1/4 (12-8x) = 2 / 3 (6x)

To find the height (x) of the right prism with a volume of 214.5 cubic feet, we need to know the base area (A) of the prism. Since you haven't provided the base shape or its dimensions, we cannot accurately calculate the height. However, once you have the base area (A), you can use the formula for the volume of a prism:

Volume = Base Area × Height

Rearranging to find the height (x):

Height (x) = Volume / Base Area

Plug in the volume (214.5 ft³) and the base area (A) to calculate the height:

x = 214.5 ft³ / A

If you provide the base shape and its dimensions, we can calculate the height for you.

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Answer:

16

Step-by-step explanation:

just use a mean absolute deviation calculator next time

Answer:

\(\dfrac{dy}{dx}=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}\)

Step-by-step explanation:

Note: I will provide links with descriptions/steps to each of the rules used in this differential equation at the bottom of this answer.

Given

\(-26x^2+4x^{39} y+y^9=-21\)

Find \(\dfrac{dy}{dx}\)

Differentiate the left side of the equation.

\(\dfrac{d}{dx}\left(-26x^2+4x^{39}y+y^9\right)= \dfrac{d}{dx}\left(-21\right)\)

Focus the left side of the equation.                                                         Apply the Sum Rule for derivatives.

\(\dfrac{d}{dx} \left[-26x^2\right]+\dfrac{d}{dx} \left[4x^{39}y\right]+\dfrac{d}{dx} \left[y^9\right]\)

Lets evaluate each derivative.

1.   Evaluate \(\frac{d}{dx} \left[-26x^2\right]\)

Differentiate using the Power Rule for derivatives.

\(\dfrac{d}{dx} \left[-26x^2\right]=2*26x^{2-1}\)

Simplify.

\(2*-26x^{2-1}\\-52x^{2-1}\\-52x\)

2.   Evaluate \(\frac{d}{dx} \left[4x^{39}y \right]\)

Differentiate using the Product Rule for derivatives.

\(4\left(x^{39}\dfrac{d}{dx}\left[y\right]+y\dfrac{d}{dx}\left[x^{39}\right]\right)\)

Rewrite  \(\dfrac{d}{dx}\left[y\right]\) as \(y'\)

\(4\left(x^{39}y'+y\dfrac{d}{dx}\left[x^{39}\right]\right)\)

Differentiate using the Power Rule for derivatives.

\(4\left(x^{39}y'+y\left(39x^{39-1} \right)\right)\)

Simplify.

\(4\left(x^{39}y'+39yx^{38} \right)\)

3.   Evaluate \(\frac{d}{dx} \left[y^9\right]\)

Differentiate using the Chain Rule for derivatives.

\(9y^8\dfrac{d}{dx} \left[y\right]\)

Rewrite  \(\dfrac{d}{dx}\left[y\right]\) as \(y'\)

\(9y^8y'\)

Add up all of the derivatives then simplify.

\(-52x+4\left(x^{39}y'+39yx^{38} \right)+9y^8y'\)

\(-52x+4\left(x^{39}y'\right)+4\left(39yx^{38} \right)+9y^8y'\)

\(-52x+4x^{39}y'+156yx^{38}+9y^8y'\)

\(4x^{39}y'+156x^{38}y+9y^8y'-52x\)

Focus the right side of the equation.

\(\dfrac{d}{dx}\left(-21\right)\)

Since \(-21\) is constant with respect to \(x\) , the derivative of \(-21\) with respect to \(x\) is 0 .

Now we have

\(4x^{39}y'+156x^{38}y+9y^8y'-52x=0\)

Finally lets solve for \(y'\).

Subtract \(156x^{38}y\) from both sides of the equation.

\(4x^{39}y'+9y^8y'-52x=-156x^{38}y\)

Add \(52x\) to both sides of the equation.

\(4x^{39}y'+9y^8y'=-156x^{38}y+52x\)

Factor \(y'\) out of \(4x^{39}y'\)

\(y'\left(4x^{39}\right) +9y^8y'=-156x^{38}y+52x\)

Factor \(y'\) out of \(9y^8y'\)

\(y'\left(4x^{39}\right)+y'\left(9y^8\right)=-156x^{38}y+52x\)

Factor \(y'\) out of \(y'\left(4x^{39}\right)+y'\left(9y^8\right)\)

\(y'\left(4x^{39}+9y^8\right)+=-156x^{38}y+52x\)

Divide each term by \(4x^{39}+9y^8\)

\(\dfrac{y'\left(4x^{39}+9y^8\right)}{4x^{39}+9y^8} =\dfrac{-156x^{38}y}{4x^{39}+9y^8} +\dfrac{52x}{4x^{39}+9y^8}\)

Cancel the common factor of \(4x^{39}+9y^8\) on the left side of the equation.

\(y'=\dfrac{-156x^{38}y}{4x^{39}+9y^8} +\dfrac{52x}{4x^{39}+9y^8}\)

Combine the numerators over the common denominator.

\(y'=\dfrac{-156x^{38}y+52x}{4x^{39}+9y^8}\)

Factor \(52x\) out of \(-156x^{38}y+52x\) and simplify.

\(y'=\dfrac{52x\left(-3x^{37}y\right)+52x}{4x^{39}+9y^8}\)

\(y'=\dfrac{52x\left(-3x^{37}y\right)+52x(1)}{4x^{39}+9y^8}\)

\(y'=\dfrac{52x\left(-3x^{37}y+1\right) }{4x^{39}+9y^8}\)

\(y'=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}\)

Rewrite \(y'\) as \(\dfrac{dy}{dx}\).

\(\dfrac{dy}{dx}=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}\)

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Answer:

51,51,78

Step-by-step explanation:

First of all equate the two angles since it is isoceles.

3x+9= 4x-5 , therefore x= 14

sub that in and find the rest of the angles.

angle G---> 4*14 -5 = 51

angle I--->3*14+9= 51

last angle 180 - 2*51 = 78

h+8= -8

h=-8-8

h=(-16)

Hope it helps. Please mark brainliest.

Answer:

-4y²- 16y

Step-by-step explanation:

   2y(-2y - 8)

   2y (-2y) + 2y (-8)  Distributive

      -4y² - 16y                Multiply (+)(-) = -   and (y)(y) = y²

Let A(t), B(t), and C(t) denote the amounts (in hg) of dye in tanks A, B, and C, respectively.

Both A and B start with 20 hg of dye, so A(0) = B(0) = 20. C starts off containing only pure water, so C(0) = 0.

The amount of dye in a given tank changes at a net rate equal to the difference between how much dye flows in and how much flows out.

• Tank A:

•• Dye flows in from an independent source at a rate of

(3 hg/L) (50 L/hr) = 3/50 hg/hr

That is,

(concentration of dye) (flow rate) = rate of change in amount of dye

and the concentration is equal to the amount of dye per unit volume.

Dye also flows in from tank B at a rate of

(B(t)/100 hg/L) (10 L/hr) = B(t)/10 hg/hr

•• Dye flows out of A into B at a rate of

(A(t)/200 hg/L) (40 L/hr) = A(t)/5 hg/hr

and out the exhaust spout at a rate of

(A(t)/200 hg/L) (20 L/hr) = A(t)/10 hg/hr

•• Then the net rate dA/dt is

\(\dfrac{\mathrm dA}{\mathrm dt} = \dfrac3{50}+\dfrac{B(t)-3A(t)}{10}\)

• Tank B:

•• Dye flows in from A at a rate of

(A(t)/200 hg/L) (40 L/hr) = A(t)/5 hg/hr

and from C at a rate of

(C(t)/100 hg/L) (10 L/hr) = C(t)/10 hg/hr

•• Dye flows out into A at a rate of

(B(t)/100 hg/L) (10 L/hr) = B(t)/10 hg/hr,

out into C at a rate of

(B(t)/100 hg/L) (30 L/hr) = 3B(t)/10 hg/hr,

and out the exhaust spout at a rate of

(B(t)/100 hg/L) (10 L/hr) = B(t)/10 hg/hr

•• The net rate dB/dt is then

\(\dfrac{\mathrm dB}{\mathrm dt} = \dfrac{2A(t)+C(t)-5B(t)}{10}\)

• Tank C:

•• Dye flows from B at a rate of

(B(t)/100 hg/L) (30 L/hr) = 3B(t)/10 hg/hr

•• Dye flows out into B at a rate of

(C(t)/100 hg/L) (10 L/hr) = C(t)/10 hg/hr

and out the exhaust spout at a rate of

(C(t)/100 hg/L) (20 L/hr) = C(t)/5 hg/hr

•• The net rate dC/dt is then

\(\dfrac{\mathrm dC}{\mathrm dt} = \dfrac{3B(t)-3C(t)}{10}\)

Condensed into a matrix equation, the system of ODEs can be expressed as

\(\dfrac{\mathrm d\mathbf X}{\mathrm dt} = \dfrac1{10}\begin{pmatrix}-3&1&0\\2&-5&1\\0&3&-3\end{pmatrix}\mathbf X + \dfrac1{50}\begin{pmatrix}3\\0\\0\end{pmatrix}\)

where

\(\mathbf X = \begin{pmatrix}A(t)\\B(t)\\C(t)\end{pmatrix}\)

and with initial condition

\(\mathbf X(0) = \begin{pmatrix}20\\20\\0\end{pmatrix}\)

Just for fun, here's a plot of the solution to this system for the first 50 hours after the pumps are started:

Answer:

The answer is 18

Step-by-step explanation:

6 × 3=18

Hope it helped!!! Sorry it was late!!!!!

Answer:

------------------------

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.

We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.

To quantify the probability of each event, we can define the following events:

Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.

Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:

To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.

Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:

Therefore, the probability of event C can be calculated as follows:

P(C) = P(A) * P(A in order) + P(B) * P(B in order)

= (1/5 * 3/5) + (1/10 * 2/5)

= 3/25

So the probability of selecting a defective unit from the order is 3/25.

To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:

P(D) = 1 - P(C)

= 1 - 3/25

= 22/25

So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.

In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.

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The system of equations solved by the elimination method gives (-2, 1)

From the question, we have the following parameters that can be used in our computation:

y = -4x + 11

y = 1/2x + 2

Subtract the equations to eliminate y

So, we have the following representation

-4 1/2x - 9 = 0

So, we have

-4 1/2x = 9

Divide the equations

x = -2

Recall that

y = 1/2x + 2

So, we have

y = 1/2(-2) + 2

This gives

y = 1

Hence, the solutions are x = 2 and y = 1

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Diners who have to wait for the longest 10% of wait times would have to wait for approximately 28.04 minutes and diners who have to wait for the shortest 15% of wait times would have to wait for approximately 20.51 minutes.

To find the number of minutes diners have to wait if their wait times are in the longest 10%, we need to find the z-score that corresponds to the 90th percentile.

Using a standard normal distribution table or calculator, we find that the z-score for the 90th percentile is approximately 1.28.

Then, we use the formula:

z = (x - μ) / σ

where z is the z-score, x is the wait time we want to find, μ is the mean wait time, and σ is the standard deviation.

Plugging in the values, we get:

1.28 = (x - 24.3) / 3.2

Solving for x, we get:

x = 28.04

To find the number of minutes diners have to wait if their wait times are in the shortest 15%, we need to find the z-score that corresponds to the 15th percentile.

Using a standard normal distribution table or calculator, we find that the z-score for the 15th percentile is approximately -1.04.

Then, we use the same formula as before:

z = (x - μ) / σ

Plugging in the values, we get:

-1.04 = (x - 24.3) / 3.2

Solving for x, we get:

x = 20.51

Therefore, diners who have to wait for the shortest 15% of wait times would have to wait for approximately 20.51 minutes.

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The number of puppies per kids is 20 puppies.

Given that, there are 180 puppies in the shelter with 9 kids.

Number of puppies per kids = Total number of puppies/Number of kids

= 180/9

= 20 puppies

Therefore, the number of puppies per kids is 20 puppies.

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Answer:

If you pacifically asking for the fraction 115/12

Step-by-step explanation:

I also looked on mathw it helps

Answer:

the part of the pizza is one -third

Step-by-step explanation:

Given that

The pizza is cut in three equal sections

And, then it gave to her four kids

So,

The part of the pizza that she give to her kids is one-third of the pizza gone for each and every kid

Therefore the part of the pizza is one -third

The same is to be considered and relevant

Serena needs 12 grams of the 40% solution and 8 grams of the 70% solution.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given Serena is making an experiment. for that, she needs 20 grams of a 52% solution of salt, one with 40% and the other with 70% of salt in them,

let her need x grams of the 40% solution and y grams of the 70% solution.

so x + y = 20.......(1)

and 0.40x + 0.40y = 20(0.52)

0.40x + 0.70y = 10.4

from equation 1 we get x = 20 - y

substitute in the equation 0.40x + 0.70y = 10.4

0.40(20 - y) + 0.70y = 10.4

8 - 0.40y + 0.70y = 10.4

0.30y = 10.4 - 8

y = 2.4/0.30

y= 8 grams

and x = 20 - 8 = 12 grams

Hence she use 12 grams of 40% solution and 8 grams of 70% solution.

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The correlation between average 2007 price and number of 2007 is 0.207

To compute the correlation between the average 2007 price and the number of 2007 wins for the 16 National League baseball teams, we can use the formula for Pearson's correlation coefficient.

First, we need to calculate the following sums:

Sum of prices (ΣX) = 19.68 + 17.07 + 34.30 + 17.90 + 14.72 + 16.70 + 26.66 + 20.09 + 18.11 + 25.28 + 26.73 + 17.08 + 20.83 + 24.53 + 29.78 + 20.88 = 387.47

Sum of wins (ΣY) = 90 + 84 + 85 + 72 + 90 + 71 + 73 + 82 + 83 + 88 + 89 + 68 + 89 + 71 + 78 + 73 = 1296

Sum of products of prices and wins (ΣXY) = (19.68 * 90) + (17.07 * 84) + (34.30 * 85) + (17.90 * 72) + (14.72 * 90) + (16.70 * 71) + (26.66 * 73) + (20.09 * 82) + (18.11 * 83) + (25.28 * 88) + (26.73 * 89) + (17.08 * 68) + (20.83 * 89) + (24.53 * 71) + (29.78 * 78) + (20.88 * 73) = 24839.87

Sum of squared prices (ΣX^2) = (19.68)^2 + (17.07)^2 + (34.30)^2 + (17.90)^2 + (14.72)^2 + (16.70)^2 + (26.66)^2 + (20.09)^2 + (18.11)^2 + (25.28)^2 + (26.73)^2 + (17.08)^2 + (20.83)^2 + (24.53)^2 + (29.78)^2 + (20.88)^2 = 19151.7899

Sum of squared wins (ΣY^2) = (90)^2 + (84)^2 + (85)^2 + (72)^2 + (90)^2 + (71)^2 + (73)^2 + (82)^2 + (83)^2 + (88)^2 + (89)^2 + (68)^2 + (89)^2 + (71)^2 + (78)^2 + (73)^2 = 94518

Using these sums, we can calculate the correlation coefficient (r):

r = (n * ΣXY - ΣX * ΣY) / sqrt((n * ΣX^2 - (ΣX)^2) * (n * ΣY^2 - (ΣY)^2))

where n is the number of data points, which in this case is 16.

Substituting the values:

r = (16 * 24839.87 - 387.47 * 1296) / sqrt((16 * 19151.7899 - (387.47)^2) * (16 * 94518 - (1296)^2))

Calculating this expression gives us:

r ≈ 0.207

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Answer: Range = (-∞, 3) U (3, ∞)

Step-by-step explanation:

The range is the set of all y-values in a function. The easiest and most straightforward way to find the range is to graph the function and find asymptotes, or locations on the graph where the function lacks y-values.

You can plug in a few points to the equation, as shown in this table below.

After you have your points, you can draw your function following the points, as shown in the next image. Notice the line at y = 3, where the function does not cross. Although it will get infinitely close to the line, the function will never meet or cross this point at any x-value. This is what is known as a "horizontal asymptote", and is not included in the range of the function.

We can represent this asymptote in a range, which is a representation of all possible y-values in the function. The possible y-values for this function start at negative infinity and end at infinity, but do not exist at y = 3, so we represent this through this mathematical expression:

Range = (-∞, 3) U (3, ∞)

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

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Answer:

2400 pages

Step-by-step explanation:

Printer 1 :  50+ 1.50/30 x  where x is the number of pages

Printer 2 :  10 + 2/30 x where x is the number of pages

Set them equal

50+ 1.50/30 x  = 10 + 2/30 x

50 + 1/20x = 10 +1/15 x

Subtract 1/20x from each side

50 + 1/20x -1/20x= 10 +1/15 x-1/20x

50 = 10 +1/15x - 1/20x

Subtract 10 from each side

40 = 1/15x - 1/20x

Get a common denominator

40 = 4/60x - 3/60x

40 =1/60x

Multiply by 60

40 *60 = 1/60x *60

2400 =x

Answer:

2400 pages

Step-by-step explanation:

First, let's make equations for the daily cost of the first printing press, with y being the total daily cost, and x being the total number of pages printed.

y=0.05x+50

Now, let's make an equation for the total daily cost of the second printing press.

y=(2/30)x+10

Since both equations are equal to y, let's use the substitution method and set them equal to each other.

0.05x+50=(2/30)x+10

Let's substitute 80 for x into both equations and see if we get a true statement.

0.05(80)+50=(2/30)(80)+10

4+50=16/3+10

54=46/3 X

Since this is a false statement, 80 pages cannot be the solution.

Now, let's try 1500 for x.

0.05(1500)+50=(2/30)(1500)+10

75+50=100+10

125=110 X

Since this is a false statement, 1500 pages cannot be the solution.

Now, let's try 2400 for x.

0.05(2400)+50=(2/30)(2400)+10

120+50=160+10

170=170

Since this is a true statement, 2400 pages is the correct solution, and it will lead to a daily cost of $170.

Given the inequality:

first we use the distributive property to get rid of the parenthesis:

Now we move the terms that got the variable g to the left side of the inequality, and the rest of the members go to the right side:

since we have that 0<=28 (and it's true), then the inequality is true for any value of g.

50%

since 98/2 = 49

Thats it

Answer: 567

Step-by-step explanation: 9*9=81  then you take 81 and times it by however many days there is in the week (aka 7) 81*7=567

Step-by-step explanation:

yo thara bhai joginder tu he ek bndr

The rate of change (slopes) and initial value (y-intercepts) are as follows:

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trend line and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

By critically observing the graph which models the given data, we can logically deduce the following rate of change (slopes) and initial value (y-intercepts):

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Answer:

if i'm correct you either divide the two numbers you have to get the answer or you multiply them to get the answer

Step-by-step explanation:

108 divided by 92

or

108 x 92

Answer:

The fraction is 3/10 = .3

Answer:

4/7

Step-by-step explanation:

If the operation is:

\(\frac{4}{5} (\frac{-2}{3} )(\frac{-15}{7} )(\frac{1}{2} )\)

The solution is:

\(\frac{4(-2)(-15)(1)}{5(3)(7)(2)} =\frac{120}{210}\)

simplified:

\(=\frac{12}{21}=\frac{4}{7}\)

Hope this helps

Answer:

The answer is 4/7

Step-by-step explanation:

- When you are multiplying fractions you multiply the numberators and the denominators like normal

- In the case where you are multiplying 2 negative numbers the product will be positive

I hope I was able to help you out with this problem. Please comment if you have any questions about this.