The probability of no loads occurring during that period is at most 0.3 exists 3.2 years.
How long must a time period be so that the probability of no loads occurring during that period?Given: Mean time between occurrence = 0.4 year
A number of loads expected to occur during a 4 year period
Period = 4
Mean time = 0.4
Let the formula = Period/Mean Time
The number of loads expected to occur during a 4-year period
= 4/0.4 = 10 loads
B. Probability that more than 11 loads occur during 4 year period
The expected number of loads during 4-year period = 10 (from A above)
mean = 10
Using Poisson distribution,
P(k events in interval)= (λ^k * e^-k)/k!
where: k = 0, 1, 2,3,4, . . ., 11 and λ = 10.
P(k = 0) = (1[tex]0^0[/tex] × [tex]e^{-10[/tex])/0! = 0.000045
P(k = 1) = (1[tex]0^1[/tex] × [tex]e^{-10[/tex])/1! = 0.000454
P(k = 2) = (10² × [tex]e^{-10[/tex])/2! = 0.00227
P(k = 3) = (10³ × [tex]e^{-10[/tex])/3! = 0.007567
P(k = 4) = (1[tex]0^4[/tex] × [tex]e^{-10[/tex])/4! = 0.018917
P(k = 5) = (1[tex]0^5[/tex] × [tex]e^{-10[/tex])/5! = 0.037833
P(k = 6) = (1[tex]0^6[/tex] × [tex]e^{-10[/tex])/6! = 0.063055
P(k = 7) = (1[tex]0^7[/tex] × [tex]e^{-10[/tex])/7! = 0.090079
P(k = 8) = (1[tex]0^8[/tex] × [tex]e^{-10[/tex])/8! = 0.112599
P(k = 9) = (1[tex]0^9[/tex] × [tex]e^{-10[/tex])/9! = 0.12511
P(k = 10) = (1[tex]0^{10[/tex] × [tex]e^{-10[/tex])/10! = 0.12511
P(k = 11) = (1[tex]0^{11[/tex] × [tex]e^{-10[/tex])/11! = 0.113736
The probability that more than 11 loads occur during a 4-year period is then given by the following Express
1 - [P(k = 0) + P(k = 1) + P(k = 2) + . . . + P(k = 11)]
substitute the values in the above equation, we get
= 1 - [0.000045 + 0.000454 + 0.00227 + 0.007567 + 0.018917 + 0.037833 + 0.063055 + 0.090079 + 0.112599 + 0.12511+ 0.12511 + 0.113736]
simplifying the equation, we get
= 1 - 0.571665 = 0.428335
C. How long must a time period be so that the probability of no loads occurring during that period is at most 0.3
(λ^0 * e^-λ)/0! = 0.3
⇒ e^-λ/1 = 0.3
simplifying the above equation, we get
⇒ e^-λ = 0.3
⇒ -λ = ln 0.3
⇒ -λ = -1.204
⇒ λ = 1.204
The time period = 4 years / 1.204
Time period = 3.2 years
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The log flume ride lasts 8 minutes. This amount of time is one minute more than twice the length of time for the teacup ride.
How long does the teacup ride last?
The time for the teacup to last is D. m = 3.5 minutes.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let the number of minutes be m.
The amount of time is one minute more than twice the length of time for the teacup ride. This will be:
= (2 × m ) + 1 = 8
2m - 1 = 8
Collect like terms
2m = 8 - 1
2m = 7
Divide
m = 7/2
m = 3.5
The correct option is D.
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Answer:
d) m = 3.5 minutes
Step-by-step explanation:
Now we have to,
→ find the time the teacup ride last.
Forming the equation,
→ 2m + 1 = 8
Then the value of m will be,
→ 2m + 1 = 8
→ 2m = 8 - 1
→ m = 7/2
→ [ m = 3.5 min ]
Hence, ride lasts for 3.5 min.
Jodi bough a new car with 14 gallon gas tank. Around the town she is able to drive 336 miles on one tank of gas. on her first trip traveling on highways, she drives 448 on one tank of gas.A: Write a compound inequality in compact from the represents how many miles Jodi can drive on a tank of gas. Let m represent the number of miles per gallon.B: Rewrite the compound inequality as two simply inequalities separate by either and or, or.C: Solve each simple inequality. Then write the solution in compact form.
We have the following:
A.
Let m represent the number of miles per gallon, the inequality would be as follows
[tex]\frac{336}{14}\leq m\leq\frac{448}{12}[/tex]B. In two simple inequalities we have this
[tex]m\ge\frac{336}{14}\text{ or }m\leq\frac{448}{14}[/tex]C.
[tex]\begin{gathered} m\ge24\text{ or }m\leq32 \\ 24\leq m\leq32 \end{gathered}[/tex]Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,7) and (4,−1)
Answer:
8.2 units (nearest tenth)
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where (x₁, y₁) and (x₂, y₂) are the two points.
Given points:
(x₁, y₁) = (6, 7)(x₂, y₂) = (4, -1)Substitute the given points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]
[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]
[tex]\implies d=\sqrt{4+64}[/tex]
[tex]\implies d=\sqrt{68}[/tex]
[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]
Therefore, the distance between the two given points is 8.2 units to the nearest tenth.
Help please I will give brainliest
The unknown angle in the triangle is as follows;
∠H = 38 degrees.How to find angles in a triangle?The angle H can be found using the exterior angle theorem.
The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Hence,
∠DFG = ∠G + ∠H
∠DFG = 14x + 1
∠G = 89°
∠H = 5x - 7
14x + 1 = 89 + 5x - 7
14x + 1 = 89 - 7 + 5x
14x - 5x = 89 - 7 - 1
9x = 81
divide both sides by 9
x = 81 / 9
x = 9
Therefore,
∠H = 5(9) - 7 = 45 - 7 = 38 degrees.
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Evelyn sells beauty supplies. She gets 5% commission for selling beauty products. How much commission will she receive if she sells 1,648 worth of beauty products?
Given:
Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.
Required:
To find the commission she receive if she sells $1,648 worth of beauty products.
Explanation:
The commission she receive if she sells $1,648 worth of beauty products is
[tex]\begin{gathered} =\frac{5}{100}\times1648 \\ \\ =82.4 \end{gathered}[/tex]Final Answer:
$82.4
As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
The sampling distribution of the sample mean approaches a Normal Distribution when the sample size becomes larger.
According to the central limit theorem for samples, if we keep drawing larger .And larger samples and calculating their means, then the sample forms its . Own normal distribution (the sampling distribution). The mean of normal distribution has the same the original distribution and a variance that is equal to the original variance divided by the sample size. The variable p is the number of values whose average is taken together ,and not the number of times we do the experiments.
Thus, for a large random sample, the sample does not resemble the regular curve but for a large random sample it will closely resemble the normal curve.
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11. The graph models the linear relationship between the cost for cleaning and the number of rooms to clean in a house of two different cleaning companies. 200 180 160 140 Home Helper 120 Cost (In dollars) 100 80 scueaky cleaners 60 40 20 0 1 2 10 3 4 5 6 7 8 9 Number of Rooms to Clean in House What is the cost (in dollars) when Squeaky Cleaners and Home Helpers clean the same number of rooms? A. $60 B. $120 C. $150 D. $210
In the graph you can see two variables: Cost and Number of rooms to clean in house.
You can find the cost when both cleaning companies clean the same number of rooms as the point when the value in the varibles (y-axis and x- axis) are the same in the lines of both companies (the point where the lines cross each other)
Then, the cost when both companies clean the same number of rooms is $150 (the number of rooms to clean is 5 in both companies)When creating a graph, it is important to _____ the x and y axis?
"When creating a graph, it is important to assign the x and y axis."
Assigning the x and y axes is crucial when making a graph because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally. A point or line's separation from the y-axis can be determined using the x-axis. The y-axis displays a point's location on a Cartesian plane in the y (vertical) direction. Additionally, it serves as the origin (zero) point for calculating how far a point is from the x-axis.
What is Graph?A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
What is x and y axis?Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.
"When creating a graph, it is important to assign the x and y axis."
Because the x-axis is referred to as the line on a Cartesian coordinate system that runs horizontally, determining the x and y axes is essential when creating a graph. The x-axis can be used to calculate a point or line's distance from the y-axis. A point's position on a Cartesian plane is shown on the y-axis in the y (vertical) direction. It also acts as the origin (zero) point for determining a point's distance from the x-axis.
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What is the solution to the inequality? 3(x+5)>12
Answer:
x>-2
Step-by-step explanation:
3 times five is fifteen, which is larger than 12, so all x needs to be is be bigger negative 2.
Consider the line whose equation is y=-1/2x+3
any line that is perpendicular to this line is
Answer:
positive
Step-by-step explanation:
for a line to be perpendicular to another line, the slope must be reciprocaled and if its positive it becomes negative (vice versa)
y = -1/2x+3 = Line A
y = 2x+3 = PERPENDICULAR to Line A
I can take a picture but I can't type it sorry
Substitute 80 for C in the formula F = 9/5C +32 to obtain the temperature in fahrenheit.
[tex]\begin{gathered} F=\frac{9}{5}\cdot80+32 \\ =9\cdot16+32 \\ =144+32 \\ =176 \end{gathered}[/tex]Thus temperature in
Screenshot down below
The number of miles that is covered is 1458 miles.
What is the gas mileage?The term gas mileage refers to the distance that have been covered by the car using a given volume of gas. It is common that the unit that is used to measure the volume of the gas is the US gallon.
We have been told that;
420 miles could be covered by the use of 20 gallons
1 mile can be covered by the use of 1 mile * 20 gallons/ 420 miles
= 0.048 gallons
If 1 mile requires 0.048 gallons
x miles requires 70 gallons
x = 1 mile * 70 gallons/0.048 gallons
x = 1458 miles
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after 5 seconds the height of the ballon is 20 feet
Question is stated in picture. Don’t forget to round to nearest hundreth!!
The volume of a cylinder is given by the following formula:
[tex]V=\pi r^2h[/tex]Where r is the radius and h is the height of the cylinder.
By replacing 8 for r and 6 for h into the above formula, we get:
[tex]V=\pi\times8^2\times6=1205.76[/tex]Then, the volume of the cylinder equals 1205.76 units³
Help me with these two question please!!!
Question 10
Lines a and b by the converse of the consecutive interior angles theorem
Question 11
Lines e and f by the converse of the alternate interior angles theorem
What is the equation of the line that passes through the point (-3,1) and has a slope of -3?
Answer:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Since line has a slope of -3, equation is y = -3x + c.
Substitute (-3,1) into the equation to find c.
1 = -3(-3) + c
c = -8
Hence, equation of line is y = -3x - 8.
3.525 divided by 0.25 find the quotient
Answer:
3.525/0.25=14.1
Step-by-step explanation:
Answer: 14.1
Step-by-step explanation:
3.525/0.25 = 14.1
Since "quotient" just means the result of two numbers being divided together. Therefore we would divide the two numbers you just gave.
Estimate 70⎯⎯⎯⎯√3 to the nearest integer.
Answer:
Step-by-step explanation:
round up
√3 = √4
70-√4= 70-2
=68
Divide $180 in the ratio of 2 : 3 : 4
By dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
Solution
Find the sum of the ratios2 + 3 + 4 = 9
Divide the amount from the sum of the ratios180 ÷ 9 = 20
Hence, we get the quotient of 20.
Multiply the quotient by the ratios20 × 2 = 40
20 × 3 = 60
20 × 4 = 80
Hence, by dividing $180 in the ratio of 2:3:4, we get 40,60 and 80
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As a speed skater Kyle cycles between sprinting and recovering on the 111. 12 m short track during practice every day for 50 minutes let T be the time and hours that Kyle sprints during the practice a right the unsimplified expression to represent the total distance Kyle skates it may help you to make a verbal model to represent the total distance Kyle skates be sure to use compatible units be interpret the parts of the expression C simplify the algebraic expression de if Kyle spent 40 minutes sprinting yesterday how far did he skate in all he sprinted for 48 KM/H and his recovery was 18 KM/H
Answer:If t= time sprinting then (50-t)= time recovering
Distance = rate x time= t(48) + (50-t)18
Step-by-step explanation:just yes
Colton has $67,696 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
Colton has $67,696 in a savings account that earns 2% interest per year. The interest is not compounded. How much interest will he earn in 1 year?
we know that
2%=2/100=0.02
so
To find out the amount of interest, multiply the total amount by the percentage in decimal form
(67,696)*0.02
=$1,353.92Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
The coordinates of point C on AB such that AC is 2/3 the length of AB is (2,0)
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
To find out how long AC is, we must first find the length of AB.
According to Pythagoras’ theorem,
[tex]a^2 + b^2 = c^2[/tex].
Thus [tex]4^2 + 6^2 = c^2[/tex].
[tex]16 + 36 = c^2[/tex].
The square root of this is;
c = √52.
AB is 7.21 units long.
2/3 of 7.21 is 4.8
The coordinate that fits this is (2,0).
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determine the measure of angle j.
The measure of the value of ∠j is 10°.
What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.
Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.
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Find the value of x in each case. Please put statement reasons.
Answer:
x = 10°
Step-by-step explanation:
Given the figure with angles 2x, 4x, 5x, and 50° marked, you want to find the value of x.
Development∠HAC = ∠HCA . . . . base angles of isosceles triangle HAC
2(∠HAC) = 4x . . . . . exterior angle 4x is equal to the sum of the equal remote interior angles HAC and HCA
∠HAC = 2x . . . . . . . divide by 2
∠AED = 180° -2x -2x = 180° -4x . . . . sum of angles in ∆AED is 180°
∠AHC = 180° -4x . . . . angles at H are a linear pair
HC ║ ED . . . . converse of corresponding angles theorem
∠FEG = ∠FCH = 50° . . . . . corresponding angles theorem
5x = 50° . . . . . substitute value of ∠FEG
x = 10° . . . . . divide by 5
Using this value for the marked angles, we get the measures shown in the attachment.
(x^4/7^-8)^7
Solve asap pls
Answer: x=2
Step-by-step explanation: (x^4/7^-8 )^7
(4x/-56)^7 (7×8=56)
4x/-8
x/-2
x = 2
Hi, can y oh please me I’m stuck on this question.
The measure of angle 2 is 81° because angles 1 and 2 are corresponding angles.
Corresponding angles:
Corresponding angle means the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Given,
Two electricity poles are built standing parallel to each other, as shown below. The measure of angle 1 is 81°.
Here we need to find the measure of the angle 2.
We know that,
If the lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet.
And as per the definition of corresponding angles, we know that, if any two lines are said to be parallel if the Corresponding angles so formed are equal.
Then the measure of the angle 2 is 81° because angle 1 and 2 are parallel.
Therefore, those angles are the corresponding angles also.
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R = ((-4,2), (3,6), (x,8), (-1,4))
Which value of r would make this relation a function?
Answer:
0
Step-by-step explanation:
the domain can’t be the same
Tell whether the data in the table can be modeled by a linear equation. Explain. A table listing pairs of x and y values. First pair. Negative 3 and 16. Second pair. Negative 1 and 10. Third pair. 1 and 4. Fourth pair. 3 and negative 2. Fifth pair. 5 and negative 8. The data be modeled by a linear equation because the rate of change constant. Question 2 If possible, write a linear equation that represents y as a function of x. If not possible, leave blank.
The table is a linear function and the equation is y = -3(x - 1) + 4
How to determine if the table represents a linear equation?From the question, we have the pairs to be
First pair = (-3, 16)Second pair.= (-1, 10)Third pair = (1, 4)Fourth pair = (3, -2)Fifth pair = (5, -8)From the above representations, we can see that:
As the values of x increase by +2, the values of y constantly increase by -6
This means that the table has a constant rate
By the definition of a linear function, the table represents a linear function
The linear equation of the functionIn (a), we have
x = +2
y = -6
The slope is calculated as
Slope = y/x
So, we have
Slope = -6/2
Evaluate
Slope = -3
The equation is then calculated as
Y = Slope * (X - x) + y
Where
(x, y) = (1, 4)
So, we have
y = -3(x - 1) + 4
Hence, the linear function is y = -3(x - 1) + 4
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please answer this following question.
on the triangle on the left, on the bottom left of that triangle it says,
[4(x +2)]
The two triangles are not similar to each other.
What is perimeter?The perimeter of the triangle is the sum of the lengths of all its sides.
The angle of triangle = 62
The two equal angles = [4(x +2)] and (5x - 7)
According to the question,
The Perimeter of triangle are;
[4(x +2)] + (5x - 7) + 62 = 180
4x + 8 + 5x - 7 + 62 = 180
9x + 63 = 180
9x = 117
x = 13
The other triangle is
6x + 62 + 6x + 6 = 180
12x + 68 = 180
12x = 112
x = 9.33
Hence, the two triangles are not similar to each other.
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x + 3y = 1 ; 7x + 8y = 11 solve by substitution.
Step-by-step explanation:
x + 3y = 1
x = 1 - 3y-(i)
7x + 8y = 11
x= 11-8y/7-(ii)
substituting eqn (i) in eqn (ii)
11-8y/7= 1-3y
11-8y=7-21y
13y=-4
y=-4/13
putting the value of y in eqn (i)
x=1-(-12/13)
x=25/13
