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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Simplify the expression. 7x + 6 + 3x -2 -5x
Answer:
5x+4
Step-by-step explanation:
5x + 6 - 2
5x + 4
Based on the family the graph below belongs to, which equation could represent the graph?
Answer:
its A
Step-by-step explanation:
just took the test
Answer:
The first graph on edge 2021
they are yes and no choices except the one that’s one the pic
helpppp
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
A linear equation is defined.A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.
Here,
Given : 2x-4=6
To prove x =5
Thus,
We have to find the value of x
[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]
Therefore , the solution of he given problem of linear equation comes out to be x = 5.
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Find the sum of the interior angles. please I need help!!
Given:
A 7-sides regular polygon.
To find:
The sum of the interior angles of the given regular polygon.
Solution:
The formula for the sum of the interior angles of a regular polygon is:
[tex]Sum=180^\circ(n-2)[/tex]
Where, n is the number of sides of the regular polygon.
The given regular polygon has 7 sides. Putting [tex]n=7[/tex] in the above formula, we get
[tex]Sum=180^\circ(7-2)[/tex]
[tex]Sum=180^\circ(5)[/tex]
[tex]Sum=900^\circ[/tex]
Therefore, the sum of the interior angles of the given regular polygon is 900 degrees.
Given f(x)+3f(-x) = 2x+6, find f(x)
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x. (A) Find the average cost per unit if 200 frames are produced. (B) Find the marginal average cost at a production level of 500 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 501 frames are produced.
The marginal average cost is -1 and The marginal average cost for 200 is $699.
What is marginal cost?The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.
Given The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x.
Average cost = Cx / x
Average cost = (40,000 + 500x)/ x
For x = 200
Average cost = (40,000 + 500 * 200)/200
Average cost = 700$ per frame
Marginal average cost = d(Cx/x)/dx
d(Cx/x)/dx = -40,000/ x^2
at x = 200
Marginal average cost = -40,000/ 200^2 = -1
Marginal average cost = -1 tells us the average cost
decrease at the rate of -1 for every x
Average cost for 200 = 700$ per frame
Average cost for 200 = 700 + 1 (-1)
The average cost for 200 = 700 -1 = 699$
therefore, the Marginal average cost for 200 is $699.
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5+1r-2=9
Please explain step by step
Answer: 6
Step-by-step explanation:
please please please help fast this is a BIG deal
Answer:
190.625 ft^2
Step-by-step explanation:
A = bh = (15.25) * (12.5) = 190.625 ft^2
Answer:
190
Step-by-step explanation:
All you have to do is multiply the dimensions(...that's what the formula states)
So, 15.2 × 12.5 = 190ft^2
NEVER FORGET YOUR UNIT, in this case it's ft^2(always 2/square when it's area)
You're very welcome and good luck :)
Which ordered pair is a solution to the inequality
y ≥ 4x-5
(3,0) (3,4) (1,1) (2,1)
Answer:
(1, 1)
Step-by-step explanation:
in the order pair you have (x, y) so if is ( 3, 0) it means is ( x=3, y=0)
substitute in the inequality those x, and y values and see if it checks
y ≥ 4x-5
for ( 3, 0) is 0 ≥ 4*3-5 false
for ( 3,4) is 4 ≥ 4*3-5 false
for (1,1) is 1 ≥ 4*1-5 true because 1 ≥ -1
for (2, 1) is 1 ≥ 4*2-5 false
What is the unit rate for 4543.08 km in 52.4 h?
The unit rate for 4543.08 km in 52.4 hours is 86.7 km.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
4543.08 km = 52.4 hours
Divide 52.4 into both sides.
86.7 km = 1 hour
Thus,
The unit rate is 86.7 km.
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Prove that limx→2 2^x=4 using the formal definition of limit.
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]
Plug in the value of 2 into the limit.
[tex](2)^{2}=4[/tex]
Thus we proved the limit.
In terms of geometric shapes, a slice of pizza closely resembles what?
Answer:
triangle
Step-by-step explanation:
It looks like a traingle
HELP ME ANSWER IS QUESTION
Answer:
A is linear
Step-by-step explanation:
check the delta y (y2 - y1) and or the delat x (x2 - x1) and see if the differences are the same from each neighboring ordered pairs
answer A has a slope (m) of (y2 - y1) / (x2 - x1) = 2/2 = 1
A wedding cake was cut into 30 slices. If 12 of the slices were eaten, what fraction represents the eaten portion of the cake? Reduce your answer to lowest terms.
Answer:
12/30, if you reduce then it would be 2/5 because you divided by 6 hope this helps! :D
Step-by-step explanation:
The fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]
Let the wedding cake be W.Let the eaten portion be E.Given the following data:
Total wedding cake slices = 30 slicesNumber of cake slices eaten = 12 slices.To find the fraction that represents the eaten portion of the cake;
In this exercise, you're required to find what fraction represents the eaten portion of the wedding cake.
[tex]Fraction = \frac{E}{W}[/tex]
Substituting the values into the equation, we have;
[tex]Fraction = \frac{12}{30}[/tex]
Dividing both sides by 6, we have;
[tex]Fraction = \frac{2}{5}[/tex]
Therefore, the fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]
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Sam bought 2 shirts. Deal A shirt was $20 and was on
sale for 10%. Deal B shirt was $ 22 dollars and was on sale for 16%. What was a better deal
was a better deal? hint: figure out the discount and the cost of each shirt
using the "What is..." question. Compare the cost of each shirt.
Answer:
Deal A was the better deal.
Step-by-step explanation:
20*.10= 2 dollar discount for a total of 20-2= $18 total
22*.16= 3.52 dollar discount for a total of 22-3.52 =$18.48
Even though deal B had the larger discount you will still be paying a bit more compared to deal A
please help find mDF!!
9514 1404 393
Answer:
72°
Step-by-step explanation:
The external angle E is half the difference of subtended arcs CG and DF.
E = (CG -DF)/2
2E = CG -DF . . . . . . multiply by 2
DF = CG -2E = 160° -2(44°) . . . . . add DF-2E to both sides; substitute values
arc DF = 72°
Round 0.295833333 to the nearest hundredth
Answer:
The answer is 0.30.
I wish you luck in your assignments.
Answer:
0.3
Step-by-step explanation:
Since 5 rounds up, that would cause the 0.09 to become a 0.1, so it would be 0.3
Jordan is making a wreath that uses different colors of ribbon
Answer:
Step-by-step explanation:
he needs 10 inches of each color to make the wreath
10
+ 10
+ 10
+ 10
= 40
40 inches of ribbon
5. Is 1/4 and 4/16 equivalent? Explain your answer.
Answer:
Yes, 1/4 and 4/16 are equivalent
Step-by-step explanation:
1/4 = 0.25
4/16 = 0.25
A system of equations is shown below
4x + 2y = 10
2x - 2y = 8
What is the value of x in the solution to the system?
4x - 2 (-x + 12) = 36
4x + 2x - 24 = 36
6x = 60
x= 10
Two regular polygons are inscribed in the same circle where the first has 1,174 sides and the second has 2,935. If the two polygons have at least one vertex in common, how many vertices in total will coincide?
Answer:
vertices in total will coincide = 1174/2 = 587
Step-by-step explanation:
1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)
2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)
360°/1174 = (360°/2935) x (5/2) (every 2.5 arc2 = 1 arc1)
It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide
vertices in total will coincide = 1174/2 = 587
check: 2935/5 = 587
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value for this test statistics is: a. 0.05 b. 0.0228 c. 0.0456 d. 0.025 brainly
Answer:
The appropriate answer is option b (0.0228).
Step-by-step explanation:
The given values are:
Random sample,
[tex]n=100[/tex]
Average length of time,
[tex]\bar{x}=3.1 \ minutes[/tex]
Waiting time,
[tex]\mu=3 \ minutes[/tex]
Standard deviation,
[tex]\sigma=0.5[/tex]
Now,
The test statistics will be:
⇒ [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]
On substituting the values, we get
⇒ [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]
⇒ [tex]=\frac{0.1}{0.05}[/tex]
⇒ [tex]=2[/tex]
hence,
⇒ [tex]P(z >2 ) = 1 - P(z <2 )[/tex]
By using the table,
⇒ [tex]=1-0.9772[/tex]
⇒ [tex]=0.0228[/tex]
At a cell phone assembly plant, 82% of the cell phone keypads pass inspection. A random sample of 101 keypads is analyzed. Find the probability that the proportion of the sample keypads that pass inspection is between 0.75 and 0.87.
The z-score for the 0.75 proportion is -1.95.
What is z-score?The Z-score calculates the deviation of the measure from the mean in standard deviations. We seek for the p-value linked with this Z-score after locating the Z-score in the z-score database.
The likelihood that the value of the measure will be less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
In a set with mean X and standard deviation μ, the z score of a measure X is given by:
Z=(X-μ)/σ
In this problem, we have that:
n=100,p=0.82
So,μ=E(X)=np=100×0.82=82
Therefore, √V(X)=√np×(1-p)=√100×0.82×0.18=3.841
For Finding the probability that less than 75 in the sample keypads pass inspection.
Using continuity correction, this is (P(75-0.5)<=P(74.5)), which is the p-value of Z when X = 74.5.
=>z= (74.5-82)/3.841
=>z= - 7.5/3.841
=>z= - 1.95 has a p-value to 0.
Hence, if a random sample of 100 keypads is analyzed and 75 pass inspection, then the z-score for 0.75 proportion is -1.95
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Explain how to find the distance between two integers
using the difference.
х
Answer:
Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them
Answer:
Find the difference between two integers by adding the additive inverse. The distance is the absolute value of the difference. Check the distance by plotting the original two integers on a number line and counting the units between them.
Step-by-step explanation:
sample answer
Can anyone help me please?
Answer:
x ≈ 8.5 cm
Step-by-step explanation:
Law of Sines
a/sinA = b/sinB
---------------------------
x/sin89 = 8/sin70
multiply both sides by sin89
x = 8/sin70 * sin89
Breakout the calculator
x = 8.512125544373626
x ≈ 8.5 cm
Darien uses 3 3/4 cups of flour for each loaf of bread he bakes enter an equation that represents the total number of cups of flower Darien uses, c, to bake n loaves of bread
Answer:
n=15/4c
Step-by-step explanation:
y=mx+b
b=0 as it does not state any initial value
y=n
x=c
m=3 3/4 or 15/4
combining these together you get:
n=15/4c+0
The equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Darien uses [tex]3\frac{3}{4}[/tex] cups of flour to make one loaf of bread, we need to establish an equation, that will represent the number of cups of flower Darien uses, c, to bake n loaves of bread,
So,
Since, she uses [tex]3\frac{3}{4}[/tex] cups for one loaf of bread so for n loaf =
(We will multiply the amount used in one loaf to the number of loafs needed)
Therefore,
To make n number of loafs = [tex]3\frac{3}{4} c[/tex]
Hence, the equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]
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The radius of a circle is 3 centimeters. What is the circle's circumference?
r=3 cm
Use 3.14 for a TT
Find the sketch the domain of the function f(x,y,z) = ln(144 - 9x² - 16y² - z²)
The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.
What is the domain?Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.
Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,
144 − 9x² − 16y² − z² > 0
9x² + 16y² + z² < 144
x²/ 4² + y²/ 3² + z²/ 12² < 1
Therefore, the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
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please be fast and pick an option
Answer:
5/14 * 5/14
Step-by-step explanation:
What's the pattern of 0, 1, 3, 7, 15, 31, 63
Answer:
a₀ = 0
aₙ = aₙ₋₁ + 2ⁿ⁻¹
Step-by-step explanation:
a₀ = 0
aₙ = aₙ₋₁ + 2ⁿ⁻¹
a₁ = a₀ + 2¹⁻¹ = 0 + 2⁰ = 1
a₂ = 1 + 2²⁻¹ = 3
a₃ = 3 + 2³⁻¹ = 7
..............