Simplify: -20w³ + 11w³
Enter the original expression if it cannot be
simplified.

Answer:

Because f(x)=y, begin by changing f(x) to the y-value, getting y=2x-4. Because we are determining the inverse of the equation, this means that the x and y-value should be switched, getting x=2y-4. Now that we're trying to isolate y, move 4 to the other side to get x+4=2y. Divide by 2 on both sides to get y=\(\frac{1}{2}\)x+2. Now, we substitute y for f(x), but this time we put \(f^{-1}\)(x), because it's the inverse of f(x).

Here are the steps in order:

y=2x-4

x=2y-4

x+4=2y

x/2+4/2=2y/2

y=1/2x+2

f^-1(x)=1/2x+2

To find the probability of the call lasting less than 230 seconds, we have to find P(X<230). Here X follows normal distribution with mean = 290

The given data: Meanμ = 290 seconds

Standard deviation σ = 30 seconds

Sample size n = 1000a) and

standard deviation = 30.

We get the value of 0.0228, which represents the area left (or below) to z = -2. Therefore, the probability that the call lasted less than 230 seconds is 0.0228 (or 2.28%). By using z-score formula;

Z=(X-μ)/σ

Z=(230-290)/30

= -2P(X<230) is equivalent to P(Z < -2) From z-table,

0.6384 (or 63.84%) P(230330) is equivalent to 1 - P(X<330)Here X follows normal distribution with mean = 290 and standard deviation = 30.From part b,

We already have P(X<330).Therefore, P(X>330) = 1 - 0.9082 = 0.0918, which is equal to 9.18%. Therefore, the probability that the call lasted more than 330 seconds is 0.1356 (or 13.56%).Answer: 0.1356 (or 13.56%). In parts a, b, and c, the final probabilities are rounded off to four decimal places as needed, as per the instructions given. However, these values are derived from the exact probabilities and can be considered accurate up to that point.

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he get gain of rupees 1500

gain percent = Profit% = [Profit/CP] × 100

1500/5000×100 = 30%

Answer: The given equation 2x + 5y = 10 can be rewritten in slope-intercept form (y = mx + b) by solving for y:

2x + 5y = 10

5y = -2x + 10

y = (-2/5)x + 2

where the slope is -2/5.

Since we want to find the equation of a line parallel to this one, the slope of the new line will also be -2/5. We can use the point-slope form of the equation of a line to find the equation of the new line, using the point (0,-3):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting m = -2/5, x1 = 0, and y1 = -3, we get:

y - (-3) = (-2/5)(x - 0)

y + 3 = (-2/5)x

y = (-2/5)x - 3

Therefore, the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3) is y = (-2/5)x - 3.

Step-by-step explanation:

Answer:

2x + 5y = - 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

2x + 5y = 10 ( subtract 2x from both sides )

5y = - 2x + 10 ( divide through by 5 )

y = - \(\frac{2}{5}\) x + 2 ← in slope- intercept form

with slope m = - \(\frac{2}{5}\)

• Parallel lines have equal slopes , then

y = - \(\frac{2}{5}\) x + c

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - \(\frac{2}{5}\) x - 3 ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fraction

5y = - 2x - 15 ( add 2x to both sides )

2x + 5y = - 15 ← in standard form

Using the continuity concept, it is found that f(2) = 4 would make the extended function continuous at x=2.

A function f(x) is continuous at x = a if it is defined at x = a, and:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

Researching this problem on the internet, from the graph of the function, we get that the lateral limits are given as follows:

\(\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2^+} f(x) = 4\)

Hence f(2) = 4 would make the extended function continuous at x=2.

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Answer:

97,988.216

Step-by-step explanation:

So, we can find this by using the following formula:

First value(change)^time

We know that the orginal, or first value, is 120,000.

We know that the time interval for this is 8 years, which is our time value.

We know that the decrease in this price is 2.5%. However, this is not our change.

Our change is the 97.5% price that is left.

This makes sense, because you would get a super small price when you use 2.5% as change.

So to sum up what we have done so far:

First value - 120,000

Change - 100%-2.5% = 97.5%. In decimal form: 0.975

Time - 8

So lets plug these into:

\(First_.value(change)^t^i^m^e\)

=

\(120,000(0.975)^8\)

And remember your order of operations here.

We dont have any equations or expressions inside the parethese, so we can move on to what comes next - exponents.

We have the exponent 8, which is attached to the 0.975.

So in your calculator, take 0.975, and put it to the 8th power.

You should get 0.816651803662261962890625

Lets leave it like this, becuase 120,000 is a very large value, and rounding what you multiply could change what you get in the end.

Now  our equation looks like:

120,000(0.816651803662261962890625)

We have done parethese, exponents - now we have multiplication and division.

We do indeed have this, since 120,000(0.816651803662261962890625) could also be written as:

\(120,000*0.816651803662261962890625\)

Now multiplying this you should get:

97,998.216439471435546875

This is where you can round your answer.

I do not know what exactly they want you to round to, so its safe to just round your answer to the hundreths place:

97,998.22

So this is the new price of the car!

Hope this helps!

oh I did a mistake earlier , pardon ^^"

Let price after 8 years be P.

Using the compound interest formula of shrinking principal :-

P = Pₒ( 1 - R/ 100) ᵀ

P = 120, 000 ( 1 - 2.5/ 100)ᵀ

P = 120, 000 { (100 - 2.5)/ 100}ᵀ

P = 120, 000{ 97. 5/ 100 }ᵀ

P = 120, 000 {0. 975 } ⁸

P = 120, 000 { 0. 8166}

P = 97,998.216 $

Since, P is is price after 8 years

The price of the car after 8 years will be 97, 998. 216 $

Step-by-step explanation:

1) 165⁰

2) 180⁰

Note:FOR initial temperature check the temperature at t=0

I hope it helped you

Answer:

To the lump sum needed to be invested to receive $10,000 in 10 years at 6.6% interest compounded daily, we can use the present value formula:

PV = FV / (1 + r/n)^(n*t)

where PV is the present value or the initial investment, FV is the future value or the amount we want to end up with, r is the annual interest rate in decimal form, n is the number of times the interest is compounded per year, and t is the time in years.

Plugging in the numbers, we get:

PV = 10000 / (1 + 0.066/365)^(365*10)

= 4874.49

Therefore, the lump sum needed to be invested is about $4,874.49.

Answer:

b

Step-by-step explanation:

Because the lines intercept at -3

The probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

To find the probability that the sum of the rolls is divisible by 6, we need to determine the favorable outcomes and the total number of possible outcomes.

First, let's identify the favorable outcomes. In this case, the sum of the rolls can be divisible by 6 if the sum is either 6 or 12.

1. For the sum of 6:
  - One possible outcome is rolling a 6 on the first roll and rolling a 1 on the remaining four rolls.
  - Another possible outcome is rolling a 5 on the first roll and rolling a 2 on the remaining four rolls.
  - We can also have rolling a 4 on the first roll and rolling a 3 on the remaining four rolls.
  - Similarly, rolling a 3 on the first roll and rolling a 4 on the remaining four rolls.
  - Finally, rolling a 2 on the first roll and rolling a 5 on the remaining four rolls.
  - This gives us a total of 5 favorable outcomes.

2. For the sum of 12:
  - One possible outcome is rolling a 6 on all five rolls.
  - This gives us a total of 1 favorable outcome.

Now let's determine the total number of possible outcomes. Since we are rolling a fair 6-sided die 5 times, the total number of possible outcomes is 6^5 (since each roll has 6 possible outcomes).

Therefore, the probability that the sum of the rolls is divisible by 6 is:

(total number of favorable outcomes) / (total number of possible outcomes)
= (5 + 1) / (6^5)
= 6 / 7776
= 1 / 1296

So, the probability that the sum of the rolls is divisible by 6 is 1/1296, which is approximately 0.00077 or 0.077%.

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We have the following:

We have coterminal angles, when you graph angles x = 30° and y = - 330° in standard position, these angles will have the same terminal side. See figure below.

Therefore, the answer is 94 degrees in the quadrant II

Answer:

hi I don't know the answer of this question but I hope anyone will answer your this question as fast as possible and iam taking free points because I needed to ask one question from someone that's why I really sorry and thank you so much for free points

The equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

Simplify LHS and RHS?

To verify whether the equation \((sin(x)cos(x))^2 = sin(2x)\) is an identity, we can simplify both sides of the equation and see if they are equivalent.

Starting with the left side of the equation:

\((sin(x)cos(x))^2 = (sin(x))^2(cos(x))^2\)

Now, we can use the trigonometric identity \(sin(2x) = 2sin(x)cos(x)\) to rewrite the right side of the equation:

\(sin(2x) = 2sin(x)cos(x)\)

Substituting this into the equation, we have:

\((sin(x))^2(cos(x))^2 = (2sin(x)cos(x))\)

Next, we can simplify the left side of the equation:

\((sin(x))^2(cos(x))^2 = (sin(x))^2(cos(x))^2\)

Since both sides of the equation are identical, we can conclude that the given equation is indeed an identity:

\((sin(x)cos(x))^2 = sin(2x)\)

Hence, the equation \((sin(x)cos(x))^2 = sin(2x)\) is verified to be an identity.

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Answer:

C) \(3x^2-14x-5\)

Step-by-step explanation:

\((5x^2-5x+1)-(2x^2+9x-6)\\\\5x^2-5x+1-2x^2-9x-6\\\\3x^2-14x-5\)

The subtraction of the given expressions gives D. 3x² - 14x + 7.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are two expressions.

5x² - 5x + 1 and 2x² + 9x - 6

We have to find the difference of the given expression.

(5x² - 5x + 1) - (2x² + 9x - 6)

= 5x² - 5x + 1 - 2x² - 9x + 6

Operating the like terms together,

= (5x² - 2x²) + (-5x - 9x) + (1 + 6)

= 3x² - 14x + 7

Hence the correct option is D.

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The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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The total number of extra points earned is approximately 214 using Simpson's Rule.

Simpson's rule is a technique of numerical integration that approximates the value of a definite integral of a function by using quadratic functions. Here, you are supposed to create a spreadsheet to estimate the total number of extra points earned on the exam using Simpson's rule.Here is the table provided:

Number of hours of study, x1 2 3 4 5 6 7 8 9 10 11

Rate of extra points 4 8 14 11 12 16 22 20 22 24 26 earned on exam, f(x) OCIED

We first calculate h and represent it as follows:  

h = (b-a)/nwhere b = 11, a = 1, and n = 10.

 Therefore, h = (11-1)/10 = 1.

Substituting the values into the Simpson's Rule formula, we have:

∫ba{f(a) + 4f(a+h) + 2f(a+2h) + 4f(a+3h) + ... + 2f(b-h) + 4f(b-2h) + f(b)} / 3n

We have 10 intervals. Thus we have:

∫1111 {4 + 4(8) + 2(14) + 4(11) + 2(12) + 4(16) + 2(22) + 4(20) + 2(22) + 4(24) + 26} / 30≈ 214.0

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Answer:

We can use the sine law to find h. First, we determine the angle between the line of sight and h:

180 - 90 - 39 = 51 degrees

The sine law states that the ratio of one triangle's angle to the opposite side's length is the same as another angle to its opposite side's length, so we can solve for h as follows:

h/sin(39) = 500/sin(51)

h = 500*sin(39)/sin(51)

When we round to the nearest whole number, we get h = 405 ft.

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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The answer is letter C. The graph of g is 3 units above the graph of h.​

Note: A vertical translation is generally given by the equation y= f(x) + b. In this example, g(x) = x^2 + 3, the +3 means to move the graph of x^2 up by 3 units. Thus, The graph of g is 3 units above the graph of h.

The best estimate for BC is 120 feet in the given triangle.

We can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We have AB = 50 feet and CD = 100 feet.

To estimate BC, we can subtract the known side length BE = 30 feet from the sum of AB and CD:

BC = AB + CD - BE

= 50 + 100 - 30

= 150 - 30

= 120 feet

Therefore, the best estimate for BC is 120 feet.

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We are given the dot-plots of sixth-grade test scores and seventh-grade test scores.

Let us first find the median of the two test scores.

Recall that the median is the value that divides the distribution into two equal halves.

Sixth Grade Geograph Test Scores:

From the dot-plot, we see that 11 is the median test score since it divides the distribution into two equal halves.

Median = 11

Seventh Grade Geograph Test Scores:

From the dot-plot we see that 13 is the median test score since it divides the distribution into two equal halves.

Median = 13

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class.

Now let us find the interquartile range which is given by

Seventh Grade Geograph Test Scores:

The upper quartile is given by

At the 10th position, we have a test score of 13

The lower quartile is given by

At the 3rd position, we have a test score of 11

So, the interquartile range is

Sixth Grade Geograph Test Scores

The upper quartile is given by

At the 9th position, we have a test score of 10

The lower quartile is given by

At the 3rd position, we have a test score of 8

So, the interquartile range is

So, the IQR is the same as the difference between medians.

Therefore, the median score of the seventh-grade class is 2 points greater than the median score of the sixth-grade class. The difference is the same as the IQR

Hence, the correct answer is option B

Answer: (6, -4)

Step-by-step explanation:

Because it translate right 4 units, so the x increase by 4, so x=6

It up 3, so y increase by 3, so y= -4

Considering that the quadrilateral EFGH is similar to quadrilateral IJKL the side LI is calculated to be

The side LI is calculated using the concept of similar polygons. This concept allows for the sides to be proportionally equal to each other.

This implies that the factor used for any side will produce same result

let the factor be r and using side HG and JK to solve for the factor r

HG * r = JK

where

HG = 16

JK = 51

substituting the values and solving for r

HG * r = JK

16 * r = 51

r = 51/16

and HE * r = LI

where HE = 9.6

LI = 9.6 * 51/16

LI = 30.6

hence side LI = 30.6

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Answer= \(50cm^{2}\)

The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Answer:

100-500

Step-by-step explanation:

Both sides of a triangle cannot be shorter than the remaining side.  Thus, the side must be less than 500 units.  With the same rule, the side must be greater or equal to 100 units, as if it was less, then 200 + 99 < 300.

The compound inequality for the range of the possible lengths for the third side will be 100- 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The meaning of inequality is to say that two things are NOT equal. One of the things may be less than, greater than, less than or equal to, or greater than or equal to the other things.

Given:

side lengths of 200 units and 300 units.

The largest value of the third side will be

200+300=500

and, the smallest value will be

300-200=100

Hence, 100<X<500

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Answer: 6,130,000

Step-by-step explanation:

No work needed