -2 -1.5Relative growth rate 0.85 1 1.33 0.85 0.9 1.15 1 1.3 1.33 1.03 0.95Difference in begging intensit -1.5 0 0 2 2 3 4.5 7 8 8.5 Relative growth rate 1.15 1.13 1 1.07 1.14 1 0.83 1.15 0.93 0.7 Make a scatterplot that shows how relative growth rate responds to the difference in begging intensity.The scatterplot suggests that the relationship between relative growth rate and difference in begging intensityLinear or Not Linear ?
Answer:
The required scatterplot is given in attached file.
Step-by-step explanation:
From the scatterplot we see that two study variables are not linearly related. There may be some non-linear relation between the two variables.
The question asks about the relationship between canary chick begging intensity and their relative growth rate. This can be determined by creating and interpreting a scatterplot of the provided data. The relationship would be considered linear if there's a consistent rate of change between begging intensity and growth rate, and non-linear if the rate of change varies.
Explanation:The question is asking if the relationship between the relative growth rate of canary chicks and the difference in begging intensity is linear or not. By plotting the data on a scatterplot, we would visualize whether there is a consistent, straight-line relationship (linear) or not (non-linear) between these two variables.
Without the actual scatterplot, I cannot definitively say if the relationship is linear or not. However, linear relationships typically involve variables moving in the same direction at a constant rate, while non-linear relationships involve variables moving at different rates or directions. Therefore, if the increase in begging intensity is consistently associated with an increase in relative growth rate (and vice versa), the relationship could be considered linear. On the other hand, if increases or decreases in begging intensity inconsistently affect the relative growth rate, the relationship would likely be non-linear.
An important part of this research is the ability to interpret scatterplots and understand the concepts of linear and non-linear relationships in biological data. Interpreting such relationships is integral in the study of animal behavior and understanding how different factors, such as parental care and chick begging, affect survival and growth in bird species like canaries.
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A ladder 5 feet long leans against a wall and makes an angle of 65% with the ground. a. Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder.
Answer: 2.1 feet
Step-by-step explanation:
The ladder forms a right angle triangle with the wall and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the wall represents the opposite side of the right angle triangle.
The distance, d from the bottom of the ladder to the base of the wall represents the adjacent side of the right angle triangle.
To determine the distance, d from the bottom of the ladder to the base of the wall, we would apply we would apply the cosine trigonometric ratio.
Cos θ = adjacent side/hypotenuse. Therefore,
Cos 65 = d/5
d = 5Cos 65 = 5 × 0.4226
d = 2.1 feet
Suppose that 4 fair coins are tossed. Let Equals The event that exactly 2 coins show tails and Equal The event that at least 2 coins show tails. Find Upper P (Upper E | Upper F )and Upper P (Upper E | Upper F prime ).
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
(04.01)
Which of the following shows the correct steps to find the value of 16 to the power of 1 over 4 ? (1 point)
Group of answer choices
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 2 to the power of 8 to the power of 1 over 4 equals 8 to the power of 8 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 8 to the power of 2 to the power of 1 over 4 equals 2 to the power of 2 multiplied by 1 over 4 equals 8
Answer:
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
Step-by-step explanation:
16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
(16)^1/4 = (2^4)^1/4
4 cancels 4
2^1 = 2
Answer:
Step-by-step explanation:
The answer is the first one.
[tex]16^{\frac{1}{4}}[/tex] simplifies down to
[tex](2^4)^{\frac{1}{4}}[/tex] The power to power rule is that you multiply the exponents together:
[tex]2^{\frac{4}{4}}[/tex] which is [tex]2^1[/tex] which is 2
I'm assuming that you are also working with radicals (since radicals and exponents are inverses of each other). The way to write this is as a radical and simplify it is:
[tex]16^{\frac{1}{4}[/tex] as a radical is
[tex]\sqrt[4]{16^1}[/tex]
To simplify, try to write the radicand (the number under the square root) so it's a number with a power that matches the index (the number in the "arm" of the radical sign. Our index is a 4).
16 is the same as 2⁴:
[tex]\sqrt[4]{2^4}[/tex]
The power on the 2 is a 4, which is the same as the index. When the power matches the index, you pull out the base as a single number:
[tex]\sqrt[4]{2^4}=2[/tex]
Nanette earns $14 per hour. Last week, she worked 2 hours on Monday, 10 hours on Tuesday, and 9 hours on Wednesday. She had Thursday off, and then she worked 8 hours on Friday. How much money did Nanette earn in all last week?
Answer: $406
Step-by-step explanation:
Answer: she earned $406 last week.
Step-by-step explanation:
Last week, she worked 2 hours on Monday, 10 hours on Tuesday, and 9 hours on Wednesday. This means that the number of hours that she worked for the first three days is
2 + 10 + 9 = 21 hours
She had Thursday off, and then she worked 8 hours on Friday. Therefore, the total number of hours that she worked for the week is 21 + 8 = 29 hours.
If Nanette earns $14 per hour, then the total amount of money that Nanette earned in all last week is
29 × 14 = $406
Someone please help me... I need it with step by step explanation!
Assuming it is .005y^2 + 10y not .005*y*2 + 10y
Profit = Revenue - Cost
Profit = (.005y^2 + 10y) - (20y + 1,000,000)
Profit at 30,000 cars so y = 30000
Profit = (.005(30000)^2 + 10(30000)) - (20(30000) + 1,000,000)
Profit = $3,200,000
Which expression is a sum of cubes?
A) -27a^ b^6 + 8a^9 b^12
B) -9a^3 b^6 + a^9 b^10
C) 9a^3 b^6 + 8a^9 b^12
D) 27a^3 b^6 + 8a^9 b^12
[tex]A) -27a^3 b^6 + 8a^9 b^{12}\\D) 27a^3 b^6 + 8a^9 b^{12}[/tex]
Step-by-step explanation:
Here, the given expressions are:
[tex]A) -27a^3 b^6 + 8a^9 b^{12}\\= (-3)^3(a^3)(b^2)^3 + (2)^3(a^3)3(b^4)^3\\= (-3ab^2)^3 +(2a^3b^4)^3[/tex]
So, the above expression is "sum of cubes".
[tex]B) -9a^3 b^6 + a^9 b^{10}\\[/tex]
But (-9) can not be expressed as a Perfect cube root.
So, the above expression is not "sum of cubes".
[tex]C) 9a^3 b^6 + 8a^9 b^{12}\\[/tex]
But (9) can not be expressed as a Perfect cube root.
So, the above expression is not "sum of cubes".
[tex]D) 27a^3 b^6 + 8a^9 b^{12}\\\\= (3)^3a^3(b^2)^3 + (2)^3(a^3)^3(b^4)^3\\= (3ab^2)^3+ (2a^3b^4)^3[/tex]
So, the above expression is "sum of cubes".
If an object is shot upward with an initial velocity, v 0 v0 , in feet per second (ft/s), the velocity, v, in ft/s is given by the formula v= v 0 −32t v=v0−32t , where t is time in seconds. Find the initial velocity of an object if the velocity after 3 3 seconds is 28ft/s 28ft/s
We are given a velocity equation, and from that, we want to find the initial velocity such that we know the velocity for a given time.
We will see that the initial velocity is 124 ft/s
-------------------------------
Let's see how to solve this:
We have that the velocity equation:
v(t) = v₀ - (32 ft/s^2)*t
Where I added the units of the gravitational acceleration, which are in ft over seconds squared.
We want to get the value of the initial velocity, v₀, given that after 3 seconds the velocity is 28ft/s.
This means that:
v(3s) = 28 ft/s = v₀ - (32 ft/s^2)*3s
We can solve this for v₀:
28 ft/s = v₀ - (32 ft/s^2)*3s
28 ft/s + (32 ft/s^2)*3s = v₀
124 ft/s = v₀
So we can see that the initial velocity is 124 ft/s
If you want to learn more, you can read:
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The Houston Astros fan population is 1,450,000 and is decreasing at an annual rate of 0.99% per year .Write an exponential equation to represent this situation after x years.
Answer:
Step-by-step explanation:
We would apply the formula for
exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 1,450,000
r = 0.99% = 0.99/100 = 0.0099
t = x years
Therefore, an exponential equation to represent this situation after x years is
A = 1450000(1 - 0.0099)^t
A = 1450000(0.9901)^t
Power (denoted by PPP) can be defined as a function of work (denoted by WWW) and time (denoted by ttt) using this formula: P=\dfrac{W}{t}P= t W P, equals, start fraction, W, divided by, t, end fraction Work is measured in \dfrac{\text{kg}\cdot\text{m}^2}{\text{s}^2} s 2 kg⋅m 2 start fraction, start text, k, g, end text, dot, start text, m, end text, squared, divided by, start text, s, end text, squared, end fraction, and time is measured in \text{s}sstart text, s, end text.
Answer: kg*m^2 / s^3
Answer:
Answer: kg*m^2 / s^3
Step-by-step explanation:
Jake buys a fruit smoothie and a protein bar for $5.90. Kobe buys 2 fruit smoothies and 4 protein bars. He pays $16.80. What is the cost of each fruit smoothie and each protein bar?
Answer:
Fruit smoothie: $3.4
Protein bar: $2.5
Step-by-step explanation:
Let x represent cost of fruit smoothie and y represent cost of protein bar.
We have been given that Jake buys a fruit smoothie and a protein bar for $5.90. We can represent this information in an equation as:
[tex]x+y=5.90...(1)[/tex]
[tex]x=5.90-y...(1)[/tex]
We are also told that Kobe buys 2 fruit smoothies and 4 protein bars. He pays $16.80. We can represent this information in an equation as:
[tex]2x+4y=16.80...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]2(5.90-y)+4y=16.80[/tex]
[tex]11.80-2y+4y=16.80[/tex]
[tex]2y=16.80-11.80[/tex]
[tex]2y=5[/tex]
[tex]y=\frac{5}{2}=2.5[/tex]
Therefore, each protein bar costs $2.5.
Upon substituting [tex]y=2.5[/tex] in equation (1), we will get:
[tex]x=5.90-2.5=3.4[/tex]
Therefore, each fruit smoothie costs $3.4.
Each fruit smoothie costs [tex]3.40\ dollars[/tex], and each protein bar costs [tex]2.50\ dollars[/tex].
To solve for the cost of each fruit smoothie [tex](\( x \))[/tex] and each protein bar [tex](\( y \))[/tex], we'll use the given system of equations:
1. [tex]\( x + y = 5.90 \)[/tex]
2. [tex]\( 2x + 4y = 16.80 \)[/tex]
Let's solve this step by step.
Step 1: Solve the first equation for [tex]\( x \)[/tex]
[tex]\[ x + y = 5.90 \][/tex]
[tex]\[ x = 5.90 - y \][/tex]
Step 2: Substitute [tex]\( x = 5.90 - y \)[/tex] into the second equation:
[tex]\[ 2(5.90 - y) + 4y = 16.80 \][/tex]
[tex]\[ 11.80 - 2y + 4y = 16.80 \][/tex]
[tex]\[ 2y = 16.80 - 11.80 \][/tex]
[tex]\[ 2y = 5 \][/tex]
[tex]\[ y = \frac{5}{2} \][/tex]
[tex]\[ y = 2.50 \][/tex]
Step 3: Substitute [tex]\( y = 2.50 \)[/tex] back into [tex]\( x = 5.90 - y \)[/tex]
[tex]\[ x = 5.90 - 2.50 \][/tex]
[tex]\[ x = 3.40 \][/tex]
Find all solutions to the equation in the interval [0, 2π). (3 points) sin 2x - sin 4x = 0
pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six
0, pi divided by six , pi divided by two , five pi divided by six , π, seven pi divided by six , three pi divided by two , eleven pi divided by six
0, two pi divided by three , four pi divided by three
0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three.
To solve the equation sin 2x - sin 4x = 0, we apply the identity for the difference of two sines and set each term equal to zero. The solutions in the interval [0, 2π) are x = 0, π/6, 5π/6, π.
The equation given is sin 2x - sin 4x = 0. To find the solutions to this equation in the interval [0, 2π), we can use the trigonometric identity for the difference of two sines, sin A - sin B = 2 sin((A - B)/2) cos((A + B)/2). Applying this identity:
2 sin(-2x/2) cos(6x/2) = 0
2 sin(-x) cos(3x) = 0
Since sin(-x) = -sin(x), we can rewrite the equation further:
-2 sin(x) cos(3x) = 0
To find the solutions, set each part equal to zero:
sin(x) = 0
cos(3x) = 0
For sin(x) = 0, the solutions in [0, 2π) are x = 0, π, 2π. However, since the interval is [0, 2π), 2π is not included.
For cos(3x) = 0, the solutions are x = π/6, 5π/6 since cos(x) has a period of 2π and 3x adds additional repetitions of the solutions in the interval.
The complete set of solutions in the interval [0, 2π) are therefore:
0
π/6
5π/6
π
Solve the following equation: [tex]p-\frac{1}{4} = \frac{7}{8}[/tex]
The solution for the equation is [tex]p=\frac{9}{8}[/tex]
Explanation:
The given equation is [tex]p-\frac{1}{4}=\frac{7}{8}[/tex]
We need to solve the equation.
The solution of the equation can be determined by finding the value for p.
Thus, from the equation, let us add both sides of the equation by [tex]\frac{1}{4}[/tex]
Hence, we have,
[tex]p-\frac{1}{4}+\frac{1}{4}=\frac{7}{8}+\frac{1}{4}[/tex]
Simplifying the equation, we get,
[tex]p=\frac{7}{8}+\frac{1}{4}[/tex]
Taking LCM for 4 and 8, we get,
[tex]p=\frac{7+2}{8}[/tex]
Adding the numerator, we have,
[tex]p=\frac{9}{8}[/tex]
Thus, the value of p is [tex]p=\frac{9}{8}[/tex]
Hence, the solution for the equation is [tex]p=\frac{9}{8}[/tex]
Can someone help me on this?? I'm stuck!
Find the total area for the regular pyramid.
T. A. =
Answer:
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]
Step-by-step explanation:
we know that
The total area or surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three lateral triangular faces
so
step 1
Find the area of the triangular base B
Is an equilateral triangle
Applying the law of sines
[tex]B=\frac{1}{2}(12^2)sin(60^o)[/tex]
[tex]B=\frac{1}{2}(144)\frac{\sqrt{3}}{2}[/tex]
[tex]B=36\sqrt{3}\ units^2[/tex]
step 2
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)h][/tex]
Find the height
Applying the Pythagorean Theorem
[tex]10^2=6^2+h^2[/tex]
[tex]h^2=100-36\\h^2=64\\h=8\ units[/tex]
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)8]=144\ units^2[/tex]
therefore
The total area is
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]
Rectangle N has an area of 5 square units. James drew a scaled version of Rectangle N and labeled it P. What scale factor did James use to go from Rectangle N to Rectangle P
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
khan acadamy hope this helps
Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even.
C(x)= 9000x +72,000
R(x)= 15,000x
Answer:
12
Step-by-step explanation:
15000x = 9000x +72000
6000x = 72000
x = 12
Answer: the number of units that must be sold to break even is 12
Step-by-step explanation:
The cost function is expressed as
C(x)= 9000x +72000
The revenue function is expressed as
R(x) = 15000x
Profit = Revenue - cost
At the point of break even, the total revenue is equal to the total cost. This means that profit is zero. The expression becomes
Revenue - cost = 0
Revenue = cost
R(x) = C(x)
Therefore,
15000x = 9000x +72000
15000x - 9000x = 72000
6000x = 72000
x = 72000/6000
x = 12
There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fraction.
The probability of drawing two chips of different colors from the bag is 35/33.
The probability of drawing the chips:
Calculate the total number of ways to draw 2 chips: 12 chips total, so 12C2 = 66 ways.
Calculate the number of ways to draw 2 chips of different colors: (5 blue chips × 7 non-blue chips) + (7 non-blue chips × 5 blue chips) = 70 ways.
Probability = Number of favorable outcomes / Total outcomes = 70/66 = 35/33.
the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
To find the probability that the two selected chips are of different colors, we can use the concept of complementary probability.
The complementary event of selecting two chips of different colors is selecting two chips of the same color.
Let's calculate the probability of selecting two chips of the same color and then subtract that from 1 to find the probability of selecting two chips of different colors.
1. Probability of selecting two blue chips:
[tex]\[ P(\text{blue, blue}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144} \][/tex]
2. Probability of selecting two red chips:
[tex]\[ P(\text{red, red}) = \frac{4}{12} \times \frac{4}{12} = \frac{16}{144} \][/tex]
3. Probability of selecting two yellow chips:
[tex]\[ P(\text{yellow, yellow}) = \frac{3}{12} \times \frac{3}{12} = \frac{9}{144} \][/tex]
Now, let's add these probabilities together because any of these scenarios results in two chips of the same color:
[tex]\[ P(\text{same color}) = P(\text{blue, blue}) + P(\text{red, red}) + P(\text{yellow, yellow}) \]\[ P(\text{same color}) = \frac{25}{144} + \frac{16}{144} + \frac{9}{144} = \frac{50}{144} \][/tex]
Finally, we subtract this probability from 1 to find the probability of selecting two chips of different colors:
[tex]\[ P(\text{different colors}) = 1 - P(\text{same color}) \]\[ P(\text{different colors}) = 1 - \frac{50}{144} = \frac{144}{144} - \frac{50}{144} = \frac{94}{144} \][/tex]
So, the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
A pool charges $4 each visit or you can buy a membership. Right and solve an inequality to find how many times a person should use a pool so that the membership is less expensive than paying each time. Interpret the solution
The inequality is:
[tex]n > \frac{m}{4}[/tex]
Membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
Solution:
Given that,
A pool charges $4 each visit or you can buy a membership
Let "n" be the number of times you visit the pool
Let the membership amount of the pool be "m"
A pool charges $4 each visit
Therefore, cost for "n" visit is: $ 4n
The inequality showing that a membership is less expensive than paying each visit to the pool is:
4n > m
Divide both sides by "4"
[tex]n > \frac{m}{4}[/tex]
Therefore, membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
The volume of a gas in a container at a constant temperature varies inversely as the pressure. The volume is 25 cubic centimeter at a pressure of 11 pounds. Use a proportion to find the pressure when the volume is 59 cubic centimeters.
Answer:
Pressure would be approximately 4.66 pounds.
Step-by-step explanation:
Given:
Volume of gas (V) = 25 cubic cm
Pressure of the gas (P) = 11 pounds
We need to find the pressure when volume is 59 cubic cm.
Solution:
Now Given:
[tex]V[/tex] ∝ [tex]\frac{1}{P}[/tex]
so we can say that;
[tex]V =\frac kP[/tex]
where k is a constant.
When V = 25 cubic cm, P =11 pounds.
[tex]25 = \frac{k}{11}\\\\k= 25\times 11 = 275\ cm^3.pounds[/tex]
So the equation becomes as.
[tex]V = \frac{275}{P}[/tex]
Now we need to find the pressure when Volume is 59 cubic cm.
[tex]59 =\frac{275}{P}\\\\P=\frac{275}{59}\\\\P\approx 4.66\ pounds[/tex]
Hence Pressure would be approximately 4.66 pounds.
The average number of field mice per acre in a 5-acre wheat field is estimated to be 14. (a) Find the probability that fewer than 12 field mice are found on a given acre. (b) Find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected.
Answer:
(a) [tex]P(X < 12)=0.26[/tex]
(b) [tex]P(X=2)=0.15[/tex]
Step-by-step explanation:
Question a
This is a Poisson distribution. The average/mean, μ = 14
So, probability that fewer than 12 field mice are found on a given acre is:
[tex]P(X < 12) = e^{-14}(\frac{14^{0}}{0!} +\frac{14^{1}}{1!} + \frac{14^{2}}{2!} + \frac{14^{3}}{3!} +\frac{14^{4}}{4!} + \frac{14^{5}}{5!} +\frac{14^{6}}{6!}+\frac{14^{7}}{7!}+\frac{14^{8}}{8!} +\frac{14^{9}}{9!}+\frac{14^{10}}{10!}+\frac{14^{11}}{11!})\\ \\P(X < 12) = e^{-14}(1+14+98+457.33+1600.67+4481.87+10457.69+20915.38+36601.91+56936.31+79710.83+101450.15)\\\\P(X < 12) = 8.315*10^{-7}(312725.1248)=0.26 \\\\P(X < 12)=0.26[/tex]
Question b
This is a Binomial distribution with:
Probability of success, p = 0.26
n = 3
[tex]P(X=2)= (3C2)p^{2}(1-p)=\frac{3!}{2!(3-2)!}*(0.26^{2})*(1-0.26)\\ \\P(X=2)=3(0.0676)(0.74)=0.15\\\\P(X=2)=0.15[/tex]
Final answer:
To find the probability that fewer than 12 field mice are found on a given acre and on 2 of the next 3 acres inspected, use the cumulative distribution function (CDF) of the Poisson distribution and the binomial distribution.
Explanation:
To find the probability that fewer than 12 field mice are found on a given acre, we need to use the cumulative distribution function (CDF) of the Poisson distribution. The average number of field mice per acre is 14, so the parameter of the Poisson distribution is also 14.
(a) To find the probability that fewer than 12 field mice are found on a given acre, we calculate P(X < 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 11), where X is the number of field mice found on a given acre
(b) To find the probability that fewer than 12 field mice are found on 2 of the next 3 acres inspected, we calculate P(X < 12) for each acre and use the binomial distribution to determine the probability of 2 successes out of 3 trials.
A painting is drawn on a cardboard 22cm long and 12cm wide such that there is a margin of 2.5 meter cm along each side. Find the total are of the margin
Answer:
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Step-by-step explanation:
We have been given that a painting is drawn on a cardboard 22 cm long and 12 cm wide such that there is a margin of 2.5 meter cm along each side. We are asked to find the area of the margin.
The total area of the margin would be equal to area of whole cardboard minus area of painting.
[tex]\text{Area of whole cardboard}=22\text{ cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of whole cardboard}=264\text{ cm}^2[/tex]
Since there is a margin of 2.5 meter cm along each side, so sides of painting would be 2,5 cm smaller on four sides. The sides painting would be [tex]22-5=17[/tex] and [tex]12-5=7[/tex].
[tex]\text{Area of painting}=17\text{ cm}\times 7\text{ cm}[/tex]
[tex]\text{Area of painting}=119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=264\text{ cm}^2-119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Therefore, the total area of the margin is 145 squared cm.
A common computer programming rule is that names of variables must be between one and eight characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example, allowable variable names include A, BB, and M3477K. How many different variable names are possible? (Ignore the difference between uppercase and lowercase letters.)
Answer:
Total number of possibilities 2,095,681,645,538.
Step-by-step explanation:
The variables can be 1 to 8 characters long.
The first space can be filled by any of the 26 letters.
The remaining n places can be filled by any of the 26 letters or any of the 10 digits.
For a single character variable the number of ways to select a variable name is,
n (1 character) = 26
For two character variable the number of ways to select a variable name is,
n (2 character) = 26 × 36 = 936
For three character variable the number of ways to select a variable name is,
n (3 character) = 26 × 36 × 36 = 26 × 36² = 33,696
For four character variable the number of ways to select a variable name is,
n (4 character) = 26 × 36 × 36 × 36 = 26 × 36³ = 1,213,056
And so on.
Similarly for the eight character variable the number of ways to select a variable name is,
n (8 character) = 26 × 36 × 36... × 36 = 26 × 36⁷ = 2,037,468,266,496
Total number of possibilities 2,095,681,645,538.
You and your friend are skiing down a hill, your friend is almost at the finish line, and you want to catch up with him, how many seconds will it take you to reach him?
Answer:It depends
Step-by-step explanation:
Half of Frank's weight added to Gary's weight equals 234. Half of Gary's weight added to Frank's weight is equal to 222 pounds. How much does Gary weigh?
Answer:
164 pounds
Step-by-step explanation:
Please see attached picture for full solution.
Universal pet house sells vinyl doghouses and treated lumber doghouses. It takes the company 5 hours to build a vinyl doghouse and 2 hours to build a treated lumber doghouse
Answer:
Step-by-step explanation:
What is the question
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?
I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.
A. I only
B. II only
C. III only
D. I and II
E. I and III
Answer:
A. I Only.
Step-by-step explanation:
To begin, we must first be clear that it is the median and that it is the arithmetic mean:
Median is the middle value of a sequence of ordered numbers, for example:
{4,4,4,4,4}, the median is 4 despite being the same numbers.
Now the arithmetic mean is the average value of the samples and is independent of the amplitudes of the intervals.
Then let's analyze each of our options:
I. At least one of the homes was sold for more than $ 165,000.
We know through the flushed:
X1 + X2 +. . . + X7 + (X8 = $130,000) + X9 +. . . + X15 = 15 ∗ 150,000 = $ 2,250,000
Now we will assume the lowest possible value from X1 to X8 = $ 130,000 and from X9 to X15 = X, which is what we want to calculate. That is to say:
X1 = X2 = X3 = X4 = X5 = X6 = X7 = X8 = 130 and X9 = X10 = X11 = X12 = X13 = X14 = X15 = X,
knowing that the total value must be the average of 15, which is equal to $ 2250000 , we have the following equation:
8 ∗ $ 130,000 + 7X = $ 2,250,000
Rearranging:
X = ($ 2,250,000 $ - $ 1,040,000) / 7
X = $ 172,857
Therefore the first statement is true, because at least one house was sold at $ 172,857 which is more than $ 165,000
Evaluating the second option
II. At least one of the homes was sold for more than $ 130,0000 and less than $ 150,000
As the example of the median in the previous case you could have 8 houses that were sold for $ 130,000 or less, therefore here it loses validity, statement II is false.
Evaluating the third option
III. At least one of the homes was sold for less than $ 130,000.
We know that the eighth house sold for $ 130,000, but houses 1 to 7 may also have been sold for that same price. The statement III is false.
Therefore the answer is A. I Only.
please help!
"solving proportions" is what needs done
please show all work clearly!
23) x = [tex]\frac{-60}{9}[/tex] = -6.666.
24) x = [tex]\frac{-12}{7}[/tex] = -1.7142.
25) x = [tex]\frac{-37}{5}[/tex] = -7.4.
Step-by-step explanation:
Step 1; For [tex]\frac{x+6}{3}[/tex] = [tex]\frac{x+4}{12}[/tex], we cross multiply the denominators and get,
3 × (x + 4) = 12 × (x + 6),
3x + 12 = 12x + 72.
We take all the x terms to the LHS and keep the constants on the RHS.
3x - 12x = 72 - 12,
-9x = 60, x = [tex]\frac{-60}{9}[/tex] = -6.6666.
Step 2; For [tex]\frac{-5}{x-4}[/tex] = [tex]\frac{9}{x+12}[/tex], we cross multiply the denominators and get,
-5 × (x + 12) = 9 × (x - 4),
-5x - 60 = 9x - 36.
We take all the x terms to the LHS and keep the constants on the RHS.
-5x - 9x = -36 + 60,
-14x = 24, x = [tex]\frac{-24}{14}[/tex] = -1.7142.
Step 3; For [tex]\frac{6}{11}[/tex] = [tex]\frac{x-1}{x-8}[/tex], we cross multiply the denominators and get,
6 × (x - 8) = 11 × (x - 1),
6x - 48 = 11x - 11.
We take all the x terms to the LHS and keep the constants on the RHS.
6x - 11x = -11 + 48,
-5x = 37, x = [tex]\frac{-37}{5}[/tex] = -7.4.
Help with this please! a, b, and c
Answer:
y = 3.6(sine( 6.2(x-4.2))+4.4
Step-by-step explanation:
(8.2-.6)/2 = altitude = 3.6
6.2 = Wavelength
(8.2+.6)/2 = 4.4 The "line" (the horizontal central line thingy whose name I forgot cuz it's 12:00)
4.2 = x shift
y = 3.6(sine( 6.2(x-4.2))+4.4
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles how far is it from Chester to durbin
Answer:
It is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.
Step-by-step explanation:
Given:
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles.
Now, to find the distance from Chester to durbin.
Distance from Alston to Barton = [tex]10\frac{3}{5} =\frac{53}{5} \ miles.[/tex]
Distance from Barton to Chester = [tex]12\frac{1}{2}\ miles =\frac{25}{2} \ miles.[/tex]
As, given the distance from Alston to Durbin, via barton and Chester, is 35 miles.
Thus, the total distance = 35 miles.
So, we add the distance of Alston to Barton and Barton to Chester and get the distance from Alston to Chester:
[tex]\frac{53}{5} +\frac{25}{2}[/tex]
[tex]=\frac{106+125}{10}[/tex]
[tex]=\frac{231}{10} \ miles.[/tex]
Distance from Alston to Chester [tex]=\frac{231}{10} \ miles.[/tex]
Now, to get the distance from Chester to durbin we subtract distance from Alston to Chester from the total distance:
[tex]35-\frac{231}{10} \\\\=\frac{350-231}{10} \\\\=\frac{119}{10} \\\\=11\frac{9}{10}\ miles.[/tex]
Therefore, it is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.