Solve: ƒ(x) = 2x(x + 1)(3x − 1)
1 and -3
0, 1, and -3
0, -1 , and 3
None of these choices are correct.

Answer: 4.

Step-by-step explanation:

Answer:

The answer is 3 7/12 Hope this helps :)

Step-by-step explanation:

Answer:

3(5+x)

Step-by-step explanation:

15+3x

5*3 + 3*x

Factor out 3

3(5+x)

Domain and range of the given data are  xt ( 2015, 2019 ) and yt ( 33.88, 47.87 ), respectively and it is not a function.

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x). Domain and Range are the two main factors of Function. The domain of a function is the set of input values of the Function, and range is the set of all function output values. A function is a relation that takes the domain’s values as input and gives the range as the output.

according to the question, The annual precipitation totals of Seattle, Washington, for various years are as follows:

2015, 44.83 inches; 2016, 45.18 inches; 2017, 47.87 inches; 2018, 35.73 inches; 2019, 33.88 inches.

a. let x represent the year and y represent the annual precipitation in inches,

x - 2015   2016   2017   2018   2019

y - 44.83  45.18  47.87  35.73  33.88

b. domain and range of the relation is

    xt ( 2015, 2019 )

    yt ( 33.88, 47.87 )

c. It is not a function as we can see there is no relation followed between the years and the inches of the annual precipitation.

Therefore, we can conclude that Domain and range of the given data that is the annual precipitation totals of Seattle, Washington, for various years  are  xt ( 2015, 2019 ) and yt ( 33.88, 47.87 ), respectively and it is not a function.

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Answer:

you pay 370.30

you saved 158.70

I believe

Answer:

$370.3

Step-by-step explanation:

If you need to find 30% of $529 you need to put 30% into a decimal. 30/100 =0.3 so if we do 0.3 x 529 we get the answer $158.7.

Then we subtract 529 by 158.7 to get 370.3 as the sale price.

The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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Solutions cannot be more concentrated than a solution that has a %T of 10%

Solutions cannot be less concentrated than a solution that has a %T of 90%.

Beer's Law:

Beer's law (sometimes called Beer-Lambert's law) states that absorption is proportional to the path length b through the sample and the concentration c of the absorbing substance: The constant of proportionality is sometimes designated by the symbol a, which makes Beer's law literal.

The linearity of the law is limited by chemical and instrumental factors. The reasons for the nonlinearity are: Absorbance deviation at high concentrations (>0.01 M) due to electrostatic interactions between adjacent molecules.

Limitation of Beer's Law:

The linearity of the law is limited by chemical and instrumental factors.

Causes of non-linearity include:

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umm whichever grade this is I don't know

Step-by-step explanation:

100%+5%=105%

105/100*200=210

100%-6%=94%

94/100*210

Answer:

Step-by-step explanation:

= 2 ± 2 √ 2

The equation of the line which is passing to a point and slope 2/3 will be y = 2/3x + 5.

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the given information in the question,

The equation for the line in the slop form is,

y = mx + b

Slope, m = 2/3

y = 2/3x + b, it is representing a partial equation.

Substitute the given point (3, 7) in the above equation,

7 = (2 ×3)/3 + b

b = 7 - 2

b = 5

So, the equation of the line will be,

y = 2/3x + 5.

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To be sure that a figure is a scaled copy there are some features we need to check:

One of them, is that no matter what, the angles of the figure must conserve the same measure to the original one.

Another one, is that the lengths of the sides of the figure, must conserve the same proportions compared to the original one (this is the scale factor).

And those are the most important features to check to know if a figure is a scaled copy.

I will show you an example:

The rectangle ABCD is a figure. Check if the rectangle EFGH is a scaled copy.

The angles of the rectangle EFGH are equal to the ones of ABCD. Nevertheless, it is necessary to check if they conserve the same proportions.

The ratio of segment AB to segment EF is 1:2. And the ratio of segment BD to segment FH is also 1:2.

The ratio of the segment AB to segment AC is 1:2. The ratio of segment EF to segment EG is also 1:2.

Once we check these feauture, we can be sure that rectangle EFGH is a scaled copy of rectangle ABCD.

Answer:

ye s1.8x10-4 is greater than 7.2x10-1

Step-by-step explanation:

The number 1.8*10⁻⁴ is smaller, not larger than 7.2*10⁻¹

We have two numbers in scientific notation, these are:

1.8*10⁻⁴

7.2*10⁻¹

We want to see if the first one is larger than the second one. This is trivial to notices, because the exponent in the first number is 3 orders of magnitude smaller than the other exponent, then the first number is smaller than the second, not larger.

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The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.

To convert the given equation from standard form to vertex form, we need to complete the square.

The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.

Given equation: y = x² - 6x + 14

Move the constant term to the right side:

y - 14 = x² - 6x

Complete the square by adding and subtracting the square of half the coefficient of x:

y - 14 + 9 = x² - 6x + 9 - 9

Group the terms and factor the quadratic:

(y - 5) = (x² - 6x + 9) - 9

Rewrite the quadratic as a perfect square:

(y - 5) = (x - 3)² - 9

Simplify the equation:

y - 5 = (x - 3)² - 9

Move the constant term to the right side:

y = (x - 3)² - 9 + 5

Combine the constants:

y = (x - 3)² - 4

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Answer:

3(x - 4)

Step-by-step explanation:

Given

3x - 12 ← factor out 3 from each term

= 3(x - 4)

The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer:

$20,000

Step-by-step explanation:

Let the new car price before tax be p.  If the sales tax was $1400, then the following is true:  0.07p = $1400, and p = $20,000

$1400 is 7% of the before-tax new car price, which is $20,000

Answer:

y=4-0.5x

Step-by-step explanation:

Step one:

given data

Alina bought an ice cream cone for $3

the weight of the ice cream is 4 ounce

the rate of melting is 0.5 ounce per minute

let the number of minutes taken for the ice cream to melt be x

and the weight after x minutes be y

Step two:

Hence the expression for the situation after x minutes is

y=4-0.5x

Answer:

\(a_{n}\) = 9 - 6n

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = - 3 - 3 = - 9 - (- 3) = - 15 - (- 9) = - 6

This indicates the sequence is arithmetic with explicit formula

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = - 6 , thus

\(a_{n}\) = 3 - 6(n - 1) = 3 - 6n + 6 = 9 - 6n

Answer:

180, 145

Step-by-step explanation:

There are 60 minutes in an hour, so we do 3*60=180 for the first one.

For the second one, we first find the minutes in 2 hours, which is 2*60=120. We add 120+25 and get 45.

Answer:

\(-n^3+7n+3\)

Step-by-step explanation:

\((f-g)(n)=f(n)-g(n) \\ \\ =4n+3-n^3+3n \\ \\ =-n^3+7n+3\)

Answer:

y = (2/5)x + 2

Step-by-step explanation:

To find the inverse of a function, we simply exchange the variables x and y and solve for y.

For this function we will write it as such:

y = -5 + (5/2)x

So to find the inverse, we will swap the x and y and solve.

y = -5 + (5/2)x

x = -5 + (5/2)y

x + 5 = (5/2)y

(2/5) * (x + 5) = y

(2/5)x + (2/5)5 = y

(2/5)x + 2 = y

Thus the inverse of the function is:

y = (2/5)x + 2

Cheers.

Two length of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. Given that the pool in this instance is 24 m long and has six loops, the wavelength is 4 m.

Wavelength = Length of Pool / Number of Loops

24 m / 6 loops

= 4 m

Wavelength

= 4 m

Two waves of the same frequency and amplitude moving in opposite directions combine to form a standing wave, which appears to be stationary. A stationary wave pattern is produced when the two waves collide and interfere with one another. Six loops make up the 24 m-long pool in this instance. As a result, the standing wave's wavelength is equal to the pool's length divided by the number of loops, or 24 m / 6 = 4 m. This indicates that the standing wave's wavelength is 4 metres. Standing waves can be used to determine a wave's speed because they are equal to wavelength times frequency. Understanding how waves behave in various contexts, such as swimming pools, oceans, or other bodies of water, can be helped by this.

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The distance between X and Y is the difference between the longitude of X and the longitude of Y, plus the radius of the Earth is 6400 km.

Longitude of X = 114 degrees

Longitude of Y = 118 degrees

Difference = 118 degrees - 114 degrees = 4 degrees

Radius of the Earth = 6400 km

Distance between X and Y = 4 degrees + 6400 km = 6404 km

Round the distance to the nearest 100 km.

6404 km = 6400 km (rounded to the nearest 100 km)

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The solution will be the intersection points thus options A (1,-3) and B (-2,0) will be correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

The solution will be the intersection points of both functions.

At the intersection point,

x² - 4 = -x - 2

x² + x - 2 = 0

x² + 2x - x - 2 = 0

x(x + 2) - (x + 2) = 0

(x - 1)(x + 2) = 0

x = 1,-2

At x = 1

y = -1 - 2 = -3 so first intersection is (1,-3)

At x = -2

y = -(-2) - 2 = 0 so second intersection is (-2,0)

Hence "The solution of the given system of equations is (1,-3) and (-2,0)".

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The process capability, Cp is calculated by dividing the upper specification limit minus lower specification limit by 6 times the process standard deviation.

This is the formula for the process capability.

Cp = (USL - LSL) / (6 * Standard deviation)

Where, Cp is process capability USL is the Upper Specification Limit LSL is the Lower Specification Limit Standard deviation is the process standard deviation.

The extrudate is subsequently cut into individual parts, and the extruded parts have a critical cross-sectional dimension = 12.50 mm with standard deviation = 0.25 mm. The mean of this distribution is the center line of the control chart and the critical cross-sectional dimension 12.50 mm is the target or specification value.

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Answer:

2.97

Step-by-step explanation:

In order to get the answer

divide 14.85 by 5

you divide by 5 because thats the amount of friends that ordered

14.85/5 = 2.97

:D

Answer:

\(\frac{3}{8}\)

Step-by-step explanation:

\(\frac{7}{8}\) - (\(\frac{1}{6}\) + \(\frac{2}{6}\))      \(\frac{1}{3}\) x \(\frac{2}{2}\)= \(\frac{2}{6}\)  (1/3  is equivalent to 2/6)  we want a common denominator so that we can add the 2 fractions

\(\frac{7}{8}\) - \(\frac{3}{6}\)      \(\frac{3}{6}\)÷\(\frac{3}{3}\) = \(\frac{1}{2}\) (3/6 is equivalent to 1/2)  These are easier numbers to work with.

\(\frac{7}{8}\) -\(\frac{1}{2}\)  We need a common denominator.  The easiest one to use would be 8

\(\frac{1}{2}\) x \(\frac{4}{4}\) = \(\frac{4}{8}\)          (1/2 is equivalent to 4/8)

\(\frac{7}{8}\) - \(\frac{4}{8}\) = \(\frac{3}{8}\)