Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following probability mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
The integral has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
Hence the probability of finding a value higher than x is given by:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
In the context of this problem, the mean and the decay parameter are given, respectively, by:
[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]
Hence the probability that a truck will be loaded in 20 minutes or more is:
[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]
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-5 < 3x -8 / means greater than or equal to
Answer:
Equation: -5 <3× -8
+8. +8
3 <3x
_ _
3. 3
Answer: 1 = X
Step-by-step explanation:
Equation: -5 <3× -8
First Step: You must add 8 to -8 and move it to both sides. The reason why we do this is because on the left side we have 1 number and on the right side we have 2 numbers. We see that the right side has more numbers than the left, so we must move the -8 turning it to a positive 8 (8-8 cancels each other making 0) and adding the +8 in -8 to -5 as well, since we're adding to both sides.
Second Step: Since we added 8 to -5, it equals 3 now 8-5=3. Changing the equation to 3 <3x. Now we have to divide 3 to both sides as well, because we want the x to be by itself. So, 3 ÷ 3 = 1 and 3x ÷ 3 = x
Results: After our extraordinary calculations we recieve
the answer 1=x
x represents a positive interger
X < 7
How should I solve this? It would help with a step by step guide
If x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
The x represents a positive integers
Positive integers are the integers greater than 0. In number line the positive number will be at the right side of the 0. The negative integers are the integers less than 0. In number line the negative number will be at the left side of the 0.
The given inequality is
x<7
The inequality is the mathematical expression represents the relation between the two values that is not equal
Here x is less than 7 and a positive integer
Therefore,
x = {1, 2, 3, 4, 5, 6}
Hence, if x represents a positive integer and x<7, then the values of x = {1,2,3,4,5,6}
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In triangle ABC, ACB = 67°, AB= 6.9 cm and
BC = 5.7 cm.
a Calculate angle BÂC.
b Hence find the area of AABC.
Please answer all questions to 3 correct sig figs.
Answer:
In triangle ABC, ACB = 67°, AB= 6.9 cm and BC = 5.7 cm.
Step-by-step explanation:
11) Translate the following phrases into algebraic expressions
a. The difference of a number k and four
b. Eight less than a number x
e. The sum of six and a number d
d. The product of a number and five
e The quotient of eight and a number
f. The product of two and a number increased by seven
g. Half of a number decreased by twelve
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
What is meant by algebraic expressions?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Arithmetic operations like subtraction, addition, division, multiplication, and exponentiation are used to combine variables and integers to produce any algebraic expression. A variable, a number, or a variable and number with an exponent as a product can all be used as the phrase.
The translation is as follows:
a) 4 - k
b) 8 - x
c) 6 + d
d) x + 5
e) 8 / x
f) 2 + x = 8
g) 1/2n-12
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Marybeth rides her skateboard 5 miles in 30 minutes. If she maintains this rate, how far will she ride her skateboard in 4 hours?
Find the length of side x in simplest radical form with a rational denominator. I will give brainliest please help asap
Answer:
[tex]x=\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
x^2+x^2=1
x^2=1/2
x=1/sqrt2
x=sqrt2/2
:]
Determine which statement completes each open sentence:
32+8+1
15 (1+2)
4²
4.2
3(x - 4 + x)
when x = 4
111
3(x-4 + x)
when x = 2
32-1
15 +1 +2
3x4+x
3x4+x
1. is equal to
2. is NOT equal to
The statement which completes each of the open sentences are given below:
32 ÷ 8 + 1 is not equal to 3² - 1
15 ÷ ( 1 + 2) is not equal to 15 ÷ 1 +2
4² is not equal to 4 . 2
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 4
3 ( x - 4 + x) is not equal to 3x - 4 + x when x = 2
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What calculation will give us the estimated volume of the Great Pyramid of Giza in cubic meters?
The option that would give the estimated volume of the Pyramid of Giza is = [tex]\frac{53,000 . 150 }{3}[/tex]
What is the volume?A pyramid is a 3-dimensional shape that is made up of a polygonal base and 4 triangular faces. The 4 triangular faces are joined at a vertex. Types of pyramids include a square pyramid, rectangle pyramid, triangle pyramid.
The volume of a pyramid is the amount of space that is a three-dimensional shape.
Volume of a pyramid = 1/3 x (base area x height)
1/3 x (53,000. 150)
= [tex]\frac{53,000 . 150 }{3}[/tex]
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Calculate the height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60 than when the angle of elevation is 30
The height of a tree whose shadow is 20m shorter when the angle of elevation of the sun is 60 is 17.3 meters.
What is elevation?The elevation is the distance above sea level. They are usually measured in meters or feet.
Let t be the height of the tree, then the length of the shadow will be:
Shadow length = t/tan(α)
where α is the angle of elevation. The difference in shadow lengths is:
20 m = t/tan(30°) -t/tan(60°) = t(√3 -1/√3)
= (20 m)/(2/√3) = 10√3 m
= 17.3 m
The height is 17.3 meters.
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Ahmed has five more CDs than one-half the number of CDs Julia has. In this situation, what does One-half c+ 5 represent?
the number of CDs Ahmed has
the number of CDs Julia has
the number of CDs Ahmed has more than Julia
the number of CDs Ahmed and Julia have altogether
Answer: A) the number of CDs Ahmed has.
Step-by-step explanation:
Please i really need help
Answer:
2:4 ratio (1:2)
2cups carrot + 4cups apple = 6cups (ratio 1:2)
Therefore 4cups carrot + 8 cups apple = 12 cups (ratio 1:2)
Hope that helps
Pleaseeeeeeeee helpppp
Answer:n= -129/t
im not sure if thats the answer ur looking for
Fill in the table using this function rule.
y=4x-3
the value of y for x values(-2,0,2,4) are {11, 3, -5, -13}
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
You want the value of y for various values of x, given that y = -4x +3.
Function evaluating
Put the value of x where x is in the function rule and do the arithmetic.
y = -4x +3
for x = -2
y = (-4)(-2) +3 = 8 +3 = 11
for x = 0
y = (-4)(0) +3 = 0 +3 = 3
for x = 2
y = (-4)(2) +3 = -8 +3 = -5
for x = 4
y = (-4)(4) +3 = -16 +3 = -13
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Solve 3x > 174, and use the interactive number line tool to graph the solution. What is true about the graph? Check all that apply.
There is an open circle at 58.
There is a closed circle at 58.
There is an open circle at 174.
There is a closed circle at 174.
The arrow points right.
The arrow points left.
Answer:
there is an open circle at 58
the arrow points right
Step-by-step explanation:
3x>174/:3
x>58 we have a strict x more than 58 that's why it's an open circle and right because x is more, but not less
The water level will be 10 feet or lower by tomorrow.
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
The given statement is "The water level will be 10 feet or lower by tomorrow."
What is a inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
The inequality for the given statement is x≤10
The inequality written for the given statement is x≤10. Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Choose the inequality that represents the statement.
The water level will be 10 feet or lower by tomorrow.
A. x≤10
B. x<10
C. x>10
D. x=10
MEAN The mean A of two numbers, x and y, is given by A =*+. Solve for y.
The mean can be written as mean A= x+ y/2
What is Mean?A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set.
Only numerical variables—regardless of whether they are discrete or continuous—can be used to determine the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it.
The mean formula is
= {Sum of Observation} ÷ {Total numbers of Observations}
Given:
mean A of two numbers, x and y
So, the mean can be written as
mean A= x+ y/2
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equivalent to 6+12x?
Answer:
Step-by-step explanation:
6 + 12x
6 ( 1 + 2x )
Basic Geomtry Help, Easy
Answer:
A
Step-by-step explanation:
Because it's has no straight to it
4) The ratio of the side length of a square to the square perimeter is always 1 to 4. Peter
drew a square with a perimeter of 28 inches.
What is the side length of the square Peter drew
The side length of a square is 7 inches drawn by the Peter.
Whats is termed as the perimeter of the square?A square's perimeter is described as the amount length of its boundary. The distance around any looped geometrical shape is used to calculate its perimeter. The perimeter of a square can be determined by adding all of its sides. It is four times this same length of every side of a square because all 4 sides are equal.According to the question, the ratio of a square's side length to its perimeter is always one to four.
According to the story, Peter drew a square with such a perimeter of 28 inches.
Divide 28 inches by 4 to get the side length of a square Peter drew.
= 28/4
= 7 inches
As a result, the side length of a square is 7 inches.
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use the aleks calculator to find 46% of 20 do not round
The value of the part of 20 that is 46% is 9.2.
How to determine the percentage of a number?Percentage is simply a number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Percentage = 46%Whole = 20Part = ?Plug the given values into the above formula and solve for the part.
Percentage = ( Part / Whole ) × 100%
46% = ( Part / 20) × 100%
46/100 = ( Part / 20 ) × 100/100
46/100 = ( Part / 20 ) × 1
46/100 = Part / 20
Cross multiply
46 × 20 = Part × 100
920 = Part × 100
Part = 920/100
Part = 9.2
Therefore, 9.2 is 46 percent of 20.
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Using the SSS congruence is criterion what additional information is needed to show that triangle RST is congruent to triangle UTS?
The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
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Answer:
Step-by-step explanation:The additional information you will need to show that triangles RST and UTS are congruent by SSS congruence is: c. RT ≅ US.
How to Prove Two Triangles are Congruent by SSS Congruence Postulate?
To prove that two triangles are congruent to each other using the SSS congruence as a criteria, we need to know or be able to show that the three sides of one triangle are congruent to the corresponding 3 sides of the other triangle.
If this criterion is met, then we have enough information needed to show the two instruments are congruent by the SSS congruence.
RS ≅ UT as marked in the diagram shown. Also, by the reflexive property, we ST ≅ TS.
We already know two pairs of sides are congruent to each other in both triangles.
In other to prove the triangles are congruent by SSS congruence, the additional information needed is: c. RT ≅ US.
In one year, a school uses 12,370 pieces of white paper, 5,670 fewer pieces of blue paper than white paper, and 3,500 fewer pieces of yellow paper than blue paper. How many pieces of paper does the school use in all?
Answer:
22270 pieces of paper
Step-by-step explanation:
White: 12370 [12,370 pieces of white paper]
Blue: 6700 (12370-5670). [5,670 fewer pieces of blue paper than white paper]
Yellow: 3200 (6700-3200). [3,500 fewer pieces of yellow paper than blue paper]
The sum is 22270 pieces of paper.
By looking at the equation of the least-squares regression line, you can see that the correlation between height and arm span is.
Step-by-step explanation:
If the data shows a leaner relationship between two variables, the line that best fits this linear relationship is known as a least-squares regression line, which minimizes the vertical distance from the data points to the regression line.
Friday
Use the equation to fill in the table.
y = 2x -7
Answer:
x=7
Step-by-step explanation:
7=2x-7
-2x-7-7
-2x=-14
x=-14÷2
x=-7
12/1-(2x+3)
How to simplify this fraction
Step-by-step explanation:
so, it is
12 / (1 - (2x + 3))
yes, that is
12 / (1 - 2x - 3) = 12 /(-2x -2) | divide both sides by -2
-6/(x + 1)
Please help or answer questions 2, 3, and 4. You may answer question 1 if you’d like but I do not need it. I have already done question 2 but confirming my answers would be nice. I will give out brainliest.
The ratios that can be used to compare the soda and punch recipes are as follows;
1. Emily:
Mason's recipe for soda is y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio's
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
2. Please see the completed values in the table in the elucidation that follows
3. The equivalent ratio relationship in each graph is given by the constant ratio of each coordinate pair.
4. The recipe that has the strongest lemon lime taste is given by the graph that has the steepest slope
What is the slope of a graph?The slope of a graph is given by the ratio of the rise to the run of a graph
1. The unit rate for Mason's recipe is (1/2) cup of lemon–lime per cup of club
While the unit rate for Tyler's recipe for club soda is (3/5) cup of lemon and lime per cup of club
Mathematically, we have
Emily;
Mason's recipe; y = (1/2)•x
Tyler's recipe; y = (3/5)•x
Julio;
Mason's recipe; y = (1/3)•x
Tyler's recipe; y = (3/8)•x
Carlos's recipe; y = (2/5)•x
Zeb's recipe; y = (1/5)•x
2. The values in the table becomes;
MasonLemon–lime; 1/3, 2/3, 1, 4/3, 5/3, 6/3
Total punch; 1, 2, 3, 4, 5, 6
Tyler'sLemon–lime; 3/8, 3/4, 9/8, 3/2, 15/8, 9/4
Total punch; 1, 2, 3, 4, 5, 6
Carlos'sLemon–lime; 2/5, 4/5, 6/5, 8/5, 2, 12/5
Total punch; 1, 2, 3, 4, 5, 6
Zeb'sLemon–lime; 1/5, 2/5, 3/5, 4/5, 1, 6/5
Total punch; 1, 2, 3, 4, 5, 6
3. Each graph represents equivalent ratios given that the value of the ratio of data point is a constant, that is, we have;
For Mason, 1:(1/3) = 2:(2/3) = 3:1...
For Tyler, 1:(3/8) = 2:(3/4) = 3:(9/8)...
For Carlos, 1:(2/5), 2:(4/5), 3:(6/5)...
For Zeb, 1:(1/5), 2:(2/5), 3:(3/5)...
4. The slope of each graph is given by the number of cups of lemon–lime per one cup of total punch,
The recipe that has the strongest lemon–lime taste is given by the recipe that has the most lemon–lime per each cup of total punch
Which gives;
The recipe that has the strongest lemon–lime can be found from the graph that has the largest slope, which is given by Carlos's recipe.
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one customer has two chances to receive a prize. if the customer keeps the higher of the two prizes awarded, what is the probability the customer will receive at least $100?
If the customer keeps the higher of the two prizes awarded, the probability the customer will receive at least $100 is 0.10
The probability that the customer will receive at least $100, P(X>100) is obtained below:
The probability that the customer will receive at least $100 is obtained by adding the corresponding probabilities of X=100 and, X=1000
Given from the table of probabilities, P(X=100)=0.08, and P(X=1,000)
P[X>100]=P(X=100)+P(X=1,000)
=0.08+0.02
=0.10
The question is incomplete, the complete question is given below:
A real estate developer is awarding one of four prizes to customers who view new properties. The prizes are awarded randomly through drawings. Prize values and their associated probabilities follow:
PRIZE VALUE PROBABLITY
$10 0.80
$20 0.10
$100 0.08
$1000 0.02
one customer has two chances to receive a prize. if the customer keeps the higher of the two prizes awarded, what is the probability the customer will receive at least $100?
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A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 238 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.
Considering the area of the rectangular lot, the width of the walkway is of 3.9 feet.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given as follows:
The area is given by A = lw.The perimeter is given by P = 2(l + w).In the context of this problem, for the garden and the walkway, the dimensions are given as follows:
Length of 15 feet.Width of 12 + w, in which w is the width of the walkway.Considering that the area is of 238 square feet, we can solve for the width of the walkway as follows:
15(12 + w) = 238
12 + w = 238/15
12 + w = 15.9.
w = 15.9 - 12
w = 3.9 feet, which is the width of the walkway.
Since the area is in square feet, the length and the width are in feet.
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peruvian cafe bought ad time on radio station wkoi. during the first four weeks, 4,000 different people heard the spot six times, while 2,000 heard it only three times during the same period. what is the average frequency?
The average frequency of people hearing the spot on the radio station is equal to 5.
Average frequency can be defined as the average number of times an individual is exposed to an Advertising schedule.
Average frequency can be calculated by using the formula;
average frequency = total / n
As 4000 people heard the spot 6 times and 2000 people heard it three times; therefore
n = 4000 + 2000 = 6000
total = number × frequency = (6 × 4000) + (3 × 2000) = 24000 + 6000 = 30,000
Substituting these values in the equation;
average frequency = 30,000 / 6000
average frequency = 5
Hence the average frequency of people hearing the spot on the radio station wkoi is calculated to be 5.
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a license plate consists of 3 letters followed by 4 digits. how many license plates are possible if the first digit cannot be 0, and letters and digits may repeat?
There are 158,184,000 possible license plates consisting of 3 letters followed by 4 digits.
Based on the given information, since the letters and digits may be repeated, there are:
26 ways to fill in the first letter
26 ways to fill in the second letter
26 ways to fill in the third letter
9 ways to fill in the first digit *(first digit cannot be 0)
10 ways to fill in the second digit
10 ways to fill in the third digit and
10 ways to fill in the first digit
Thus, by Fundamental Principle of Counting, there are 158,184,000 possible license plates.
26 x 26 x 26 x 9 x 10 x 10 x 10 = 158,184,000
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