Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%
If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.
To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:
F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]
where μ is the mean, σ is the standard deviation, and erf(z) is the error function.
Plugging in the given values, we get:
F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2
Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:
P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5
So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.
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Graph y = - 1/2x + 3 use the line tool and select two points on the line
The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image
How to graph the equation of a line?y = - 1/2x + 3
In order to graph the equation of the line:
First, find the value of x when y = 0:
y = - 1/2x + 3 , when y = 0:
0 = - 1/2x + 3
1/2x = 3
x = 3 × 2
x = 6
Also, find the value of y when x = 0:
y = - 1/2x + 3, when x = 0:
y = - 1/2(0) + 3
y = 3
Therefore, the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached
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PLSS GUYS HELP MEEEEEEEE PLS
The value of x is 10°.
What is a measure of an angle?
Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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The value of x is 10°.
What is a measure of an angle?Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.
What is angle?An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex.
Here, we have
The measure of ∠AOC is 90°.
3x° + 46° +14° = 90°
3*10° + 46 + 14° = 90°
Hence, the value of x is 10.
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50 POINTS Answer the following questions and draw a rough sketch of the function:
f(x)=-x^4+8x^3+8x^2-96x-144
What is the function’s general shape?
Does the function face up or down?
What is the function’s y-intercept?
If one of the factors is (−6), how would you show that on the graph?
The function's general shape is a downward-opening parabola.
The function faces down The function's y-intercept is -144x - 6 is a factorWhat is the function’s general shape?
From the question, we have the following parameters that can be used in our computation:
f(x)=-x^4+8x^3+8x^2-96x-144
Express properly
So, we have
f(x) = -x⁴ + 8x³ +8x² - 96x - 144
Next, we plot the graph (see attachment)
From the attached graph, we can see that the function opens down
This means that the general shape is a downward-opening parabola.
Does the function face up or down?The function faces down (as shown on the graph)
What is the function’s y-intercept?Here, we set x = 0
So, we have
f(0) = -(0)⁴ + 8(0)³ + 8(0)² - 96(0) - 144
Evaluate
f(0) = -144
So, the y-intercept is -144
How to show that one of the factors is (x - 6) on the graph?We start by setting the factor to 0
So, we have
x - 6 = 0
Solve for x
x = 6
From the graph;
When x = 6, y = 0
This means that x - 6 is a factor
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Evaluate this problem
Answer:
78
Step-by-step explanation:
a + 8b = 6 + 8 x 9 = 6 + 72 = 78
Answer: 78
Step-by-step explanation:
value of a=6
value of b=9
a+8b= 6+8*9
as the 8 will be multiplied by 9
6+8*9= 6+72
6+72 = 78
How do I even do this?
Answer:
going to have to to get the house ready
Consider the following problem:
The length s(t) of the side of the base of a square prism is decreasing at a rate of 7
kilometers per minute and the height h(t) of the prism is increasing at a rate of 10
kilometers per minute. At a certain instant to, the base's side is 4 kilometers and the
height is 9 kilometers. What is the rate of change of the surface area A(t) of the
prism at that instant?
Match each expression with its given value.
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
What does rate of change mean?
An indicator of how one quantity changes in proportion to another is called a rate of change. If x and y are the independent and dependent variables, respectively, then the rate of change is equal to y-to-x conversions. Positive or negative change rates are possible.
Surafce area of a prism is equal to
2(Area of base) + (perimeter of base)(height)
2b^2+4bh
[tex]S=2b^2+4bh[/tex]
[tex]\frac{ds}{dt}=4b\frac{db}{dt} + 4b\frac{db}{dt} + 4h\frac{db}{dt} \\[/tex]
It is given that db/dt= -7 and dh/dt -=10.
At a particular instant b= 4km, h=9 km.
Now we will substitute the values in this formula:
[tex]\frac{ds}{dt}=-4*4*7-4*4*7+ 4*9*10\\\frac{ds}{dt}=136[/tex]
The rate of change of the surface area A(t) of the prism is 136 kilometers per minute.
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profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, what were profits last year.
The profits last year were $2041.66
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here, profits of calculess corporation this year were 140% of profits last year. if profits this year were $4900, then let the profit last year be x then we have 2.4x=4900
x=4900/2.4
x=2041.66
Hence, The profits last year were $2041.66
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b.) Suppose the Governor of Louisiana decided that all license plates must begin with the
letter A on each license plate. How many fewer license plates would
Louisiana be able to issue using the Governor's mandate for license plates?
Answer: atleast alot
Step-by-step explanation:
SELECT ALL of the numbers that are included within the range of the line segment.
ANSWERS ↓
-6
-4
-3
-2
0.5
1.5
3.5
Answer: -2, -3, and -4.
Step-by-step explanation:
The range is all the Y Values the graph uses, and the Y values range from -0.5 to -5.5, making every number in between those included.
Solve systems of equations by elimination -3x-3y=3 3x+6y=9
Answer: x = -5, y = 4
Step-by-step explanation:
Align the two equations according to their terms:
[tex]\left \{ {{-3x-3y = 3} \atop {3x+6y = 9}} \right.[/tex]
Add the two equations. Because -3x and 3x equals zero, they can be eliminated from the equation. This results in:
[tex]3y = 12\\y = 4[/tex]
Plug in y = 4 into the first equation:
[tex]-3x - 3(4) = 3\\[/tex]
Solve for x:
[tex]-3x-12 = 3\\-3x = 15\\x = -5[/tex]
Check by plugging in both x and y:
[tex]-3(-5) - 3(4) = 3\\15 - 12 = 3\\3 = 3[/tex]
So, x = -5 and y = 4
A rectangle with an area of 5050 units^2
2
is the image of a rectangle that was dilated by a scale factor of \frac{1}{3}
3
1
. Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]
How can I inflate my model?Add the square of the scaling factor s to the area of the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of the figure after dilation Ad. a d = s2a p .
To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]
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What is the coefficient in the expression 6 – 2 + 4n
Answer:
4
Step-by-step explanation:
The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.
Hope this helps! :)
Anything would help please
When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)
what is triangle ?A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
area of the polygon ( triangle ) = 1/2 * b * h
= 1/2 * 4 * 4
= 8 units
so When the points are (2, 6), (2, -2), and (8 units), the polygon's or triangle's area is 8. ( 4 , -2)
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What's the equation and solution?
Using the Algebraic tile method we get x=2 solution for equation model
What is Algebraic Tile method?The algebra tile method is a method of solving equations by using visual models, such as tiles with different values on them, to represent the unknowns and constants in the equation. It is often used to help students understand the process of solving equations and to see how the operations of addition and subtraction correspond to the process of combining or separating algebraic expressions.
In the question, we have 3 kinds of tile
X tilesunit positive tilesunit negative tilesEquation will be :
⇒ 3x - 1 - 1 = 1 + 1 + 1 + 1
⇒ 3x - 2 = 4
⇒ 3x = 6
⇒ x = 2
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To purchase 12,100 worth of machinery for her business, Latoya made a down payment of 1800 and took a business loan for the rest. After 3 years of paying monthly payments of 313.36, she finally paid off the loan.
A, what was the total amount latoya ended up paying for the machinery. (including down payment and monthly payments)
B. How much interest did latoya pay on the loan
The total amount that Latoya ended up paying for the machinery, was $ 13, 080 .96
The amount of interest that Latoya paid was $ 980.96
How to find the total amount paid ?The total amount paid by Latoya for the machinery can be found as :
= Down payment of the machinery + ( Monthly payments x Number of months per year x Number of years )
= 1, 800 + ( 313. 36 x 12 x 3 )
= $ 13, 080 .96
The total interest paid on the loan was :
= ( Monthly payments x Number of months per year x Number of years ) - Worth of the machine - down payment
= ( 313. 36 x 12 x 3 ) - 12, 100 - 1, 800
= $ 980.96
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Assume the Poisson distribution applies. Use the given mean to find the indicated probability.
Find P(5) when μ = 9
Answer: 0.155
Step-by-step explanation:
To find the probability of a certain event occurring in a Poisson distribution, we can use the formula:
P(k) = (μ^k * e^(-μ)) / k!
Where:
P(k) is the probability of the event occurring k timesμ is the meane is the base of the natural logarithm ( approximately 2.71828)k! is the factorial of k (k factorial)Plugging in the given values, we get:
P(5) = (9^5 * e^(-9)) / 5! = 126,441 * 0.000123 = 0.1550
So the probability of the event occurring 5 times is approximately 15.5%.
on Monday in December, it was -8 degrees Celsius in Harbin China and -2 degrees Celsius and Beijing China on Tuesday and Beijing it was 5 degrees colder than it was the day before what was the new temperature?
The required temperature in Beijing China is -7°C on Tuesday.
As mentioned in the numeral,
On Monday in December
The temperature in Harbin China is -8°C,
Now,
The Temperature in Beijing china is -2°C
According to the condition, the temperature on the next day in Beijing is 5° degrees colder than it was yesterday since the temperature is becoming colder implying that the temperature is getting decreased by -5°C.
The temperature on Tuesday is given as,
T = -2°C - 5°C [subtracting -5 because the temperature is decreased]
T = - 7°C
Thus, the required temperature in Beijing China is -7°C on Tuesday.
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An English teacher reviewed 2 3 of an essay in 1 4 of an hour. At this rate, how many essays can she review in 1 hour? Simplify your answer and write it as a proper fraction, mixed number, or whole number. essays
The essays that she can review in 1 hour would be; 2 2/3.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.
Thus, Fraction of the essay reviewed = 2/3
Amount of time used = 1/4
Therefore, the fraction of essay for an hour can be calculated as;
= Fraction of the essay reviewed / Amount of time used
= 2/3 ÷ 1/4
= 2/3 × 4
= 8/3
= 2 2/3
Hence, She will review 2 2/3 essay.
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During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes. Based on this relative frequency, how many pars or better could he be expected to make on the remaining 150 holes? Round to the nearest whole number if necessary.
70 pars or better
60 pars or better
65 pars or better
53 pars or better
Dirk will make 70 pars or better.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that During the first several rounds of a golfing league, Dirk made par or better on 42 out of 90 holes.
Out of 90 holes, Dirk made par or better on 42 holes.
At this rate, Out of 1 hole, Dirk made par or better on (42/90) holes.
Then, Out of 150 holes, Dirk will make par or better on -
(42/90 x 150) holes
(42/90 x 150)
70
Therefore, Dirk will make 70 pars or better.
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What's the sum of 3 3/8 and 4 3/4? A.9 1/4 B. 8 3/4 C. 7 3/4 D. 8 1/8
Answer:
D
Step-by-step explanation:
3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex] Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]
3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]
7[tex]\frac{9}{8}[/tex]
7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex] Another name for [tex]\frac{8}{8}[/tex] is 1
7 + 1 + [tex]\frac{1}{8}[/tex]
8[tex]\frac{1}{8}[/tex]
2 copies of 1/10 write fraction for each statement
2 copies of 1/10 can be written as 2/10
What is a fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here 2 copies of 1/10 thus 2×1/10=2/10
=1/5
Hence, 2 copies of 1/10 can be written as 2/10
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A moving sidewalk carries people at a rate of 400 feet per minute. How long is this moving sidewalk if it takes 4 minutes to travel from one end to the other?
A 25 feet
B 100 feet
C 404 feet
D 1600 feet
*process
Mario had 8 1/5
yards of ribbon for a project. Sue gave him 2 3/4 more yards of ribbon. Which is closest to the number of yards of ribbon Mario had altogether?
The closest to the number of yards of ribbon Mario had altogether will be ;
⇒ 11 yards
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Now,
Since, Mario had 8 1/5 yards of ribbon for a project.
And, Sue gave him 2 3/4 more yards of ribbon.
Hence, Total ribbon for the project Mario have = 8 1/5 yards + 2 3/4 yards
= 41/5 + 11/4
= (164 + 55) / 20
= 219 / 20 yards
= 10.95 yards
≈ 11 yards
Thus, Total ribbon for the project Mario have = 11 yards
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-50 POINTS- If you guess will be reported.
If P=(1,6), Find: D3 (P)
Answer:
(3,18)
Step-by-step explanation:
You do not give the center of dilation, so I am using the origin (0,0)
You multiply the x and y by 3
(1,6)
1 x 3 = 3
(1,6)
6 x 3 = 18
(3,18)
The graph below represents the linear equation y = 1/2x - 3.
A second linear equation is represented by the data in the table.
x | y
-1 | 1
0 | 0
2 | -2
3 | -3
What is the solution to the system of equations?
A) (-2, -4)
B) (1, -1)
C) (2, -2)
D) (4, -4)
Answer:
(2,-2)
Step-by-step explanation:
The answer is the intercept point of both lines, so we need to find the point when both the line touches, with out graphing we can see by the table that point (2, -2) intercepts with the line on the graph.
hope this helps :)
Answer:
C) (2, -2)--------------------------
From the table we see each y-coordinate is the negative of the corresponding x-coordinate. It gives us the second line:
y = - xThe first line is given y = 1/2x - 3, equate both to get:
- x = 1/2x - 3-2x = x - 6x + 2x = 63x = 6x = 2Then the value of y:
y = - x = - 2The solution is (2, - 2).
What is 15% of 12 meters?
Answer:
1.8 meters
Step-by-step explanation:
Multiply 12 by 0.15 to get your answer. You multiply because the question says "15% of 12 meters" which means you need to multiply.
Answer: 1.8
Step-by-step explanation:
Multiply 12 by .15 (15% as a decimal), and you'll get 1.8 meters. You multiply, because it says 15% of 12 meters.
graph f and h , write h in terms of f, describe the transformation from the graph of f to the graph of h .
the equation :
f(x) = 3x ; h(x) = 3x - 5
h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
What is the graph of the function?A graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of a function. It is a way to visualize the behavior of the function and its relation to the x and y axes.
Here,
We can draw the graph as
h(x) = 3x - 5 can be written in terms of f(x) by adding 5 to the output of f(x)
h(x) = f(x) + 5
The transformation from the graph of f(x) to the graph of h(x) is a vertical shift of 5 units down. This is because the original function f(x) is shifted down by 5 units to get h(x). The slope of the two lines is still the same, 3, but the y-intercept of f(x) is (0,0) and the y-intercept of h(x) is (-5/3,0). The transformation causes the graph of h(x) to be shifted down 5 units along the y-axis, while the slope and x-intercept of the graph remain the same.
Hence, h(x) = f(x) + 5 represents a vertical shift of 5 units down from the graph of f(x) = 3x. The slope of the two lines is the same, but the y-intercept of h(x) is different from f(x).
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Please help me solve
On solving the provided question, we can say that - the linear equation
y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y=mx+b
x=gallons of fuel
y=total weight of plane including fuel
m=slope=6.4
b=weight of plane, no fuel....a constant to be calc'd
[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]
82gallons fuel is 2424.80 lbs
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5) Is y = x^3 a function. Why or why not; please use complete sentences.
Yes, the expression; y = x³ is a function because it passes the vertical line test.
What is function?Function from a set x to a set y assigns to each element of x exactly one element of y. The set x is called the domain of the function and the set y is called the codomain of the function.
There are 4 types of functions:
Functions with arguments and return values Functions with arguments and without return valuesFunctions without arguments and with return valuesFunctions without arguments and without return valuesOn this note, the set containing all possible values of x is called the domain of the function and the set y is called the co-domain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
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1. The height of a right triangular prism is 1 5/6 inches. Each side of the triangular base measures 10 inches, and the height of the base is 8 2/3 inches. The triangular prism is placed atop a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.
What is the surface area of the solid formed?
100 POINTS!!! IF YOU DRAW AN ACCURATE DIAGRAM TOO, YOU WILL BE AUTOMTIC BRAINLIEST!!!!!!
If the height of a right triangular prism is 1⁵/₆ inches. The surface area of the solid formed is 598.33 in².
What is surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
First step:-
Right triangular prism=1⁵/₆ inches= 11/6 inches
Height of the base=8²/₃ inches = 26/3 inches
Second step:-
Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)
Surface area = 5(100) +43.33+ 3(18.33)
Surface area = 500) +43.33 + 55
Surface area = 598.33 in²
Therefore the surface area of the solid formed is about 598.33 in²
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