Answer:
The dimension of box=[tex]2ft\times 2ft\times 1ft[/tex]
Step-by-step explanation:
We are given that
Volume of box=4 cubic feet
Let x be the side of square base and h be the height of box
Volume of box=[tex]lbh=x^2h[/tex]
[tex]4=x^2h[/tex]
[tex]h=\frac{4}{x^2}[/tex]
Now, surface area of box,A=[tex]x^2+4xh[/tex]
[tex]A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}[/tex]
[tex]\frac{dA}{dx}=2x-\frac{16}{x^2}[/tex]
[tex]\frac{dA}{dx}=0[/tex]
[tex]2x-\frac{16}{x^2}=0[/tex]
[tex]2x=\frac{16}{x^2}[/tex]
[tex]x^3=8[/tex]
[tex]x=2[/tex]
[tex]\frac{d^2A}{dx^2}=2+\frac{32}{x^3}[/tex]
Substitute x=2
[tex]\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0[/tex]
Hence, the area of box is minimum at x=2
Therefore, side of square base,x=2 ft
Height of box,h=[tex]\frac{4}{2^2}=1 ft[/tex]
Hence, the dimension of box=[tex]2ft\times 2ft\times 1ft[/tex]
Consider the series 7/9+7/27+7/81+7/243
Answer:
=1 37/243
Step-by-step explanation:
the series is that the numerator is all 7
srry if its wrong i dont rlly understand what its asking
Answer:
= 1.1522....
Step-by-step explanation:
7/9 +7/27 +7/81 + 7/243
189 + 63 + 1,701 + 567
243. 19,683
= 252 + 2,268
243. 19,683
= 4,960,116 + 551,124
4,782,969
= 5,511,240
4,782,969
= 1.15
What is the value of ⅝ ÷ ⅖
Answer:
25/16
Step-by-step explanation:
Remember, keep-change-flip
Turn this into a multiplication equation
[tex]\frac{5}{8} * \frac{5}{2}[/tex]
Multiply to get 25/16
SOMEONE PLEASE PLEASE HELP!!!!!
Answer:
1800
Step-by-step explanation:
At the start of the school year, there were 72 boxes of coloring pencils in the art room, with each box containing 12 packs. During the school term , 58 boxes were used. How many packs of coloring pencils were left?
Answer:
Take away the 58 boxes from the 72 boxes and you will have 14 boxes left.
Then you have to multiply the 14 boxes left, by the 12 packs of pencils what gives you 168 packs of colouring pencils left.
What is the mean absolute deviation
of the following set of data?
4
6
6
2
Pls help.
Answer:
72
Step-by-step explanation:
4+6+6+2=18
and u added 4 numbers so 18×4=72
Mr.perkins has $120 in a savings account .the interest rate is 5% per year and it is not compounded how much will he have in 2 years
Answer:
The answer is $132
Step-by-step explanation:
120+ (5% of 120) (2)
120+(6)(2)
120+12
=132
HELP ME PLS I WILL CRY I HAVE SO MUCH TESTS AND ESSAYS DUE PLS SHOW WORK
Answer:
180 minutes
Step-by-step explanation:
60x3
4 times 4 times 4 times 4 times4 times 4. Using exponents, the expression is?
Answer:
It will have a 4 and then a five on the top right of it.
Step-by-step explanation:
4^5
Answer:
4^{5}
Step-by-step explanation:
Just basically what the other person said.
4 exponent 5
Which expression is equivalent to +7?
Which expression is equivalent to 5/6 divide to 7
Answer:
(5/6)/7!
5/(6*7!)=5/(6*7*6*5*4*3*2*1)=1/(6*7*6*4*3*2*1)=1/6048=0.0001653439
Step-by-step explanation:
The answer is 5/6x1/7
-1<9+n<17 and graph the answer after
Answer:
We get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
Or we can write as: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below:
Step-by-step explanation:
We need to solve the inequality [tex]-1<9+n<17[/tex] and graph the answer.
Solving the inequality
[tex]-1<9+n<17[/tex]
We know that if a<u<b then we can write a<u and u<b
So, we can write
[tex]-1<9+n \:and\: 9+n<17[/tex]
Solving these equations and finding values of n
[tex]-1<9+n \:and\: 9+n<17\\9+n>-1\:and\:9+n<17\\n>-1-9\:and\:n<17-9\\n>-10\:and\:n<8[/tex]
So, we get [tex]\mathbf{n>-10\:\:and\:\:n<8}[/tex]
We can write it as: -10< n and n<8
Overlapping we get: [tex]\mathbf{-10<n<8}[/tex]
The graph is shown is figure attached below:
The ratio of 6:5 can be expressed as
Answer:
the ratio of 6:5 can be expressed as 6/5
Let
P be a polynomial function, and
P(x) = 23 – dx2 - 4x – 20. If
(2 – 2) is a factor of the polynomial, what is the value of
d?
Answer:
The value of d = -5
The polynomial function x³ +5 x² - 4x -20 =0
Step-by-step explanation:
Explanation
Given that the equation is third degree polynomial
p(x) = x³ - d x² - 4x -20
Given factors x= 2 and x=-2
Substitute 'x' = 2 in given polynomial
8 -d(2²)-4(2) - 20 =0
⇒ 8 - 4 d - 8 -20=0
⇒ - 4 d-20 = 0
⇒ - 4 d = 20
⇒ d = - 5
The value of d = -5
Verification:-
After substitution d =-5 in given polynomial
x³ - (-5) x² - 4x -20 =0
put x=2
8 +5(4)-8-20 =0
20 =20
The factors are x= 2 and x=-2 of the given polynomial
A wheel assembly is
made from 2 wheels,
each weighing 2.6
pounds, and a steel
axle, which weighs
1.8 pounds. What is
the total weight of
the assembly?
Answer:
The total weight of the assembly is 7 pounds.
Step-by-step explanation:
The total weight of the assembry is found by the sum of the weights of each components.
We have:
2 wheels, each weighing 2.6 pounds, so 2*2.6 = 5.2 pounds
An axle, which weighs 1.8 pounds, so 5.2+1.8 = 7 pounds
The total weight of the assembly is 7 pounds.
I'm Jeff Bezos. AMA (ask me anything)
Answer:
CAN I GET AMAZON GIFT CARD AND SOME MULLA THANKS LOVE YOU SUGAR ZZZADDY
Step-by-step explanation:
20 points need help math equation
Answer:
47.3
Step-by-step explanation:
180-90-42.7=47.3
Answer:
47.3
Step-by-step explanation:
this is a right triangle, which means that Angle O is 90°
90 + 42.7 = 132.7
180 - 132.7 = 47.3
triangle KLM ~ triangle KQP are similar. Solve for x.
The value of x is 5.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
ΔKLM ≈ ΔKQP
This means,
KL/KQ = KM/KP
(3x - 1) / 7 = 8/4
Cross multiply.
3x - 1 = 2 x 7
3x - 1 = 14
3x = 14 + 1
Divide both sides with 3.
3x = 15
x = 5
Thus,
x is 5.
Learn more about triangles here:
https://brainly.com/question/25950519
#SPJ1
If Janet maintains the same driving rate can she drive more than 600 miles in 10 hours?Explain
In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?
(a) n = 10, p = 0.5
(b) n = 40, p = 0.88
(c) n = 100, p = 0.2
(d) n = 100, p = 0.99
(e) n = 1000, p = 0.003
Answer:
(c) n = 100, p = 0.2
Step-by-step explanation:
To approximate to use the normal distribution for a binomial, we need that:
[tex]np \geq 10, n(1-p)\geq 10[/tex]
So, for each option
(a) n = 10, p = 0.5
[tex]np = 10*0.5 = 5 < 10[/tex]
So not appropriate
(b) n = 40, p = 0.88
[tex]np = 40*0.88 = 35.2 > 10[/tex]
[tex]n(1-p) = 40*0.12 = 4.8 < 10[/tex]
So not appropriate.
(c) n = 100, p = 0.2
[tex]np = 100*0.2 = 20 > 10[/tex]
[tex]n(1-p) = 100*0.8 = 80 > 10[/tex]
So appropriate
(d) n = 100, p = 0.99
[tex]np = 100*0.99 = 99 > 10[/tex]
[tex]n(1-p) = 100*0.01 = 1 < 10[/tex]
So not appropriated
(e) n = 1000, p = 0.003
[tex]np = 1000*0.003 = 3 < 10[/tex]
So not appropriate
A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.
Given that,
Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.
We have to determine,
In which of the following situations would it be appropriate to use a normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.
According to the question,
Probabilities for a binomial distribution with the given values of n and p.
(a) n = 10, p = 0.5
(b) n = 40, p = 0.88
(c) n = 100, p = 0.2
(d) n = 100, p = 0.99
(e) n = 1000, p = 0.003
To approximate to use the normal distribution for a binomial is given as,
[tex]np\geq 10 , \ n(1-p)\geq 10[/tex]
When n = 10 and p = 0.5,[tex]= np \geq 10\\\\= 10 \times 0.5 = 5<10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 40 and p = 0.88,[tex]= n.p \geq 10\\\\= (40).(0.88) \geq 10\\\\= 35.2\geq 10\\\\Then,\\=n(1-p) = 40(1-0.88) \geq 10 \\\\= 40\times 0.12 \geq 10 = 4.8\leq 10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 100 and p =0.2,[tex]= n.p \geq 10\\\\= (100).(0.2) \geq 10\\\\= 20\geq 10\\\\Then,\\=n(1-p) = 100(1-0.2) \geq 10 \\\\= 100\times 0.8\geq 10 = 80\geq 10[/tex]
The normal distribution is greater than 10 so, this appropriate.
When n = 100 and p = 0.99,[tex]= n.p \geq 10\\\\= (100).(0.99) \geq 10\\\\= 99\geq 10\\\\Then,\\=n(1-p) = 100(1-0.99) \geq 10 \\\\= 100\times 0.01\geq 10 = 1\leq 10[/tex]
The normal distribution is less than 10 so, this not appropriate.
When n = 1000 and p = 0.003,[tex]= np \geq 10\\\\= 1000 \times 0.003 = 3<10[/tex]
The normal distribution is less than 10 so, this not appropriate.
Hence, A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.
To know more about Binomial Distribution click the link given below.
https://brainly.com/question/16776778
Game stop buys a game for $28 and marks the game up 64%. How much will you pay for the game?
Explain it and answer it please.
HELPP PLEASE WILL GIVE BRAILIEST
3
Solve for x.
-2x + 6 + 4x = -12
11/12 x 6/11 in simplest form
Please help. I need to know the answer. I will give brainliest
9514 1404 393
Answer:
1 4 8 9Step-by-step explanation:
blank 1
Locate x = 7 and find the y-value where the blue curve crosses.
f(7) = 1
blank 2
Locate x = -9 and find the y-value where the red curve crosses.
g(-9) = 4
blank 3
Locate y = 0 (the x-axis) and find the x-value where the blue curve crosses.
f(8) = 0
blank 4
Locate y = 2 and find the x-value where the red curve intersects.
g(9) = 2
A company sells, amongst other products, a medicated shampoo. The shampoo is sold in container sizes that are labeled as containing 500 ml. The volume of liquid that is actually put into the containers is normally distributed with a mean of 510 ml and a standard deviation of 10 ml.
(a) Estimate the probability that a container chosen at random will hold
(i) more than 520 ml
(ii) between 495 ml and 515 ml
(iii) less than the advertised amount
Answer:
between (ii)
Step-by-step explanation:
Write an equation of the line with a slope of 3 and a y-intercept of 4.5.
Answer:y= 3x + 4.5
Step-by-step explanation:
A coffee shop sells refill mugs for $7.50 each. Each coffee refill costs $1.75. Last month, Cody spent $42.50 on a mug and refills. Which equation can you use to find how many refills Cody bought. (Let x = the number of refills) How many refills did Cody buy last month? 10, 12, 20, or 25
Answer:
cannot see equations to select from but I got '7.50 + 1.75x = 42.50'
20 refills
Step-by-step explanation:
7.50 + 1.75x = 42.50
1.75x = 35
x = 35 / 1.75
x = 20
The letters from the word MATHEMATICS are placed in a hat. What is the probability of selecting an M and then selecting a T if the letters are selected at random and not replaced?
Please please help
Find the measure of the missing angle.
63°
Answer:
27 degrees
Step-by-step explanation:
Answer:
a = 27° ______
Step-by-step explanation:
~~~~~~~~~~
Solve for t in terms of u, v, w, and x.
Answer:
there's no image lol
Step-by-step explanation
URGENT PLEASE HELP
Consider this equation.
cos(0)= -2√5/5
If 0 is an angle in quadrant II, what is the value of sin(0)?
Answer:
I hope this can help
Step-by-step explanation:
The value of sin(0) should be considered as the [tex]\sqrt{5} \div 5[/tex]
Calculation of the value of sin(0):Since the equation is [tex]cos(0)= -2\sqrt 5/5[/tex]
Also in the case when 0 is an angle in quadrant II
So based on this, we can say that value of sin(0) should be considered as the [tex]\sqrt{5} \div 5[/tex]
Learn more about an equation here: https://brainly.com/question/4874021