Any piece of luggage must have a length, width, and height combined that is less than or equal to 150 cm. A traveler requests to take a package with the maximum permitted volume. if the length and width are to be equal, then the dimensions would be 48*96*72
Any piece of luggage must have a length, breadth, and height combined that is 216 cm or less.
L+W+H=216 (because we want the max volume, we may ignore the "less than part" and set them equal) (since we want the max volume, we can ignore the "less than part" and set them equal)
L = W if the length and width are equal.
Let's construct this new equation by swapping L for W.
Arrange H to the left so that H=216-2W when 2W+H = 216
Consequently, what is volume V=L*W*H=W=W2*(216-2W) =216W2-2W3 div./dW=432W-6W?
2\s432W-6W^2=0
72w-w2=0 divided by 6 on both sides.
W = 72 L H = 72 cm
L=2W is the only item that has altered.
Given that L+W+H=216 and that V=L*W*H=2W*W*(216-3W) =432W2-6W, 3W+H=216
864W-18W2 x 3 V prime
Set V prime to 0, solve it by dividing both sides by 18, and you'll get W = 48. dimensions will be
48, 96, and 72 cm in width ,lenght and height
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a pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. this plan randomly selects and tests 21 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. what is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects? (report answer as a decimal value accurate to four decimal places.) p(accept shipment)
0.9660 is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationIf the number of tablets in a shipment is sufficiently large, we can consider the testing procedure you describe (selecting a random sample of 29 ibuprofen tablets and counting the number of defective tablets in the sample) to be a binomial probability experiment.
Let X = (Number of defective ibuprofen tablets in a random sample of 29 tablets.) Then we may reasonably assume that X follows a binomial distribution. For each "trial" (that is, each tablet selected), there are two possible outcomes, "success" (the tablet is defective), or "failure" (the tablet is not defective). Note that the word success as used in the binomial distribution does not carry the connotation of being a "good" outcome. A "success" is simply the outcome you are interested in counting, which in this case is the number of defectives in the sample. The important parameters for a binomial distribution are n (the number of trials) and p (the probability of success on any one trial.) For this situation, we have p = .01 (since we are told 1% of the tablets in the shipment are defective) and n = 29. The general formula for the binomial distribution is
P(x) = nCx·px·(1 - p)n-x
where x is the number of successes in n trials (In this problem, x is the number of defectives in a random sample of 29 tablets.) The symbol nCx is the "number of combinations of n things taken x at a time". This is the number ways of choosing x distinct objects from a set of n objects, without regard to order. It is given by
nCx = n!/[x!·(n-x)!]
where ! is the factorial symbol.
We want to find the probability that the shipment is accepted. We are told that a shipment will be accepted if at most one tablet doesn't meet the required specifications. That is, the number of defectives must be less than or equal to one.
P(Shipment accepted) = P(X ≤ 1). (In this case, X ≤ 1 if and only if X=0 or X=1)= P(0) + P(1).
So we calculate P(0) (the probability of 0 defective tablets in the shipment), and P(1) (the probability of 1 defective.) Using the formula for the binomial distribution, we have
P(0) = 29C0·(.01)0·(1 - .01)29 - 0.
But 29C0 = 1, so
P(0) = 1·(.01)0·(.99)29 ≅ .74717
Also,
P(1) = 29C1·(.01)1·(1 - .01)29 - 1.
Calculating 29C1, we have
29C1 = 29!/[1!·(29-1)!] = 29, so
P(1) = 29·(.01)1·(99)28
P(1) ≅ .21887
Finally, then, we have
P(Shipment accepted) ≅ .74717 + .21887 ≅ .9660 (to 4 decimal places.)
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make x the subject of the formular 6x+a=5(x+t)
The value of x is (5t-a) when the formula is 6x+a=5(x+t).
According to the question,
We have the following information:
6x+a=5(x+t)
Now, from this formula, we have to mark the value of x or in other words, we have to find the value of x.
Now, multiplying 5 into the bracket on the right hand side:
6x+a = 5x+5t
Subtracting 5x from both sides of the equation:
6x-5x+a = 5t
x+a = 5t
Subtracting a from both sides of the equation, we will get the final value of x in terms of t and a:
x = 5t-a
Hence, the value of x is (5t-a) when the formula is 6x+a=5(x+t).
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What is the probability of selecting a king or queen from a standard deck of 52 cards
Target buys masks wholesale for $15 a piece. they mark them up 150% for resale. if
kara bought one from them and paid 12% sales tax, how much did she spend
altogether?
Target buys masks wholesale for $15 a piece. They mark them up 150% for resale. If Kara bought one from them and paid 12% sales tax, then
The amount spent by Kara overall is $42.
Here, we need to determine how much money she spent overall. Finding the mask’s cost after adding the 150% mark is the first step in determining how much is spent.
She purchased it for $37.5 but had to pay 12% tax on it. Consequently, she spent $42 total.
Use proportional relationships to solve multi step ratio and percent problems. Examples include simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
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There are 3 boys for every 2 girls in a dance competition. Does it make sense for there to be a total of 9 people in the competition?
According to the ratio, it doesn't make sense to have a total of 9 people in the dance competition.
What is a ratio?In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
The ratio of boys to every girls is 3:2 in a dance competition.
Let's find if it will make sense to have a total of 9 people in the competition.
Therefore,
number of boys = 3 / 5 × 9 = 27 / 5 = 5.4
number of girls = 2 / 5 × 9 = 18 / 5 = 3.6
Therefore, it doesn't make sense to have 9 people in the competition because the actual number of boys and girls will be in decimal which is impossible.
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What is the solution to this system of linear equation 3x 2y 14?.
The solutions to this system of linear equation 3x−2y=14 is ( [tex]\frac{2y + 14}{3}[/tex] , [tex]\frac{3x}{2}[/tex]-7).
Add 2y to both sides.
3x=14+2y
The equation is in standard form.
3x=2y+14
Divide both sides by 3.
[tex]\frac{3x}{3}[/tex] = [tex]\frac{2y + 14}{3}[/tex]
Dividing by 3 undoes the multiplication by 3.
x = [tex]\frac{2y + 14}{3}[/tex]
Now,
3x−2y=14
Subtract 3x from both sides.
−2y=14−3x
Divide both sides by −2.
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{14 - 3x}{-2}[/tex]
Dividing by −2 undoes the multiplication by −2.
y = [tex]\frac{14 - 3x}{-2}[/tex]
Divide 14−3x by −2.
y = [tex]\frac{3x}{2}[/tex] - 7
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5x+6y +39 = 0
3y = 4x
Answer:
Step-by-step explanation:
Move all terms not containing xx from the center section of the inequality.
Inequality Form:
0<x<30<x<3
Interval Notation:
(0,3)
Answer:
y=-4
x=-3
Step-by-step explanation:
x=3y/4
5*(3y/4) +6y+39=0
15y/4+6y+39=0
3.75y+6y+39=0
9.75y=-39
y=-4
x=-3
if the zeroes of the quadric polynomial 2x^2-5x+k are reciprocal to each other then find the value of k
Answer:
The value of k is 1.
Step-by-step explanation:
Answer:
The value of k=1
Step-by-step explanation:
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of f(x) = (3/4)ˣ is attached. The values are f(-2) = 16/9, f(-1) = 4/3, f(0) = 1, f(1) = 3/4 and f(2) = 9/16
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the exponential function:
f(x) = (3/4)ˣ
Hence:
f(-2) = (3/4)⁻² = 16/9
f(-1) = (3/4)⁻¹ = 4/3
f(0) = (3/4)⁰ = 1
f(1) = (3/4)¹ = 3/4
f(2) = (3/4)² = 9/16
The graph of f(x) = (3/4)ˣ is attached.
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Question 7
7. Line segment RS has endpoints at (4. 9) and (12,-4). What are the coordinates of the midpoint?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 12 +4}{2}~~~ ,~~~ \cfrac{ -4 +9}{2} \right) \implies \left(\cfrac{ 16 }{2}~~~ ,~~~ \cfrac{ 5 }{2} \right)\implies \left( 8~~,~~2\frac{1}{2} \right)[/tex]
Plot 5/3 and it oppoite on the number line. Select the point on the line to plot the point
[tex]\frac{5}{3}[/tex]The point on the number line to plot the point which is opposite [tex]\frac{5}{3}[/tex] is [tex]\frac{-5}{3}[/tex]
What is a number line?A number line is a horizontal representation of a number of parts with equal intervals.
What exactly is a number line?
A number line is a horizontal line with evenly spaced numerical increments. It shows how to answer plotted the number on the line.
Which points on the number line are diametrically opposed?If two numbers are the same distance from 0 and on opposite sides of the number line, they are opposites.
For example, 4 is the inverse of -4, and -4 is the inverse of 4. They are both equal distances from zero.
Given: number is [tex]\frac{5}{3}[/tex]
The opposite of 5/3 is the additive inverse let x be the additive inverse
[tex]\frac{5}{3}[/tex] + x = 0
x = 0 - [tex]\frac{5}{3}[/tex]
x= - [tex]\frac{5}{3}[/tex]
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If my current grade in math is 93.73% and I get a 74% on my test that is 40% of my grade, what is my new grade?
His new grade will be 85.838 , this can be calculated using simple fraction.
What is fraction?
As the components of a whole, fractions are by definition. The entire can be a single item or a collection of items.
Main Body:
Initial percentage of child = 93.73%
Child's percentage at test = 74%
according to the question his 40% of test grade is accounted
Parts of grade is from test = 4/10
So his new grade = (4/10)*74 + (6/10) *93.73
New grade = 29.6 +56.238
Hence the new grade for the child will be 85.838%
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Gabriella, Leah and Juan, cut up a golden delicious apple and a granny Smith apple for a snack after school. They split the apples evenly between how many apples did each person get right your answer as a proper fraction or mixed number.
Step-by-step explanation:
What is the value?
Please put the full question
Then only I would be able to help you
Find x and y so that the quadrilateral is a parallelogram. Answer below and show work.
Answer:
x = 2 , y = 29
Step-by-step explanation:
if the quadrilateral is to be a parallelogram , then
• opposite sides are congruent
• opposite angles are congruent
Then
2x + 9 = x + 11 ( subtract x from both sides )
x + 9 = 11 ( subtract 9 from both sides )
x = 2
and
3y + 19 = 106 ( subtract 19 from both sides )
3y = 87 ( divide both sides by 3 )
y = 29
with reference to time series data patterns, a cyclical pattern is the component of the time series that
Answer:
Step-by-step explanation:
10125. POGO STICK On her pogo tick, Lula made 24 hop in 30 econd. At thi rate, how many hop will he make in 50 econd?
Answer:
3
Step-by-step explanation:
Find the nth term of this sequence
15,12,9,6
Answer: an = 18 - 3n
Step-by-step explanation:
so the next term should be 3
please help! I need help asap
Step-by-step explanation:
5.
normally no.
just think - we are talking about people. it's it possible to have half of a friend at a game ?
no, the input is not possible.
but if this function is used in the context or a larger analysis, and mean values are created and checked, then it might be valid.
it all depends on the context of how the function is used.
2.
we don't see all answer options, but the range is the interval or set of all valid y-values (the 2nd number in an ordered pair).
we see : -1, 3, 4, 6
whichever answer option shows this is correct.
Determine the inverse of the function f (x) = 3(x − 4)2 + 5.
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity of the quantity x minus 5 end quantity over 3 end quantity such that the domain of f (x) is x ≤ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≥ 4
inverse of f of x is equal to 4 minus the square root of the quantity x over 3 minus 5 end quantity such that the domain of f (x) is x ≤ 4
Question 4(Multiple Choice Worth 2 points)
(02.06 MC)
Determine the inverse of the function f(x) = log2(3x + 4) − 5.
f inverse of x is equal to 2 to the power of x plus 3 all over 2
f inverse of x is equal to the quantity x plus 5 end quantity squared minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x plus 5 end quantity minus 4 all over 3
f inverse of x is equal to 2 to the power of the quantity x minus 5 end quantity plus 4 all over 3
Question 5(Multiple Choice Worth 2 points)
(02.06 MC)
Given the graph of f(x), determine the range of f−1(x).
Rational function with one piece increasing from the left in quadrant 2 asymptotic to the line y equals 1 and passing through the point 2 comma 2 and asymptotic to the line x equals 3 and another piece increasing from the left in quadrant 4 asymptotic to the line x equals 3 passing through the point 4 comma 0 asymptotic to the line y equals 1.
Answer: The inverse of the function f(x) = 4(x-3)² + 2 is
The given function is:
f(x) = 4(x - 3)² + 2
To find the inverse of the function:
Make x as the subject of the formula
Replace x by and replace f(x) by x
Therefore, the inverse of the function is:
Step-by-step explanation:
if this rate of growth remains the same and the population is 550,000 in the year 2020, approximately how many people will there be after 15 years?
\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
Answer:
no
Step-by-step explanation:
\frac{1}{6}f^3a=
6
1
\frac{1}{6}f^3a=
6
1
f
3
a=
\,\,D
D
katie has £1200. she gives 1/3 of the money to her sister. Then katie give 1/4 of the remaining money to her brother. how much money does katie have left?
Answer:
£600
Step-by-step explanation:
Katie gives 1/3 of the money to her sister.
1/3 of 1200 is 400, because 1200 divided by 3 is 400. So she gives 400 to her sister, which means she has 1200-400= 800 left.
When she gives 1/4 of the remaining to her brother, that means that we need to figure out how much 1/4 of 800 is. 800 divided by 4 is 200. So Katie gives 200 to her brother.
800 that she has remaining minus the 200 she gives to her brother leaves her with 800-200 = 600
Input(x):a number output(y):2less than 4 times x
The equation to describe the information that 2 less than 4 times x is 4x - 2.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, 2 less than 4 times will be:
= (4 × x) - 2
= 4x - 2
Therefore, the equation is 4x - 2.
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The telephone company offers two billing plans for local calls. Plan 1 charges $35 per month for unlimited calls and Plan 2 charges $19 per month plus $0.05 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2. b. Explain the meaning of the answer to part a.
help ASAP! answers to part a and b
The inequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,
x > 320.
And x > 320 means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.
(a) Given, that the telephone company offers two billing plans for local calls. Plan 1 charges $35 per month for unlimited calls.
Plan 2 charges $19 per month plus $0.05 per call.
Let x calls be made,
Now, according to the Plan 1,
the charges for 'x' calls be $35 only
according to the Plan 2,
the charges for 'x' calls be
$19 + $0.05x
Now, Plan 1 is more economical than Plan 2 for,
$35 < $19 + $0.05x
On solving the inequality, we get
$16 < $0.05x
On dividing both the sides by 0.05, we get
16/0.05 < x
320 < x
i.e. the monthly calls be more than 320.
(b) Now, as in part (a) we got,
320 < x
which means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.
Hence, theinequality for the number of monthly calls for which Plan 1 is more economical than Plan 2 is,
x > 320.
And x > 320 means that the monthly calls should be more than 320, for Plan 1 to be more economical than Plan 2.
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please help me this is geometry
Answer:
50
Step-by-step explanation:
Since 45-45-90 tri, x^2+x^2=100^2
So 2x^2=10000
2x=100 and x=50
Answer:
a = 70.71068 = 50√2
Step-by-step explanation:
Given c=100 and ∠β=45°,a = 70.71068 = 50√2a = √c^2 - b^2
= √1002 - 70.7106781186552
= √5000
= 70.71068 = 50√2
Thanks.
If the regular price of the pair of glasses was $72 how much did Gabriela pay wit the discount
The amount Gabriela paid with the discount is $50.4.
How to find the amount paid with the discount?Discount is a reduction in price. Discount means reducing the price or value of an object or item.
Gabriela bought a new pair of glasses at the store when they were 30% off the sale.
The regular price of the glasses is 72 dollars. The amount Gabriela paid with the discount can be calculated as follows:
discount = 30% off of the sale
discount = 30 / 100 × 72
discount = 2160/ 100
discount = 21.6 dollars
Therefore,
price paid with the discount = 72 - 21.6
price paid with the discount = 50.4 dollar
Therefore, the amount she paid with the discount is 50.4 dollars
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find the slop of the line passing through the points (2,7) and (-1,4)
Answer:
1
Step-by-step explanation:
Change is y over the change in x
The y's are 4 and 7.
The x's are -1 and 2
[tex]\frac{4-7}{-1-2}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
Factor. 49x^8-16y^14 Enter your answer in the box.
The factor of the expression is [tex]49x^8-16y^{14} =(7x^4-4y^7)(7x^4+4y^7)[/tex].
What is factor?
A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.
Given, 49x⁸ − 16y¹⁴ is an expression.
We can write it as (7x⁴)² − (4y⁷)²
we know, [tex]a^2-b^2=(a-b)(a+b)[/tex]
using this identity, we get
49x⁸ − 16y¹⁴ = (7x⁴ - 4y⁷)(7x⁴ + 4y⁷)
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Someone solve this with solution than you.
15-8k+15k - 8 = 42
Answer:
k=5
Step-by-step explanation:
15-8k+15k-8=42
15+7k=50
7k=35
k=5
Eduardo decided to invest money in an account that earns 3% compounded semi-annually. If he initially
deposited $750 into the account, how much will it be worth in 8 years? Round answer to the nearest
hundredth.
Answer:
$951.74
Step-by-step explanation:
You want the future value of $750 earning 3% per year for 8 years, compounded semi-annually.
Compound interestThe value of an account earning interest at rate r on principal P compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
For P=750, r=0.03, n=2, t=8, this is ...
A = 750(1 +0.03/2)^(2·8) = 750(1.015^16) ≈ 951.74
The account will be worth about $951.74 in 8 years.
__
Additional comment
All spreadsheets and many graphing calculators have the necessary financial functions for computing this value. Apps are available for the purpose, as well.
