To calculate the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean, one must find the corresponding z-scores and use a standard normal distribution table. The probability is approximately 39.58%.
Explanation:To find the probability that a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime of three years, we can use the properties of the normal distribution. We are given a mean (μ) of 3 years and a standard deviation (σ) of 2 years. We are interested in the probability that a wiper lasts less than 1.3 years (3 - 1.7) or more than 4.7 years (3 + 1.7).
First, we need to calculate the z-scores for 1.3 and 4.7 years:
Z1 = (1.3 - 3) / 2 = -0.85
Z2 = (4.7 - 3) / 2 = 0.85
Using a standard normal distribution table or a calculator, we find the probabilities corresponding to these z-scores. The probability of a wiper lasting less than 1.3 years is P(Z < -0.85), and the probability of lasting more than 4.7 years is P(Z > 0.85).
Since the normal distribution is symmetric, P(Z < -0.85) is equal to P(Z > 0.85). Thus, we only need to calculate one of these probabilities and double it to find the total probability. Let's say P(Z > 0.85) = p, then the total probability is 2p.
Assuming P(Z > 0.85) = 0.1979 (from standard normal distribution tables), the total probability is:
Probability = 2 * 0.1979 = 0.3958
Therefore, the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean lifetime is approximately 0.3958 or 39.58%.
Final answer:
By standardizing the values and using a standard normal distribution table, we can find the probability to be approximately 0.7422 or 74.22%.
Explanation:
To solve this problem, we can use the normal distribution. Given that the mean lifetime of the windscreen wipers is 3 years with a standard deviation of 2 years, we want to find the probability that the wiper lasts for a time that is not within 1.7 years of the mean lifetime.
First, we need to standardize the values by calculating the z-scores.
The z-score formula is (x - mean) / standard deviation. In this case, we have x = 1.7, mean = 3, and standard deviation = 2.
Plugging in these values, we get a z-score of -0.65.
Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.65.
The area under the curve to the left of -0.65 is approximately 0.2578. Since we want the probability that the wiper lasts for a time that is not within 1.7 years of the mean, we subtract this probability from 1.
Therefore, the probability is approximately 1 - 0.2578 = 0.7422, or 74.22%.
1. A bag of chips costs $3.79 including tax Mr.Connor wants to purchase chips for his class and has a $15 budget. Write and inequality to solve for the number of bags of chips Mr.Connor can purchase with his budget
A. $15x > $3.79
B.$15x < $3.79
C $3.79 > $15
D. $3.79 < $15
(There is a flat line under all the greater than and less than signs)
2. A cab charges $1.75 for the first mile $0.25 for each additional mile. Write and solve an inequality to determine how many miles eddie can travel if he has $15
A. $1.75 + $0.25x < $15; x < 53 miles
B. $1.75 + $0.25x > $15; x >53 miles
C. $0.25 + $1.75x < $15; x< 8 miles
D.$0.25 + $1.75x > $15; x > 8 miles
Translate the phrase into a math expression.
Twenty divided by the sum of 4 and 1.
(1+4) ÷ 20
20 ÷ (1+4)
1 + (4÷20)
(20÷4) + 1
Answer:
[tex]\displaystyle 20 \div (1 + 4)[/tex]
Explanation:
It is EXACTLY how it sounds, and of course, you must include grouping symbols to separate both parts of the expression.
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8 foot piece of wood cut into how many 7/8 inches?
Which of the following best describe perpendicular lines? A.lines that are not in the same plane B. Lines that meet at a 90* angle C. Lines that meet at a 45' angle D. Lines that are coplanar and do not intersect
A line is said to be perpendicular to another line if the two lines intersect at a right angle. An angle is said to be a right angle if its measure is 90 degrees.
The question is asking us to select the option which best describes a perpendicular lines.Among all the options given option B states :Lines that meet at a 90* angle.
Option B is the right answer.
The perpendicular lines are those lines that meet at a 90* angle. That is option B.
Perpendicular linesPerpendicular lines are those lines that meet at an angle of 90°. To further explain the perpendicular lines, a diagram above is used.
Line AB is perpendicular to XY because AB and XY intersect each other at 90°.
Some of the characteristics of perpendicular lines include:
These lines always intersect at right angles.Adjacent sides of a square and a rectangle are always perpendicular to each otherTherefore, perpendicular lines are those lines that meet at a 90* angle.
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Consider the functions f(x) = x2 − 13 and g(x) = x + 5. What is the value of (f − g)(−4)? ...?
Answer- The Answer is -12
Step-by-step explanation:
I took the test
If x2 − 8xy + 12y2 = 8 and x − 6y = 3, then x − 2y =
The graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.
True
False
Answer:
true
Step-by-step explanation:
The statement 'The graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.' is True.
What s graph of a function?"It is a set of points that satisfy given function."
What is transformation of a function?"It means that the curve representing the graph either 'moves to left / right/ up/ down' or 'it expands or compresses' or 'it reflects'."
What is translation of function?"A shift of the graph of a function up, down, left, or right, without changing the shape, size, or dimensions of the graph."
For given question,
We have been given a function y = 6cos x - 3
Also we have been given a transformed function y = 6cos(x - 2) - 3
We know that when function f(x) is transformed to f(x - k) then the graph of f(x) is translated 'k' units right.
So, the graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.
Therefore, the statement 'The graph of y = 6cos(x - 2) - 3 is obtained by shifting the graph of y = 6cos x - 3 horizontally 2 units to the right.' is True.
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Any ordered pair that makes all equations in a system of equations true is a(n) ...?
What number represents the same amount as 2 hundreds 14 tens 3 ones
The representation of the given number will be given below such that it sum should be 343.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation.
There might simply be two terms, but there might also be 100,000 or a million. Summations exist with an infinite number of parameters.
The summation is to add or subtract any two or more terms by doing the operation.
The representation of 200, 14, and 3 will be
200 hundred
14 tens
+ 3 ones
--------------------
343
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PRE-ALGEBRA HELPPPP!!
Answer:
yeet
Step-by-step explanation:
Can someone help me...again?
"The graph below shows the population of mice in an ecosystem where the mice are not allowed to enter or leave.
Which best describes the population at point A?
A.The death rate is higher than the birthrate.
B.The population is decreasing.
C.The birthrate is higher than the death rate.
D.It has reached carrying capacity"
The point marked A is the point where the birth rate is higher than the death rate.
What is birth rate/ death rate?The term birth rate refers to the rate at which new organims are introduced into the population and the death rate refers to the rate at which individuals exit in the population.
In this case, when we observe the graph, we can see that the point marked A is the point where the birth rate is higher than the death rate.
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a cheese pizza cost $8.75 each additional cost topping costs $1.25. if you order one pizza and have $12.50. how many toppings can you have on the pizza.
how do i work out sinx+2sinxcosx=0 in radians?
Tom gets $12 off a box of chocolates that had an original price of $48. What percentage is the discount ?
Geometry question help
15 pts will award brainliest if explained
Answer if you understand it only
the sum of two numbers is 85. twice one number plus four times the other is 218. find the numbers
what is the solution set of the equation?
8/x+2=(x+4)/(x-6)
a. {-12,4}
b. {12}
c. {4,6}
d. {-4,12}
The ordered pairs (1, 6), (2, 36), (3, 216), (4, 1296), and (5, 7776) represent a function. What is a rule that represents this function?
Answer:
The rule is [tex]\\ f(x) = 6^{x}[/tex]
Step-by-step explanation:
The resulting values are powers of 6:
[tex]\\ 6^{1} = 1[/tex]
[tex]\\ 6^{2} = 36[/tex]
[tex]\\ 6^{3} = 216[/tex]
[tex]\\ 6^{4} = 1296[/tex]
[tex]\\ 6^{5} = 7776[/tex]
One factor that is not defined in the question is whether the domain (the set of values for which a function is defined [WolframAlpha, 2019]) of the function [tex]\\ f(x) = 6^{x}[/tex] is only for x = {1, 2, 3, 4, 5} or defined for all possible values this function can take, that is, x = (-∞;∞) or all real numbers.
As you can see from the graph attached:
Theoretically, this function could take all values for x = (-∞;∞). If this were the case, the function is a continuous line with resulting values (that is, the range of the function) for f(x)>0 (0;∞). The graph below shows only positive values (x > 0) and values for x ≤ 5.For values x = {1, 2, 3, 4, 5}, the function is discrete (not a continuous line) and only defined for these values. In this case, the function would be represented only by the points in the graph, and the values it could take would be only f(x) = {6, 36, 216, 1296, 7776}, which would represent the range for this function.In the last case, we have to redefine the function as:
[tex]\\ f(x) = 6^{x}[/tex] for [tex] x = \{1, 2, 3, 4, 5\}[/tex].
the area of a rectangle is 15x^2y^5. if the length is 5xy^3, what is the width?
tan^4x-sec^4x=1-2 sec^2(x)
verify
Find equation of the axis of symmetry of Y= -3x^2+12x-7
you are driving at a constant velocity of 100 km per hour. the first landmark you see is your favorite restaurant which happens to be 10 km from your house. which sequence describes the distances you cover at intervals of one hour, starting when you pass the restaurant?
The graphs of the function f (given in blue) and g (given in red) are plotted above. Suppose that u(x)=f(x)g(x) and v(x)=f(x)/g(x). Find each of the following:
u'(1) =
v'(1) =
This is a problem of calculus where the product and quotient rules are used to find the derivatives of functions u and v at x=1. The values need to be taken from the provided graph.
Explanation:This is a calculus question related to the product rule and the quotient rule of derivatives. First, let's explore the definitions: the product rule states that the derivative of the product of two functions is the derivative of the first times the second plus the first times the derivative of the second. The quotient rule states that the derivative of the quotient of two functions is the bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared. From the graph, we have to find out the values of f(1), g(1), f'(1), and g'(1).
Then, we can calculate u'(1) by using the product rule: u'(1) = f'(1)g(1) + f(1)g'(1). In the same way, we can calculate v'(1) by using the quotient rule: v'(1) = [g(1)f'(1) - f(1)g'(1)] / [g(1)]^2. The specific values need to be derived from the provided graph
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(u’(1) = 5)
[tex](v’(1) = \frac{-13}{4})[/tex]
We have two functions:
(u(x) = f(x)g(x))
[tex](v(x) = \frac{f(x)}{g(x)})[/tex]
We need to find the derivatives of both (u(x)) and (v(x)) at (x = 1).
1. Derivative of (u(x)):
Using the product rule, we have:
[ u’(x) = [tex]v \cdot \frac{du}{dx} + u \cdot \frac{dv}{dx} ][/tex]
Where:
(v = g(x))
[tex](\frac{du}{dx})[/tex] is the derivative of (f(x))
[tex](\frac{dv}{dx})[/tex] is the derivative of (g(x))
From the graph:
At (x = 1), we have (f(1) = 3) and an estimated slope of the tangent line for (f’(1)[tex]\approx -2).[/tex]
Similarly, at (x = 1), we have (g(1) = 2) and an estimated slope of the tangent line for [tex](g’(1) \approx 3).[/tex]
Now let’s calculate (u’(1)):
[ u’(1) = [tex]g(1) \cdot f’(1) + f(1) \cdot g’(1)[/tex] = (2)(-2) + (3)(3) = 5 ]
2. Derivative of (v(x)):
Using the quotient rule, we have:
[ v’(x) = [tex]\frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2} ][/tex]
Substitute the values we found earlier:
(v = g(x) = 2)
[tex](\frac{du}{dx}[/tex] = f’(x) = -2)
[tex](\frac{dv}{dx} = g’(x) = 3)[/tex]
Now let’s calculate (v’(1)):
[tex][ v’(1) = \frac{(2)(-2) - (3)(3)}{2^2} = \frac{-13}{4} ][/tex]
Therefore:
(u’(1) = 5)
[tex](v’(1) = \frac{-13}{4})[/tex]
Find the measure of an angle whose measure is 18 degrees less than one-half of the measure of its complement.
If x represents the measure of the angle, then which of the following expressions would equal x?
90 - (0.5x - 18)
0.5(90 - x - 18)
0.5(90 - x) - 18
Answer:
The answer is C, 0.5(90 - x) -18
Step-by-step explanation:
The cost of a service call to fix a washing machine can be expressed by the linear function y=45x+35 where y represents the total cost and x represents the number of hours it takes to fix the machine. What does the slope represent?
a-the cost for each hour it takes to repair the machine
b=the cost for coming to look at the machine
c-the total cost for fixing the washing machine
d-the amount of time that it takes to arrive at the home to make the repairs
Answer:
The slope represents the cost for each hour it takes to repair the machine.
Step-by-step explanation:
We are given that the cost of a service call to fix a washing machine can be expressed by the linear function
[tex]y=45x+35[/tex]
Where
y=Total cost of a service to fix the machine.
x=Number of hours takes to fix the machine
We have to find that slope in this function what represents.
General equation of line is given by
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y- intercept
Comparing the general equation with the given function
We get m=45,c=35
m=45 represents the cost for each hour it takes to repair the machine because when number of hours multiplied by 45 then we get total cost of x hours.
Hence, the slope represents the cost for each hour it takes to repair the machine.
How do you factorise xy zy?
Does this set of ordered pairs represent a function? Why or why not?
{(–2, 2), (–1, 2), (3, –1), (3, 1), (4, 11)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
The table contains data on the mileage displayed on a bicycle odometer as it relates to the number of days since the bicycle was purchased. Using the Scatter Plot tool, find the value of the correlation coefficient for this data set.
0.8
1.0
0.3
0.1
Answer:
Hence, the correlation coefficient is:
r=1.0
Step-by-step explanation:
We know that the correlation coefficient ''r'' is calculated by the formula:
[tex]r=\dfrac{\sum{XY}}{\sqrt{\sum{X^2}\sum{Y^2}}}--------------(1)[/tex]
Let x denote the data point (Number of days since purchase)
Let y denote the data point (Mileage Displayed on odometer)
x y X=x-x' Y=y-y' XY X² Y²
15 67 -20 -95 1900 400 9025
25 122 -10 -40 400 100 1600
35 164 0 2 0 0 4
45 210 10 48 480 100 2304
55 247 20 85 1700 400 7225
x' be the mean of the data of the x-values.
[tex]x'=\dfrac{15+25+35+45+55}{5}\\\\\\x'=\dfrac{175}{5}\\\\\\x'=35[/tex]
Also let y' denote the mean of the y-values.
[tex]y'=\dfrac{67+122+164+210+247}{5}\\\\\\y'=\dfrac{810}{5}\\\\\\y'=162[/tex]
Now we have:
∑ XY=4480
∑ X²=1000
∑ Y²=20158
Hence, we put all the values in the formula (1) to obtain:
r=0.997 which is close to 1.0
Also from the scatter plot we could observe that the relationship is linear and also strong positive relationship.
Hence, the correlation coefficient is 1.0
"If a parallelogram has four right angles, then it is a rectangle." What is the inverse of this conditional statement? A. If a parallelogram has four right angles, then it is a rectangle. B. If a parallelogram does not have four right angles, then it is a rectangle. C. If a parallelogram has four right angles, then it is not a rectangle. D. If a parallelogram does not have four right angles, then it is not a rectangle.
Answer:
If a parallelogram does not have four right angles, then it is not a rectangle.
Step-by-step explanation:
"If a parallelogram has four right angles, then it is a rectangle."
To get the inverse of the conditional statement, we take the negation of both the hypothesis and the conclusion.
So, the inverse of the given statement will be :
If a parallelogram does not have four right angles, then it is not a rectangle.