the mean of the data set {9, 5, y, 2, x } is twice the data set {8, x, 4, 1, 3}. What is (y-x)^2?​

Step-by-step explanation:

First, we can try to factor out the greatest common factor, which is 1 in this case. Then, we can try to factor by grouping:

x³ - 5x² - 8x + 12

= x²(x - 5) - 4(x - 3)

= x²(x - 5) - 4(x - 3)

Now we can see that we have a common factor of (x - 3), which we can factor out:

x²(x - 5) - 4(x - 3)

= (x - 3)(x² - 4x + 4)(x - 5)

The expression is now fully factorised, so the complete factorisation of x³ - 5x² - 8x + 12 is:

(x - 3)(x - 2)²(x - 5)

Answer:

Step-by-step explanation:

First make a ratio,

6:62.64

Now make an equation

6/62.64=4/x

solve for x...

x=41.76

Answer:

c. y=x2+9x+18

Step-by-step explanation:

If we factor y=x2+9x+18 using the x method, the factors 3 and 6 mutliply to 18 as well as add to 9. that means y=x2+9x+18=(x+3)(x+6). From the graph, we can see that when y=0, it is at the x's -3 and -6. If we set (x+3)and(x+6) equal to zero (for ex. x+3=0), our x's are -3 and -6 which are the same zeros as the graph

The quadratic function that best describe the graph is y =  x² + 9x + 18.

The solution of the given graph is determined from the intersection of the curve on the horizontal axis.

The two points of intersection of the curve are -6 and - 3.

The quadratic function is determined from the solutions of the curve.

x = -6 or x = -3

x + 6 = 0 or x + 3 = 0

(x + 6)(x + 3) = 0

expand the bracket as follows;

x² + 3x + 6x + 18 = 0

x² + 9x + 18 = 0

y = x² + 9x + 18

Thus, the quadratic function that best describe the graph is y =  x² + 9x + 18.

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Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.

To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).

The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

The slope of the given line is -2/3.

Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:

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

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

To convert this equation into slope-intercept form, we can simplify and rearrange:

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

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

y = (-2/3)x - 7

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The given equation is verified using double angle identities showing that 2cos^4(x) - 2sin^4(x) = 4cos(2x)

To use the double angle identities, we can start with the identity:

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

We can rearrange this to get:

cos^2(x) = (1 + cos(2x))/2

sin^2(x) = (1 - cos(2x))/2

Substituting these into the left-hand side of the equation we want to verify, we get:

2cos^4(x) - 2sin^4(x)

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

= 2[(1 + cos(2x))/2]^2 - 2[(1 - cos(2x))/2]^2

= (1 + cos(2x))^2 - (1 - cos(2x))^2

= 1 + 2cos(2x) + cos^2(2x) - 1 + 2cos(2x) - cos^2(2x)

= 4cos(2x)

Thus, we have shown that:

2cos^4(x) - 2sin^4(x) = 4cos(2x)

So, the given equation is verified using double angle identities.

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Step-by-step explanation:

144° + m5 = 180°

m5 = 180° - 144°

m5 = 36°

m5 + 56° + m4 = 180°

m4 = 180° - 56° - 36°

m4 = 88°

m3 + 56° = 180°

m3 = 180° - 56°

m3 = 124°

since the 2 horizontal lines are parallel:

m1 = m5 = 36°

m2 = 56°

The probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

The probability mass function (PMF) and cumulative mass function (CMF) for the random variable x, which denotes the number of parts correctly classified in an optical inspection system, can be determined.

Since the classifications of the parts are independent, we can use the binomial probability distribution to model this scenario. The PMF gives the probability of obtaining a specific value of x, and the CMF gives the probability of obtaining a value less than or equal to x.

The PMF of x is given by the binomial probability formula:

P(x) = (n C x) * p^x * (1 - p)^(n - x)

where n is the number of trials (number of parts inspected), x is the number of successes (number of parts correctly classified), and p is the probability of success (probability of correct classification of any part).

In this case, n = 3 (three parts inspected) and p = 0.98 (probability of correct classification).

Let's calculate the PMF for x:

P(x = 0) = (3 C 0) * (0.98^0) * (1 - 0.98)^(3 - 0) = 0.0004

P(x = 1) = (3 C 1) * (0.98^1) * (1 - 0.98)^(3 - 1) = 0.0588

P(x = 2) = (3 C 2) * (0.98^2) * (1 - 0.98)^(3 - 2) = 0.3432

P(x = 3) = (3 C 3) * (0.98^3) * (1 - 0.98)^(3 - 3) = 0.941192

The PMF for x is:

P(x = 0) = 0.0004

P(x = 1) = 0.0588

P(x = 2) = 0.3432

P(x = 3) = 0.941192

To calculate the CMF, we sum up the probabilities up to x:

F(x) = P(X ≤ x) = P(x = 0) + P(x = 1) + ... + P(x = x)

Using the calculated probabilities, the CMF for x is:

F(x = 0) = 0.0004

F(x = 1) = 0.0592

F(x = 2) = 0.4024

F(x = 3) = 1.0

Therefore, the probability mass function (PMF) for x is {0.0004, 0.0588, 0.3432, 0.941192}, and the cumulative mass function (CMF) for x is {0.0004, 0.0592, 0.4024, 1.0}.

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Answer:

a: 4

b: package and shopping costs

c: 1/2 (   (6-3)/(16-10) )

d: cost of shipping per pound

e: y= 1/2x + 4

f: 92

Step-by-step explanation:

Okay bunch of answers

10.5

Answer:

10.5

Step-by-step explanation:

did it on khan

In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).

A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.

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Step-by-step explanation:

Decimals can always be put over 1, as they're part of a whole number.

\(\frac{0.75}{1}\)

Multiply both numerator and denominator by 100:

\(\frac{0.75 \times 100}{1\times 100} =\frac{75}{100}\)

\(\frac{0.75}{1} \: and \: \frac{75}{100} \: are \: fractions \: of \: 0.75\)

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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Answer: m=5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

471.3 = 3.142×10×H

H= 471.3÷31.42

H=15

Answer:

it's A 10

Step-by-step explanation:

10+20= 30

so 15×2=30

5+10=15

2( = ×2

A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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Remember that

the area of the circle is

A=pi*(r^2)

we have

r=9.2/2=4.6 m ------> the radius is half the diameter

substitute

A=pi*(4.6^2)

using a calculator

(Note: the value of pi is the value that appear in the calculator)

Answer:

\(\huge\boxed{D)\frac{3p}{p-3} }\)

Step-by-step explanation:

The first thing that can help you here is factoring every term.

\(p^2-4p-12\)

Factor.

\((p-6)(p+2)\)

\(6p+12\)

Factor.

\(6(p+2)\)

18p

Factor, keeping in mind the denominator of the other term.

\(6(3p)\)

\(p^2-9p+18\)

Factor.

\((p-6)(p-3)\)

Now you have simplified your original problem:

\(\frac{p^2-4p-12}{6p+12} *\frac{18p}{p^2-9p+18}\)

into:

\(\frac{(p-6)(p+2)}{6(p+2)} *\frac{6(3p)}{(p-6)(p-3)}\)

Now, after multiplying the numerator and denominator of the fractions:

\(\frac{(p-6)(p+2)(6)(3p)}{(6)(p+2)(p-6)(p-3)}\)

Then, you can simplify the fraction by cancelling terms:

\(\frac{3p}{p-3}\)

Hope it helps :) and let me know if you want me to elaborate.

Answer:

2/5, option 4.

Step-by-step explanation:

When you are dividing 2 fractions, the first fraction stays the same, and the 2nd fraction becomes the reciprocal, and the division sign becomes a multiplication sign.

The reciprocal of 2/3 is 3/2.

Now you need to change the division sign to a multiplication sign.

The equation will now become 4/15 x 3/2.

4 times 3 is 12, and 15 times 2 is 30.

12/30 isn't an option, so you will need to simplify.

Find a common factor, then divide.

6 is a common factor, so you divide both 12 and 30 by 6, to get 2 and 5.

2/5 is what you are left with.

Option 4.

4/15 divided by 2/3 is 2/5.

Answer:

hi

Step-by-step explanation:

\( \frac{4}{15} \div \frac{2}{3} = \frac{4}{15} \times \frac{3}{2} = \frac{2}{5} \)

have a nice day

Answer:

D.(-4,-8) and(2,4)

Step-by-step explanation:

y=-2x

y=x²-8

this means that the two equations are equal because they both add up to y

thus; x²-8=-2x

formulae=Ax²+bx+c=0

x²+2x-8=0

find two numbers which multiplied will give you x² and when added will give you 2x that is x and x

x²+x+x-8=0

x(x+1)+1(x-8)=0

(x+1)(x-8)=0

1)x+1=0. x= -1

1)y=-2x

y=-2(-1)=2

y=2

2)y=x²-8

y=1²-8= -8

y= -8

note*this means that the answer should have both 2 and -8 thus d is the answer

Answer:

C) 253. 3 cm²

Step-by-step explanation:

1. Sector area formula can be in degrees or radians. I will use degrees because we are given 240 degrees as a unit.

2. SA= \(\frac{x}{360}\) times \(\pi r^{2}\) where x is the degrees of the sector

3. 240/360 times 3.14(11)²

4. 0.66666667 times 379.94

5. approximately 253. 3 cm²

Answer:

Step-by-step explanation:

Answer:

slope is ((3,0).

intercept is (0, 1)

Step-by-step explanation:

so y=3x+1?

*see attachment below showing the dot plot and box plot created by Tia

Answer:

Dot plot

Step-by-step explanation:

In a dot plot, the temperature of a day is represented by 1 dot. There are 30 dots on the box plot shown in the attachment that was made by Tia.

This dot plot display makes it easier to find how many days had a temperature that is higher than 15°.

Thus, from the dot plot, we have:

2 dots representing 2 days having a temperature of 16°C each

2 days also have daily temperature of 17°C

2 days have temperature of 18°C as well, and

1 day has temperature of 19° C.

Therefore, the number of days that had a temperature above 15°C is 7 days.

Answer:

Dot Plot, Box Plot

Step-by-step explanation:

I got the other guy's answer wrong but mine is right =)

Answer:

The Inverse Property of Addition states that \(a + (-a) = 0\): The sum of a real number and its additive inverse is zero, the additive module.

Step-by-step explanation:

From the Algebra of Real Numbers we know that the Inverse Property of Addition, also know as Existence of Additive Inverse states that for all real number \(u\) exist only a real number \(v\) so that:

\(u+v = 0\)

Where \(v = -u\) and \(0\) is also known as additive module.

Therefore, we can complete the phrase below:

The Inverse Property of Addition states that \(a + (-a) = 0\): The sum of a real number and its additive inverse is zero, the additive module.

Answer:

The Inverse Property of Addition states that : The sum of a real number and its additive inverse is zero, the additive module.

Step-by-step explanation:

ive done it!

Answer:

Step-by-step explanation:

So first you do y=z and1+2=3 so 6=y=-0 is your answer :)

2600 pens.

the remaining pens Ali have after giving 1547 away.

2600 - 1547

= 1053

so, Ali has 1053 pens with him.

Ali has 2600 pens.

the amount of pens Ali has left after he gave away 1547 pens.

subtract 2600 from 1547.

\(2600 - 1547\)

\( = 1053 \: pens\)

hence, Ali has 1053 pens left with him after giving 1547 pens away.

The required answer is :

a. The third side of the reflective sticker cannot be 12 cm long.

b. It is not possible to form a triangle with side lengths of 6 cm, 8 cm, and 2 cm.

According to the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side.

In this case, the sum of the two given sides (6 cm + 8 cm = 14 cm) is less than the length of the third side (12 cm).

Therefore, it is not possible to form a triangle with side lengths 6 cm, 8 cm, and 12 cm.

(b) The third side of the reflective sticker cannot be 2 cm long.

Applying the triangle inequality theorem, the sum of any two sides of a triangle must be greater than the third side.

The sum of the two given sides (6 cm + 8 cm = 14 cm) is greater than the length of the third side (2 cm).

Hence, it is not possible to form a triangle with side lengths 6 cm, 8 cm, and 2 cm.

Therefore, a. The third side of the reflective sticker cannot be 12 cm long.

b. It is not possible to form a triangle with side lengths of 6 cm, 8 cm, and 2 cm.

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