3. (07.05 MC) An equation is shown below: 12x + 3(x - 5) = 6x + 9x - 15
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points)​

The notation "||v||" typically refers to the Euclidean norm (also known as the magnitude or length) of a vector v in a Euclidean space. The Euclidean norm of a vector v in n-dimensional space is defined as the square root of the sum of the squares of its components:

||v|| = sqrt(v1^2 + v2^2 + ... + vn^2)

Given that ||v|| = 8, we can find the Euclidean norm of -7v as follows:

||-7v|| = 7 * ||-v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2)

Since -v has the same magnitude as v but points in the opposite direction, we can replace each vi in the above expression with -vi:

||-7v|| = 7 * sqrt((-v1)^2 + (-v2)^2 + ... + (-vn)^2) = 7 * sqrt(v1^2 + v2^2 + ... + vn^2)

But we know that ||v|| = sqrt(v1^2 + v2^2 + ... + vn^2) = 8, so we can substitute:

||-7v|| = 7 * ||v|| = 7 * 8 = 56

Therefore, ||-7v|| is 56.

The area of the fiqure is 132 cm².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the area is 132 cm².

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There are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).

Assuming that the distance between adjacent lattice points is equal to 1 unit, we can find the number of paths from [tex]a$ to $b$[/tex] consisting of exactly six line segments by using the concept of permutations and combinations.

To reach [tex]b$ from $a$[/tex] using exactly 6 line segments, we need to make 3 horizontal and 3 vertical moves, with each move covering a distance of 1 unit. The order in which we make these moves is important.

Out of the 6 moves, we can choose 3 moves to be horizontal and the remaining 3 to be vertical. The number of ways of doing this is given by the combination formula:

[tex]$C(6,3) = \frac{6!}{3!3!} = 20$[/tex]

Once we have selected the 3 horizontal moves and 3 vertical moves, we can arrange them in any order. The number of ways of doing this is given by the permutation formula:

[tex]$P(6,6) = 6! = 720$[/tex]

Therefore, the total number of paths from[tex]$a$ to $b$[/tex]consisting of exactly six line segments (vertical, horizontal or inclined) is given by the product of the number of ways of choosing 3 horizontal moves out of 6, and the number of ways of arranging the 6 moves:

[tex]$20 \times 720 = 14,400$[/tex]

Hence, there are 14,400 paths from $a$ to $b$ consisting of exactly six line segments (vertical, horizontal or inclined).

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There are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or inclined).

We can use the concept of permutations and combinations.

First, we need to consider the possible directions for each line segment:

vertical, horizontal, and inclined (assume inclined in both the top-right and bottom-right directions).

So there are 4 possible directions for each segment.

Since we have 6 line segments, we need to find the total number of paths that can be formed by arranging the 4

directions for the 6 segments.

We can use the formula for permutations with repetition, which is [tex]n^r[/tex], where n is the number of possible directions (4)

and r is the number of segments (6).

Plug in the values into the formula:

[tex]4^6[/tex] = 4096.

So, there are 4096 paths from point a to point b that consist of exactly six line segments (vertical, horizontal, or

inclined).

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The length of the second shelf is 98 centimeters.

Let's denote the length of the first shelf as x centimeters. According to the problem, we have the following equations for the lengths of the other shelves:

Second shelf: 2x + 18 cm

Third shelf: x - 12 cm

Fourth shelf: x + 4 cm

Robert must use the entire 2.5-meter board for the shelves, so the sum of the lengths of the four shelves should be equal to 2.5 meters, or 250 centimeters. Thus, we can write an equation:

x + (2x + 18) + (x - 12) + (x + 4) = 250

Simplify the equation:

x + 2x + 18 + x - 12 + x + 4 = 250

Combine like terms:

6x + 10 = 250

Subtract 10 from both sides:

6x = 240

Now, divide by 6:

x = 40

Now that we have the length of the first shelf (x = 40 cm), we can find the length of the second shelf:

Second shelf = 2x + 18 = 2(40) + 18 = 80 + 18 = 98 cm

So, the length of the second shelf is 98 centimeters.

Answer:

114 cm

Step-by-step explanation:

Let's start by finding the shortest shelf.

The second shelf is 18 centimeters longer than twice the length of the first shelf. The first shelf is smaller than the second shelf.

The third shelf is 12 centimeters shorter than the first shelf. The third shelf is shorter than the first shelf, so, the third shelf is the shortest shelf.

Let's call the length of the third shelf s.

We know that the third shelf is 12 centimeters shorter than the first shelf. In other words, s is 12 centimeters shorter than the first shelf. So, we can write the length of the first shelf as:

[tex]s+12[/tex]

We also know that the second shelf is 18 cm longer than twice the length of the first shelf.

Start by multiplying the length of the first shelf by 2.

[tex]2(s+12)=2s+24[/tex]

Now, let's add 18.

[tex]2s+24+18=2s+42[/tex]

So, the length of the second shelf is 2s+42.

The remaining shelf is 4 centimeters longer than the first shelf. Remember that the first shelf is s+12. Let's add 4.

[tex]s+12+4=s+16[/tex]

So, the first shelf is s+12, the second shelf is 2s+42, the third shelf is s, and the remaining shelf is s+16.

When you add them all together, you will get the 2.5 meter board.

2.5 meters is equal to 250 cm.

So, the first shelf plus the second shelf plus the third shelf plus the remaining shelf is equal to the entire board, or 250 cm.

Let's rewrite that in terms of s:

[tex](s+12)+(2s+42)+s+(s+16)=250=\\5s+70=250=\\5s=180=\\s=36[/tex]

We now know that s=36 cm.

The problem asks how long the second shelf is. Recall that the second shelf is 2s+42.

Let's plug in 36 to this expression:

[tex]2s+42=\\2(36)+42=\\72+42=\\114[/tex]

So, the second shelf is equal to 114 cm.

In 2016, the total number of cars produced in the world was 72 million (rounded to the nearest whole number) by forming linear equation.

In 2011, the total number of cars produced in the world was 59.9 million.

In 2016, the total number of cars produced in the world was 21% greater than the total number produced in 2011.

Let us say in 2016 the total number of cars produced in the world was N million.

Therefore, by expressing the given problem in a linear equation we get,

Total number produced in 2016, N = 59.9 + (21% of 59.9 )     in millions

⇒ N = 59.9 + [tex][ \frac{21}{100} ] 59.9[/tex]     ( in millions )

= 59.9 + 12.579    ( in millions )

= 72.479  ( in millions )

= 72 millions ( rounded to the nearest whole number)

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The transformations of the functions compared to the parent function are given as follows:

C. Reflection over the x-axis, vertical stretch by a factor of 2, and shift right units.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

y = sqrt(x).

Hence the transformations are given as follows:

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Answer:

Jessica has 400 cm^3 of material. She uses 35cm^3 to make a right triangular prism. She wants to make a second prism that is a dilation of the first prism with a scale factor of 2.5.

The volume of the first prism is 35 cm^3. Since the second prism is a dilation of the first prism with a scale factor of 2.5, its volume will be (2.5)^3 = 15.625 times greater than that of the first prism. Therefore, the volume of the second prism will be 35 x 15.625 = 546.875 cm^3.

To make the second prism, Jessica needs an additional material of 546.875 - 35 = 511.875 cm^3.

So Jessica needs an additional material of 511.875 cm^3 to make the second prism.

Step-by-step explanation:

The statement that is true is:

The probability that a randomly selected player on Team C is 10 years old is 5/16.

Option A is the correct answer.

We have,

The probability that a randomly selected player on Team C is 10 years old.

= Number of 10 years old players in Team C / Total players in Team C

= 5./16

The probability that a randomly selected player on Team A is 8 years old.

= Number of 8 years old players in Team A / Total players in Team A

= 4/15

The probability that a randomly selected 8-year-old player is on Team C.

= Number of 8 years old players in Team C / Total  8 years old players

= 8/21

The probability that a randomly selected 10-year-old player is on Team B.

= Number of 10 years old players in Team C / Total 10 years old players

= 5/14

Thus,

The probability that a randomly selected player on Team C is 10 years old is 5/16.

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A rhombus is a quadrilateral with all four sides of equal length. When AB¯¯¯¯¯¯ || CD¯¯¯¯¯¯ and AB¯¯¯¯¯¯ ≅ CD¯¯¯¯¯¯, we know that ABCD is a parallelogram with opposite sides parallel and equal in length. The correct Answer is B.

To show that it is a rhombus, we need to prove that all four sides are equal.

Since the diagonals of a parallelogram bisect each other, we know that AP = CP and BP = DP.

If we can show that BC = AD, we can conclude that ABCD is a rhombus.

Using the fact that AB¯¯¯¯¯¯ || CD¯¯¯¯¯¯, we can show that ΔABP ≅ ΔCDP

Therefore, we have: BP/DP = AB/CD

Hence, the correct answer is B.

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Jamar would need to invest approximately $12,115.77, rounded to the nearest ten dollars, for the value of the account to reach $18,000 in 7 years using compound interest.

We can use the formula for compound interest to solve for the initial investment amount, which is:

A = P(1 + r/n)^(nt)

where A is the future value, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, we want to find P, and we know that A = $18,000, r = 0.047, n = 4 (quarterly compounding), and t = 7. Substituting these values, we get:

$18,000 = P(1 + 0.047/4)^(4*7)

$18,000 = P(1.01175)^28

P = $12,115.77

Therefore, Jamar would need to invest approximately $12,115.77, rounded to the nearest ten dollars, for the value of the account to reach $18,000 in 7 years.

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Answer:

Step-by-step explanation:

One way for Paul to display his data is by using a scatter plot. A scatter plot is a graph that uses ordered pairs to represent data points. In this case, each data point would represent a friend's score and the number of minutes they spent studying science over the weekend.

To create a scatter plot, Paul would plot each data point as an ordered pair on a coordinate plane. The x-coordinate would represent the number of minutes spent studying, and the y-coordinate would represent the friend's score on the science test. Paul could then use a title and labels for the x and y axes to make the graph clear and informative.

A scatter plot is a good choice for this data because it allows Paul to easily see any relationship between the amount of time spent studying and the scores on the science test. He can also use the graph to identify any outliers or patterns in the data.

The area of the circle in the graph is 113 square units.

Remember that for a circle of radius R, the area is given by the simple formula you can see below.

A = pi*R²

Where pi = 3.14, so we can use this formula to find the area of the circle.

On the diagram we can see that the radius of the circle is:

R = 6 units

Replacing that in the area formula we will get.

A = 3.14*(6 units)²

A = 113.04 units ²

The correct option is the third one.

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The inverse of the graphs are added as an attachment

To plot the inverse of a graph, you can follow these steps:

See attachment for the graphs

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Answer:

A

Step-by-step explanation:

because when we say statical data we mean numerical data (asking u about number) so the answer yes i have 5 or no they r more or less.

Answer: 136

Step-by-step explanation: it's the only big number

Answer:

Step-by-step explanation:

To find the point that is a certain fraction of the way between two given points, we can use the midpoint formula and the scalar multiplication of vectors.

Let's first find the vector that points from point A to point B:

�

�

⃗

=

(

4

−

3

)

−

(

−

3

−

2

)

=

(

7

−

1

)

AB

=(

4

−3

​

)−(

−3

−2

​

)=(

7

−1

​

)

The scalar multiplication of a vector with a scalar value scales the length of the vector. To find the point that is 3/4 of the way from point A to point B, we can multiply the vector $\vec{AB}$ by 3/4:

3

4

�

�

⃗

=

3

4

(

7

−

1

)

=

(

21

4

−

3

4

)

4

3

​

AB

=

4

3

​

(

7

−1

​

)=(

4

21

​

−

4

3

​

​

)

Finally, we can add this vector to point A to get the point that is 3/4 of the way from point A to point B:

(

−

3

−

2

)

+

(

21

4

−

3

4

)

=

(

3

4

,

−

11

4

)

(

−3

−2

​

)+(

4

21

​

−

4

3

​

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)=

(

4

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​

Answer: I'm not really sure what you're trying to find but 250in³

Step-by-step explanation:

10in x 5in x 5in = 250 in³

The size of Justin's painting that needs to be to fit in this frame is  530 square inches

It is important to note that the formula for the area of a rectangle is expressed with the equation;

A = lw

Such that the parameters of the formula are;

From the information given, we have that;

Width of the frame = 22 1/2 inches

Length of the frame = 26 1/2 inches

But the width around the frame = 221/2 - 2 1/2 = 45/2 - 5/2 = 20 inches

Substitute the values

Area = 20(53/2)

multiply the values

Area = 530 square inches

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An equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

What is the slope-intercept form?

The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

Here, we have

Given graph and we have to find the equation for the line shown in the given graph.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 20)/(0 + 3)

Slope (m) = -15/3

Slope (m) = -5.

At data point (0, 5) and a slope of -5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -5(x - 0)

y - 5 = -5x

y = -5x + 5

Hence, an equation in slope-intercept form for the line shown in the given graph is equal to y = -5x + 5.

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The probability of drawing two hearts without replacement is 0.0588. The probability of drawing an ace followed by a king without replacement is 0.006.

Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.

6) To find the probability of drawing two hearts without replacement, we can use the formula:

P(two hearts) = (number of ways to choose 2 hearts) / (number of ways to choose 2 cards from a deck)

As there are 13 hearts in a standard deck of 52 cards, the number of ways to choose 2 hearts is given by the combination:

13 choose 2 = 13! / (2! * (13-2)!) = 78

The number of ways to choose 2 cards from a deck of 52 cards is:

52 choose 2 = 52! / (2! * (52-2)!) = 1326

Therefore, the probability of drawing two hearts without replacement is:

P(two hearts) = 78 / 1326 ≈ 0.0588 (rounded to four decimal places)

7) To find the probability of drawing an ace followed by a king without replacement, we can use the formula:

P(ace, then king) = P(ace) * P(king|ace not drawn)

The probability of drawing an ace is given by:

P(ace) = 4/52 = 1/13

After drawing an ace from the deck, there are 51 cards remaining, of which 4 are kings. Therefore, the probability of drawing a king given that an ace has not been drawn is:

P(king|ace not drawn) = 4/51

Hence, the probability of drawing an ace followed by a king without replacement is:

P(ace, then king) = (1/13) * (4/51) ≈ 0.006 (rounded to three decimal places).

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Answer:1,041

Step-by-step explanation:

The surface area of the tetrahedral die is 1353 square millimeters

To find the surface area of the tetrahedral die, we need to find the area of each of the four equilateral triangular faces and add them together.

The formula for the area of an equilateral triangle is A = (√(3)/4) x s², where s is the length of the side.

In this case, the base edge of the tetrahedral die is 26 millimeters, so the length of each side of the equilateral triangles is also 26 millimeters.

Using the formula for the area of an equilateral triangle, we can find the area of one face:

A = (√(3)/4) x 26²

A = 338.3 square millimeters (to the nearest tenth)

Since there are four faces, we can multiply the area of one face by 4:

4 x 338.3 = 1353.2 square millimeters

Therefore, the surface area of the tetrahedral die is approximately 1353 square millimeters (to the nearest ten square millimeters).

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The values of x and y using trigonometric ratios are: 12) x = 8, y = 4√3 and 14) y = 11√2, x = 11√2

Some of the common trigonometric ratios are:

Using the above as a guide, we have the following:

12) Let us solve for x and y using trigonometric ratios to get:

4/x = sin 30

4/0.5 = x

x = 8

Similarly:

4/y = tan 30

y = 4/tan 30

y = 4√3

Using the above as a guide, we have the following:

14) Let us solve for x and y using trigonometric ratios to get:

y/22 = sin 45

y = 11√2

Similarly:

x/22 = cos 45

x = 11√2

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The values of x and y using trigonometric ratios are:

12) x = 8, y = 4√3

14) x = 11√2, y = 11√2

The three most common trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = adjacent/hypotenuse

12) We can find x and y using trigonometric ratios as follows:

4/x = sin 30

x = 4/sin 30

x =4/0.5

x = 8

We can solve for y as:

4/y = tan 30

y = 4/tan 30

y = 4(1/√3)

y = 4√3

14) We can find x and y using trigonometric ratios as follows:

y/22 = sin 45

y = 22 * 1/√2

Rationalizing the denominator gives:

y = 11√2

We can find x as:

x/22 = cos 45

x = 22 * 1/√2

Rationalizing the denominator gives:

x = 11√2

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The probabilities for the given events are:

P(a vowel) = 3/11

P(N or S) = 2/11

P(not C) = 9/11

The probability is given by the quotient between the outcomes that meet the event and the total possible outcomes.

In Candlestick there are 11 letters.

4) There are 3 vowels, then this probability is:

P(a vowel) = 3/11

5) The letters N and S appear 2 times, then the probability is:

P(N or S) = 2/11

6) The letter C appears 2 times, then the other 9 letters are not C, so the probability is:

P(not C) = 9/11

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Answer:

9 inches

Step-by-step explanation:

A foot is 12 inches long. To find a fourth of a foot, divide 12 by four to get 3. This means that Julio has already dug a hole one foot and three inches deep. To make his hole two feet deep, he will need to dig the other 3/4 of the foot. To find 3/4 of a foot, take 1/4 of a foot (3 inches) and multiply by 3 (9 inches).
Julio will have to dig 9 more inches.

Multicollinearity refers to a situation in multiple regression where the independent variables, or predictors, in a statistical model are correlated with each other. Option B multicollinearity is correct.

Multicollinearity can result in several problems, including:

It is important to identify and address multicollinearity in a multiple regression model to ensure accurate and reliable interpretation of the results. This can be done through techniques such as variance inflation factor (VIF) analysis, principal component analysis (PCA), or using a subset of predictors with low intercorrelation.

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The term used to describe the case when the independent variables in a multiple regression model are correlated is

b. multicollinearity  is correct.

Multiple regression is a typical method in statistical modelling for determining the association between a dependent variable and two or more independent variables.

The fundamental tenet of multiple regression is that there is no correlation between the independent variables. Multicollinearity is the outcome when this assumption is broken, which can happen in real life.

When two or more independent variables in a multiple regression model have a high correlation with one another, multicollinearity arises.

Due to these issues, the model's coefficients may not be correctly interpreted, producing estimates that are inaccurate and unstable.

It is challenging to separate the distinct impacts of each independent variable on the dependent variable when multicollinearity is present because these effects are entangled and difficult to separate.

b. multicollinearity is correct option.

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Answer:

angle EDC = 64 degrees

The requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.

Here,
AC is the perpendicular bisector of side GH, But this bisector also bisects the triangle in two equal halves.
So,
GH =2GB
FH = 2 * 8 = 16

CH = CG
CH = 12

Thus, the requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.

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Answer: 26 degrees

Step-by-step explanation:

12/24 = 1/2

0.3895 Answer

Step-by-step explanation:

I thought you meant it on paper.

Answer:

0.3895

Step-by-step explanation:

Write out the division problem: 389.5 ÷ 1000.

Since we're dividing a decimal number by 1000, we can simply move the decimal point three places to the left to convert 1000 to 1.000: 389.5 ÷ 1.000.

Moving the decimal point three places to the left also means we need to add three trailing zeroes to the dividend: 389.5 becomes 389.500.

Now we can perform the long division: divide 3 by 1, write the quotient 3 above the 8, and subtract 3 from 8 to get 5 as the new remainder. Bring down the next digit 8 to get 58.

Divide 58 by 1, write the quotient 58 above the 9, and subtract 58 from 89 to get 31 as the new remainder. Bring down the next digit 5 to get 315.

Divide 315 by 1, write the quotient 315 above the decimal point, and subtract 315 from 389 to get 74 as the new remainder.

Since there are no more digits to bring down, we've reached the end of the long division. The final quotient is 0.3895.

Don't forget to include the decimal point in the answer, since we moved it three places to the left in step 2. The final answer is 0.3895.

So, 389.5 ÷ 1000 = 0.3895.