The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:
1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)
2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).
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The probability of the sum of the two recorded numbers being less than 4 is [tex]\frac{3}{4}[/tex].
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.
1) both numbers are 1 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} = \frac{1}{16}[/tex])
2) one number is 1 and the other is 2 (probability of [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{4} =[/tex] [tex]\frac{1}{16}[/tex])
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the length of a rectangle is increasing at a constant rate of 3 cm/s, and its width is increasing at a constant rate of 0.5 cm/s. at the time the length is 5 cm and the width is 1.2 cm, how fast is the area of the rectangle increasing?
The area of a rectangle is increasing at a constant rate of 3.5 cm²/s when the length is increasing at a constant rate of 3 cm/s and the width is increasing at a constant rate of 0.5 cm/s.
The area of a rectangle is calculated as length multiplied by width (A = L x W). At the given time, the length is 5 cm and the width is 1.2 cm, so the area is 6 cm². When the length is increasing at a constant rate of 3 cm/s, and the width is increasing at a constant rate of 0.5 cm/s, then the area is increasing at a rate of 3.5 cm²/s. This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5). This is the rate of increase of the area and is expressed as 3.5 cm²/s This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5).
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If A(2, 3) and B(-4, -6), find AB. Round to the nearest tenth.
The value of a ring ($1000) increases exponentially so that it has a value of $3,000 after 5 years. Find the rate.
Answer: [tex]\sqrt[5]{3}-1[/tex]
Step-by-step explanation:
Let the annual rate of increase be [tex]r[/tex].
[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]
Solve for X, Leave in simplest radical form.
Hope it helps.
If you have any query, feel free to ask.
more workers what sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in exercise 36(b)? justify your answer.
On solving the provided question, we can say that the sample size would have to be multiple by 4 = 4048
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
the sample size would have to be multiple by 4
n = 1012
n X 4
= 1012 X 4
= 4048
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What is a point that divides a line segment into 2 equal parts called?
Answer: Midpoint
Step-by-step explanation:
Can anyone help me with the answer. Sorry if it’s hard to see , please just zoom in
Answer:
NOLO
Step-by-step explanation:
the radius of a sphere is decreasing at a constant rate of 6 feet per second. at the instant when the volume of the sphere is 163163 cubic feet, what is the rate of change of the volume? the volume of a sphere can be found with the equation v
865.96 is the rate of change of the volume. This can be solved using the concept of rate of change of the volume.
What is volume of sphere?The volume of a sphere is the maximum volume of air that may be contained within it. Volume of sphere = 4/3 πr³ is the formula for computing the volume of a sphere of radius "r."
As we know,
volume (V) = 4/3 πr³
Given that,
volume of the sphere is 163 cubic feet
the radius of a sphere is decreasing at a constant rate of 6 feet per second (dr/dt) = 6
So, 163 = 4/3 × 22/7 r³
or, r³ = (3423/88)
or, r = [tex][\frac{3423}{88}]^{1/3}[/tex]
again, dv/dt = 4/3 × π × 3 r² × dr/dt
or, dv/dt = 4 × π × r² × dr/dt
or, dv/dt = 4 × 22/7 ×[tex][\frac{3423}{88}]^{2/3}[/tex] × 6
or, dv/dt = 75.43 × [tex][\frac{3423}{88}]^{2/3}[/tex]
or, dv/dt = 865.96
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Write an abolute value inequality comparing the ditance of the tour guide and the diver to eal level. Who i cloer to ea level? Explain how you know. Sea level = -18 ft
Tour guide = 5 ft
One diver = -11 ft
The diver is closer to sea level since their distance to sea level (7 ft) is less than the distance of the tour guide to sea level (23 ft).
As we know,
|Tour guide - sea level| < |One diver - sea level|
The distance between the tour guide and sea level is 5 - (-18) = 23 feet.
The distance between one diver and sea level is -11 - (-18) = 7 feet.
Since the absolute value of the difference between the tour guide and the sea level is greater than the absolute value of the difference between one diver and the sea level, we can conclude that the diver is closer to the sea level.
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Two APs have same common difference. If the first term is -1 and that of the other is -8. then the difference between their 4th term is?
Answer:
7
Step-by-step explanation:
Let the common difference of the two APs be" D"
Let 1st term of 1st AP be A₁ i.e = -1
And the first term of the second AP b₁ i.e = -8
We know that the nth term of an AP is;
an = a+(n-1)d
4th term of first AP,
a₁ + (4-1)d = − 1 + 3d. --Eqn. 1
And 4th term of the second AP,
b₁ + (4-1) d=-8+ 3d -- Eqn 2
Now, the difference between their 4th terms is i.e.
= (- 1+ 3d ) - (-8 + 3d )
= -1 + 3d + 8 - 3d = 7
So, the answer is 7.
it takes 3 people 12 hours to paint a room. How long would it take 1 person to paint the same room?
Answer:
36 hours
Step-by-step explanation:
3 x 12 = 36
Answer:
36 hours
Step-by-step explanation:
if it took 3 people to paint a room in 12 hours, we have,
3 people = 12 hours
divide by 3. multiply by 3
1 person = 36 hours.
f(n)=n+3
g(n)=2n-4
Find (fog)(-3)
Answer:
-7
Step-by-step explanation:
(fog)(-3) = f(g(-3)) = f (2(- 3) - 4) = f(-10) = -10 + 3 = -7
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Given the following point on the unit circle, find the angle, to the nearest tenth of a
degree (if necessary), of the terminal side through that point, 0° ≤ 0 < 360°.
P=
√15
5
√10
5
Answer:
60°
Step-by-step explanation:
To find the angle of the terminal side through a point P on the unit circle, we can use the coordinates of the point. The angle is given by the inverse tangent (atan) of the y-coordinate divided by the x-coordinate.
The point P is given as (√15/5, √10/5)
Using the arctan function we have:
theta = arctan(√10/5/√15/5) = arctan(√2/√3)=atan(√2/√3) = pi/3
The angle theta is in radians, to convert it to degree we multiply it by 180/pi
Theta = (pi/3) * (180/pi) = 60. Therefore, the angle of the terminal side through the point P is 60°.
3x + 3y = 3
\y=-1/x+2
y=-2
y = 0
y = 3
y = 1
Answer: [tex]y=3[/tex]
Step-by-step explanation:
The intersection point of the graphs is the solution. So, you need to find the [tex]y[/tex]-coordinate of the intersection point.
Becky has 14 pints of pudding. How many cups of pudding does she have?
Answer:
28 cups
Step-by-step explanation:
[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{14}[/tex]
1 x 14 = 14, so 2 x 14 = 28
Pls help!! URGENT!!
What is RU? Use the figure below.
Answer: 20 ( Choice A )
Step-by-step explanation: You can prove that triangle RTS and triangle RTU are the same using the Side-Angle-Side method, so ultimately, side RS should equal RU. Therefore, 8x = 6x + 5.
x should equal 2.5. The question is asking you how long side RU is, simply plug in 2.5 and you get 20.
A large church has a niche in one wall. On the floor plan it appears as a semicircular indentation of radius 2.60 m. A worshiper stands on the center line of the niche, 1.70 m out from its deepest point, and whispers a prayer. Where is the sound concentrated after reflection from the back wall of the niche
40m is the sound concentrated after reflection from the back wall of the niche.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
with radius 2.60m , the cylindrical wall is a highly efficient mirror for sound , with focal length
f = R/2 = 2.60/2 = 1.30
in a vertical plane the sound disperses as usual butthat radiated in a horizontal plane is concentrated in a soundimage at a distance q from the back of niche ,
so 1/p+1/q = 1/f
so 1/1.70 +1/q = 1/1.3
1/q = 1/1.3 - 1/1.70
q = 40m
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The US has a population of approximately 330 million people. Given that 0. 35 of the population have blue eyes, calculate the number of people in the US who do not have blue eyes.
The number of people in the US who do not have blue eyes is 214.5 million.
The given question has been solved using Probability. It is given that the number of people in the US is 330 million
for the time being, we let P=330 which represents the population of the US
also, it is given that the number of people having blue eyes is 0.35 times the Population
So, Pb= 0.35 × P
here, Pb represents the number of people having blue eyes
So the number of people that do not have blue eyes must be the number of people having blue eyes subtracted from those having blue eyes
i.e, Pnb=P-Pb
=P-(P × 0.35)
=P(1-0.35)
=330 (0.65 )
=214.5
Thereby, the number of people that do not have blue eyes is 214.5 million.
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At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.11 and the probability that the flight will be delayed is 0.14. The probability that it will not rain and the flight will leave on time is 0.82. What is the probability that it is raining if the flight has been delayed? Round your answer to the nearest thousandth.
The probability that the flight would be delayed when it is not raining is 12.46%.
What is probability?Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
To determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:
Probability that it will not rain = 1 - probability that it will rain
X = 1 - 0.11
X = 0.89
Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed
X = 0.89 x 0.14
X = 0.1246
0.1246 x 100 = 12.46
Therefore, the probability that the flight would be delayed when it is not raining is 12.46%.
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Write the slope-intercept form of the equation of each line.
7) y - 9 =2/3 (x + 6)
8) y + 4 = 8(x - 2)
Answer:
7) y = [tex]\frac{2}{3}[/tex]x + 13
8) y = 8x - 20
Step-by-step explanation:
Question 7
y - 9 = [tex]\frac{2}{3}[/tex](x + 6)
Step 1: Distribute [tex]\frac{2}{3}[/tex] to (x + 6); y - 9 = [tex]\frac{2}{3}[/tex]x + 4
Step 2: Add 9 to both sides; y = [tex]\frac{2}{3}[/tex]x + 13
Question 8
y + 4 = 8(x - 2)
Step 1: Distribute 8 to (x - 2); y + 4 = 8x - 16
Step 2: Subtract 4 from both sides; y = 8x - 20
A 7x1 board is completely covered by mx1 tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the board. Each tile is either red, blue, or green. Let N be the number of tilings of the 7x1 board in which all three colors are used at least once. For example, a 1x1 red tile followed by a 2x1 green tile, a 1x1 green tile, a 2x1 blue tile, and a 1x1 green tile is a valid tiling. Note that if the 2x1 blue tile is replaced by two 1x1 blue tiles, this results in a different tiling. Find the remainder when N is divided by 1000.
The remainder when N is divided by 1000 is 106.
What is the Principle of Inclusion-Exclusion?The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.
From the question,
First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.
Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways
Four pieces = 6C3 = 20
Five pieces = 6C4 = 15
Six pieces = 6C5 = 6
Seven pieces =6C6 = 1
Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:
Three pieces : 3³ - 3 × 2³ + 3 = 6
Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36
Five pieces : 3⁵ - 3 × 2⁵ + 3 = 150
Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540
Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806
Adding them together, we get
15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106
Hence, the remainder when it is divided by 1000 is 106.
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Answer:
106
Step-by-step explanation:
if the radius of a circle is 12 ft what is the area in terms of π
Step-by-step explanation:
The area of a circle is radius²· π
12x12=144
So the answer is 144π.
Answer:
37.71428571425567788
What is the best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24
The best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24 are x = 43 and y = 22
How to determine the solutionFrom the information given, we have the expressions;
X minus Y equals negative 65X plus 3Y equals 24This is represented as;
x - y = -65
x + 3y = 24
Make 'x' the subject from equation 1
x = -65 + y
Now, substitute the expression into equation (2), we get;
-65 + y + 3y = 24
collect the like terms
4y = 24 + 65
Add the like terms
4y = 89
Divide the values by the coefficient of y
y = 89/4 = 22
Substitute the value in eqation3
x = -65 + 22
Add the values
x = 43
Hence, the values are 43 and 22
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what are the four conditions necessary for x to have a binomial distribution? mark all that apply.
Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process
a set number of trials, such as three rolls of the dice or five flips of the coin.Each trial can either be successful or unsuccessful. Note that the example with the die seems to have six possible outcomes. We must take into account options like "get a 6" (success) or "not obtain a 6." (failure).The likelihood of success must be constant (equal for every try). P(6) = 1/6 for each roll of the die in the example.The trials are separate. The likelihood of success in future trials is unaffected by the outcome of the first.Know more about binomial at:
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How do I do this help me please
Answer: A. p + 3 = 49
B. p = 46
Step-by-step explanation:
A. represents the equation that represents the word problem. In this case, the original number of paintbrushes Kaitlyn had is represented by (p) and Claire gives her 3 more paintbrushes, the total number of paintbrushes she has is 49.
B. represents the original number of paintbrushes Kaitlyn had. To find this, we can simply solve the equation from part A for (p) by isolating it on one side of the equation.
Therefore, Kaitlyn originally had 46 paintbrushes.
Nikhil and Mae work at the same company. Nikhil has been at the company 4 times as long as Mae. Nikhil's time at the company is 8 more than 2 times Mae's time. The following system of equations models the scenario:
x = 4y
x = 8 + 2y
How many years has each person been employed by the company?
Nikhil has been with the company for 16 years, while Mae has been there for 4 years.
Nikhil has been with the company for 24 years, while Mae has been there for 6 years.
Nikhil has been with the company for 20 years, while Mae has been there for 5 years.
Nikhil has been with the company for 12 years, while Mae has been there for 3 years.
Answer:
1) Nikhil 16 years & Mae 4 years
Step-by-step explanation:
x = 4y {equation 1}
Hence, x - 4y = 0 { equation 2}
x = 8 + 2y {equation 3}
Then, x - 2y = 8 { equation 4}
{equation 4-2}
x -x -2y - ( - 4y) = 8 -0
-2y +4y = 8
2y = 8
2 2
y = 4
By substituting { equation 1}
x = 4y
x = 4 × 4
= 16//
(Deleted Answer)
Paul usually makes the 100 km journey to visit his family. The trip involves three separate stages:
a) A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
b) A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
c) A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.
The length of the section of roadworks was 121 km.
What is the concept of time and distance?
Time is directly proportional to distance. It means that speed remains constant, if we have two vehicles moving two distances for two different time duration then the time is directly proportional to the distance. Speed is directly proportional to distance.
1) Total time = 1 hr 55 minutes
2) Distance = 121 km
To calculate Matthew's journey we have to use the formula of :
Time = distance /speed
Are doing the calculations for each Stage, like this:
Stage A, we know that:
Distance: 20 km
speed: 30 km/h
Time = 20/30
T = 2/3h
Time = 40 minutes
Stage B, we know that:
Distance: 50 km
speed: 100 km/h
Time = 50/100
T = 0.5 h
Time = 30 minutes
Stage C, we know that:
Distance: 30 km
speed: 40 km/h
Time = 30/40
T = 3/4 h
Time = 45 minutes
1) So using all the values calculated above, let's calculate the total value of the trip that will take place by:
Total = (40 + 30 + 45)minutes
Total = 115 minutes
Total = 1 hour 55 minutes
2) For the second part of this question we want to calculate the total distance of travel hours so:
Speed: 60 km/h
Time: 6 minutes + x
x =1 hr 55 minute + 6 minutes 2 hr 1 minute
Time = 2.01666667
Distance = speed * time
Distance = 60 * 2.01666667
Distance = 121 km
hence, the length of the section of roadworks was 121 km.
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Ages Numbers of students 15-18 2 19-22 7 23-26 5 27-30 5 31-34 6 35-38 3 Based on the frequency distribution above, find the relative frequency for the class with lower class limit 27 Relative Frequency =%Give your answer as a percent, rounded to one decimal place
Relative frequency for the class with lower class limit 27 is 20.0%.
To find the relative frequency for the class with lower class limit 27, we must first find the total frequency of the data set. The total frequency is 28 (2+7+5+5+6+3=28). Since the class with lower class limit 27 has a frequency of 5, we can calculate the relative frequency of this class by dividing the frequency of the class by the total frequency.
Formula:
Relative Frequency = (Number of Students in the Class)/(Total Number of Students in the Group) x 100
Relative Frequency = (5)/(28) x 100
Relative Frequency = 0.1786 x 100
Relative Frequency = 17.86%
Rounded to one decimal place, Relative Frequency = 20.0%.
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suppose you are offered one slice from a round pizza, that is, a sector of a circle, and the slice must have a perimeter of 32 inches. what diameter pizza will produce the largest slice?
On solving the provided question, we can say that D, diameter pizza will produce the largest slice is 16
what is diameter?Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.
Let r be the radius and be the angle of a circle.
According with the graph, the area of the sector is given by
A = 1/2r^2∅
The arc length of a circle with radius r and angle∅ is r∅
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
2r + r∅ = 32 in
r∅ = 32 - 2r
∅ = 32- 2r / r
Now,
A = 1/2r^2[32- 2r / r]
A = 16r - r^2
A' = 16 - 2r 16 -2r = 0
r = 8
A" = -2
so, D, diameter pizza will produce the largest slice is 16
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Between what two consecutive integers does the square root of 12 lie
The two consecutive integers that the square root of 12 lies between are 3 and 4.
How to find the integers ?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. This therefore means that integers can only be whole numbers and consecutive integers follow each other. For instance, 1, 2, and 3 are consecutive integers.
To find the two consecutive integers that the square root of 12 lies between, find the square root of 12 :
= √ 12
= 3.46
This means that the lower integer would be 3 and the consecutive integer following would be 4.
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