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Which ordered pair is a solution to the system of inequalities?

The equation in standard form will be 4x^2 - 8x - (5 + f(x)) = 0.

The given equation f(x) = (2x + 1) (2x-5) can be simplified by multiplying the two binomials together to get:

f(x) = 4x^2 - 8x - 5

This equation is in general form, not standard form. Standard form of a quadratic equation is given by:

ax^2 + bx + c = 0

where a, b, and c are constants and a ≠ 0.

To convert the given equation to standard form, we need to set it equal to zero by subtracting f(x) from both sides:

4x^2 - 8x - 5 - f(x) = 0

Since f(x) is an arbitrary constant, we can combine the constant terms to get:

4x^2 - 8x - (5 + f(x)) = 0

This equation is now in standard form, with a=4, b=-8, and c=-(5+f(x)).

In summary, to convert a quadratic equation in general form to standard form, we need to set it equal to zero and combine constant terms. The resulting equation should have the form ax^2 + bx + c = 0, with a, b, and c being constants and a ≠ 0.

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The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.

What is linear equation?

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

Given, the equation y = 2x -4

Which is linear function and have y a dependent variable and x be the independent variable,

because value of y depends upon the value of x.

Hence, a is the correct answer.

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Answer: A

Step-by-step explanation: Trust me

Answer:

P = 3/11

Step-by-step explanation:

There are:

6 red marbles

4 blue marbles

2 yellow marbles.

So there are a total of 12 marbles in the bag, such that each one has the same probability of being randomly picked.

We want to find the probability that the first pick is not yellow (so it can be either blue or red), and the second pick is a blue marble.

Now there are two cases.

The first marble is red and the second blue

the first marble is blue and the second blue

We need to find the probability in each case.

The probability that the first marble is red is equal to the quotient between the number of red marbles (6) and the total number of marbles (12)

p = 6/12

Now, for the second draw, we need a blue marble, the probability in this case is the quotient between the number of blue marbles (4) and the total number of marbles in the bag (now there are 11, because one is already taken)

q = 4/11

The joint probability is equal to the product of the individual probabilities, then:

P₁ = p*q = (6/12)*(4/11) = 2/11

And for the other case, we draw two blue marbles:

For the first draw, the probability is:

p = 4/12

And for the second draw, now there are 3 blue marbles and 11 total marbles, then the probability is:

q = 3/11

The joint probability is:

P₂ = (4/12)*(3/11) = 1/11

The total probability is then:

P = P₁ + P₂ = 2/11 + 1/11 = 3/11

K-Means uses Euclidean distance. The output includes average and maximum distances, separation, and convergence after iterations related to the number of starting seeds.

In the output of a K-Means cluster analysis, "Ave Distance" refers to the average distance between the data points and their assigned cluster centroids.

"Max Distance" represents the maximum distance between any data point and its assigned centroid. "Separation" indicates the distance between the centroids of different clusters, reflecting how well-separated the clusters are.

Convergence in K-Means clustering refers to the point when the algorithm reaches stability and the cluster assignments no longer change significantly.

When the video mentions convergence after 4 iterations, it means that after four rounds of updating cluster assignments and re-computing centroids, the algorithm has achieved a stable result.

The "Number of starting seeds" option determines how many initial random seeds are used for the algorithm, and it can affect the number of iterations needed for convergence. Increasing the number of starting seeds may result in faster convergence as it explores different initial configurations.

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Answer:

\(\{58198.2573,58239.7427\}\)

Step-by-step explanation:

We assume that the following conditions are true before constructing the confidence interval:

Assumption #1: Random Sampling.

Assumption #2: Independence.

Assumption #3: Large Sample.

Assumption #4: The 10% Condition (sample size is no bigger than 10% of population

Assumption #5: The Success / Failure Condition.

Assumption #6: Homogeneity of Variances.

A 95% confidence level correlates to a critical value of \(z^*=1.96\), hence:

\(\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=58219\pm 1.96\biggr(\frac{56}{\sqrt{28}}\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}\)

Therefore, we are 95% confident that the true mean of the average yearly income for a married couple living in city C is between $58,198.2573 and $58,239.7427

For C we get

C = (A-b)/εm

Substract your y-intercept from the absorbance and divide by the slope

Beer's law, or Beer-Lambert law, is a relation between the concentration, degree of attenuation, optical path length, and absorbance of a solution. This law is often employed in the analysis of chemicals as it is a straightforward relation. The law was named after August Beer and Johann Heinrich Lambert.

The basic idea here is to use a graph plotting Absorbance vs. Concentration of known solutions. Once you have that you can compare the absorbance value of an unknown sample to figure out its concentration.

You will be applying Beer's law to calculate the concentration.

The equation for Beer's law is: A = εmCl

(A=absorbance, εm = molar extinction coefficient, C = concentration, l=path length of 1 cm)

You should have a data set which was used to create a standard curve. The graph should plot concentration (independent variable) on the x-axis and absorption (dependent variable) on the y axis.

You'll need to add a line of best fit to the data points and determine the equation for the line. The equation should be in y=mx + b form.

y = absorbance (A)

Note: no unit for absorbance

x = concentration (C)

Note: unit is M or mol/L

m = (εm) = slope or the molar extinction coefficient in beers law which has units of \(M^-^1cm^-^1\)

So A = εmC +b

If you solve for C you should get

C = (A-b)/εm

So if you substract your y-intercept from the absorbance and divide by the slope, you are finding the concentration of your sample.

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The given question is incomplete, So we take the similar question:

How do you calculate concentration from absorbance?

Answer:

Given,

y=x³ ,0≤x≤2

We have to find the surface area of the surface by rotating the curve about the x axis.

For rotation about the x axis, the surface area formula is given by-

s=2π∫ᵇₐ y√1+(y)² dx

y=x³

y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

s=2π∫₀²(x³)√1+(3x²)² dx

let u=1+9x⁴

du=36x³dx

dx/36x³

Substituting u and du in the integral,

s= 2π∫₀²(x³)√u du/36x³

s= 2π∫₀²√u du

s= 2π/36.2/3[u.3/2]₀²

s= π/27[(145)³/²-(1)³/²]

s= π/27 [1746.03-1]

s= π/27 [1745.03]

s= 64.67π

s= 64.67(3.14)

s=203.06 square units.

therefore, the exact surface area is 203.06 square units.

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Answer:

      In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.                       

         Given:    y=3x, for x is in [1,125] about the y axis.

                                            y=x³ ,0≤x≤2

Lets find the surface area of the rotating curve,

Finding surface area for rotation along x-axis,

                                    s=2π∫ᵇₐ y√1+(y)² dx

                                     y=x³

                                     y'=3x²

By rotating the curve y=x³ about the x axis in the interval [0,2]

                           s=2π∫₀²(x³)√1+(3x²)² dx

                          Assuming  u =1+9x⁴

                                           du=36x³dx

                                               =dx/36x³

Substituting respective values of u and du in the integral,

                              s= 2π∫₀²(x³)√u du/36x³

                              s= 2π∫₀²√u du

                              s= 2π/36.2/3[u.3/2]₀²

                              s= π/27[(145)³/²-(1)³/²]

                              s= π/27 [1746.03-1]

                              s= π/27 [1745.03]

                              s= 64.67π

                              s= 64.67(3.14)

                              s=203.06 square units.

hence, the surface area is 203.06 square units.

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Answer:

1208.9

Step-by-step explanation:

To figure out the answer we have to separate it two parts

So the surface area of the piñata is

=The surface area of first cone + the area of the second second cone

=π×r×(r+s)+π×r×(r+s)

=3.14×7×(7+24)+3.14×7×(7+17)

=3.14×7×31+3.14×7×24

=681.38+527.52

=1208.9

Note:I am not sure so if you have any doubts. You can go with others

Given:

\(m\angle L=m\angle Z=70^\circ\)

\(m\angle N=m\angle Y=90^\circ\)

To find:

The value of \(m\angle 1\).

Solution:

In triangle XYZ,

\(m\angle Y=m\angle N=90^\circ\)        (Given)

\(m\angle Z=m\angle L=70^\circ\)         (Given)

\(m\angle X+m\angle Y+m\angle Z=180^\circ\)        [Angle sum property]

\(m\angle 1+90^\circ+70^\circ=180^\circ\)

\(m\angle 1+160^\circ=180^\circ\)

\(m\angle 1=180^\circ-160^\circ\)

\(m\angle 1=20^\circ\)

Therefore, the \(m\angle 1\) is 20°.

Answer:

Step-by-step explanation:

( 9^2 ) = 23

The distance between ping's home to aris's home will be 1 street and 12th avenue.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given,

Ping house ⇒ 3rd street and 6th avenue

Ari's home ⇒  21st street and 18th avenue

So, the distance between them

21 - 3 = 18 street

18 - 6 = 12 avenue.

Hence "The distance between ping's home to aris's home will be 1 street and 12th avenue".

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The answer is y = 2x - 15

The equation of a line is y = mx +c

m = slope

c = y intercept

From this equation y=2x+6

m = 2

Since the lines are parallel their gradients are also the same

Equation of the line using point (8,1) is

y - 1 = 2(x-8)

y - 1 = 2x - 16

y = 2x - 15

Hope this helps

Answer: y=2x-15

Step-by-step explanation: Since the lines are parallel their slopes will be the same, so all you need to do is plug in (8,1) in the x and y values of the equation: y=2x+b. When you do this you get 1=2(8)+b. Simplify. The b value will be -15 which is the y-intercept so the answer is y=2x-15

In a basket holding 35 pieces of fruit with an apple-to-orange ratio of 2:5, there are 10 apples.

To find the number of apples in the basket, we need to determine the ratio of apples to the total number of fruit pieces.

Given that the ratio of apples to oranges is 2:5, we can calculate the total number of parts in the ratio as 2 + 5 = 7.

To find the number of apples, we divide the total number of fruit pieces (35) by the total number of parts (7) and multiply it by the number of parts representing apples (2):

Apples = (2/7) * 35 = 10.

Therefore, there are 10 apples in the basket of 35 pieces of fruit.

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Answer: 125.6 ml

Step-by-step explanation: V = (3.14) (2^2) (10)

V = (3.14) (4)(10)

V= 125.6 cm^3

1 cubic centimeter = 1 milliliter

The solution of given Expression without using the absolute value Symbol is  -(x/3), (x/3)

If x < 0, then -x > 0. Therefore, we can write:

|x/3| = |-x/3| = (-x)/3 = -(x/3)

So, the expression |x/3| can be written as -(x/3) when x < 0 and

(x/3) when x>0

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\(|7x|>21\\7|x|>21\\|x|>3\\x>3 \vee x<-3\\x\in(-\infty,-3)\cup(3,\infty)\)

Answer:

Sure here O- cookie

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

Answer:

12.89

Step-by-step explanation:

use a calculator

Answer:

y = 200 + 50x

Step-by-step explanation:

y = cost

x = number of months

The cost is equal to the cost to open the plan plus the monthly fee times the number of months

y = 200 + 50x

Answer:

y = 200 + 50x

Step-by-step explanation:

the cost = the base cost plus the monthly charge ($50 per the number of months you pay it)

hope this helps (/o.o)/<3

Answer:

what do you have to do or solve... it doesn't make sense what's got to happen

Answer:

there is no real solution

Step-by-step explanation:

There is no number that, when squared, produces a negative value. A negative multiplied by a negative gives a positive, and a positive times a positive gives a positive. You can however have a ± symbol to indicate that the root of 36 could be either positive or negative

Answer:

6. 7.5/1

7. 2.4/1

8. 40/1

Step-by-step explanation:

All you have to do is divide the 2 numbers to find the unit rate.

Answer:

6: 7.5 pizzas per Classroom

7: 2.4 Liters per test

8: 40 Points per Game

Answer:

-2/3

Step-by-step explanation:

x1 = -1, y1 = 4;

x2 = 2, y2 = 2;

Use the given slope formula to get the answer by yourself.  

To find the volume of the solid obtained by revolving the region enclosed by the curve y=e^x, the x-axis, and the lines x=0 and x=1 around the x-axis, we can use the method of cylindrical shells.First, we need to find the equation of the curve y=e^x. This is an exponential function with a base of e and an exponent of x. As x varies from 0 to 1, y=e^x varies from 1 to e.

Next, we need to find the height of the cylindrical shell at a particular value of x. This is given by the difference between the y-value of the curve and the x-axis at that point. So, the height of the shell at x is e^x - 0 = e^x.
The thickness of the shell is dx, which is the width of the region we are revolving around the x-axis.
Finally, we can use the formula for the volume of a cylindrical shell:
V = 2πrh dx
where r is the distance from the x-axis to the shell (which is simply x in this case), and h is the height of the shell (which is e^x).So, the volume of the solid obtained by revolving the region enclosed by the curve y=e^x, the x-axis, and the lines x=0 and x=1 around the x-axis is given by the integral:
V = ∫ from 0 to 1 of 2πxe^x dx
We can evaluate this integral using integration by parts or substitution. The result is:
V = 2π(e - 1)
Therefore, the volume of the solid is 2π(e - 1) cubic units.

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The solution to the equation is y = 5.

Therefore, the correct answer is "O y = 5."

Option C.

Here,

Let's solve the equation step by step to find the value of y:

Combine the y terms on the left side of the equation:

y + 3y + 6 = 26

Combine the y terms on the left side of the equation:

4y + 6 = 26

Move the constant term to the other side of the equation:

4y = 26 - 6

Simplify the right side:

4y = 20

Now, solve for y by dividing both sides of the equation by 4:

y = 20 / 4

y = 5

So, the solution to the equation is y = 5.

Therefore, the correct answer is "O y = 5."

Option C.

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The fraction of the value given as 125% can be expressed by the term of  125% = 5/4.

A ratio in which the total value is always 100 is a ratio, and a percentage is a portion of that ratio.

To represent a portion of a whole, we utilise fractions. Now, we must translate a percentage to a fraction.

Use the instructions below to convert 125% to a fraction:

First, add the percent sign.

Divide the supplied percentage by 100 to express it as a fraction.

As a result, we can write as 125/100.

To simplify the fraction, divide the numerator and denominator by their respective HCFs.

Now, 125 percent can be expressed as 125/100.

When the given fraction is simplified, we obtain

[Dividing the numerator and denominator by their HCF, which is 25]: 125/100 = 5/ 4

Hence, the fraction of 125% is 5/4.

Using a percent to fraction calculator is another way to confirm.

Hence, the fraction of 125% is 5/4.

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Answer:

C. n = 90; p = 0.8

Step-by-step explanation:

According to the Central Limit Theorem, the distribution of the sample means will be approximately normally distributed when the sample size, 'n', is equal to or larger than 30, and the shape of sample distribution of sample proportions with a population proportion, 'p' is normal IF n·p ≥ 10 and n·(1 - p) ≥ 10

Analyzing  the given options, we have;

A. n = 45, p = 0.8

∴ n·p = 45 × 0.8 = 36 > 10

n·(1 - p) = 45 × (1 - 0.8) = 9 < 10

Given that for n = 45, p = 0.8, n·(1 - p) = 9 < 10, a normal distribution can not be used to approximate the sampling distribution

B. n = 90, p = 0.9

∴ n·p = 90 × 0.9 = 81 > 10

n·(1 - p) = 90 × (1 - 0.9) = 9 < 10

Given that for n = 90, p = 0.9, n·(1 - p) = 9  < 10, a normal distribution can not be used to approximate the sampling distribution

C. n = 90, p = 0.8

∴ n·p = 90 × 0.8 = 72 > 10

n·(1 - p) = 90 × (1 - 0.8) = 18 > 10

Given that for n = 90, p = 0.9, n·(1 - p) = 18 > 10, a normal distribution can be used to approximate the sampling distribution

D. n = 45, p = 0.9

∴ n·p = 45 × 0.9 = 40.5 > 10

n·(1 - p) = 45 × (1 - 0.9) = 4.5 < 10

Given that for n = 45, p = 0.9, n·(1 - p) = 4.5 < 10, a normal distribution can not be used to approximate the sampling distribution

A sampling distribution Normal Curve

45 × (1 - 0.8) = 9

90 × (1 - 0.9) = 9

90 × (1 - 0.8) = 18

45 × (1 - 0.9) = 4.5

Now we will investigate the shape of the sampling distribution of sample means. When we were discussing the sampling distribution of sample proportions, we said that this distribution is approximately normal if np ≥ 10 and n(1 – p) ≥ 10. In other words

Therefore;

A normal curve can be used to approximate the sampling distribution of only option C. n = 90; p = 0.8