Given that the weights of bags of potato chips are normally distributed with an average weight of 16 ounces and a standard deviation of 0.4 ounces, find the following probability.
That a randomly selected bag weighs between 15.6 ounces and 16.4 ounces
That a randomly selected bag weighs between 15.2 ounces and 16.8 ounces.
That a randomly selected bag weighs less than 14.8 ounces.
probability of a randomly selected bag weighing between 15.6 ounces and 16.4 ounces is 0.68269.
probability of a randomly selected bag weighing between 15.2 ounces and 16.8 ounces is 0.9545.
probability of a randomly selected bag weighing less than 14.8 ounces is 0.0013499.
What is Z-Sore?The relationship between a value and a set of values' mean is described by the statistical measurement known as the Z-score. Standard deviations from the mean serve as a unit of measurement for the Z-score. A Z-score of zero means the data point's score is the same as the mean score.
Given, Given that the weights of bags of potato chips are normally distributed with an average weight of 16 ounces and a standard deviation of 0.4 ounces. thus,
μ = 16
σ = 0.4
for randomly selected bags weighing between 15.6 ounces and 16.4 ounces
x₁ = 15.6
x₂ = 16.4
Z score = ( x - μ)/σ
z₁ = (15.6 - 16) / 0.4
z₁ = -1
z₂ = (16.4 - 16)/ 0.4
z₂ = 1
From the table of normal distribution (z²)
the probability of getting the value between -1 to 1 is = 0.68269
for randomly selected bags weighing between 15.2 ounces and 16.8 ounces
x₁ = 15.2
x₂ = 16.8
Z score = ( x - μ)/σ
z₁ = (15.2 - 16) / 0.4
z₁ = -2
z₂ = (16.8 - 16)/ 0.4
z₂ = 2
From the table of normal distribution (z²)
the probability of getting the value between -2 to 2 is = 0.9545
for randomly selected bags weighing less than 14.8 ounces.
x = 14.8
Z score = ( x - μ)/σ
z = (14.8 - 16) / 0.4
z = -3
From the table of normal distribution (z²)
the probability of getting a value less than 14.8 = 0.0013499
Therefore, The probability that a randomly chosen bag will weigh between 15.6 and 16.4 ounces is 0.68269. The probability that a randomly chosen bag will weigh between 15.2 and 16.8 ounces is 0.9545. The probability that a randomly chosen bag will weigh less than 14.8 ounces is 0.0013499.
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The first equation from the system of equations is graphed. Graph the second equation to find the solution of the system of equations. y = –x, y = 2x + 6 What is the point of intersection? (2, 1) (–1, 2) (0, 6) (–2, 2)
Answer:D
Step-by-step explanation:
just took it on edge
Answer:
The answer is d
Step-by-step explanation:
I GIVE BRAINLIEST!
Someone explain please!
Answer: 7 8 9 7 6 12 2 0
Step-by-step explanation:
Answer:
1) -8m +4+p
2) 10-3t
3)im not sure for the rest
Step-by-step explanation:
Find the maximum revenue for the revenue function R(x) = 395x − 0.9x2
The maximum revenue obtained for the given revenue function is 43340.
What is termed as maxima and maximum value?Maxima and minima are the highest and lowest values of a function within a given set of ranges.
The maximum value of the function under the entire range is known as the absolute maxima, and the minimum value is recognized as the absolute minima.Range refers to the difference between both the maximum and minimum values of observations in a data set.Now, as per the given question;
The given revenue function is; R(x) = 395x − 0.9x²
Differentiate the given function with respect to x.
dR/dx = 395 − 2×0.9x
dR/dx = 395 - 1.8x
Put the given equation equal to zero and find the critical point for which the function will become maximum.
395 - 1.8x = 0
x = 219.44
x ≈≈ 220.
Substitute the obtained value of x in the revenue function to find its maximum value.
R(x) = 395x − 0.9x²
R(220) = 395×220 − 0.9(220)²
R(220) = 86900 - 43560
R(220) = 43340.
Therefore, the maximum revenue calculated for the given revenue function is 43340.
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Please help me out!!!
Answer:
Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]
Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]
Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]
Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]
Step-by-step explanation:
We are given [tex]f(x)=2x-6[/tex]
We need to match the transformations.
1) shifts f(x) 4 units down.
When function f(x) shifts k units down the new function becomes f(x)-k
In our case
[tex]g(x)=2x-6-4\\g(x)=2x-10[/tex]
So, Shifts 4 units down ---> [tex]g(x)=2x-10[/tex]
2) Stretches f(x) by a factor of 4 away from x-axis
When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)
[tex]g(x)=2(4x)-6\\g(x)=8x-6[/tex]
So, Stretches f(x) by a factor of 4 away from x-axis--->[tex]g(x)=8x-6[/tex]
3) Shifts f(x) 4 units right
When function f(x) shifts h units right the new function becomes f(x-h)
[tex]g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14[/tex]
So, Shifts f(x) 4 units right---> [tex]g(x)=2x-14[/tex]
4) Compress f(x) by a factor of 1/4 toward the y-axis
When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)
[tex]g(x)=1/4(2x-6)\\g(x)=1/2x-3/2[/tex]
Compress f(x) by a factor of 1/4 toward the y-axis ---> [tex]g(x)=1/2x-3/2[/tex]
(Option Not given)
(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)
C
After concluding his research, which statements would Virchow agree with? Check all that apply.
Living things come from nonliving things.
Cells can come from nonliving materials.
Frogs can come from mud.
Living things can only come from living things.
Cells come from pre-existing cells.
Answer:
Cells come from pre-existing cells.
Answer:
(A) Living things can only come from living things.
(B) Cells come from pre-existing cells.
Step-by-step explanation:
i just answered this on e d g e n u i t y.
hope this helps <3
When tomás simplified the expression -2.6 + [-5.4], he got2.8. What mistake did tomás likely make?
Answer: he probably didn't pay attention to the - sign on -5.4
Given the points below, find XY. Round to
the nearest hundredth.
X(-9, 2) and Y(5, -4)
The distance between X(-9,2) and Y(5,-4) is 15.23 units.
The distance formula states that if there are 2 points A(x1, y1) and B(x2, y2), then the distance between the two points is given by the formula-
[tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]
Here, we are given that there are 2 points- X(-9, 2) and Y(5, -4)
So here we can say that,
x1 = -9, y1 = 2
and x2 = 5, y2 = -4
Now, plugging in the values given above in the distance formula we will find XY as follows-
XY = [tex]\sqrt{(-9-5)^{2} + (5+4)^{2} }[/tex]
XY = [tex]\sqrt{(-14)^{2} + (9)^{2} }[/tex]
XY = [tex]\sqrt{196+ 81 }[/tex]
XY = [tex]\sqrt{277 }[/tex]
The square root of 277 is approximately 15.23.
Thus, XY = 15.23
Therefore the value of XY to the nearest hundredth is 15.23 units.
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A man has mislaid his wallet. He thinks there is a 0.4 chance that the wallet is somewhere in his bedroom, a 0.1 chance it is in the kitchen, a 0.2 chance it is in the bathroom, and a 0.15 chance it is in the living room. What is the probability that the wallet is a) somewhere else? b) in either the bedroom or the kitchen?
Answer:
a. Probability = 0.15
b. Probability = 0.3
Step-by-step explanation:
Given
[tex]P(Bedroom) = 0.4[/tex]
[tex]P(Kitchen) = 0.1[/tex]
[tex]P(Bathroom) = 0.2[/tex]
[tex]P(Living\ room) = 0.15[/tex]
Solving (a): Probability of being somewhere else
This is calculated by subtracting the sum of given probabilities from 1.
[tex]Probability = 1 - (0.4 + 0.1 + 0.2 + 0.15)[/tex]
[tex]Probability = 1 - 0.85[/tex]
[tex]Probability = 0.15[/tex]
Solving (b): Probability of being in bedroom or kitchen
This is calculated as:
[tex]Probability = P(Bedroom) + P(Kitchen)[/tex]
[tex]Probability = 0.2 + 0.1[/tex]
[tex]Probability = 0.3[/tex]
Write an equation to model each situation and solve. Be sure to label the solution.
7. A rectangle has a length of 2x - 12 units and a width of 3 units. The value of the
rectangle's area is equal to the value of its perimeter. Write an equation to represent this
situation. Then, solve the equation.
Need a equation and a solution.
Answer:
A. 3(2x - 12) = 2(3 + 2x - 12)
B. Length = 6, width = 3
Step-by-step explanation:
l = 2x - 12
w = 3
Area = 3(2x - 12)
Perimeter = 2(3 + 2x - 12)
if A = P
3(2x - 12) = 2(3 + 2x - 12)
6x - 36 = 6 + 4x - 24
6x - 4x = 6 - 24 + 36
2x = 18
x = 9
Length = 2x - 12 = 2(9) - 12 = 18 - 12 = 6
How many edges does this shape have?
Answer:8
Step-by-step explanation:
It has the same number of edges, planes, and vertices as a cuboid. Therefore, there are 12 edges in the shape.
What is the rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
A rectangular prism has 12 edges.
It has the same number of edges, planes, and vertices as a cuboid.
The shape can be a rectangular prism or cuboid.
Therefore, there are 12 edges in the shape.
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Simplify 42 ⋅ 48.
416
410
1616
1610
If a position vector v has a magnitude of 5 and is located in the first quadrant, then which of the following could be the terminal point of 2v?
(4, 6)
(2, 8)
(6, 8)
(10, 10)
Answer:
I think its (6,8) if im wrong i will write the correct answer here or i will right it in the comments
Step-by-step explanation:
What number is 75%of32
Answer: 24
I am bad at explaining so i wouldn't help there
Answer:
24
Step-by-step explanation:
75% is also 3/4. 3/4 out of 32 can be 3 x 32/4 which is 3 x 8, or 24.
A bag contains coins consisting of quarters and dimes.
The total value of the coins is $8.65. There are 6 more
dimes than quarters. Which system of equations can be
used to determine the number of quarters, x, and the
number of dimes, y, in the bag?
x = y + 6 & 25x + 10y = 865
y = x + 6 & 10x + 25y = 8.65
10 = x +y & .25x + .10y = 8.65
y = x + 6 & 25x + 10y = 8.65
A (i think)
Step-by-step explanation:
Suppose that the functions q and r are defined as follows.
q (x)=–2x+1
r(x) = 2x²+2
Find the following.
(r og)(-1) = 0
0/6
Х
(q or)(-1) = 0
5
?
Answer:
(r o q)(-1) = 20
(q o r)(-1) = -11
Step-by-step explanation:
Given
[tex]q(x) = -2x + 1[/tex]
[tex]r(x) = 2x^2 + 2[/tex]
Solving (a): (r o q)(-1)
In function:
(r o q)(x) = r(q(x))
So, first we calculate q(-1)
[tex]q(x) = -2x + 1[/tex]
[tex]q(-1) = -2(-1) + 1[/tex]
[tex]q(-1) = 2 + 1[/tex]
[tex]q(-1) = 3[/tex]
Next, we calculate r(q(-1))
Substitute 3 for q(-1)in r(q(-1))
r(q(-1)) = r(3)
This gives:
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(3) = 2(3)^2 + 2[/tex]
[tex]r(-1) = 2*9 + 2[/tex]
[tex]r(-1) = 20[/tex]
Hence:
(r o q)(-1) = 20
Solving (b): (q o r)(-1)
So, first we calculate r(-1)
[tex]r(x) = 2x^2 + 2[/tex]
[tex]r(-1) = 2(-1)^2 + 2[/tex]
[tex]r(-1) = 2*1 + 2[/tex]
[tex]r(-1) = 6\\[/tex]
Next, we calculate r(q(-1))
Substitute 6 for r(-1)in q(r(-1))
q(r(-1)) = q(6)
[tex]q(x) = -2x + 1[/tex]
[tex]q(6) = -2(6) + 1[/tex]
[tex]q(6) =- 12 + 1[/tex]
[tex]q(6) = -11[/tex]
Hence:
(q o r)(-1) = -11
Monday
American Industries charges
$5 a day and $3.50 and hour
to rent a drill. Write and solve
an equation to show how
much it will cost you to rent a
drill for 6 hours.
Answer:
Step-by-step explanation:
so the equation will be: y = 5 + 3.50x. y is the total cost, and x is the number of hours. To solve for 6 hours, just plug 6 into the equation so: y = 5 + 3.50(6) = 26. So the answer is: it costs $26.00 to rent a drill for 6 hours.
help, I need help. please
Answer:
4 1/2 and 7 1/4
Step-by-step explanation:
Question 1 (10 points)
(04.02 MC)
A proportional relationship between the number of pounds of kiwis (x) and the price in dollars (y) can be graphed, and the ordered pair (3, 2) would be on the graphed line.
Part A: What is the price of 1 pound of kiwis? Show your work. (8 points)
Part B: What does the ordered pair (6, 4) which is the line in the graph represent? Explain in words. (2 points)
Your answer:
Answer:
[tex]1\ pound = \$ \frac{2}{3}[/tex]
6 pounds of kiwis cost $4
Step-by-step explanation:
Given
[tex]x = pound\ of\ kiwis[/tex]
[tex]y = price\ in\ dollars[/tex]
[tex](x,y) = (3,2)[/tex]
Solving (a): Price of 1 pound kiwi
The given parameters can be translated to be:
3 pounds costs $2
i.e.
[tex]3\ pounds = \$2[/tex]
To get the cost of 1 pound, we divide both sides by 3
[tex]\frac{3\ pounds}{3} = \frac{\$2}{3}[/tex]
[tex]1\ pound = \frac{\$2}{3}[/tex]
[tex]1\ pound = \$ \frac{2}{3}[/tex]
Solving (b): What does (6,4) represent
This can be rewritten as:
[tex](x,y) = (6,4)[/tex]
Recall that the representation is:
[tex]x = pound\ of\ kiwis[/tex]
[tex]y = price\ in\ dollars[/tex]
By comparison:
[tex]x = 6\\ y = 4\\[/tex]
So, the above can be translated to mean.
6 pounds of kiwis cost $4
Answer:
6 pounds of kiwis cost $4
Step-by-step explanation:
What is the discriminant of the quadratic equation 5x^2-8x+4=0?
Use a parametrization to express the area of the surface as a double integral. Then evaluate the integral. The portion of the cylinder x^2+y^2=16 between the planes z=4 and z=5
Let u=z and v=θ and use cylindrical coordinates to parameterize the surface. Set up the double integral to find the surface area.
Answer:
The answer is "[tex]8\pi[/tex]"
Step-by-step explanation:
[tex]\to r(v,u) =(4 \cos v, 4 \sin v,u) \\\\0\leq v \leq 2\pi, \ \ 4\leq u\leq 5\\\\\to r_v= (-4 \sin v, 4 \cos v, 0)\\\\\to r_u=(0,0,1)[/tex]
[tex]\to r_v\times r_u = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\-4 \sin v& 4 \cos v& 0\\0&0&1\end{array}\right| \\\\[/tex]
[tex]= (4 \cos v, -4 \sin v, 0)[/tex]
[tex]|r_v \times r_u| = \sqrt{16 \cos^2 v +16 \sin^2 v}\\\\[/tex]
[tex]= \sqrt{16( \cos^2 v + \sin^2 v)}\\\\= \sqrt{16(1)}\\\\= \sqrt{4^2}\\\\=4[/tex]
Calculating the surface area:
[tex]=\int^{2\pi}_{0} \int^{5}_{4} 4 \ du \ dv \\\\=\int^{2\pi}_{0} 4[4]^{5}_{4} \ dv \\\\=\int^{2\pi}_{0} 4[5-4] \ dv \\\\=\int^{2\pi}_{0} 4 \ dv \\\\=4 [v]^{2\pi}_{0}\\\\= 4 \times 2\pi\\\\= 8\pi[/tex]
This question is based on the parametrization. Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
Given:
The portion of the cylinder [tex]x^{2} +y^{2} = 16[/tex] between the planes z=4 and z=5.
Let u=z and v=θ and use cylindrical coordinates to parameterize the surface.
We need to express the area of the surface as a double integral.by using parametrization.
According to the question,
It is given that u=z and v=[tex]\theta[/tex],
Therefore, r(v,u) = (4 Cos v,4 Sin v, u)
Range of v : 0 [tex]\leq[/tex] v [tex]\leq[/tex] 2[tex]\pi[/tex]
Range of u : 4 [tex]\leq[/tex] u [tex]\leq[/tex] 5
[tex]\rightarrow r_v= (-4 \;sin\; v,4\;cos\; v,0)\\\rightarrow r_u=(0,0,1)[/tex]
[tex]\rightarrow r_u \times r_v =\begin{bmatrix} \hat{i}& \hat{j} & \hat{k}\\ -4\; sin\;v & 4\; cos\; v & 0 \\ 0 & 0 & 1\end{bmatrix}\\\\=(4 cos v,\;-4 sin v ,0)\\\\\left | r_v \times r_u \right | = \sqrt{16cos^{2}v+16sin^2v } \\\\= \sqrt{16(cos^{2}v+sin^2v) }\\\\=\sqrt{16}\\\\=4[/tex]
Now calculating the surface area,
[tex]=\int\limits^{2\pi}_0\int\limits^5_4 4 du\; dv\\\\=\int\limits^{2\pi}_0 4[u]^5_4 dv\\\\=\int\limits^{2\pi}_0 4[5-4] dv\\\\\\=\int\limits^{2\pi}_0 4dv\\\\\\=4[v]^{2\pi}_0 = 4(2\pi-0)= 8\pi[/tex]
Therefore, 8[tex]\pi[/tex] is the surface area as a double integral by using parametrization.
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Rudy invested $2460 in a money market account for 3 and 1/2 years. He earned $452 in simple interest. Which best represents the annual interest rate?
A. 3 and 3/5 percent
B. 5 and 1/4 percent
C. 5 and 3/4 percent
D. 6 and 2/5 percent
Answer:
B. 5 and 1/4 percent
Step-by-step explanation:
Step one:
given
principal= $2460
time= 3 and 1/2 years= 3.5 years
SI= $452
Required
The rate
Step two:
we know that
SI= PRT/100
substituting our data we have
452= 2460*R*3.5/100
452=8610R/100
cross multiply
452*100= 8610R
divide both sides by 8610
45200/8610= R
R= 5.25%
R= 5 and 1/4 percent
Solve | =
711.6Y/
K²
for K².
The answer is K^2 = 711.6Y on solving the given equation.
Given that, 1 = 711.6Y/K^2 and we have to solve it for the value of K^2. For this we simply have to solve the given equation steps wise. So, let's proceed to solve the equation.
1 = 711.6Y/K^2
Now, multiply K^2 with 1, we get
K^2 = 711.6Y
So, the value of k^2 will be equal to Y times 711.6 and further we can solve it for the various value of Y.
Let us suppose, we have to solve the above equation for the specific value of Y.
So, put Y = 1
On solving, we get
K^2 = 711.6x1
K^2 = 711.6
K = (711.6)^(1/2)
K = 26.67
∴ K^2 = 711.6Y is the equation we will get on solving the equation given to us in the question.
Hence, K^2 = 711.6Y is the required answer.
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Please answer this correctly without making mistakes
Answer:
The second coupon
Step-by-step explanation:
Answer:
First coupon ($250.00)
Step-by-step explanation:
Figure out the new price with first coupon:
$453.00 - $250.00 = $203.00Figure out the new price with second coupon:
55% of $453 = [tex]\frac{55}{100}[/tex] × [tex]\frac{453}{1} = \frac{24915}{100} = 249.15[/tex] Because we now know that 55% ($249.15) is less than $250.00, we automatically know that the first coupon will save Braden more moneyI hope this helps!
Find the difference
$9.36 - $1.12
plzz i need fasssssst
Answer: 1. a) 0 b) -4 2. a) 3 b) -9 3. a) -80 b) -339 c) -14 4. a) 110 b) -87
Step-by-step explanation: This took forever
Which is the best estimate for 6,193 ÷ 48 using compatible numbers?
A. 100
B. 120
C. 150
D. 160
Round 6193 to 6000
Round 48 to 40
6000/50 = 120
The answer is B. 120
A small drink holds 50% as much as a large drink. If the large drink holds 24 ounces, how much does the small drink hold?
Answer:
12
Half of 24 is 12
I hope this helps C:
Answer:
23.5
Step-by-step explanation:
i hope this is helpful :)
Need help asap plz will give brainliest
Answer:
[tex]z - 0.05z = 236.60[/tex]
Step-by-step explanation:
Given
[tex]Discount = 5\%[/tex]
[tex]Total\ Cost = 236.60[/tex]
Represent the cost of goods bought with z
When the coupon is applied, the discount becomes
[tex]Discount = 5\% * z[/tex]
This gives:
[tex]Discount = 0.05 * z[/tex]
[tex]Discount = 0.05z[/tex]
The discount subtracted from the cost of good will gives the total amount paid.
So, we have:
[tex]Cost\ of\ Goods - Discount = Total\ Cost[/tex]
This gives:
[tex]z - 0.05z = 236.60[/tex]
Hence, option (a) is correct
Choose the model that represents the same function as the graph of f (x)
y=1/2x-3
The graph shows that the line moves up 1 and right 2, up 1 and right 3, etc., and that b is the y intercept. It denotes a positive 1/2 slope.
The y intercept is -3 because the line crosses the y axis at -3. The shaded region has to be below the line. Our response is the second graph in the first row.
so
y= 1/2x -3
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