How much would the volume of this cube decrease if you reduced the length of each side by 3 cm?

Answer:

1080 total inches of ribbon. 60 pieces of ribbon can be cut.

Step-by-step explanation:

Firstly, the dressmaker has 15 rolls of ribbon that are 6 feet in length. Multiply those to see how many feet in total, 90. Then multiply this by 12 (there are 12 inches in a foot) to get the amount of total inches: 1080.

This is the answer to the question below the problem.

To answer the bigger question at hand:

You would need to take 1080 divided by 18 to find how many pieces the dressmaker can cut. She can cut exactly 60 pieces from her 15 rolls of ribbon.

By definition, a trinomial is an algebraic expression that has 3 terms.

In the given polynomial:

We can identify the following terms:

Then, we can say it is a trinomial.

Answer:

A=L*W

Let w be width

L=(w+6)

40=(w+6)*w

40= w^{2} +6w

w^{2} +6w-40=0

w^{2}+10w-4w-40=0  

w(w+10)-4(w+10)=0

(w-4)(w+10)=0

w=4

Length= 10 units

Width=4 units

Step-by-step explanation:

Solution to the differential equation is y = y_h + y_p = c1 cos(x) + c2 sin(x) + (1/2)(sin(x) + x

We first find the solutions to the homogeneous equation y'' + y = 0, which has characteristic equation r^2 + 1 = 0. The roots are r = ±i, so the general solution to the homogeneous equation is y_h = c1 cos(x) + c2 sin(x).

To find the particular solution using variation of parameters, we let y_p = u1(x) cos(x) + u2(x) sin(x). Then we have y_p' = u1' cos(x) + u2' sin(x) + u1(-sin(x)) + u2 cos(x) and y_p'' = -u1 cos(x) - u2 sin(x) + u1'' cos(x) + u2'' sin(x) + 2u1'(-sin(x)) + 2u2' cos(x).

Substituting y_p and its derivatives into the differential equation, we get:

(-u1 cos(x) - u2 sin(x) + u1'' cos(x) + u2'' sin(x) + 2u1'(-sin(x)) + 2u2' cos(x)) + (u1 cos(x) + u2 sin(x)) = sec(x)tan(x)

Simplifying and equating coefficients, we get the system of equations:

u1'' cos(x) + u2'' sin(x) - u1' sin(x) + u2' cos(x) = 0

u1'' sin(x) - u2'' cos(x) - u1' cos(x) - u2' sin(x) = sec(x)tan(x)

Solving for u1'' and u2'' and substituting them into the first equation, we get:

(u1' sin(x) - u2' cos(x))' = 0

Integrating both sides, we get:

u1' sin(x) - u2' cos(x) = C1

for some constant C1. Differentiating this equation and substituting it into the second equation, we get:

C1 cos(x) + u1 sin(x) + u2 cos(x) = sec(x)tan(x)

Simplifying, we get:

u1 sin(x) + u2 cos(x) = sec(x)tan(x) - C1 cos(x)

To find u1 and u2, we differentiate this equation and use the fact that u1' sin(x) - u2' cos(x) = C1:

u1' cos(x) + u1 sin(x) - u2' sin(x) - u2 cos(x) = sec(x)sec(x)

Simplifying and using the identity sec^2(x) = 1 + tan²(x), we get:

u1' cos(x) - u2' sin(x) = 1 + tan²(x) - C1 cos(x)

Multiplying the first equation by cos(x) and the second equation by sin(x) and adding them, we get:

u1' = (1 + tan²2(x))cos(x) - C1 sin(x)

u2' = (1 + tan²(x))sin(x) + C1 cos(x)

Integrating these expressions, we get:

u1 = (1/2)(sin(x) + xcos(x)) - C1cos(x) + C2

u2 = -(1/2)(cos(x) - xsin(x)) + C1sin(x) + C3

Therefore, the general solution to the differential equation is:

y = y_h + y_p

= c1 cos(x) + c2 sin(x) + (1/2)(sin(x) + x

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Answer:

the answer is *a sorry if wrong

The type of statistical technique that is employed in future predictions of outcomes based on presented data is: C. linear regression.

Linear regression can be described as a statistical technique that is used to make future predictions using the regression equation of a line of best fit that models the relationship between variables Y and X.

Through the regression equation, outcomes of the future can be predicted. This statistical technique is known as: C. linear regression

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Y would be undefined as any value because x is always equal to to, so y can be any number

Answer:

28 m,  112 m

Step-by-step explanation:

x = length of short piece

4x = length of long piece

x + 4x = 140

5x = 140

x = 140/5 = 28

4x = 4(28) = 112

The common denominator of the fractions is 24. Therefore:

\( \bold{4 + \dfrac{3}{8} - \dfrac{2}{6 } = \dfrac{96}{24} + \dfrac{9}{24} - \dfrac{8}{24} = \dfrac{96 + 9 - 8}{24} = \dfrac{97}{24} } \)

Since, once reduced to a common denominator, the sum of fractions is limited to the sum of their denominators (integers), the properties of the addition of rational numbers are the same as those of the addition of integers.

Answer:

x = 31; AB = 74

Step-by-step explanation:

if ABC = JKL then AB = JK

2x + 12 = 4x - 50

2x + 12 - 4x + 50 = 0

- 2x = - 62

x = 31

AB = 2 * 31 + 12 = 62 + 12 = 74

Answer: the height of the pole is 16.782 meters

Step-by-step explanation: Let us take the height of the pole as "h".

i) Finding the height of the pole:

distance from the pole is 20m.

The angle of elevation is 40°

\(tan(40°) = h/20\)

Multiply both sides by 20:

\(20 * tan(40°) = h\)

\(h ≈ 20 * 0.8391 ≈ 16.782 meters\)

Therefore, the height of the pole is 16.782 meters.

ii) Finding the angle of depression

The angle of depression is the angle formed between the horizontal ground and the line of sight from the point of observation to the foot of the pole.

angle of depression = angle of elevation = 40°

Therefore, the angle of depression of the foot of the pole from the point of observation is 40°.

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Using trigonometric methods, it is determined that the height of the pole is found by using the formula for tangent, and adding the height of the observer. The angle of depression equals the angle of elevation, so both are 40 degrees.

To solve the problem, we use the properties of a right triangle and trigonometric functions. Since we know the angle of elevation and the length of one side, we can find the length of the other side using the tangent function.

For the height of the pole: we know that tan(θ) = opposite/adjacent, so,
tan(40) = height/20
height = tan(40) * 20

Let's denote the observer's height as h=1.54m, so the total height of the pole is height + h.

For the angle of depression: In a right triangle, the angle of depression and the angle of elevation are equal. Therefore, the angle of depression is also 40 degrees.

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Therefore, the indefinite integral of the given function is x^3 + (4/3)x^4 - (4/9)x^(9/2) + C, where C is the constant of integration.

We can begin by simplifying the integrand as follows:

x^2(3 + 4x - 4x^(3/2)) dx

= 3x^2 dx + 4x^3 dx - 4x^(7/2) dx

= x^3 + (4/3)x^4 - (4/9)x^(9/2) + C

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The minimum sample size needed to estimate the population mean with a 98% confidence interval, a population standard deviation of 8.8, and a margin of error of 1 is 421.

the minimum sample size n needed to estimate u for the given values of c, o, and E is 458. This means that we would need to collect data from at least 458 individuals in order to obtain a sample mean that is within 1 unit of the population mean with 98% confidence, assuming a population standard deviation of 8.8.

To find the minimum sample size n needed to estimate the population mean (µ) with a confidence level (C) of 0.98, a population standard deviation (σ) of 8.8, and a margin of error (E) of 1, follow these steps: Determine the confidence level: C = 0.98, which implies a 98% confidence interval. Identify the corresponding z-score for the given confidence level: For a 98% confidence interval, the z-score is 2.33 Use the formula for the minimum sample size n: n = (Z * σ / E)²
Plugging in the given values: n = (2.33 * 8.8 / 1)² n = (20.504 / 1)² n ≈ 420.16 Since the sample size must be a whole number, round up to the nearest whole number: n = 421.

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Answer:

Here is the answer.

Step-by-step explanation:

Answer:

(-3.5,-6.5)

Step-by-step explanation:

Like terms are those terms that are having the same variables and order. The simplified form of the given equation 7z+2=8+2z+1z is 4z=6.

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

The given equation to us is 7z+2=8+2z+1z, simplifying the equation we will get,

\(7z + 2 = 8 + 2z + 1z\\\\\text{Bring the like terms on the same side of the equation}\\\\7z -2z-1z = 8 -2\\\\7z-3z=6\\\\4z = 6\)

Hence, the simplified form of the given equation 7z+2=8+2z+1z is 4z=6.

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Answer:

47

Step-by-step explanation:

Answer:

logx a + logx b

Step-by-step explanation:

Answer:

Answer: The arc PS would be a minor arc · Step-by-step explanation: As a minor arc is one that is less that 180 degrees, it would be the only viable ...

If the Wilson family drove 472 miles in 8 hours. The family that traveled at the higher rate of speed  and  rate is: D: Wilson; 59 mi/h

Using this formula to find the speed

Speed = Distance /Time

Let plug in the formula

Rate of speed for Gonzalez family

Rate of speed  = 342 ÷ 6

Rate of speed = 57 mph

Rate of speed  for Wilson family

Rate of speed = 472 ÷ 8

Rate of speed = 59 mph

Therefore the correct option is D.

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Answer:

Dylan must spend 45 minutes of his time on studies.

Step-by-step explanation:

Natasha gets 30 minutes less than Dylan. Total there can be 1 and half hour for studies which means there are 90 minutes for the studies. Dylan must spend half of his time on his studies.

90 minutes * 50% = 45 minutes.

Answer:

Step-by-step explanation:

Straight line equation is in the form of:

Lets verify the options:

Answer:

4x+31

Step-by-step explanation:

2(x + 4) – 3(x – 6) + 5(x + 1)

Distribute

2x+8 -3x+18 +5x +5

Combine like terms

2x-3x+5x  +8+18+5

4x+31

Answer:

y=1/3x

Step-by-step explanation:

the slope (rise/run) is 1/3 and the y-intercept ("b" in y=mx+b) is just 0, so you dont have to write it

Answer:

x = 20

Step-by-step explanation:

Hello!

Solve for x by isolating the variable.

The value of x is 20.

The value of x when the scale factor of Figure A to Figure B is 4:5 is 12.

Therefore, the answer is 12.

Scale factor is the ratio of corresponding dimensions of an object to another object. If scale factor is less than 1, it is scaling down of the figure and if the scale factor is greater than 1, it is scaling up of the figure. Here the ratio is 4:5, so it is less than 1.

As the scale factor is 4:5, the ratio of corresponding sides is 4 is to 5.

That is x/15 = 4/5.

Therefore, x = 4/ 5 × 15

x = 12

-- The question is incomplete without the figure, the complete question is:

__If the scale factor of Figure A to Figure B is

4:5, find the value of x.__

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π/16 is the area enclosed by the curve r= sin(4θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(4θ) =0

=> sin(4θ) =0

=> 4θ = 0,π

=> θ = 0, π/4

so a=0 , b= π/4

now  

  A =  \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)   ------(i)

so   \(r^2\) = (sin(4θ))^2

=>   \(sin^2\)( 4θ )

ans we know that

cos(2α) = 1 -  \(2sin^2\)2 α

so     \(sin^2\)= (1- cos(8θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)

=> 1/4*  \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)

here a=0 and b=π/4

after putting the value and solving the integral

A = π/16

so A is the area enclosed by r=sin(4θ) is π/16

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At the upper triple point, solid graphite, liquid carbon, and gaseous carbon dioxide coexist in equilibrium.

In a phase diagram for carbon, the upper triple point represents a specific combination of temperature and pressure where all three phases of carbon—solid (graphite), liquid (carbon), and gas (carbon dioxide)—coexist in equilibrium.

At this point, there is a delicate balance between the three phases, and any deviation from the exact temperature and pressure values would cause one or more phases to dominate.

The upper triple point is a unique set of conditions where solid graphite, liquid carbon, and gaseous carbon dioxide can exist simultaneously.

It's important to note that the precise values of temperature and pressure at the upper triple point may vary depending on the specific phase diagram being referenced.

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Answer:

3/13 which is 0.23 as a decimal

Step-by-step explanation: