The dimensions of the package of maximum volume that can be sent are 20 inches by 40 inches.
Let us represent the length of the square cross-section of the postal package with x, and the width of the package with y.
So, the perimeter is given by the equation -
y + 4x = 120
y = 120-4x -----------(1)
the volume will be
V = [tex]x^{2} y[/tex] -----------(2)
Now, substitute (1) in (2), and we get,
V = [tex]x^{2}[/tex] (120-4x)
V = 120[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
Differentiating with respect to x, we get,
V' = 240x - 12[tex]x^{2}[/tex]
V'=0
hence, 240x - 12[tex]x^{2}[/tex] = 0
12[tex]x^{2}[/tex] = 240x
dividing by 120x on both sides,
hence, x=20
Now, we know that,
y = 120 - 4x
y = 120-4(20)
y = 120-80
y=40
Hence, the dimensions that maximize the volume of the package are 20 inches by 40 inches.
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For what type of variable does it make sense to construct a confidence interval about a population proportion?.
Given that a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level. For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.
The sample size, sample variability, and confidence level are all variables that have an impact on the CI's width
Assuming all other factors remained constant, a larger sample would result in a narrower confidence range. Additionally, more sample variability results in a wider range of.
Hence, a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.
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You are separating 16 tomatoes equally among 3 baskets.
Drag tomatoes to show how many tomatoes will be in each basket and how many tomatoes will be left over.
A type of green paint us made by mixing 2 cups of yellow with 3.5 cups of blue. a. Find a mixture that will make the same shade of green but larger amount.
Step-by-step explanation:
easiest example : multiply both (it is important to do it to both) by 2 :
2×2 = 4 cups of yellow
3.5×2 = 7 cups of blue
will make the same shade of green, as the mixing ratio is the same.
just, instead of 5.5 cups, it gives us 11 cups of green paint (surprise, surprise, this is also twice as much) .
Ari earned $356.74 the first week he
worked. The second week he earned
$427.19. To the nearest dollar ABOUT
how much less did he earn the first
week?
Select the correct answer.
What are the solutions of this quadratic equation?
x² + 2x = -2
OA.
OB.
O C.
OD.
x = 1 ti
x= -1 ti
x = 0
x = ti
Answer:
The answer might be C.(x=0)
Step-by-step explanation:
hope this helps!
Solve: cosine (x + pi) = one-half over the interval left-bracket startfraction pi over 2 endfraction, pi right-bracket.
The values that represent the solution to [tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex] ,
x ∈ [0, 2·π) are:
[tex]x = (\frac{\pi }{2} , \frac{3\pi }{2} )[/tex]
Sine and Cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle θ the sine and cosine functions are denoted simply as sinθ and cos θ.
Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse:
Sin (α) = [tex]\frac{opposite}{Hypotenuse}[/tex] and Cos (α) = [tex]\frac{Adjacent}{Hypotenues}[/tex]
Given in the question:
The given function is presented as follows;
[tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex]
Where;
x ∈ [0, 2·π)
We have;
cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)
[tex]cos (\frac{\pi }{4} ) = \frac{\sqrt{2} }{2} , sin( \frac{\pi }{4)} =\frac{\sqrt{2} }{2}[/tex]
Which gives
[tex]cos(\frac{\pi }{4} - x ) = \frac{\sqrt{2} }{2} cos x +\frac{\sqrt{2} }{2} sinx[/tex]
Therefore, we get;
[tex]\frac{\sqrt{2} }{2} cos x = \frac{\sqrt{2} }{2} sinx - \frac{\sqrt{2} }{2} = 0[/tex]
cos x = 0
[tex]cos (\frac{\pi }{2} ) =0[/tex]
Therefore;
The possible solutions (x-values) to cos x = 0 are;
[tex]0\leq \frac{n.\pi }{2} \leq 2\pi[/tex]
Where;
n = 1, 3, 5, ...
x ∈ [0, 2·π)
We get; [tex]x = \frac{\pi }{2} or \frac{3\pi }{2}[/tex]
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does the sequence { y k } converge? recall that there are four notions of convergence of random variables viz., almost sure, mean square, in probability and in distribu- tion. you should answer this question for each of these four modes of convergence. whenever you have convergence, also indicate what the limiting random variable is
Consider a sequence of random variables X1, X2, X3, ⋯ that is defined on an underlying sample space S. For simplicity, let us assume that S is a finite set, so we can write
S = {s₁, s₂,⋯,sₙ }.
Remember that each Xₙ is a function from S to the set of real numbers. Thus, we may write
Xₙ (sₐ) = xₙₐ, for a=1,2,⋯,k.
After this random experiment is performed, one of the sₐ' s will be the outcome of the experiment, and the values of the Xₙ's are known. If sₐ is the outcome of the experiment, we observe the following sequence:
x₁ₐ ,x₂ₐ,x₃ₐ,⋯.
Mean Square Convergence:Let [Xₙ] be a sequence of square integral random variables defined on a sample space Omega. We say that [Xₙ] is mean-square convergent (or convergent in mean-square) if and only if there exists a square integral random variable X such that
[tex]\lim_{n \to \infty} E[ X_{n} - X^{2} ][/tex]
Distribution Convergence:Convergence in distribution is in some sense the weakest type of convergence. All it says is that the CDF of Xₙ's converges to the CDF of X as n goes to infinity. It does not require any dependence between the Xₙ's and X. We saw this type of convergence before when we discussed the central limit theorem. To say that Xₙ converges in distribution to X, we write:
Xₙ →d X.
Probability Convergence:Convergence in probability is stronger than convergence in distribution. In particular, for a sequence X₁, X₂, X₃, ⋯ to converge to a random variable X, we must have that P(|Xₙ−X|≥ϵ) goes to 0 as n→∞, for any ϵ>0. To say that Xₙ converges in probability to X, we write:
Xₙ →p X.
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a surveyor took some measurements of a piece of land. the owner needs to know the area of the land to determine the value. what is the area of the piece of land?
The area of the piece of land is 849 ft².
The area of the piece of land
=22 x 30 x [tex]\frac{1}{2}[/tex] x 2 + (30-12) x 21 x [tex]\frac{1}{2}[/tex]
=660 + 18 × 21×[tex]\frac{1}{2}[/tex]
=660 + 189
=849 ft²
The area is the amount that expresses the volume of a place on the plane or on a curved surface. The location of an aircraft region or aircraft place refers back to the area of a shape or planar lamina, at the same time as floor region refers to the location of an open floor or the boundary of a three-dimensional object. the area may be understood as the amount of fabric with a given thickness that could be essential to style a model of the shape, or the amount of paint vital to cowl the surface with a single coat. it's miles the 2-dimensional analog of the length of a curve (a one-dimensional concept) or the extent of a strong (a three-dimensional concept).
The place of a shape can be measured by way of evaluating the form to squares of a hard and fast size. inside the global gadget of devices (SI), the usual unit of the vicinity is the rectangular meter (written as m²), that's the location of a rectangle whose sides are one meter long. A shape with a place of three rectangular meters would have the equal region as 3 such squares. In mathematics, the unit square is described to have placed one, and the location of another shape or floor is a dimensionless real variety.
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How do you say 7.793 in word
Answer:
seven and seven hundred nintey three thousandths
Step-by-step explanation:
help guys i don’t understand
Answer:
Step-by-step explanation:
You need to set the problem up like this:
VX=VW+WX. 4x=3x+5subtract 3 from both sides. x=5because 'x' equals 5, plug that 4(5)=3(5)+5back in for all the 'x's
simplify the equation 20=20The length of the line segmentshould be 20
Which is the best prediction for the number of fish in year 6 ? Round your answer to the nearest whole number .
The number of fish in year 6 will be;
⇒ y = 438.60
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The exponential regression equation is,
⇒ y = 14.08 × 2.08ˣ
Where, x is represent the year.
Now,
Since, The exponential regression equation is,
⇒ y = 14.08 × 2.08ˣ
Where, x is represent the year.
Hence, The number of fish in year 6 will be;
⇒ y = 14.08 × 2.08ˣ
⇒ y = 14.08 × 2.08⁶
⇒ y = 14.08 × 31.15
⇒ y = 438.60
Thus, The number of fish in year 6 will be;
⇒ y = 438.60
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An event manager is tracking participation in a tournament by age group. The manager created the following histogram:
Histogram with title Tournament Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 30, the second goes to 50, the third goes to 40, and the last goes to 10.
What percentage of the tournament participants are under the age of 20? Round to the nearest whole percent.
10%
23%
30%
77%
Round to the closest whole percent, 23% of the participants in the event are under the age of 20.
Define the term percentage of the number?Rather than being expressed as a fraction, a percentage is a piece of a whole presented as a number ranging from zero and 100. None of this is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the overall number by the entirety and multiply the result by 100 to get the percentage.For the stated question-
Total number of people = 30 + 50 + 40 + 10
Total number of people = 130
Number of participants are under the age of 20 = 30.
Let 'x' be the % of the participants are under the age of 20.
Thus,
x% of 130 = 30
x = 30 x 100 / 130
x = 23.07
x = 23%
Thus, round to the closest whole percent, 23% of the participants in the event are under age of 20.
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what is the proportion of 27/15 = 72/a
Answer:
a = 40
Step-by-step explanation:
Aume that the average number of waking hour per day i 16. If we pend 70 percent of our waking hour for communicating, how many hour do we pend communicating each day?
The total number of hours spend on the communicating is 11.2 hours each day..
Explain the term percentage of the number?A value or ratio that may be stated as a portion of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.The proportion ultimately refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.As the stated question-
Average number of waking hour per day = 16.
Communicating hours = 70% of total hours.
Thus,
Communicating hours = 70 x 16 / 100
Communicating hours = 11.2 hours
Thus, the total number of hours spend on the communicating is 11.2 hours.
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6 friends are coming to a party and each friend want 5 cookies but each box has twelve cookies so how many boxes do they need
Answer: 3 boxes
Step-by-step explanation:
6 x 5 = 30
36(closest multiple of 12 to 30) divided by 12 = 3
Answer:
2.5 boxes
Step-by-step explanation:
So, if each friend wants 5 cookies then you would multiply 6*5 which =30. Then you would divide 30 by 12 boxes which = 2.5. So you need 2.5 boxes or 3 if they need to be whole.
Set 1 angles a and c are ? and are also ? Set 2 angles b and d are ? and are also?
2.
2.
1)
a = 62⁰
b
d
O
2)
b = 120°
a
d
All Harriet wants for her 12th birthday is a pet dawef hamster, maybe even mire than one so the hamster doesnt get lonley. To prove to her parents how responsible she can be, sje bought a cage that has a 12- inch by 2 1/3 foot floor space and even did some research on the needs of dwarf hamsters. Harriet found out that each dwarf hamster requires atkeast 2/3 square foot of living soace. How mahy dwarf hamsters can live in the cage Harriet purchased?
Mathematically, three dwarf hamsters can live in the cage Harriet purchased.
How is the number determined?The number of dwarf hamsters that can live in Harriet's cage is determined using mathematical operations, including multiplication and division.
Mathematical operations involve the manipulation of numbers, variables, and mathematical operands to determine mathematical results.
The result of an addition is known as the sum while for a subtraction operation is the difference.
The result of a multiplication operation is known as the product like a dvision operation (also called the quotient).
The height of the cage = 12 inches or 1 foot
The length of the cage = 2¹/₃ feet
The area of the cage = 2¹/₃ ft² (1 x 2¹/₃)
The living space required by each dwarf hamster = ²/₃ ft²
The number of dwarf hamsters that can live in the cage = 3.499 (2¹/₃ ÷ ²/₃).
= 3
Thus, using mathematical operations, we can determine that the highest number of dwarf hamsters that can live in Harriet's cage is three.
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I have 13 nutcrackers and 14 snowmen on my tree. How many stars are there? Let s repentant the amount of stars.
Hint there is 29 in all.
Answer:
There are 2 stars
Step-by-step explanation:
There are 29 items in total.
As we are given the number of two of the items(nutcrackers and snowmen)we can easily find the number of the last item(stars) by subtracting the number of nutcrackers and snowman by the number of total items.(29)
So the solution would be :
29 - (13 + 14) = number of stars
==> add 13 and 14
29 - 27 = number of stars
==> simplify
2 = number of stars
What is a formula for the nth term of the given sequence?
180, -240, 320...
im lost
this is due in 1 hour. please help!
Place the figures in order from least volume to greatest volume.
Solve the equation for v.
0.5v + 0.06 < 3.46
v > 1.8
v < 1.8
v > 6.8
v < 6.8
Answer:
[tex]\boxed{\tt v < 6.8}[/tex]
Step-by-step explanation:
[tex]\tt 0.5v+0.06 < 3.46[/tex]
Multiply both sides by 100:-
[tex]\tt 0.5v\times\:100+0.06\times\:100 < 3.46\times\:100[/tex]
[tex]\tt 50v+6 < 346[/tex]
Subtract 6 from both sides:-
[tex]\tt 50v < 340[/tex]
Divide both sides by 50:-
[tex]\tt \cfrac{50v}{50} < \cfrac{340}{50}[/tex]
[tex]\tt v < \cfrac{34}{5}[/tex]
Or
[tex]\tt v < 6.8[/tex]
Therefore, your answer is v < 6.8!!! :)
______________________
Hope this helps!
Have a great day!
What number is 0.44 more than 0.25?
Answer: 0.69
Step-by-step explanation:
0.44 + 0.25 = 0.69
The correct answer is [tex]\boxed{0.69}[/tex]
How did figure out this?For this question we will be adding the numbers given.
Given:
[tex]0.44\\0.25[/tex]
Therefore, the equation is:
[tex]\boxed{0.44 +0.25}[/tex]
Adding the given numbers 0.44 and 0.250.44 + 0.25 = 0.69Therefore, the correct answer is [tex]\boxed{0.69}[/tex]
There are 8 red marbles and 6 blue marbles in a bag.
(a) What is the ratio of blue marbles to red marbles?
(b) What is the ratio of all marbles in the bag to blue marbles?
the ratio of blue marvel is 4/3
the ratio of Al marbles to blue is 7/3
its making me type something here but question in the pic thanks :)
The value of the definite integral is 10 after breaking the limits of the integral.
What is integration?It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
The piecewise function is given:
[tex]\rm \int\limits^4_0 {x} \, dx = \int\limits^2_0 {2} \, dx +\int\limits^4_2 {x} \, dx[/tex]
[tex]\rm \int\limits^4_0 {x} \, dx = x^2|^2_0+(1/2)x^2|^4_2[/tex]
= 4 + (1/2)[16 - 4)
= 4 + 6
= 10
Thus, the value of the definite integral is 10 after breaking the limits of the integral.
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A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 44 cables and apply weights to each of them until they break. The 44 cables have a mean breaking weight of 778. 1 lb. The standard deviation of the breaking weight for the sample is 15. 5 lb
(767.47, 777.13) is the confidence interval in the given situation.
What is the confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.
[tex]\begin{aligned}&\mathrm{CI}=(772.3-4.83,772.3+4.83) \\&\mathrm{CI}=(767.47,777.13)\end{aligned}[/tex]
Therefore, (767.47, 777.13) is the confidence interval in the given situation.
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wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. based on this information, what is a possible amount of time, in hours, that it could take wyatt to husk 72 dozen ears of cor
Wyatt can husk anywhere from 12 to 18 dozen ears of corn per hour.
To find the possible amount we need to calculate the maximum and minimum time period in hours
Thus, if we need to find the time taken to husk 72 dozen ears of corn, the maximum time would be ,
=72 / 12 hours
=6 hours
And the minimum time would be used for the does wyatt takes to husk the 72 dozen of corn
=72/18 hours
=4 hours
Thus, depending on his speed, Wyatt takes anywhere from 4 to 6 hours to husk 72 dozen ears of corn.
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What value does each equation need to be multiplied by in order to eliminate the y-terms?
Equation 1: 6x − 5y = -4
Equation 2: 4x + 2y = 28
Please Help, I don't get it
Equation 1 needs to be multiplied with + 2
Equation 2 needs to be multiplied with + 5.
Step-by-step explanation:
Here, the given system of equation is given as:
Equation 1 : 6 x − 5 y = -4
Equation 2: 4 x + 2 y = 28
Here, in equation 1, the coefficient of y = - 5
Also, in the equation 2, the coefficient of y = + 2
Now, in order to eliminate the y coefficients,
Coefficient of y in 1 = - Coefficient of y in 2
Now, to make -5 and + 2 to eliminate each other,
Multiply -5 with 2, we get -5 x 2 = -10
And Multiply the coefficient + 2 with 5, we get +2 x 5 = + 10
The new coefficient of y is equation 1 = - 10 y
The new coefficient of y in equation 2 = + 10 y
They will cancel out each other, when both equations are ADDED.
Hence, equation 1 needs to be multiplied with + 2
and the equation 2 needs to be multiplied with + 5.
need help on 10,12, and 13 please
Answer:
Step-by-step explanation:
Answer:
(10) x=1, y=-3
(12) x=3, y=22
(13) x= 6, y= 7
Step-by-step explanation:
[10] 6x -9 =-3x
6x+3x=9
9x=9
x=9,
you are the manager of a restaurant for a fast-food franchise. last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.6 minutes. you select a random sample of 81 orders. the sample mean waiting time is 3.45 minutes, with a sample standard deviation of 0.9 minute. complete parts (a) and (b) below. question content area bottom part 1 a. at the 0.05 level of significance, is there evidence that the population mean waiting time is different from 3.6 minutes? state the null and alternative hypotheses.
There is not evidence that the population mean waiting time is different from 3.6 minutes.
What is the p-value?
A statistical measurement known as a p-value is employed to check a hypothesis' validity against actual data. A p-value calculates the likelihood of getting the outcomes that were observed, presuming that the null hypothesis is correct. The statistical significance of the difference that was found increases with decreasing p-value.
From the question, we know that the size (n), the mean (x), and the standard deviation (s) of the sample are 81, 3.45 minutes and 0.9 minutes. Additionally, we are going to decide if the waiting time is different or not from 3.6 minutes, so the null and alternative hypotheses are:
H0: m=3.6
H1: m≠3.6
Where m is the mean of the population.
Then, we don't need to be concerned about the shape of the population distribution because the value of the n is bigger than 30 and we can use the statistic z as:
[tex]z = \frac{x-m}{\frac{a}{\sqrt{n} } }[/tex]
So, replacing the values, the test statistic is:
[tex]z = \frac{3.45 - 3.6}{\frac{0.9}{\sqrt{81} } }[/tex]
= 2.50
On the other hand, the p-value for this test is calculated as:
p-value = 2P(z >2.50) = 2(0.0668) = 0.134
Taking into account that the p-value is bigger than the level of significance 0.01, the null hypothesis is not rejected, and there is not evidence that the population mean waiting time is different from 3.6 minutes.
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