Answer:
56
Step-by-step explanation:
Multiply it out 2×2×2×7 = 56
Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box).
Dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm² : (√2/3 , √2/3 ,√2/3)
Given, rectangular box with largest volume.
Let f(x , y , z) = xyz
Ф ≡ xy + yz + xz - 2 = 0
[tex]F =[/tex] [tex]f + \lambda[/tex][tex]\phi[/tex]
[tex]F = xyz + \lambda (xy + yz + xz - 2)[/tex]
[tex]F_x = 0\\yz + \lambda(y + z) = 0......1\\\\F_y = 0\\xz + \lambda(x+z)= 0......2\\\\F_z = 0\\xy + \lambda(x + y) = 0..........3[/tex]
xy + yz + xz - 2 = 0........4
Solving the above 4 equations,
[tex]yz + \lambda(y + z) = 0\\\lambda = -yz/(y+z)\\\\xz + \lambda(x + z) = 0\\\lambda = -xz / (x+z)[/tex]
Evaluating the lambda values,
x = y
Similarly, y = z
Therefore, x² + x² + x² - 2 = 0
x = √2/3
y = √2/3
z = √2/3
Hence, Dimensions : (x , y , z) = (√2/3 , √2/3 ,√2/3)
Know more about rectangle,
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A pair of $72 sneakers is marked with a sign "$20 OFF or 20% OFF.
The $20 on final price is ________
The 20% Off final price is ________
Which deal will give you the cheaper final price?
Answer:
$52
$57.6
Step-by-step explanation:
$20 off $72 is equal to 72-20=$52
20% of $72 is $14.4 which will then lead to 72-14.4=$57.6
The figure shows the letter W and four of its transformed images—A, B, C, and D:
Which of the four images was formed by a reflection of the letter W?
A
B
C
D
Answer:
The answer is c
Step-by-step explanation:
Beacuse when u the shape is transfrromed that what u get
I need help with mixed numbers when subtracting plz
Answer:
turn it into an improper fraction then subtract
Step-by-step explanation:
5×6=30
30+1=31
31/6
3×6=18
18+5=21
21/6
31/6 - 21/6 = 10/6
simplify: 5/3 ♡
I'm not sure tho lol
an airplane is change in alitude before landing is shown in the table
Answer:
wheres the table can you please provide one
Step-by-step explanation:
AnswerA= -4,000m
Step-by-step explanation:
1 35,000
2 31,000
3 27,000
4 23,000
Youre subtracting 4,000 everytime.
Help me please is the math
Answer:
2nd) which is 4 multiplied by 5 multiplied by 2
Which is the correct comparison symbol to make the number sentence true ( )? 6.53 _____ 6.534
Answer:
<
Step-by-step explanation:
6.53 < 6.534
The auxiliary equation for the given differential equation has complex roots. Find a general solution. y''-10y' 29y=0
Answer:
[tex]y = Acos5x - Bsin5x[/tex]
Step-by-step explanation:
Given the differential equation y''-10y'+29y=0
First, we need to rewrite it as an auxiliary equation as shown:
Let y'' = m²y and y' = my
Substitute the values into the general equation
m²y-10my+29y = 0
Factor out y:
(m²-10m+29)y = 0 [The auxiliary equation]
Solve the auxiliary equation and find the roots of the equation
m²-10m+29 = 0
m = -b±√(b²-4ac)/2a
a = 1, b = -10, c = 29
m = -10±√(10²-4(1)(29))/2(1)
m = -10±√(100-116)/2
m = -10±√-16/2
m = (-10±4i)/2
m = -10/2 + 4i/2
m = -5+2i
Comparing the complex number with a+bi, a = -5 and b = 2
The general solution for complex solution is expressed as:
[tex]y = Acosax + Bsinax[/tex]
Substitute the value of a in the equation
[tex]y = Acos(-5)x + Bsin(-5)x\\y = Acos5x-Bsin5x[/tex]
Hence the general solution to the differential equation is [tex]y = Acos5x - Bsin5x[/tex]
Typically, an MBA student who has a GMAT score above 710 is eligible for financial support. Given that a student is eligible for financial support, what is the probability that the student’s GMAT score is higher than 725 ?Typically, an MBA student who has a GMAT score above 710 is eligible for financial support. Given that a student is eligible for financial support, what is the probability that the student’s GMAT score is higher than 725 ?
The correct and complete question is shown below;
The random variable X denotes the GMAT scores of MBA students who were accepted to top MBA programs in Fall 2012. Assume that is normally distributed with a mean [tex]\mu_x[/tex] = 675 and a standard deviation [tex]\sigma_x = 30[/tex]
Typically, an MBA student who has a GMAT score above 710 is eligible for financial support. Given that a student is eligible for financial support, what is the probability that the student’s GMAT score is higher than 725?
Answer:
The probability that the student's GMAT score is higher than 725 = 0.3928
Step-by-step explanation:
From the given information:
Let X be the random variable that follows a normal distribution;
Then;
[tex]X \sim N( \mu_x = 675, \sigma_x = 30)[/tex]
To objective is to determine the probability that [tex]P(X > 725 | X > 710)[/tex]
[tex]P(X > 725 | X > 710)= \dfrac{P(X > 725 \cap X > 710 )}{P(X > 725)}[/tex]
[tex]\dfrac{P(X > 725 )}{P(X > 710)}=\dfrac{1 - P(X < 725) }{1- P(X < 710)}[/tex]
By using the EXCEL FORMULA: [tex]"= NORMDIST(x, \mu_x , \sigma_x , 1)"[/tex]
P(X< 725) = [tex]" = NORMDIST(725,675,30,1)"[/tex]
P(X< 725) = 0.9522
P(X< 710) = [tex]" = NORMDIST(710,675,30,1)"[/tex]
P(X< 710) =0.8783
[tex]P(X > 725 | X > 710)=\dfrac{1 - 0.9522}{1- 0.8783}[/tex]
[tex]P(X > 725 | X > 710)=\dfrac{0.0478}{0.1217}[/tex]
[tex]P(X > 725 | X > 710)=0.3928[/tex]
Suppose the time it takes a certain printer to print a document is an Exponential random variable with an average time of 15 seconds. You send a document to the printer at 1:00pm, and it is the third document in the queue. What is the probability that your printout will be ready by 1:01pm
Answer:
0.8046
Step-by-step explanation:
We're asked to calculate the probability that the job will be ready by 1.01 pm
From the question, we can note that the parameter of an Exponential is E(X)= 15
Next, to calculate the third job probability, we will have to use Poisson Distribution with parameter 1/λ
Therefore, E(Y) = 1/15
Then, The third job will be ready for 1:01 pm, and thus E(Y) = 61/15
Therefore, the required probability is
P(X ≥ 3) = 1 - P(X < 3)
= 1 - Poisson(3,4, true)
= 1 - 0.1954
= 0.8046
Lilliana is training for a marathon. She runs the same distance every day for a week on Monday,
Wednesday, and Friday, she runs 2 laps on a running trail and then runs 6 more miles. On Tuesday and
Sunday, she runs 4 laps on the trail and then runs 2 more miles. On Saturday, she just runs laps. How
many laps does Lilliana run on Saturday?
Answer: 6 miles
Step-by-step explanation:
WEDNESDAY + FRIDAY (# OF MILES)
The Miles Covered by Each Lap = 3x
The Miles on Top of That = 6
TUESDAY + SUNDAY (# OF MILES)
The Miles Covered by Each Lap = 5x
The Miles on Top of That = 2
You want to now put that into an equation! Therefore, you want to put the number of miles from Wednesday and Friday on one side and the number of miles from Tuesday and Sunday on the opposite side.
SOLVING EQUATION FOR MILES PER LAP
Step 1) 3x + 6 = 5x + 2
given equation from what we put together.
Step 2) -3x + 3x + 6 = 5x + 2 -3x
subtract 3x from both sides.
Step 3) -2 + 2x + 2 = 6 -2
subtract 2 from both sides.
Step 4) 2 × x = 4
divide both sides by 2 because you want to put the variable (x) on one side.
Step 5) x = 2 miles for each lap
Now you want to go look back at the equation and plug in 2 for the variable x.
Step 6) 5 ×2 + 2 = 12
PEMDAS!
Step 7) 12 ÷ 2 = 6
SHE RUNS 2 MILES ON SATURDAYS!
I’ll mark brainliest tysm
-13 EX: 2(-4) - 5 = -8 -5 = -13
-7
-1
1
3
THESE ARE THE ANSWERS
Jan designs a new logo for Kim's website. Kim pays Jan $45 for 5 hours of work. How much will Kim pay Jan for 15 hours of work?
am not sure but i think its 135$
i divided 45 by 5 to get the pay per hour
then multipled 9 by 15 to get the answer
am not the best in maths so its better u get someone to check if before u submit.
Answer:
675
Step-by-step explanation:
$45✖15 hours=675
so you see what we did here is multiply the money amount by the hour .
HOPE IT HELPS :)PLEASE GIVE ME brilliant!!!Thirty-seven school buses arrived at the zoo, each carrying thirty-seven to forty-three students per bus.
Estimate the number of students visiting the museum.
A: 16,000
B: 160
C: 1,600
D: 160,000
Answer:
C 1,600
Step-by-step explanation:
because If you multiply 37*43 It will get you 1591 and it's asking for the estimated answer which is 1600
What is the number that comes in 21,7,15,11 times table
Answer:
i think it is 105
but 105 divide by 11 is 9.54
Please answer correctly, will give brainlist.
Answer:
the answer is 77
Step-by-step explanation:
A measures 32 and B measures 109 so you subtract 109 and 32 and your answer will be 77
Suppose you are working with a data set that is normally distributed, with a mean of 350 and a standard deviation of 48. Determine the value of x from the following information.
a. 70% of the values are greater than x.
b. x is less than 10% of the values.
c. 24% of the values are less than x.
d. x is greater than 60% of the values.
Answer:
324.848
288.464
316.112
337.856
Step-by-step explanation:
Given that :
Mean (m) = 350
Standard deviation (σ) = 48
Determine the value of x for the following :
Using the z probability calculator :
a.) 70% of the values are greater than x.
1 - 0.7 = 0.3
P(x < 30%) = P(x < 0.3) = - 0.524 = z
Z = (x - m) / σ
x = (z * σ) + m
X = (- 0.524 * 48) + 350 = 324.848
b.) x is less than 10% of the values.
P(x < 0.1) = - 1.282 = z
X = (- 1.282 * 48) + 350 = 288.464
C.) 24% of the values are less than x
P(x < 0.24) = - 0.706 = z
X = (- 0.706 * 48) + 350 = 316.112
D.) x is greater than 60% of the values
P(x > 0.6) = -0.253 = z
X = (- 0.253 * 48) + 350 = 337.856
Evaluate the function for the indicated values of x.
[Look at image]
Answer:
f(-10) = -19
f(2) = 4
f(-5) = -9
f(-1) = 1
f(8) = -5
Step-by-step explanation:
Maggie makes blankets to sell. The table shows Maggie’s expense, f(x), her revenue, g(x), and her profit, h(x), per unit of yarn used, x.
Which expresses h(x) as a combined function?
h(x) =
x + f(x)
(f+g)(x)
(f-g)(x)
(g-f)(x)
Answer:
(g-f)(x)
Step-by-step explanation:
You have to subtract expenses from revenue and multiply by yarn to equal profit
3 5 of students at a school are boys. If there are 2610 students at the school, how many are girls?
Answer:
1044 girls in the school
Step-by-step explanation:
3/5*2610=1566 boys
2610-1566-1044 girls
it should be 1044 because
3/5=.6 or 60%boys and 40% girls
2610 * 60% or .6 = 1566 boys
2610 - 1566boys = 1044 girls
or
2610 * 40% or .4 = 1044 girls
so there are 1044 girls at the school
Choose the letter of the correct answer Write your answer on a separate
sheet
1. What do you call an expression in fraction form in which the numerator and
the denominator are polynomials?
A. rational algebraic equation
C. rational algebraic expression
B. linear algebraic expression
D. finear algebraic equation
2. In a rational algebraic expression written in the form of where P and Q are
polynomials, the polynomial Q must not be equal to
AO
C 2
B.
D. 3
3. Which of the following is a rational algebraic expression?
Answer:
1. Rational Algebraic Expression
2. 0
3. See explanation
Step-by-step explanation:
Solving (1):
From the list of given options, Option C. Rational Algebraic Expression answers the question.
And it is always of the form P/Q where P and Q are polynomials
Take for instance
P = x² - x + 2 and Q = x² + 2x - 4
P/Q = (x² - x + 2)/(x² + 2x - 4)
The above expression is a perfect example of a Rational Algebraic Expression
Solving (2): The denominator of a rational algebraic expression must not equal 0
Hence, option A answers the question
Solving (3): The options are missing.
However, a perfect example has been sighted on (1) above
A squirrel needs to look for some nuts in the forest every day. It can find 24 nuts on a sunny
day and 10 nuts on a rainy day. If the squirrel found 98 nuts last week, write and solve a
system of equations in order to find:
How many sunny days were there in last week? |
sunny days
How many rainy days were there in last week?
rainy days
Answer:
24x+10y=98
2sunny days
5rainy days
Step-by-step explanation:
x=number of sunny days
y=number of rainy days
(2*24)+(10*5)=98
vualah :)
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples. 30 + 5m; $36 30 + m; $36 30 + 5m; $24 30 + m; $24
Answer:
m + 30 ; $36
Step-by-step explanation:
Given that:
Total fruits needed = 15
Fruits needed :
Apple (m) ; cost = $3 per piece
Oranges (o) ; cost = $2 per piece
Amount spent on fruits :
[(cost of apple * number of apples) + (cost of orange *(total fruits - number of apples)]
3m + 2(15 - m)
3m + 30 - 2m
3m - 2m + 30
m + 30
Amount spent if 6 apples is purchased :
m = 6
m + 30
6 + 30 = $36
Insurance withholding varies depending on whether an entire family is covered or only the employee is covered. True False
Answer:
it would True
Step-by-step explanation:
Three Rivers publishes a catalog each year, last year it had 198 pages back and front. We
print 150 copies. How much does it cost the college if a ream, 500 pages, cost
$7.40 each?
Answer:
$222
Step-by-step explanation:
We need to find how many ream was used in the printing forts, to determine how much the College spent.
The catalog is 198 pages, back and front, which means, 1 leaf will take 2 pages. Therefore, 99 pages were used in printing 1 copy of the catalog.
No of pages that were used in printing 150 copies = 150*99 = 14,850 pages.
If 500 pages = 1 realm, therefore,
14,850 pages = 14,850/500 = 29.7.
Since, it's a full team that is sold, let's approximate the number of reams bought to be 30 reams.
If 1 ream costs $7.40, therefore,
30 reams = 30*7.40 = $222
I'm Using my last points will give brainliest geometry - finding angles with justification (level 1) delta math Please do step by step and pick reasoning for each
here are reasonings to pick from:
verticle angles
Linear pair (or triples)
Congruent angles
sum of angles in a triangle
sum of angles in a quadrilateral
Base angles of an isosceles triangle
Angle bisector definition
corresponding angles
alternate interior angles
alternate exterior angles
same - side interior angles
angle addition postulate
angle subtraction postulate
perpendicular lines form right angles
Answer:
m<GFC = 69 degrees
Step-by-step explanation:
The angle with 37 degrees is congruent with the angle on the left of 74 because of the Alternate Interior Angles Postulate
The last angle in the triangle that you don't know the degrees of is on the right of angle 74 because of the Alternate Interior Angles Postulate
So 37+74+ (the degree we don't know of the triangle) = 180 because of linear triples
180 - (37+74) = 69
So the angle on the right of angle 74 = 69
So m<GFC = 69 degrees
Answer:
Its 69
Step-by-step explanation:
the three measures will add up to 180 so all you hace to do is add the angles given and subtract that from 180 to find x
estimated answer for 3 3/7 x 1 3/4 simplify and type a whole number
Answer:
6
Step-by-step explanation:
3 3/7 * 1 3/4
~Turn into improper fractions
24/7 * 7/4
~Multiply both numerators and denominators.
168/28
~Simplify
6
Best of Luck!
Tom took a trip of 1,020 miles. He traveled by train at 55 miles an hour and the same number of hours by plane at 285 mph. How many hours did the trip take?
Answer:
3 hours
Step-by-step explanation:
285+55+285+55+285+55=1020
or another way
285+55×3= 1020
3/15 divided by 5/6
7 divided by 1/6
2 1/5 divided by 1 1/3
2 1/7 divided by 3/28
Answer:
0.2400000096
1.16666666667
1.92307692308
0.02551020238
Step-by-step explanation:
hope this helps :)
3/15 divided by 5/6: 6/25
7 divided by 1/6: 21/50
2 1/5 divided by 1 1/3: 21/50
2 1/7 divided by 3/28: 20
Hope this helps!
Same Thing as the first one