Answer:
[tex]x=6+3\sqrt{2}[/tex] is the size of the square
Step-by-step explanation:
Let the side of the square cut from the cardboard be “x”
Size of the square base = [tex]12 -2x[/tex], height of the box = x
Volume of square box = Area * height = [tex](12-2x)^2 * x[/tex]
Differentiating the above equation and equating it to zero, we get –
d/dx [tex]((12-2x)^2 * x)[/tex]
d/dx[tex]{(144 + 4x^2 -48x)*x}[/tex]= d/dx [tex](144x + 4x^3 -48x^2)[/tex]
d/dx [tex](144x + 4x^3 -48x^2) = 0[/tex]
[tex]144+8x^2-96X= 0\\18 +X^2-12X = 0[/tex]
On solving above equation, we get –
[tex]x=6+3\sqrt{2} \\ x=6-3\sqrt{2}[/tex]
29
A person invests $5000 in a bank account paying 4.5% interest compounded continously. To the nearest tenth
of a year, how long must the person leave the money in the bank until it reaches $10,200?
6.9 years
10.2 years
20.1 years
15.8 years
Answer
15.8
Step-by-step explanation:
PLEASE I NEED HELP I DONT UNDERSTAND HOW TO DO ILL GIVW MORE IF RIGHT
Answer: Choice D
[tex]\frac{9\sqrt{2}}{2}[/tex]
=============================================
Explanation:
We have a 45-45-90 triangle. If x is the leg length, then y = x*sqrt(2) is the hypotenuse.
Solving for y gets us [tex]x= \frac{y}{\sqrt{2}} = \frac{y\sqrt{2}}{2}[/tex]
In this case, y = 9 is the hypotenuse which then leads to choice D.
------------
Another way to find the answer is to use the pythagorean theorem
a = x and b = x are the two congruent legs
c = 9 is the hypotenuse
Solving a^2+b^2 = c^2, aka x^2+x^2 = 9^2, will lead to [tex]x = \frac{9\sqrt{2}}{2}[/tex]
Enter the slope-intercept equation of the line shown below. ??!!!!!
Answer:
y=2x+4
Step-by-step explanation:
2x is the gradient and the y intercept is 4 so we just put them into the equation y=mx+c
Find the inverse of function f. A.f-1(x)=7x+9 B.f-1(x)=1/9x-7/9 C.f-1(x)=7/9x-1/9 D.f-1(x)=-9x-7
Answer:
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Step-by-step explanation:
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helpppp!!!
Make a conjecture about the number of units produce in 50 hours
what is the solution to 8t - 2 - 9t < 5?
Answer:
t > -7
Step-by-step explanation:
8t - 2 - 9t < 5
Combine like terms
- 2 - t < 5
Add 2 to each side
-2-t+2 < 5+2
-t <7
Multiply each side by -1, remembering to flip the inequality
t > -7
To rent a certain meeting room, a college charges a reservation fee of 13 and an additional fee of 6 per hour. The chemistry club wants to spend less than 73 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answe
I LIKE YR CUT G!
Step-by-step explanation:
PLEASE HELP! i will give brainliest
Answer:
2) $300
Step-by-step explanation:
I used the the following two points to find slope:
(9,400) and (8,350) to get a slope of 50
therefore, f(x) = 50x
f(6) = 50(6)
f(6) = 300
I keep getting the wrong answers someone help please.
Answer:
1. 8.9
2. 14.5
3. 10.3
4. 18.8
5. 8.0
6. 15.0
(All to the nearest tenth)
The code is the sum of all missing sides
So adding all
=75.5
Plz help me anyone it’s being timed
Answer:
consistent.
Step-by-step explanation:
if lines cross they're consistent. If they dont they're inconsistent and if they overlap completely they're equivalent
The sphere at the right fits snugly inside a cube with 18-in. edges. What is the approximate volume of the space between the sphere and cube?
Answer:
2,778 in³
Step-by-step explanation:
Volume cube
v = 18³
v = 5,832
Volume sphere
v = (4/3)π9³
v = 3,053.6280592893
Volume space
v = 5,832 - 3,053.6280592893
v = 2,778.3719407107
2,778 in³
Answer:
Step-by-step explanation:
We need to first find the volume of the cube, then subtract from it the volume of the sphere. This is what we are being asked to find. First, the volume of the cube is length times width times height. Since this is a cube, all of the sides are the same length, making the volume
V = 18³ so
V = 5832 inches cubed. Now for the sphere.
The formula for the volume of a sphere is
[tex]V=\frac{4}{3}\pi r^3[/tex] and we will use 3.1415 for π.
[tex]V=\frac{4}{3}(3.1415)(9)^3[/tex] which gives us
V = 3053.538
Subtracting the volume of the sphere from the volume of the cube:
V = 5832 - 3053.538
V = 2778.462 inches cubed
The weight of oranges growing in an orchard is normally distributed with a mean weight of 5 oz. and a standard deviation of 0.5 oz. From a batch of 1500 oranges, how many would be expected to weight less than 5 oz., to the nearest whole number?
Answer:
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 6
Standard deviation = 0.5
Middle 95% of weights:
By the Empirical Rule, within 2 standard deviations of the mean.
6 - 2*0.5 = 5
6 + 2*0.5 = 7
The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.
what divided by 6 = 0.2
Answer:
6 divided by 30 is equal to 0.2.
Step-by-step explanation:
You make the fraction into 6/30, you reduce it to 1/5 which then you do 1 divided by 5 which also gets you to 0.2.
im giving points and brainliest
Answer:
cool
Step-by-step explanation:
ok
-4i+ 3i= i- 8+ 3i- 12
Answer:
Step-by-step explanation:
-4i+3i=i-8+3i-12
-i=4i-20
20=4i+i
20=5i
20/5=i
4=i
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Please help me!
Find the indicated sum for each sequence.
S9 of –9, 36, –144, 576, ...
Answer:
the answer is to multliply it by -4
This is for math pls help I need this done
Answer:
its upside down turn it around
Step-by-step explanation:
please help if i don't pass I'm done
Answer:
500cm^3
Step-by-step explanation:
Can be divided intI a square and cuboid
Volume of square= Length^4
Volume= 5^3
V=125cm^3
Volume of cuboid= L× B × H
Volume= 15× 5× 5
Volume=375cm^3
375+125= 500
is 3 bigger than 3.3
Answer:
No.
Step-by-step explanation:
3.3 is bigger than 3 by .3: )
Answer:
no.
3.3 > 3
Step-by-step explanation:
4x+2=-13 solve for x
Answer:
Solution given
4x+2=-13
subtract each term by 2
4x+2-2=-13-2
divide both side by 4
4x/4=-15/4
we get
x=-15/4
is a required answer.
Let's solve:
[tex]4x+2=−13[/tex]
Step 1: Subtract 2 from both sides.
[tex]4x+2−2=−13−2 \\ 4x = - 15[/tex]
Step 2: Divide both sides by 4.
[tex] \frac{4x}{4} = \frac{ - 15}{4} [/tex]
Answer:
[tex] \frac{ - 15}{4} [/tex]
(trigonometry) solve for x
Answer:
x around 53.7
Step-by-step explanation:
We use cosine^-1 to solve for x
In the calculator put in cos^-1 (16/27)
What is the slope of the line shown below?
Answer: b
Step-by-step explanation:
someone please help with this!! 10 points available!!
The approximate volume is ___ cubic centimeters. Do not round your answer.
Use 3.14 for π.
Answer:
19329.84
Step-by-step explanation:
3.14×18 which is squared so it 324×19
3.14×324×19= answer
Simplify.
7/8 x 1 1/3
A. 7/24
B. 28/24
C. 1 1/6
D. 1 7/24
Solve the angle using trigonometry
Answer:
Step-by-step explanation:
Um angle T and R don't exist on this triangle. Only sides and Angles A B C.
But remember Sin = Opposite / Hypotenuse
Cos = Adjacent / Hypotenuse
Tan = Opposite / Adjacent
S o/h C a/h T o/a
Please help me ASAP And show work please
Answer:
X = 11
Step-by-step explanation:
3^(x-7) = 81
Find what exponent makes three into 81
The answer: x = 11
Answer:
x = 11
Step-by-step explanation:
Given
[tex]3^{x-7}[/tex] + 4 = 85 ( subtract 4 from both sides
[tex]3^{x-7}[/tex] = 81
[tex]3^{x-7}[/tex] = [tex]3^{4}[/tex]
Since the bases on both sides are equal, both 3 then equate the exponents
x - 7 = 4 ( add 7 to both sides )
x = 11
Anyone please I need Help plssssss
Answer: 1/8
1 goes in the green blank space
8 goes in the gray blank space
========================================================
Explanation:
H = heads
T = tails
HHH means we get 3 heads in a row, HHT means heads twice then tails the third time, and so on.
Here are the 8 ways to flip three coins (note: 2^3 = 2*2*2 = 8).
HHHHHTHTHHTTTHHTHTTTHTTTWe see that HHH only comes up once out of 8 total times. Therefore, the probability of getting HHH is 1/8
------------
Another way to see the answer is note that P(H) = 1/2 is the probability of getting heads on a single coin flip
Then with two coin flips, we have P(HH) = P(H)*P(H) = (1/2)*(1/2) = 1/4. Each coin flip is independent of one another.
And finally, P(HHH) = P(H)*P(H)*P(H) = (1/2)*(1/2)*(1/2) = 1/8
Priyah’s weekly earnings were proportional to the number of hours she worked. The table shows the number of hours Priyah worked and the amount she earned. How much money did Priyah earn per hour?
Answer:
$17.50 is how much Priyah makes per hour
Explain how
you know you would use sine, cosine or tangent to
solve this. Explain thorougly
C
X
10
B В
Answer:
To solve for x, I would use Cosine.
This is because cosine holds the ratio of adjacent/hypotenuse. Based on the diagram, we can see that HYPOTENUSE = x, so we are solving for x. We know the angle, is 17 degrees. Lastly, we know the triangle leg ADJACENT to the angle is 10 units long. So we would use cosine, implementing the ratio adjacent/hypotenuse. Solving this, we would use cos(17)=10/x. Then our goal is to isolate x, so cos(17)=10/x becomes cos(17)*x=10, we are still trying to isolate x, so, x=10/cos(17). Therefore, our answer x = 10.457 units. cosine would be the best way to go.
Step-by-step explanation: