A box manufacturer is to make a closed box of volume 288in3, where the base is a rectangle whose length is three times its width. What is the length of the box that uses the least amount of material

The time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

To find the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (triple the initial deposit)

P = Principal amount (initial deposit)

r = Annual interest rate (6.1% or 0.061 as a decimal)

n = Number of times interest is compounded per year (weekly compounding means n = 52)

t = Time in years

In this case, we have:

A = 3P (triple the initial deposit)

P = P100,000

r = 0.061

n = 52

t = Time (unknown)

Substituting these values into the formula, we have:

3P = P(1 + r/n)^(nt)

Simplifying further, we get:

3 = (1 + 0.061/52)^(52t)

To isolate t, we can take the natural logarithm (ln) of both sides of the equation:

ln(3) = ln((1 + 0.061/52)^(52t))

Using the logarithmic property, we can bring down the exponent:

ln(3) = 52t * ln(1 + 0.061/52)

Now we can solve for t:

t = ln(3) / (52 * ln(1 + 0.061/52))

Using a calculator, the value of t comes out to approximately 6.12 years (rounded to two decimal places).

Therefore, the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

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The perimeter of the hexagon is the sum of its side lengths

The perimeter of the hexagon is 48.5 ft

The given parameters are:

\(\mathbf{Area = 169.74}\) --- the area of the hexagon

\(\mathbf{a = 7}\) -- the apothem

Let the perimeter of the hexagon be p.

So, the area is calculated as:

\(\mathbf{Area = \frac 12 pa}\)

Substitute values for Area and (a)

\(\mathbf{169.74 = \frac 12 \times p \times 7}\)

Multiply both sides by 2

\(\mathbf{339.48= p \times 7}\)

Divide both sides by 7

\(\mathbf{48.5= p }\)

Rewrite as:

\(\mathbf{p = 48.5}\)

Hence, the perimeter of the hexagon is 48.5 ft

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Answer:

Read the explanation down

Step-by-step explanation:

This is a linear equation, because the equation does not have any exponents. Graph it by putting the equation into either slope-intercept form y=mx+b or point-slope form y−y1=m(x−x1).

Isolate y by first adding 6x to each side:

9y=6x−18

Divide each side by 9:

y=23x−2

Now graph the line y=23x−2 by first plotting the y intercept at (0,−2), then connecting points with a slope of 23.

graph{2/3x-2 [-10, 10, -5, 5]}

Answer:

425

Step-by-step explanation:

The curve that has a slope of 3 when x = 2 is y = 3x² - x - 2.

The curve that has a slope of 3 when x = 2 is y = 3x² - x - 2.

Step-by-step explanation: Given curves:

y = 3exy = 0y= 43y = - 3 - 2 ln xy = x² - 13x²2 - xy = 3x² - x - 2

Differentiate all the curves one by one with respect to x:y = 3exdy/dx = 3ex, when x = 2, y = 3e2

therefore slope = 3e2y = 0dy/dx = 0.

There is no slopey = 43dy/dx = 0.

There is no slopey = - 3 - 2 ln xdy/dx = -2/x, when x = 2, y = -3 - 2 ln 2, slope = -2/2 ln 2 = -1.4427y = x² - 1dy/dx = 2x, when x = 2, y = 3, slope = 4y = 3x² 2 - x - 2dy/dx = 6x - 1, when x = 2, y = 10, slope = 11

Therefore, the curve that has a slope of 3 when x = 2 is y = 3x² - x - 2.

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The curve with a slope of 3 when x = 2 is y = x² - 1.

The slope of a curve at a point is the tangent to the curve at that point.

To find the slope at the point where x = 2, we must first find the derivative of each curve.

The derivative will give us the slope of the tangent to the curve at any point, including the point where x = 2.

Then, we can substitute x = 2 into the derivative and find the slope.

The correct answer is y = x² - 1.To find the derivative of each curve, we use differentiation rules as follows:

dy/dx = 3e^x

dy/dx = 0

dy/dx = 0

dy/dx = -2/x + 0

dy/dx = 2x

For the curve y = x² - 1,

we have dy/dx = 2x.

Substituting x = 2 into the derivatives of each curve, we get:

dy/dx = 3e²

dy/dx = 0

dy/dx = 0

dy/dx = -2/2 + 0

= -1

dy/dx = 2(2)

= 4

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Answer:    $1,147.20.

Step-by-step explanation:

The total amount accrued for principal plus interest in the calculation simple interest

= principal * (1+ rate * number of years)

= $800 *(1+ 6.2% * 7)

= $1,147.20.

Hopefully his helped, if not HMU and I will try my best to get u a better answer! :)

It is enough for him to use a simple random sample of 172 cars.

It is required that there are at least 10 successes and 10 failures to test a hypothesis that involves a proportion p in a sample of size n.

Following conditions are required for it:

1) np ≥ 10

2) n (1-p) ≥ 10

p = 6% = 0.06

n = 172

So, there are at least 10 successes and 10 failures in the 172 cars sample, it is enough for him to use a simple random sample of 172 cars.

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Answer:

She lives in the Southern Hemisphere.

Step-by-step explanation:

Did you figure it out?

To prove that triangle FGE and triangle IJH we need information like the two sides of each triangle and the included angle to be congruent.

To prove two triangles are similar by the SAS is that you need to show that two sides of one triangle are proportional to two corresponding sides of another triangles, with the included corresponding angles being congruent.

For the SAS postulate you need two sides and the included angle in both triangles.

Side-Angle-Side (SAS) postulate:-

If two sides and the included angles of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. SAS postulate relate two triangles and says that two triangles are congruent if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle.

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Answer: mg they left u hanging for some time here hol up,

y=−25

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y/5-2-(-7)=0

y/5          

(y/5 -  2) -  -7  = 0  

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

   2 =  2/1=2.5/5

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

y - (2.5/5 5)=y - 10

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 y+25

 ———— • 5 = 0 • 5

  5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  y+25  = 0

4.2      Solve  :    y+25 = 0  

Subtract  25  from both sides of the equation :  

                     y = -25

9514 1404 393

Answer:

  log(35)/log(7)

Step-by-step explanation:

The change of base formula is ...

  \(\log_b(a)=\dfrac{\log(a)}{\log(b)}\)

You have b=7, a=35, so the rewrite is ...

  \(\log_7(35)=\boxed{\dfrac{\log(35)}{\log(7)}}\)

Answer:

∠ ADC = 122°

Step-by-step explanation:

ABCD is a cyclic quadrilateral.

opposite angles in a cyclic quadrilateral sum to 180° , that is

∠ ADC + ∠ ABC = 180∠

∠ ADC + 58° = 180° ( subtract 58° from both sides )

∠ ADC = 122°

Answer:

7 + 2s = 15

4 shirts

Step-by-step explanation:

Let's say w denotes sweaters and s denotes shirts.

Since there are 7 more sweaters than shirts:

w = 7 + s

There are a total of 15 sweaters and shirts in all, so:

w + s = 15

Substitute 7 + s in for w in the second equation:

w + s = 15

7 + s + s = 15

7 + 2s = 15

Solving for s:

7 + 2s = 15

2s = 15 - 7 = 8

s = 8/2 = 4 shirts

Thus, the equation is 7 + 2s = 15, and there are 4 shirts.

~ an aesthetics lover

The given vectors are:
Vector A = (-11, b, 2)
Vector B = (b, b^2, b)

The values of b for which the given vectors are orthogonal are 0, -3, and 3.

To find the values of b for which the given vectors are orthogonal, we need to use the dot product of the vectors.

To determine if two vectors are orthogonal, their dot product should be equal to zero.

The dot product is calculated as follows:

Dot Product (A, B) = A1 * B1 + A2 * B2 + A3 * B3

Substituting the components of Vector A and Vector B:

(-11 * b) + (b * b^2) + (2 * b) = 0

Now, simplify the equation:

-11b + b^3 + 2b = 0
b^3 - 9b = 0

Factor the equation:

b(b^2 - 9) = 0

Now, we can find the values of b:

b = 0
b^2 - 9 = 0
b^2 = 9
b = ±3

So, the values of b for which the given vectors are orthogonal are 0, -3, and 3.

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The angle a = 12.3699 degrees can be converted to degrees, minutes, and seconds form as follows: 12 degrees, 22 minutes, and 11.64 seconds.

To convert the angle a = 12.3699 degrees to degrees, minutes, and seconds form, we need to separate the whole number of degrees, minutes, and seconds.

First, we take the whole number of degrees, which is 12.

Next, we focus on the decimal part, 0.3699, which represents the remaining minutes and seconds.

To convert the decimal part to minutes, we multiply it by 60. So, 0.3699 * 60 = 22.194.

The whole number part of 22.194 represents the minutes, which is 22.

Finally, we need to convert the remaining decimal part, 0.194, to seconds. We multiply it by 60, which gives us 0.194 * 60 = 11.64.

Therefore, the angle a = 12.3699 degrees can be expressed as 12 degrees, 22 minutes, and 11.64 seconds when written in degrees, minutes, and seconds form.

Note that in the seconds part, we kept two decimal places for accuracy, but it can be rounded to the nearest whole number if desired.

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At STP (standard temperature and pressure), the molar volume of an ideal gas is 22.4 L/mol. To calculate the grams of Ne (neon) gas in 25.0 L, we first need to find the moles of Ne gas and then convert it to grams using its molar mass.

1. Find moles of Ne:
25.0 L Ne * (1 mol Ne / 22.4 L) = 1.1161 mol Ne

2. Convert moles to grams:
Ne has a molar mass of 20.18 g/mol.
1.1161 mol Ne * (20.18 g/mol) = 22.51 g Ne

Answer: There are 22.51 grams of Ne contained in 25.0 L of Ne gas at STP.

Part B:
To find the volume in liters occupied by 32.0 g of Ar (argon) gas at STP, we first need to find the moles of Ar gas and then convert it to volume using the molar volume at STP.

1. Find moles of Ar:
Ar has a molar mass of 39.95 g/mol.
32.0 g Ar * (1 mol Ar / 39.95 g) = 0.8010 mol Ar

2. Convert moles to volume:
0.8010 mol Ar * (22.4 L/mol) = 17.94 L Ar

Answer: 32.0 g of Ar gas occupies 17.94 liters at STP.

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The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.

First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.

Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.

Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.

Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.

Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸

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Answer:

0.65g

Step-by-step explanation:

Decay rate = 50%

Decay rate = 0.5

\(A = Aoe {}^{ - kt} \)

where Ao = initial amount at start, k = rate of decay or growth, t = time, e = euler's number and A = value at time 't'

Ao = 4.8

t = 88/44 = 4

k = 0.5

substitute these values in the equation

\(A = 4.8e {}^{ - 0.5 \times 4} \)

\(A = 0.6496\)

\(A = 0.65 \: (2dp)\)

At the start of the maze, the value of d, representing the direction the robot is facing, would be 1

Based on the given information, the arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. In programming the robot, let the complex number d represent the direction the robot is facing.

In the complex plane, the positive real axis (usually the rightward direction) corresponds to the positive real number line, and the positive imaginary axis (usually the upward direction) corresponds to the positive imaginary number line.

Since the arrow at the maze entrance indicates that the robot will be heading east, we can represent this direction as a complex number. In the complex plane, the eastward direction can be represented by the positive real axis, which corresponds to the positive real number line.

Therefore, at the start of the maze, the value of d, representing the direction the robot is facing, would be 1.

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Answer:

1. x = z / y + w, x ≠ 0

2. x = z / y + w

3 (Simularities). They are both simular because the second equation includes the same properties but with an x in each part of the question except for the answer.

(Also people at brainly are on here 24/7 doesn't matter what day it is <3)

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

Answer:

m = -2

Step-by-step explanation:

slope of AB

(4-3)/(-1-2)= 1/-3 = -1/3

parallel lines have the same slope

slope of CD = -1/3

we can now find the line that passes through the point C

y-5= -1/3(x-4)

y = -1/3 x +4/3 +5

y = -1/3 x + (4+15)/3

y = -1/3 x + 19/3

this line must passes also through the point D

we know its y, so:

7 = -1/3 x + 19/3

(7 * 3) = (-1/3 x + 19/3) * 3

21 = - x + 19

x = 19 - 21

x = -2

Based on the information provided, the suggested interval (0 < x < 2) could potentially be an interval during which the water balloon's height is increasing.

In general, if the height of the water balloon is increasing, it means that as time progresses, the height of the balloon is getting larger. This corresponds to a positive rate of change of the height with respect to time.

If we have a function that describes the height of the water balloon over time, we can calculate the derivative of that function with respect to time. If the derivative is positive within the interval (0 < x < 2), it means that the height is increasing during that interval.

However, without the specific function or more information, it is not possible to determine with certainty whether the water balloon's height is increasing within the given interval.

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Answer:

\(\frac{1}{36}\)

Step-by-step explanation:

The probability of rolling a 4 is 1/6.

Using the multiplication rule, the required probability is \((1/6)^2=\frac{1}{36}\).

Step-by-step explanation:

1235

Now when we talk about place values we have ones tens hundreds thousands ten thousands and so on. So when you look at no.1 its place value is ones because 1 is the first value.

So 2 is in tens.

Now the difference of tens and hundreds is tens follows the 2 place value and hundreds the next.

HOPE ITS HELPFUL

Answer:

4544

Step-by-step explanation:

The underlined sentence means that the 2nd and third values must be different, for example

4554 has 5 in the 2nd and 3rd place so cannot be this

4545 and 4544 have 4 and 5 in 2nd/3rd place so this is fine

Since the number is even then it is 4544

Answer:

Step-by-step explanation:

are the what???

Answer: x =400

Step-by-step explanation:

Answer:

180 + 0.4x = 400

Answer:

2/3=More

1/4=less

7/8=more

2/6=less

2/4=equal

Step-by-step explanation:

Look at each model that shows each fraction and also look at the denominators and the numerators of each fraction.

#1

Greater than 1/2

#2

Less than 1/2

#3

Greater than 1/2

#4

Less than 1/2

#5

Equal to 1/2