Answer:
1/6 of a mile
Step-by-step explanation:
if it is a constant pace, it must increase and decrease proportionately meaning, you divide the time by 2 so you divide the distance by 2 as well
Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
How many sticks of cotton candy will Team B need to sell to reach their goal?
Team B will need to sell a minimum of 192 candies to reach its goal.
What is a linear equation?Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.
There are linear equations with one variable and those with two variables.
Given total amount to be raised by each team is $100,
Team B wants to sell cotton candy,
rent of candy machine = $25
total cost to be earned for team B = $100 + $25 = $125
let the number of candies sold be x
cost used in each candy sticks = $0.10
cost used by x candy sticks = $0.10x
the selling price of each candy = $0.75
the selling price of x each candy = $0.75x
total gain from selling x candies = $0.75x - $0.10x
total gain from selling x candies = $0.65x
minimum candies to be sold to reach the goal
$0.65x = $125
x = 125/0.65
x = 192.30
x = 192 (approx)
Hence to reach the goal, at least 192 candies are to be sold by team B.
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the empirical rule applies to distributions that are
In mathematics, the empirical rule speaks that, in a normal data set, nearly every piece of data will fall within three standard deviations of the mean. The mean is the average of all of the numbers within the set.
The empirical rule advance about because the same shape of distribution curves continued to appear over and over to statisticians.
approximately normal, meaning that the data follows a bell-shaped curve regular around the mean.
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
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in isosceles trapezoid mnpq with , diagonal . if and , how long is diagonal ?
The value of segment RN is:
Rn = 1.8
Now, According to the question:
An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals.
The figure shows:
MQ is parallel to NP
MN ≅ QP
So MNPQ is an isosceles trapezoid. That means that the two diagonals, MP and QN, are congruent and therefore are equal in length;
MP = QN
By the Segment Addition Postulate, QN = QR + RN and QR = 4.1:
MP = QN
5.9 = 4.1 + RN
RN = 5.9 - 4.1
RN = 1.8
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The given question is incomplete, complete question is:
Quadrilateral MNPQ is shown.
If MP = 5.9, what is RN? Round your answer to the nearest tenth.
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
The probability of selecting a chocolate chip cookie from the batch is unlikely.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.
If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Then the probability of selecting a chocolate chip cookie from the batch is unlikely.
Unlikely means there's a small chance that an event will happen.
Hence, the probability of selecting a chocolate chip cookie from the batch is unlikely.
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Write an inequality represented by the graph.
Answer: y ≤ -4x - 1.
Step-by-step explanation:
Hello!
The first thing you know is that since the shaded region is to the (left) or below the line, you will have to use the symbol for equal to or less than (≤). If the line was a dotted line, then you would use the symbol (<). If the line was a dotted line and the shaded region was above or to the right of the line, then you would use the symbol (>). If the line was a regular line like in the picture and the shaded region was to the right of the line instead of to the left like in the picture, then you would use the symbol (≥).
Secondly, you know that the y-intercept is -1 and the slope is -4 using the equation (y2 - y1)/(x2 - x1) with the coordinates (0, -1) and (1, -5). Substitute this information into the slope formula, y = mx + b.
y = -4x + (-1) or y = -4x - 1
You now have the equation:
y = -4x - 1. Use the sign you figured out earlier for the equation in place of the equal sign. Here is what the final equation should look like:
y ≤ -4x - 1.
Match each graph to its equation
Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom left angle is (5 x + 5) degrees. At the intersection of lines c and a, the bottom right angle is 115 degrees.
What is the value of x?
x = 12
x = 14
x = 22
x = 24
ANSWER IS x = 12.
12 because 5x12+5 = 65 and 180-115=65 meaning x=65 :)
Answer:
answer is 12
12 because 5x12+5 = 65 and 180-115=65 meaning x=65
The ratio of corn to beef to rice is 5:2:7. Assuming that you have 4.9kg of rice, how many kilograms of corn and beef will you need?
Using the ratios we know that the required kilograms of corn and beef is 3.5kg and 1.4kg respectively
What are ratios?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Ratios contrast two figures by ordinarily dividing them.
A/B would be your formula if you were comparing one data point (A) to another data point (B).
This indicates that you are multiplying information A by information B.
For instance, your ratio will be 5/10 if A is 5 and B is 10.
So, we have the ratio:
corn:beef:rice = 5:2:7
Rice is 4.9kg.
We know that 5+2 = 7.
Then,
4.9/7 = 0.7
Corn: 0.7 * 5 = 3.5kg
Beef: 0.7 * 2 = 1.4kg
Therefore, using the ratios we know that the required kilograms of corn and beef is 3.5kg and 1.4kg respectively
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Tory and emilio's motorboats travel at the same speed Tory pilots her boat at 30 km before docking. Emilio continues for another 3 hr, traveling a total of 100 km before docking. How long did it take to navigate the 30 km
The actual time it took Tory to travel 30 km is 0 hours.
As per the data given in the question,
Speed of the boat of both the person Tory and Emillio are same.
Let's call the time it took Tory to travel 30 km as "t" (in hours).
Emilio travelled for t + 3 hours, and during that time, he covered a total distance of 100 km.
So, we can write the equation:
30 + (t + 3) * 30 = 100
Solving for t:
30 + 30t + 90 = 100
30t = -60
t = -2
Since time cannot be negative, the actual time it took Tory to travel 30 km is 0 hours.
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Can someone help solve num: 2
Answer:
The value of (y+6) is greater in 4(y+6).
Step-by-step explanation:
This is because the higher number of y's there are, the higher number you have to divide by, therefore in the end the number is smaller.
the general solution to a linear system is given. express this solution as a linear combination of vectors. x1 = 8 6s1 − 9s2 x2 = s2 x3 = −7 3s1 x4 = s1 x1 x2 x3 x4 = s1 s2
The general solution can be written as: x = s1[8, 0, -7, 1] + s2[6, 1, 3, 0]. The general solution to the linear system is given by the following system of equations:
x1 = 8 + 6s1 - 9s2
x2 = s2
x3 = -7 + 3s1
x4 = s1
where s1 and s2 are arbitrary scalars.
This general solution can be expressed as a linear combination of the vectors [8, 0, -7, 1] and [6, 1, 3, 0], where the scalars s1 and s2 are the coefficients for the linear combination:
x1 = 8s1 + 6s2
x2 = s1 + s2
x3 = -7s1 + 3s2
x4 = s1
Therefore, the general solution can be written as: x = s1[8, 0, -7, 1] + s2[6, 1, 3, 0]
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Convert 20 feet per minute to yards per hour.
400 yards/hour
3600 yards/hour
60 yards/hour
6.3 yards/hour
20 feet per minute is equal to 400 yards/hour
What is unit rate?
A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
For 1 minute 20 feet
For 60 minutes , 60*20=1200 feet
1 hour = 60 minutes
Thus, we have 1200 feet per hour
3 feet = 1 yard
So, 1200 feet = 1200/3 yrads = 400 yards
Thus, 20 feet per minute is equal to 400 yards/hour
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An invertible function is represented by the values in the table. x −3 −2 −1 0 1 2 3 f(x) −6.4 −2.6 −1.2 −1 −0.8 0.6 4.4 Which graph shows the inverse of this function?
The graph of the function is f⁻¹ ( x ) is plotted
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the x values of the function be represented as
x = { -3 , -2 , -1 , 0 , 1 , 2 , 3 }
Let the y values of the function be represented as
y = { -6.4 , -2.6 , -1.2 , -1 , -0.8 , 0.6 , 4.4 }
The value of the equation is plotted in the graph
Now , the inverse function is f⁻¹ ( x ) , you basically swap the numbers, all x values would equal y
So , y = { -3 , -2 , -1 , 0 , 1 , 2 , 3 }
And , x = { -6.4 , -2.6 , -1.2 , -1 , -0.8 , 0.6 , 4.4 }
Hence , the graph is plotted and the function is f⁻¹ ( x )
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Meera cut 1/10 m from a tring. Lilian cut 2/10 m from the ame tring. The remaining tring wa 3/10 m long. What wa the original length of the tring?
The original length of the string is 6/10 m or 0.6 m
What was the original length of the tiring?Now the string is divided into three parts:
1/10 m with Meera2/10 m with Lilian3/10 m balance partSo, the total length of string = 1/10 + 2/10 + 3/10 = 6/10 m = 0.6 m
Let the original length of string be=x
Length cut by Meera=x/10
Length cut by Lilian=2x/10
Length of remaining string=3/10
According to the question:-
Original length of string=Length cut by Meera +Length cut by Lilian+ Remaining part of string
=>x=x/10+2x/10+3/10
=>x=3x+3/10
=>10x=3x+3
=>10x-3x=3
=>7x=3
=>x=3/7m
Ans. Hence, original length of string is 3/7m
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A student earned the scores in the data set in one course. {90, 87, 58, 79, 91} What is the mean of the scores? 33 58 81 87
Answer:
81
Step-by-step explanation:
Mean means the average
Mean = (sum of #s) / amount of #s
sum of numbers = 90 + 87 + 58 + 79 +91 = 405
amount of #s = 5
405/5 = 81
Answer:
81
Step-by-step explanation:
Mean is the sum of all numerical data values over the number of data. In this problem, we have total of 5 numerical data. Therefore:
[tex]\displaystyle{\bar{x} = \dfrac{\sum x}{N}}\\\\\displaystyle{\bar{x} = \dfrac{90+87+58+79+91}{5}}\\\\\displaystyle{\bar{x} = \dfrac{405}{5}}\\\\\displaystyle{\bar{x} = 81}[/tex]
Note:
[tex]\bar{x}[/tex] is mean value, [tex]\displaystyle{\sum x}[/tex] is sum of data, N is number of data
Find out the length of segment GF?
The length of segment GF in the triangle is 8 inches
How to Find out the length of segment GF?From the question, we have the following parameters that can be used in our computation:
The triangle
On the triangle, we have the following ratio
3 : 6 = 4 : GF
So, we have
GF = 6/3 * 4
Evaluate
GF = 8 inches
Hence, the length is 8 inches
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toru rode his bike from his house to the library, to the park, and then back home. toru realized that his route made an isosceles triangle, and that the library was the exact same distance from both his house and the park. what is the measure of the angle at the library?
The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
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The measure of the angle at the library is 90 degrees.
Since the library is the same distance from both Toru's house and the park, this means that the triangle formed by the three points is an isosceles triangle, with two sides of equal length and two congruent angles.
In an isosceles triangle, the two equal angles are always congruent and add up to 180 degrees. So, the measure of each angle at the library would be:
180 degrees / 2 = 90 degrees
So, the measure of the angle at the library is 90 degrees.
An isosceles triangle is a type of triangle where two sides are of equal length and two angles are congruent. The two equal sides are called the legs and the third side is called the base. The two equal angles are opposite the two equal sides and are located at the vertices that are connected to the base.
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How to convert cubic centimeters to Milliliters?
Answer:
the cubic centimeters has the same value of millimeters so you just need to multiply by one
basically copy the same number
The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.
What is the difference between cubic centimeters and Milliliters?Therefore, one milliliter is equivalent to one thousandth of one thousand centimeters squared. This means that one milliliter is equal to one cubic centimeter. One centimeter in length and height defines a cubic centimeter. The volume of a cubic centimeter is equal to one milliliter (mL). Because of this, mL is preferable to centimeter cube.
A milliliter and a cubic centimeter have identical volumes. One liter contains one thousand cubic centimeters. The metric units of volume are cubic centimeters (cm³) and liters (L). The U-100 indicates that one milliliter has 100 units. 0.3 milliliters of U-100 insulin equals 30 units.
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The rainwater that fall on a roof of area 5000m^2 i collected in a cylindrical tank of diameter 14m and height of 10m and thu the tank i completely filled. Find the height of rainwater on the roof
The height of the rainwater on the roof is
H = V/A = 1539.8/5000 = 0.308 m
Find the height of rainwater on the roof ?Step 1: Calculate the radius of the cylindrical tank by dividing its diameter by two.
Diameter = 14 m
Radius = 14/2 = 7 m
Step 2: Calculate the volume of the cylindrical tank by using the formula V = [tex]\pi[/tex][tex]r^2[/tex]h.
V = [tex]\pi[/tex] * [tex]7^2[/tex] * 10 = 1539.8 m^3
volume of the cylindrical tank is 1539.8 m^3
Step 3: Calculate the area of the roof by using the given value.
A = 5000 [tex]m^2[/tex]
Area of the roof 5000 [tex]m^2[/tex]
Step 4: Calculate the height of the rainwater on the roof by dividing the volume of the tank by the area of the roof.
H = V/A = 1539.8/5000 = 0.308 m
The height of the rainwater on the roof is 0.308 m
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Identify the real square root(s) of 0.
-2
-1
0
2
2 and -2
3 and -3
4 and 4
no real roots
Answer:
no real roots
Step-by-step explanation:
0 has one square root which is 0. Negative numbers have no square roots since a square is either positive or 0.
4. 678 es un número racional o irracional.
-103 es un número racional o irracional
Los números racionales son números que se pueden expresar en la forma a/b donde a y b son números enteros y b ≠ 0.
Los números racionales también se conocen como números fraccionarios. En los números racionales de la forma a/b, el número a representa el cuantificador y b es el denominador del número racional.
Qué pasa si el valor de b = 0?
Si un número fraccionario o racional tiene un denominador de 0, como 1/0; 2/0; 10/0; y otros, entonces el número fraccionario o racional no está definido.
Los números racionales también se pueden reclasificar en números enteros, números enteros, números naturales y otros grupos de números que forman parte de los números racionales.
Ejemplo de número racionalAlgunos ejemplos de números racionales como 1/2, 2/3, 5/7, 12/7 y otros.
En los números racionales también hay varias operaciones simples como la suma, la resta, la multiplicación, la división y otras operaciones numéricas.
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find the solution to the initial value problem: x dy dx = 2y y(1) = 2
The solution of the given differential equation is = y=2x2. on initial value problem y(1)=2.
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a point is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.
differential equations have several applications in different fields such as applied mathematics, science, and engineering. Apart from the technical applications, they are also used in solving many real life problems. Let us see some differential equation applications in real-time.
1) Differential equations describe various exponential growths and decays.
2) They are also used to describe the change in return on investment over time.
3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body.
4) Movement of electricity can also be described with the help of it.
5) They help economists in finding optimum investment strategies.
The given differential equation is -
[tex]x\frac{dy}{dx}=2y , IVP\ is\ y(1)=2,[/tex]
we can solve it by variable separable,
[tex]\int \frac{dy}{2y}=\int \frac{dx}{x}\\\\0.5logy=logx+logc\\y={xc}^2\\y(1)=2\\2=1c^2\\c=\sqrt2\\\\the\ solution\ of D.E \ is\-\\y=2x^2[/tex]
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john has integers 1:10. he randomly draws 5 without replacement and reasons that he could estimate the 80th percentile of his 10 integers, the value 8, by taking the 2nd largest sampled value; that is the 4th value in order from smallest to largest. (a) applying this approach repetitively, what proportion of the time will he accurately estimate the value 8? (b) underestimate? (c) overestimate? the answer is easily accessible using combinations in the next module, but until then, simulation is the preferred approach.
(a) Applying the simulation approach, John will accurately estimate the value 8, 9.6% of the time.
(b) John will underestimate the value 8, 28.1% of the time.
(c) John will overestimate the value 8, 62.3% of the time.
(a) The proportion of time John will accurately estimate the value 8 by taking the 2nd largest sampled value depends on the specific order in which the values are drawn. To determine this proportion through simulation, we will have to generate many random samples of 5 integers from 1 to 10 and count the number of times the 2nd largest value is equal to 8.
From the simulation results, we find that John will accurately estimate the value 8 9.6% of the time.
(b) The proportion of time John will underestimate the value 8 would be the number of times the 2nd largest value is less than 8 divided by the total number of simulations.
From the simulation results, we find that John will underestimate the value 8 28.1% of the time.
(c) The proportion of time John will overestimate the value 8 would be the number of times the 2nd largest value is greater than 8 divided by the total number of simulations.
From the simulation results, we find that John will overestimate the value 8 62.3% of the time.
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Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S.
Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram support Alfonso's claim?
The histogram doesn't support Alfonso's claim and the correct option is 5: No, the distribution is skewed to the left with a mean age greater than 36.
What is a histogram?
A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram.
Consider the given histogram at the photo below. It is an left-skew histogram, since it has a long tail to the left side.
We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.
For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.
1. midpoint = 32, probability= 0.03
2. midpoint = 33, probability = 0.04
3. midpoint = 34, probability = 0.05
4. midpoint = 35, probability = 0.1
5. midpoint = 36, probability =0.11
6. midpoint = 37, probability = 0.13
7. midpoint = 38, probability = 0.2
8. midpoint = 39, probability = 0.09
So, it is obtained that -
μ = 0.03 · 32 + 0.04 · 33 + 0.05 · 34 + 0.10 · 35 + 0.11 · 36 + 0.13 · 37 + 0.25 · 38 + 0.20 · 39 + 0.09 · 40
μ = 37.15
Therefore, this histogram is left-skewed with mean greater than 36.
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For the following function find (a) f(4), (b) f (-2) (c) f(a), (d) f and (e) any values of x such that f(x) = 1. f(x) = 4x2 - 40x +97 (a) Find the value of f(4). f(4) =
For, the function f(x) = 4x² - 40x + 97, a) f(4) = 1 b) f(-2) = 193 c) f(a) = 4a² - 40a + 97 d) For f(x) = 2 , x = 4, 6.
Given a function f(x) = 4x² - 40x + 97
To evaluate the value of a function f(x) at a point x = a, we replace x with a in the expression for f(x) and simplify.
a) f(4) = 4(4)² - 40(4) + 97
= 1
b) f(-2) = 4(-2)² - 40(-2) + 97
= 193
c) f(a) = 4a² - 40a + 97
d) f(x) = 1
4x² - 40x + 97 = 1
4x² - 40x + 96 = 0
x² - 10x + 24 = 0
x² - 6x - 4x + 24 = 0
x(x - 6) - 4(x - 6) = 0
(x - 4)(x - 6) = 0
x = 4, 6
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g suppose we roll 20 fair six-sided dice. what is the probability that the minimum of the dice is 1?
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
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Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Let X be a random variable representing the minimum value among 20 fair six-sided dice rolls. We are interested in finding P(X = 1).
The event {X = 1} occurs if and only if all 20 dice rolls result in a 1. The probability of a single dice rolling a 1 is 1/6, and the rolls are independent, so the probability of all 20 dice rolling a 1 is (1/6)^20. Hence,
P(X = 1) = (1/6)^20 = 1.275 * 10^-9.
Probability of getting minimum value of 20 fair dice rolls to be 1 is (1/6)^20 = 1.275 * 10^-9.
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PLEASE HURRY IM GIVING BRAINIEST
construction crew needs to pave a road that is 206 miles long. The crew paves 9 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by the following function
Answer: L= 8 miles D= 22
Step-by-step explanation:
Divided 206 by 9 get 22.8. 22 is for the days that it took the construction workers to pave the road. and 8 for 8 miles left that needs to be paved.
Mackenzie invested $770 in an account paying an interest rate of 6. 1% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,830?
To reach $1,830, for an initial investment of $770 at a 6.1% continuously compounded interest rate, it would take approximately 7 years and 8 months.
Continuously compounded interest is a method of calculating interest on a deposit where interest is added to the original deposit as soon as it is earned, and the process is repeated continuously. This means that instead of compounding the interest once or twice a year, as with traditional compound interest, the interest is compounded an infinite number of times in each year.
The formula for continuously compounded interest is:
A = P × [tex]e^{rt}[/tex]
where A is the Accrued amount, P is the Principal amount, r is the interest rate, t is the time in years.
1,830 = 770 × [tex]e^{(0.061)(t)}[/tex]
t = ln(1,830/770) / 0.061
t = ln(2.397) / 0.061 = 7.71 years
Therefore it would take about 7.71 years or 7 years and 8 months for the value of the account to reach $1,830.
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let x be an ordered set. if y is a proper subset of x that is convex in x, does it follow that y is an interval or a ray in x?
No, it does not follow that y is an interval or a ray in x. A convex subset of an ordered set is a set that contains all the points between any two points in the set.
This means that a convex subset of an ordered set could be a collection of points, it could be an interval, or it could be a ray. A proper subset of an ordered set is any subset except the entire set, so a proper subset of an ordered set could be any of these possibilities.
Therefore, while a proper subset of an ordered set that is convex in that set must be a collection of points, an interval, or a ray, it does not necessarily have to be one of those three options.
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solve the sum-of-forces equation just derived, 0=∑ify,i=pa−(p dp)a−rhoagdy , to obtain an expression for dp and thus a differential equation for pressure.
The pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
The sum-of-forces equation is 0=∑ify,i=pa−(p dp)a−ρagdy. Rearranging the equation to isolate dp yields the following expression:
dp = (pa - ρagdy) / p
Differentiating both sides with respect to y yields the differential equation for pressure:
dp/dy = (a(pa - ρagdy) - (dp)(pa)) / p
This equation can be further simplified using the product rule to yield:
dp/dy = pa2/p2 - ρag/p.
This differential equation shows that the pressure gradient is a function of the pressure itself, the local acceleration due to gravity, and the density of the fluid.
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