Using the normal distribution, it is found that 2.64% of all the nails produced by this machine are unusable.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of 3 inches, hence [tex]\mu = 3[/tex].The standard deviation is of 0.009 inches, hence [tex]\sigma = 0.009[/tex].Nails that are more than 0.02 inches from the mean are unusable, hence:
[tex]Z = \frac{0.02}{\sigma}[/tex]
[tex]Z = \frac{0.02}{0.009}[/tex]
[tex]Z = 2.22[/tex]
The proportion is P(|Z| > 2.22), which is 2 multiplied by the p-value of Z = -2.22.
Z = -2.22 has a p-value of 0.0132.
2 x 0.0132 = 0.0264
0.0264 x 100% = 2.64%
2.64% of all the nails produced by this machine are unusable.
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the Following table shows alexandra's investment options over the course of three years. Her initial investment was $1,000 . write one function for each option to describe the value of the investment f(n), in dollars, after n years.
The pattern in the given series of amount in the account are in the form of
arithmetic and geometric progression.
The function for Option 1 is; [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]The function for Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Reasons:
The given table of values is presented as follows;
[tex]\begin{tabular}{c|c|c|c|}Number of years&1&2&3\\Option 1 (Amount in dollars)&1,100&1,200&1,300\\Option 2 (Amount in dollars)&1,100&1,210&1,331\end{array}\right][/tex]
In Option 1, the amount in dollars for each year has a common difference of d = 100
The first term, a = 1,100
Therefore;
The Option 1 can be represented as an arithmetic progression , A.P. in the
form, tₙ = a + (n - 1)·d as follows;
For the Option 1, we have;
The amount in dollars after n years, [tex]\underline{ f(n) = 1,100 + (n - 1) \cdot 100}[/tex]For Option 2, it is possible to find;
1,331 ÷ 1,210 = 1,210 ÷ 1,100 = 1.1
Therefore;
The terms in the Option 2 have a common ratio of r = 1.1
The Option 2 is a geometric progression, G.P.
The first term in Option 2 is a = 1,100
Which gives, the nth term, tₙ = a·r⁽ⁿ ⁻ ¹⁾
Therefor;
The function for the Option 2 is; [tex]\underline{f(n) = 1,100 \times 1.1^{(n - 1)}}[/tex]Learn more about arithmetic and geometric progression here:
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What two numbers multiplied together equal 8 but when added together equal -6
Answer:
i believe its -4 and -2
Step-by-step explanation:
hope tha work
Maija is bicycling north on a straight path. She bicycles for
17.
4
kilometers when she realizes she is
thirsty. Maija remembers passing a water fountain
2 kilometers earlier By rounding to the nearest
whole number, estimate the distance from the beginning of Maija's ride to the water fountain
Answer:
The awnser is 19 Kilometers
Last week, you finished Level 2 of a video game in 32 minutes. Today, you finish Level 2in 28 minutes. What is your percent of change
Answer:
12.5% decrease
Step-by-step explanation:
[(V2 - V1) / V1] x 100 = Percent Change
What is the product of 44(4-7)(4)?
-16
O
ОО
-1 -12
-100
8
DONE
Hey there!
44(4 - 7)(4)
= 44(-3)(4)
= -132(4)
= -528
Therefore, your answer is: -528
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
y=-2x2+12x-26
Rewrite the equation in vertex form and identify the vertex, the axis of symmetry, and the y-intercept.
Answer:
y = 12x - 22
Step-by-step explanation:
If we first write the equation in vertex form and we identify it (I think you meant to simplify y) we get y = 12x - 22 as your answer!
Oscar has baskets that each contain 25 apples. Each day 2 apples are
eaten from each basket. Oscar has (25 – 2d) apples left afterd days in
one basket. If Oscar has 7 baskets of apples, how many apples are left
after d days?
Answer:
175 -14d
Step-by-step explanation:
There will be 7 times as many as in one basket.
7(25 -2d) = 175 -14d . . . . total apples left
3х + 4y= 4
12х + 16y = 8
Answer:
No Solution.
Step-by-step explanation:
3x+4y=4
12x+16y=8
--------------
-4(3x+4y)=-4(4)
12x+16y=8
--------------------
-12x-16y=-16
12x+16y=8
-----------------
0=-8
no solution
PLLZ HELLP QUESTION IS BELOW!! :D
Answer:
The answer to the first question is 32 but I don't know the slope of the line, sorry
what expressions are equivalent to 7 ^ 8 x 7 ^ -4
Answer:
7^4
Step-by-step explanation:
The equivalent expression 7^8 x 7^-4 using a single exponent is 7^4
How to write the expression using a single exponent.From the question, we have the following parameters that can be used in our computation:
7 ^ 8 x 7 ^ -4
This means that
7^8 x 7^-4
Apply the law of indices
So, we have
7^8 x 7^-4 = 7^(8 - 4)
This gives
7^8 x 7^-4 = 7^4
Hence, the solution is 7^8 x 7^-4 = 7^4
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Question 14
Determine if the given lines are parallel or perpendicular or neither.
3y=2-x
y=-1/3x+4
Answer:
The given lines are parallel.
Step-by-step explanation:
3y=2-x
y=-1/3x+4
-------------
y=2/3-1/3x
y=-1/3x+2/3
y=-1/3x+4
----------------
Since the two lines have exact same slopes, it follows that these two lines are parallel.
Use the quadratic formula to solve for x.
9x^2-3x=1
Round the answer to the nearest hundredth
Last question.
find x,y,z : 4x^2+2y^2+2z^2-4xy-4xz+2yz-2y+6z+10=0
I hope this helps.
Answer:-
∴x−3y−4z=0
Explanation:
First we rearrange the equation of the surface into the form f(x,y,z)=0
x2+2z2=y2
∴x2−y2+2z2=0
And so we have our function:
f(x,y,z)=x2−y2+2z2
In order to find the normal at any particular point in vector space we use the Del, or gradient operator:
∇f(x,y,z)=∂f∂xˆi+∂f∂yˆj+∂f∂zˆk
remember when partially differentiating that we differentiate wrt the variable in question whilst treating the other variables as constant. And so:
∇f=(∂∂x(x2−y2+2z2))ˆi+
(∂∂y(x2−y2+2z2))ˆj+
(∂∂z(x2−y2+2z2))ˆk
=2xˆi−2yˆj+4zˆk
So for the particular point (1,3,−2) the normal vector to the surface is given by:
∇f(1,3,−2)=2ˆi−6ˆj−8ˆk
So the tangent plane to the surface x2+2z2=y2 has this normal vector and it also passes though the point (1,3,−2). It will therefore have a vector equation of the form:
→r⋅→n=→a⋅→n
Where →r=⎛⎜⎝xyz⎞⎟⎠; →n=⎛⎜⎝2−6−8⎞⎟⎠, is the normal vector and a is any point in the plane
Hence, the tangent plane equation is:
⎛⎜⎝xyz⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠=⎛⎜⎝13−2⎞⎟⎠⋅⎛⎜⎝2−6−8⎞⎟⎠
∴(x)(2)+(y)(−6)+(z)(−2)=(1)(2)+(3)(−6)+(−2)(−8)
∴2x−6y−8z=2−18+16
∴2x−6y−8z=0
∴x−3y−4z=0
Why is the slope the same on a line when different points are used to identify the slope?
Different points can be used to identify the slope as follows -
We have a straight line.
We have to investigate why is the slope same on a line when different points are used to identify the slope.
What is Slope of a Line ?The slope of a line is denoted by m and is defined as the change in y coordinate with respect to the change in x coordinate.
According to question -
Different points can be used to identify the slope provided that they all lie on the same straight line. Line is a collection of points and these set of points can be used top determine the rate of change of y with respect to x. The slope of a line can also be found out using y - intercept of the line using the general equation of straight line -
y = mx + c.
Hence, the slope is same on a line provided that they all lie on the same straight line
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Solve the following system of equations.
4x + 7y= 18
- 7x - 8y = -23
X =
y =
im lazy to solve in my paper hope it helps
what is the approximate value of a local maximum for the polynomial
Answer:
D) 2.5
Aaliyah- ツ
Can i get some help ?:
Answer:
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
Step-by-step explanation:
7 + 3² - 2.5 / 4 - 1.2 = 4.82142857
( 3/4 + 1/8 ) ÷ 1/8 - 2² = 3
Which means :
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
a store is handing out scratch-off cards to its customers .for each card a customer wins either a coupon or a free t-shirt .the ratio of coupon cards to t-shrits is 9:2 .the total of 8,250 cards how many of the cards are t-shirts cards
Step-by-step explanation:
Ratio 9:2, therefore total number of shares is 11.
because 9+2 = 11
total cards = 8,250
8,250/11 = 750
This is the value for one of the shares.
As the ratio is 9:2 we can find:
9 X 750 : 2 X 750
To see what everyone has won.
T-shirts : 2 X 750 = 1,500.
Hope you understand how it's done, if not leave a comment and I'll try to be more thorough
find the domain of f(x). f(x) = √9x+36
Answer:
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]
Step-by-step explanation:
I'm assuming the 9x and the 36 are in the root
[tex]\sqrt{9x+36}[/tex]
first we must solve for x
[tex]{9x+36}\geq 0[/tex]
substract 36 to both sides
[tex]{9x}\geq -36[/tex]
divide by 9 to both sides
[tex]\frac{9x}{9} }\geq \frac{-36}{9}[/tex]
simplify left side
[tex]x\geq \frac{-36}{9}[/tex]
simplfy right side
[tex]x\geq -4[/tex]
The domain in interval notation is [-4,∝) or set build: {x|x[tex]\geq[/tex]-4}
Which number is closest to 1/2
Answer:
0.56
it's basically the number closest to 50. Don't get tricked by the 0.05 because that's only 5% not 50%
If a new car is valued at $26,000 and 10 years later it is valued at $7000, then what is the average rate of change
of its value during those 10 years?
Answer:
The change in value is 19,000 altogether and 1900/year
Step-by-step explanation:
Change in value:
initial value - final value
= $26,000 - $7000
= $19,000
Change in value/year:
change in value/time
= $19,000/10
= $1900/year
how do you evaluate numbers in math?
To evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.
Assuming we are given the expression, 3x + (2x - 1), and we are required to evaluate the expression, the following shown below is how to evaluate the expression if we are told that x = 1.
First step is to plug in the value of the variable, x, into the expression:3(1) + (2(1) - 1)
3 + 2 - 1
Using the order of operation, simply4
Therefore, to evaluate an expression in maths, plug in he value of the variable, then simplify the expression following the order of operation.
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Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.
Answer:
Are there any numbers?
Step-by-step explanation:
Marhannah must make a costume for the school play. She needs a piece of fabric that’s is 8/3 yards long and 3/2 yards wide. What is the area of the piece of fabric Marhannah needs?
Answer:
Our material is 54" wide. Here is a helpful chart to help you quickly convert linear yards into inches and feet.
How big is one linear yard of fabric?
Yards Length Width
3 108 Inches (9 Feet) 54 Inches (4.5 Feet)
4 144 Inches (12 Feet) 54 Inches (4.5 Feet)
Step-by-step explanation:
C A R R Y
O N
L E A R N I N G
2a- 1-4 1/3a+ 7-a consider the linear expression what are the like terms in the expression simplify the linear expression
Answer:
2a7-1
Step-by-step explanation:
Given the function f(x) x^2-2x/x^3 +9x^2-10x Find any holes, vertical asymptotes, and horizontal asymptotes there may be.
Answer:
See below
Step-by-step explanation:
I assume you mean [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex]:
Holes: Since [tex]f(x)=\frac{x^2-2x}{x^3+9x^2-10x}[/tex] reduces to [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex], then there is a hole at [tex]x=0[/tex] as [tex]x[/tex] exists in both the numerator and denominator (however, its limit as x approaches 0 is 1/5).
Vertical Asymptotes: If we further reduce [tex]f(x)=\frac{x(x-2)}{x(x^2+9x-10)}[/tex] to [tex]f(x)=\frac{x-2}{(x+10)(x-1)}[/tex], then we see that there are vertical asymptotes at [tex]x=-10[/tex] and [tex]x=1[/tex]
Horizontal Asymptotes: As the degree of the numerator is less than the degree of the numerator ([tex]2<3[/tex]), then there is a horizontal asymptote at [tex]y=0[/tex]
which is a better deal? 5 pens for $1.85 OR 8 pens for $3.12 ? find the unit rate
Answer:
5 pens
Step-by-step explanation:
1.85 divided by 5 is .37
3.12 divided by 8 is .39
so 1.85 is a better deal
What is the area of a cross section that is parallel to
face ABCD?
Enter your answer in the box.
cm2
Answer:
1296cm².
Step-by-step explanation:
= 12×36×6÷2 ................
plz check weather correct or notn
A basket contains four apples, three pears, two peaches, if we draw one fruit from the basket, what is the probability of getting a peach or an apple?
Answer:
The probability of getting a peach or an apple is 2/3.
Step-by-step explanation:
There are two peaches and four apples, so six fruits we want to know the probability of getting, and there are also three pears, which means we have nine fruits total. The chance of getting an apple or a pear is six out of nine, which simplifies to two out of three.
4.8 multiplied to 10 to the power -9
Answer:
000000004.8
Hope it help!