A closed box with a square base is to have a volume of 16000 cubic centimeters. The material
for the top and bottom of the box costs $3 per square centimeter while the material for the sides
costs $1.50 per square centimeter. Find the dimensions of the box that will minimize the total
cost of materials. What is the minimum total cost?

Answer:

Step-by-step explanation:

why is it so hard omg

Proportionately, if they do half and half of 50% and 80% of the two bags, Bob is correct.

A proportion is a mathematical measure that compares two variables or numbers.

Proportions can be stated in percentages or ratios, as decimals or fractions.

Content of 16-ounce bag of nuts = 60% chocolate-covered nuts

Content of first bag = 50/50 plain and chocolate-covered nuts

Content of second bag = 80% chocolate-covered nuts

A mixture of half of 50% bag with half of 80% bag will result in 65% (50% + 80%)/2.

Thus, since the promise for each 16-ounce bag is for at least 60% chocolate-covered nuts, Bob is correct.

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Is Bob correct?

When [tex]n=1[/tex],

[tex]10^{2\cdot1 - 1} + 1 = 10^1 + 1 = 11[/tex]

which is of course divisible by 11.

Assume this holds for [tex]n=k[/tex], that

[tex]11 \mid 10^{2k - 1} + 1[/tex]

In other words,

[tex]10^{2k - 1} + 1 = 11\ell[/tex]

for some integer [tex]\ell[/tex].

Use this to show the claim is true for [tex]n=k+1[/tex].

[tex]10^{2(k+1) - 1} + 1 = 10^{2k + 1} + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k+1} + \left(10^{2k-1} + 10^{2k-1}\right) + 1 \\\\ ~~~~~~~~~~~~~~~~~~~~ = \left(10^{2k+1} - 10^{2k-1}\right) + \left(10^{2k-1} + 1\right) \\\\ ~~~~~~~~~~~~~~~~~~~~ = 10^{2k-1} \left(10^2 - 1\right) + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 99\times10^{2k-1} + 11\ell \\\\ ~~~~~~~~~~~~~~~~~~~~ = 11\left(9\times10^{2k-1} + \ell\right)[/tex]

which is indeed divisible by 11. QED

On the off-chance you meant [tex]10^{2^n-1}+1[/tex], notice that [tex]2n-1[/tex] is odd for any integer [tex]n[/tex]. Similarly [tex]2^n-1[/tex] is odd for all [tex]n[/tex], so the above proof actually proves this automatically.

9x - 4(x - 2) =x + 20

We move all terms to the left:

Multiply

We get rid of the parentheses.

We add all the numbers and all the variables.

We move all terms containing x to the left hand side, all other terms to the right hand side

The table that represents exponential growth is the second table.

Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.

In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the Xs increase by 1, the Ys increase by a multiple of 4.

One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.

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Answer: B

Step-by-step explanation:

❄ Hi there,

keeping in mind that the sum of complementary angles is 90°,

set up an equation, letting [tex]\angle2[/tex]  be x  –

[tex]\triangleright \ \sf{\angle1+x=90}[/tex]                 {and we know that [tex]\boxed{\angle1=45}[/tex]}

[tex]\triangleright \ \sf{45+x=90}[/tex]

[tex]\triangleright \ \sf{x=90-45}[/tex]

[tex]\triangleright \ \sf{x=45}[/tex]

[tex]\triangleright \ \sf{\angle2=45\textdegree}[/tex]

      __________

Keeping in mind that a right angle is 90°,

set up an equation, letting [tex]\angle1[/tex] be x:

[tex]\triangleright \ \sf{x+\angle2=90}[/tex]                       {and we know that [tex]\boxed{\angle2=63}[/tex]}

[tex]\triangleright \ \sf{x+63=90}[/tex]

[tex]\triangleright \ \sf{x=27}[/tex]

[tex]\triangleright \ \sf{\angle1=47\textdegree}[/tex]

❄

Answer:(5-1)(7-1)

Step-by-step explanation:

We have give 4 numbers that are 1,1,5,7. we have to apply operations on it to make it 24.

» ( 7 - 1) × (5 - 1)

» (6) × (4)

» 24

Here's our answer..!!

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]x + y = 10\implies y = -x+10\implies y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+10 \leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so, we're really looking for the equation of al ine whose slope is -1 and that passes through (-1 , 5)

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{-1}( ~~ x-\stackrel{x_1}{(-1) ~~ }) \\\\\\ y-5 = -(x+1)\implies y-5=-x-1\implies y=-x+4[/tex]

There are different ways to construct an angle. The steps used in making a line segment are; First, you have to put the compass at one specific end of the line segment. Then you shift the compass slowly a little bit so it will be longer than half the length of the line segment. Then you have to draw arcs up and down the line. while using the same compass width, you then draw arcs from one specific end of the line. and thereafter you put your ruler at the point where the arcs cross, and you then draw the line segment. The difference is that to bisect an angle, one has to divide the shape or angle into two congruent parts while in the construction of a line segment, there are differences in length. What is the construction process of Angles? This entails a good construction process in making angles. They are step-by-step processes used to produce detailed and exact geometric figures.

**Disclaimer** Hi there! I assumed the question is to represent W in terms of all other variables (P, L). The following answer corresponds to this understanding. If it is incorrect, please let me know and I will modify my answer.

Answer: W = (P/2) - L

Step-by-step explanation:

Given equation

P = 2L + 2W

Factorize 2 out

P = 2 (L + W)

Divide 2 on both sides

P / 2 = 2 (L + W) / 2

P / 2 = L + W

Subtract L on both sides

(P / 2) - L = L + W - L

[tex]\Large\boxed{W=\frac{P}{2} -L}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

[tex]\displaystyle{W = \dfrac{P}{2} - L}[/tex]

Step-by-step explanation:

To solve for W, we have to isolate the W-variable. First, we can factor the expression 2L + 2W to 2(L+W):

[tex]\displaystyle{P = 2(L+W)}[/tex]

Next, we'll be dividing both sides by 2:

[tex]\displaystyle{\dfrac{P}{2} = \dfrac{2(L+W)}{2}}\\\\\displaystyle{\dfrac{P}{2} = L+W}[/tex]

Then subtract both sides by L:

[tex]\displaystyle{\dfrac{P}{2} - L= L+W-L}\\\\\displaystyle{\dfrac{P}{2} - L= W}[/tex]

Therefore, we'll obtain W = P/2 - L.

Note that the given formula is perimeter formula of a rectangle where Perimeter = 2 * Length + 2 * Width.

So if we solve for W (Width) then we'll get Width = Perimeter / 2 - Length which can be useful to find width with given perimeter and length.

Last box

As it's 7:2

Difference between x and y must increase in big number as x and y increases

Option D is correct in that manner

Let's double check

Answer:

9:50 am

Step-by-step explanation:

because 10 x 60 is equal to 1 hour, so you get 600 seconds subtracted from 10am. 600 seconds is equal to 10 minutes. so 10 am - 10 minutes = 9:50am

[tex]s = c(1 + in) \\ s = 4000(1 + 0.03 \times 1) [/tex]

[tex]s = 4120.00[/tex]

Step-by-step explanation:

(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)

Answer: 40

Step-by-step explanation:

Sub x=4 into 3x²-2x+1

∴ 3(4)²-2(4)+1

=3(16)-8+1

=48-8+1

=40

Answer:

41

Step-by-step explanation:

substitute the x to 4

so 3(4)² - 2(4) + 1 = 41

Answer:

c

Step-by-step explanation:

consider points (0,2) and (-4,0)

slope=(0-2)/(-4-0)=-2/-4=1/2

y-intercept=2

y=mx+c

y=1/2 x+2

Answer:

y=1/2x+2

Step-by-step explanation:

answer

is true statement w= 4

The options Patel has to solve the quadratic equation 8x² + 16x + 3 = 0 is x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot.

8x² + 16x + 3 = 0

8x² + 16x = -3

8(x² + 2x) = -3

8(x² + 2x + 1) = -3 + 8

8(x² + 1) = 5

(x² + 1) = 5/8

(x + 1) = ± √5/8

x = -1 ± √5/8

Therefore,

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

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Answer: slope is 1/3

Step-by-step explanation: make a graph of y=1/3x+9

Answer:

√3/2

Step-by-step explanation:

This is compound angle of cosine

cos(11+19)

=cos(30)

=√3/2

There is no answer because there cannot be one to one function inverse.

With the use of formula, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams

First analyze the problem and represent them in exponential function. The decay rate is different from increase rate with minus and plus sign.

Given that a tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. Let

An exponential model representing the amount of Iodine-125 remaining in the tumor after t days will be

A = I( 1 - R%)^t

Let us use the formula to find the amount of Iodine-125 that would remain in the tumor after 60 days by substituting all the given parameters into the formula

A = 0.9 ( 1 - 1.15/100)^60

A = 0.9 ( 1 - 0.0115)^60

A = 0.9 ( 0.9885)^60

A = 0.9 x 0.4995

A = 0.45 grams

Therefore, the amount of Iodine-125 that would remain in the tumor after 60 days is 0.45 grams

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Answer:

1 section should be labelled "bilingual".

4 sections should be labelled "monolingual".

Step-by-step explanation:

If 20% of students in the school are bilingual, then 80% of students in the school are monolingual, since 100% - 20% = 80%.

If the spinner is to be divided into 5 equally sized sections, with each section labeled as "bilingual" or "monolingual" to represent the corresponding proportion of students in the school, then:

Bilingual

  20% of 5

= 20/100 × 5

= 100/100

= 1 section

Monolingual

  80% of 5

= 80/100 × 5

= 400/100

= 4 sections

Therefore:

The graph of the parabola can be seen in the image below.

We need to find some points on the parabola, and then draw a curve that connects them.

On the graph you already have the x-intercepts, so you already have two points.

Now let's get another point which is the vertex.

For our parabola:

[tex]y = -x^2 + 10x - 24[/tex]

The vertex is at:

[tex]x = -10/(2*-1) = 5[/tex]

Evaluating in x = 5 we get:

[tex]y = -5^2 + 10*5 - 24 = 1[/tex]

So we also have the point (5, 1), now we can just connect the points and get the parabola:

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Answer:

[tex]\frac{5}{100}\times35[/tex]

[tex]0.05\times35[/tex]

Step-by-step explanation:

Given:

Which of the following options have the same value as 5% 35, percent of 35?

Following Options:

[tex]5 \times 35[/tex]

[tex]\frac{5}{100}\times35[/tex]

[tex]0.5\times0.35[/tex]

[tex]0.05\times35[/tex]

[tex]\frac{5}{10}\times35[/tex]

Solve:

[tex]5[/tex] % [tex]= 0.05=\frac{5}{100}[/tex]

Thus the following options:

[tex]5 \times 35[/tex]           [ False x ]

5 does not equal 5%

[tex]\frac{5}{100}\times35[/tex]         [True √ ]

[tex]5[/tex]% [tex]=\frac{5}{100}[/tex]

[tex]0.5\times0.35[/tex]      [ False x ]

[tex]0.5 = 0.50[/tex]

[tex]0.05\times35[/tex]       [True √ ]

[tex]5[/tex]% [tex]= 0.05=\frac{5}{100}[/tex]

[tex]\frac{5}{10}\times35[/tex]          [ False x ]

[tex]\frac{5}{10}=0.50[/tex]

Therefore, the options [B] [tex]\frac{5}{100}\times35[/tex] and [D] [tex]0.05\times35[/tex] is True.

Kavinsky

Answer:

a. 33

Step-by-step explanation:

a straight line is 180° so

3x = 180 - 81

3x = 99

to find x divide by 3

x = 99/3

x = 33

Step-by-step explanation:

(2^2x²/xy²) for x=3 and y=2

we have

2^2(3)²/((3)(2²))

2^2(9)/((3)(4))

2^18/12

262144/12

21845.3

The value of  expression [tex]2^{2} x^{2}/xy^{2}[/tex]  for x=3 and y=2 is, 3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  [tex]2^{2} x^{2}/xy^{2}[/tex]

The value of expression when, x = 3 & y = 2

⇒  2²×3²/3×2²

⇒  3

Hence, The value is 3

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It can be said that the total amount of fuel that was used by Michael when he was away to his friends was 12 gallons.

The question said that the tank was full before he left to his friends. This was after he checked the gauge of the gas tank.

The question says that the required quantity needed to fill up this tank is 24 gallon. Hence if it is full, then the total gallon it had before he made this trip was 24 gallon.

Then we are told that he went ahead to check the gauge when he finished and was at home. The quantity of fuel he had at this time was 1/2 of what was there.

This would be 1/2 * 24

12

Hence he made use of 12 gallons when he was away.

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