Find x
8(x-27)+49=87+28x

Answer:

hope this will help you

Answer: The lowest possible product would be -6724 given the numbers 82 and -82.

We can find this by setting the first number as x + 164. The other number would have to be simply x since it has to have a 164 difference.

Next we'll multiply the numbers together.

x(x+164)

x^2 + 164x

Now we want to minimize this as much as possible, so we'll find the vertex of this quadratic graph. You can do this by finding the x value as -b/2a, where b is the number attached to x and a is the number attached to x^2

-b/2a = -164/2(1) = -164/2 = -82

So we know one of the values is -82. We can plug that into the equation to find the second.

x + 164

-82 + 164

82

Step-by-step explanation: Hope this helps.

The sum of the polynomials is 3x² + 6x + 4.

The population was 6.98 million in 1900. The population of New York decreased with respect to time.

What is an exponential function?

An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

The population of New York state can be modeled by

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}\)

P is the population and t is the number of years since 1800.

The difference between the year 1900 to 1800 is 100.

Putting t = 100 in the given model:

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}\)

\(P(t)=\frac{19.71}{1+61.22e^{-3.513}}\)

P(t) = 19.71/2.8248

P(t) = 6.9774

P(t) = 6.977 (rounded to the nearest thousands)

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Given that the graph of f(x) consists of four line segments .We need to find g(0).We know that g(x) is defined as follows that there are four line segments on the graph of f(x).We must ascertain g(0).

\($$g(x) = \begin{cases} 3x + 1,& x < 0\\ 2x - 1,& 0 \le x < 2\\ -x + 5,& x \ge 2\end{cases}$$\)

We have to evaluate g(0).The value of g(0) will be equal to 2x - 1 when x is equal to 0.

Since 0 is in the interval 0 ≤ x < 2, we use the second equation of the piecewise function to evaluate g(0).So, g(0) = 2(0) - 1 = -1Therefore, g(0) is equal to -1.

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When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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Answer:

see explanation

Step-by-step explanation:

x and y are same- side interior angles

they are on the same side of the transversal and are in the interior of the parallel lines.

Answer:

These are same side interior.

Step-by-step explanation:

They are both interior of the lines and are on the same side of it. Therefore, they are same side interior.

I hope this helps!

-No one

Answer:

n = 84

Step-by-step explanation:

18 + 3 = 21, so that means the quotient of the number and 4 is 21.

21 * 4 = 84

CHECK:

84 / 4 = 21

21 - 3 = 18

Answer:

x = \(\frac{32}{3}\) (see below)

Step-by-step explanation:

First, use distributive property:

5 (x + 8) = 8 (x + 1)

5x + 40 = 8x + 8

Then, simplify the equation by combining like terms. You want to isolate the variable to one side of the equation so you can solve for it. Here what I'm talking about:

5x + 40 = 8x + 8

-5x            -5x

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

40 = 3x + 8

-8           -8

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

32 = 3x

Now, divide both sides by 3 to get the value of x:

3x = 32

x = \(\frac{32}{3}\)

or

x ≈ 10.7

Answer:

x= 32/3

Step-by-step explanation:

5(x+8)= 8(x+1)

5x+40=8(x+1)

5x=40=8x+8

5x+40=8x+8

5x+40-40=8x+8-40

5x=8x-32

5x=8x-32

5x-8x=8x-32-8x

-3x=-32

-3x = -32

(Divide both by -3)

x=32/3

The length of the microorganism in millimeters is 0.005 mm.

The theory behind converting length units from one unit to another is based on the conversion factor principle. In the International System of Units (SI), the conversion factor between two units of length can be obtained by comparing the number of meters represented by each unit. For example, 1 millimeter is equal to 0.001 meters, and 1 micrometer is equal to 0.000001 meters.

To convert from one unit of length to another, we multiply the length by the appropriate conversion factor. In this case, to convert from micrometers to millimeters, we multiply the length in micrometers by 0.001 to obtain the length in millimeters.

To convert the length of the microorganism from micrometers (μm) to millimeters (mm), we divide by 1000.

5 μm / 1000 = 0.005 mm

Therefore, the length of the microorganism in millimeters is 0.005 mm.

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Answer:

< B = 180-30-65=85°

< E = 85°

< D = 30°

< C = 65°

BC = 20/35 × 28 = 16

Its not must that 3x have to be the one to be subtracted. You could take 8x as well.

But always subtract from the smaller one (in this case 3x) because its easier.

If you are subtracting 3x-3x and 8x-3x, the equation would be like

4 = 5x - 16

5x = 4+16

5x = 20

x = 4

The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.

To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.

From the first sentence, we know that:

4x + y = 13 ...(1)

From the second sentence, we know that:

3y + 2x = 14 ...(2)

Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.

Multiplying equation (1) by 3, we get:

12x + 3y = 39 ...(3)

Subtracting equation (2) from equation (3), we get:

10x = 25

x = 2.50

Substituting x = 2.50 into equation (1), we get:

4(2.50) + y = 13

y = 3

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Answer:

a)3⁴

b)7⁵

c)10²

d)5⁷

Step-by-step explanation:

a)3²×3² = 3^2+2=3⁴

b)7×7⁴=7¹×7⁴=7^1+4=7⁵

c)10⁹÷10⁷=10^9-7=10²

d)5⁸÷5=5⁸-5¹=5^8-1=5⁷

Answer:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 .

Step-by-step explanation:

Answer:

32 degrees.

Step-by-step explanation:

A triangle is 180 degrees.

180 - 85 - 63 = 32 degrees.

Answer:

x = 32

Step-by-step explanation:

All interior angles in a triangle equal to 180

use this to solve for x

180 = 85 + 63 + x

180 - 85 - 63 = x

32 = x

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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I divided 56 by 4 to see how much per CD Brad payed. This got me $14. $42 divided by $14 is $3, so he can buy 3 CDs.

Answer:

3

Step-by-step explanation:

For each CD:

$56÷4=$14

Therefore for $42,

$42÷$14=3

Brad can purchase 3 CD'S.

Hope this helps!

Hope this helps!please mark BRAINLIEST.

(a) The phasor representation of F₁(t) is:

F₁ = (5/√2) - j(5/√2)

(b) The phasor representation of F₂(t) is:

F₂ = (√2/2 - 1) - j(√2/2 + √3 + 1)

(c) The time domain waveform for F₃ is: F₃(t) = 2cos(ωt) + 2sin(ωt)

(d) The time domain waveform for F₄ is: F₄(t) = 2\(e^{(3+j(\omega\ t-4))\)

(e) The time domain waveform for F₅(x) is: F₅(x) = Re{((1+j)\(e^{(j(\omega\x-2))\))}

To find the phasors of the given time domain waveforms and the time domain waveforms for the given phasors, we need to convert between the two representations using Euler's formula and basic trigonometric identities.

(a) For the waveform F₁(t) = 5sin(π/4 - ωt):

To find the phasor, we can express it in complex form as follows:

F₁(t) = 5sin(π/4)cos(ωt) - 5cos(π/4)sin(ωt)

     = (5/√2)cos(ωt) - (5/√2)sin(ωt)

The phasor representation of F₁(t) is:

F₁ = (5/√2) - j(5/√2)

(b) For the waveform f₂(t) = cos(ωt + π/4) - 2sin(ωt + π/3):

Using trigonometric identities, we can rewrite f₂(t) as:

f₂(t) = cos(π/4)cos(ωt) - sin(π/4)sin(ωt) - 2sin(π/3)cos(ωt) - 2cos(π/3)sin(ωt)

     = (√2/2)cos(ωt) - (√2/2)sin(ωt) - √3sin(ωt) - sin(ωt)

Combining like terms, we have:

f₂(t) = (√2/2 - 1)cos(ωt) - (√2/2 + √3 + 1)sin(ωt)

The phasor representation of f₂(t) is:

F₂ = (√2/2 - 1) - j(√2/2 + √3 + 1)

(c) Given the phasor F₃ = 2 - 2j, we can convert it to the time domain waveform:

F₃(t) = Re{F₃ * \(e^{(j\omega\ t)\)}

= Re{(2 - 2j) * \(e^{(j\omega\ t)\)}

= 2cos(ωt) + 2sin(ωt)

The time domain waveform for F₃ is: F₃(t) = 2cos(ωt) + 2sin(ωt)

(d) Given the phasor F₄ = 2\(e^{(3-4j)\), we can convert it to the time domain waveform:

F₄(t) = Re{F₄ * \(e^{(j\omega\ t)\)}

= Re{(2\(e^{(3-4j)\)) * \(e^{(j\omega\ t)\)}

= 2\(e^{(3-4j+j\omega\ t)\)

The time domain waveform for F₄ is: F₄(t) = \(e^{(3+j(\omega\ t-4))\)

(e) Given the phasor F₅(x) = (1+j)\(e^{(-2jx)\), we can convert it to the time domain waveform:

F₅(x) = Re{F₅ * \(e^{(j\omega\ x)\)}

= Re{((1+j)\(e^{(-2j)\)) * \(e^{(j\omega\ x)\)}

= (1+j)\(e^{(-2j+jωx)\)

The time domain waveform for F₅(x) is: F₅(x) = Re{((1+j)\(e^{(j(\omega\ x-2))\))}

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Answer:

\(61600\)

Step-by-step explanation:

\(10^4\\\\10*10*10*10\\\\100*100\\\\10000\\\\\\10000*6.16\\\\61600\)

The person above this should have the answer. It seems like nobody else is answering.

1. The most likely color for the taxi = green

2. The probability that the taxi is blue = 0.25

Let us assume that tg represents the taxi was green and tb represents the taxi was blue;

Also yg represents the taxi appeared green and yb  represents the taxi appeared blue.

9 out of 10 athenian taxis are green

So, P(tg) = 0.90

And, P(tb) = 1 - P(tg)

                = 1 - 0.90

                = 0.10

As under the dim lighting conditions, discrimination between blue and

green is 75% reliable,

P(yb | tb) = 0.75.

So, P(yg | tb) = 1 - P(yb | tb)

                     = 0.25

Similarly P(yg | tg) = 0.75

Thus, P(yb | tg) = 1 - P(yg | tg)

                         = 0.25

P(tb | yb) = P(tb, yb) / P(yb)

               = [P(yb | tb) P(tb)] / [P(yb, tg)P(tg) + P(yb | tb) P(xb)]

               = 0.25

Thus the probability that the taxi is blue = 0.25

P(tg | yb) = 1 - P(tb | yb)

              = 0.75

We can observe that P(tb | yb) > P(tb) but the posterior P(tb | yb) is smaller than 0.5, since the prior P(tb) is very small. Thus, the taxi was most likely green.

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The complete question is:

Suppose you are a witness to a nighttime hit-and-run accident involving a taxi in Athens.All taxi cars in Athens are blue or green. You swear under oath that the taxi was blue.Extensive testing shows that, under the dim lighting conditions, discrimination between blue and green is 75% reliable.

1. is it possible to calculate the most likely color for the taxi? (*hint:* distinguish carefully between the proposition that the taxi *is* blue and the proposition that it *appears* blue.)

2. what is the probability of the taxi being blue, if you know that 9 out of 10 athenian taxis are green?

The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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Answer:

Hypotenus property a2 +b2 =c2

If one wants to examine the relationship between college students' decision on where to live near campus and their academic performance, the predictor variable would be the "decision on where to live near campus."

The decision on where to live near campus refers to the choice made by college students regarding their residential location in relation to their educational institutions.  

This variable encompasses various factors, including proximity to campus, housing costs, availability of amenities, and other relevant considerations.

By investigating this predictor variable, researchers can analyze how students' living arrangements impact their academic performance.

They can explore whether students who choose to live closer to campus or in areas with certain amenities have better academic outcomes compared to those who choose different living arrangements.

To examine this relationship, researchers would collect data on students' living arrangements, such as whether they live on-campus, off-campus, or commute from a distance.

They would also collect data on academic performance measures, such as GPA, course grades, or graduation rates.

By comparing these variables, researchers can determine if there is a correlation or association between living decisions and academic performance.

Understanding the relationship between living decisions and academic performance can provide insights into factors that contribute to student success.

It can inform university housing policies, support services, and provide guidance to students in making informed decisions about their living arrangements during their college years.

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Question: The complete question may be like: If one wants to examine the relationship between college students' decision on where to live near campus and their academic performance, the _____ will be the predictor variable.

Fauvist artists extended the visual vocabulary of Post-Impressionism by making their primary subject matter Color

Fauvist artists, a group of early 20th-century painters, indeed extended the visual vocabulary of Post-Impressionism primarily through their innovative use of color. The Fauvist movement emerged in France in the early 1900s and was characterized by bold, vibrant colors and expressive brushwork.

Prior to the Fauvists, Post-Impressionist painters, such as Vincent van Gogh and Paul Cézanne, had already begun to break away from the naturalistic color palette of Impressionism. They explored new ways of using color to convey emotion and form, but it was the Fauvists who took this exploration to new levels.

Fauvist artists, including Henri Matisse, André Derain, and Raoul Dufy, embraced intense, non-naturalistic colors. They used bold, contrasting hues that were often unrelated to the actual appearance of their subjects. This departure from traditional color usage was a radical departure from the subdued, more subdued palettes of earlier movements.

By focusing on color as their primary subject matter, the Fauvists aimed to evoke powerful emotional responses from the viewers. They believed that color had the ability to express emotions and convey meaning on its own, without being limited to realistic representations of objects. Instead of relying on naturalistic color schemes, they used vivid and arbitrary colors to create a sense of energy and vitality.

The Fauvists also liberated color from its traditional role as a means to depict light and shadow. They applied colors freely and spontaneously, often using broad brushstrokes, without concern for accurate representation. This allowed them to create highly expressive and subjective interpretations of their subjects, whether they were landscapes, portraits, or still lifes.

In summary, Fauvist artists extended the visual vocabulary of Post-Impressionism primarily through their revolutionary use of color. By breaking away from the naturalistic color palette and embracing bold, vibrant hues, they explored the expressive potential of color itself, going beyond traditional notions of representation. Their approach opened up new avenues for artistic expression and paved the way for further experiments in color by future generations of artists.

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Answer:

D

Step-by-step explanation:

5 x 8 = 40

2 x 2 = 4

4 x 7 = 28

40 + 4 + 28 = 72