write the complex number in standard form
√-180

The expression for the perimeter of the frame is 128 inches + 10w.

Width of the mat = 4w

width of the frame = w

Now,

Let the length of the poster be = L

Let the width of the poster = W.

Therefore,  According to the question,

L = 48 inches and W = 16 inches.

The total width of the mat and frame around the poster will be -

= 4w + w

= 5w.

Calculating the perimeter of the frame -

= 2 (L + W + 5w),

= 2 (48 + 16  + 5w)

= 2 (64 + 5w)

= 128 + 10w.

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The solution x = 1 of the equation log Subscript 3 Baseline (x + 2) = 1 is shown in figure.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ log₃ (x + 2) = 1

Now, We can draw the graph of expression log₃ (x + 2) = 1.

Here, The expression is,

⇒ log₃ (x + 2) = 1

⇒ x + 2 = 3¹

⇒ x + 2 = 3

⇒ x = 3 - 2

⇒ x = 1

Thus, The solution x = 1 is shown in figure.

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Answer:

y = log x + 3

Step-by-step explanation:

The answer above is incorrect.

Answer:

The solution to the two functions is (1, 3) and it represents the temperature at which the number of people visiting the zoo equals the number of people leaving the zoo.

Answer:

138

Step-by-step explanation:

i took the same quiz.

It is, indeed, a function. The function domain is {3,6,12,18} and the function range is {5,7,9,10}.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.

Here,

domain={3,6,12,18}

range={5,7,9,10}

Yes, it is a function. The domain of function is {3,6,12,18} and range of function is {5,7,9,10}.

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Answer:

amounts of

Step-by-step explanation:

In a principal + interest loan, the principal (original amount borrowed) is divided into equal monthly amounts, and the interest (fee charged for borrowing) is calculated on the outstanding principal balance each month.

Hope this helps!

a) Distance between given points = 11 unit ; Midpoint is (0 , -1/2)

b) Distance between given points = 7 unit ; Midpoint is (-1/2 , 0)

c) Distance between given points = 4.47 unit ; Midpoint is (6 , 4)

d) Distance between given points = 8.06 unit ; Midpoint is (-1 , 1/2)

e) Distance between given points = 5 unit ; Midpoint is (4 , 5/2)

f) Distance between given points = 13 unit ; Midpoint is (1/2 , 2)

g) Distance between given points = 5√5 unit ; Midpoint is (5/2 , 5)

h) Distance between given points = √5 unit ; Midpoint is (3 , 1/2)

i) Distance between given points = 6 unit ; Midpoint is (6 , 1)

j) Distance between given points = 15 unit ; Midpoint is (1 , -5/2)

Distance between two points with coordinates (x₁ , y₁)  and (x₂ , y₂). is given by

D = √[(x₁ - x₂)² + (y₁ - y₂)²]

This formula is derived from the Pythagoras Theorem, as the points form a right triangle in plane, with the hypotenuse representing the distance between them.

Given,

a)  (0, 5) and (0 -6)

Distance = √[(0 - 0)² + (5 - -6)²] = √11² = 11 unit

Midpoint = [(x₁ + x₂)/2 + (y₁ + y₂)/2]

= [(0+0)/2 , (5 + -6)/2]

⇒ Midpoint = (0, -1/2)

b) (3, 0) and (-4, 0)

Distance = √[(3 - -4)² + (0 - 0)²] = √7² = 7 unit

Midpoint =  [(x₁ + x₂)/2 + (y₁ + y₂)/2]

= [(3+ -4)/2 , (0 + 0)/2]

⇒ Midpoint = (-1/2, 0)

Similarly,

c) (5, 2) and (7, 6)

Distance = 4.47 unit

Midpoint = (6 , 4)

d) (-3, 4) and (1, -3)

Distance = 8.06 unit

Midpoint = (-1 , 1/2)

e) (6, 4) and (2, 1)

Distance = 5 unit

Midpoint = (4 , 5/2)

f)(-2, -4) and (3, 8)

Distance = 13 unit

Midpoint = (1/2 , 2)

g) (0, 0) and (5, 10)

Distance = 5√5 unit

Midpoint = (5/2 , 5)

h) (2, 1) and (4, 0)

Distance = √5 unit

Midpoint = (3 , 1/2)

i) (6, 4) and (6, -2)

Distance = 6 unit

Midpoint = (6 , 1)

j) (-5, 2) and (7, -7)

Distance = 15 unit

Midpoint = (1 , -5/2)

Hence,

a) Distance between points is 11 unit ; Midpoint = (0 , -1/2)

b) Distance between points is 7 unit ; Midpoint = (-1/2 , 0)

c) Distance between points is 4.47 unit ; Midpoint = (6 , 4)

d) Distance between points is 8.06 unit ; Midpoint = (-1 , 1/2)

e) Distance between points is 5 unit ; Midpoint = (4 , 5/2)

f) Distance  between points is 13 unit ; Midpoint = (1/2 , 2)

g) Distance between points is 5√5 unit ; Midpoint = (5/2 , 5)

h) Distance between points is √5 unit ; Midpoint = (3 , 1/2)

i) Distance between points is 6 unit ; Midpoint = (6 , 1)

j) Distance between points is 15 unit ; Midpoint = (1 , -5/2)

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The direction of t+ u+ v is 155°.

A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.

Given:

The magnitude and direction of vectors t, u, and v are shown in the table.

Vector   Magnitude  Direction

t                 5                 250°

u                6                  60°

v               12                 330°

The coordinates of the resultant vectors:

t + u + v,

= (5 cos250° + 6cos60° + 12cos330°, 5 Sin250° + 6Sin60° + 12Sin330°)

= (11.7, -5.5)

Now, the direction of t+ u+ v = arc tan(-5.5/11.7)

= 155°

Therefore, 155° is the direction.

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Answer:

335°

Step-by-step explanation:

I took the test and got it right :)

Grouped/color-coded scatter plot: a scatter plot with a third categorical variable added, shown by color or shape, to visualize relationships between two numerical variables.

Scatter plots that include a categorical variable are known as a "Grouped Scatter Plot" or a "Color-Coded Scatter Plot". In these plots, the points on the scatter plot are color-coded or shaped according to a third categorical variable, allowing for an easy visualization of the relationship between two numerical variables while taking into account the categorical variable.

Grouped scatter plots can help to visualize patterns and trends in the data that might not be immediately apparent in a regular scatter plot. For example, you can use a scatter plot to compare the relationship between the two numerical variables for different categories. This can give insights into how the relationship between the variables changes across the different categories, and can help to identify any outliers or exceptions to the general trend.

In a color-coded scatter plot, the color of each point on the plot represents the value of the categorical variable. This can help to quickly identify patterns and trends in the data based on the color of the points, and can make it easier to see how the relationship between the two numerical variables varies across different categories.

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The normal distribution is a probability distribution used to describe the probability of a given value of a continuous variable.

The normal distribution is characterized by two parameters, the mean and standard deviation. The mean, μ, represents the center of the distribution, and the standard deviation, σ, represents the spread of the distribution.

In a production process, the normal distribution can be used to predict the probability of defects and the number of defects expected for a given mean and standard deviation. The probability of a given defect can be calculated using the formula p = 1-N(x; μ, σ), where N(x; μ, σ) is the cumulative normal distribution function, x is the number of defects, μ is the mean, and σ is the standard deviation.

For example, if a production process produces items with a mean weight of 10 grams and a standard deviation of 1 gram, then the probability of a defect occurring is calculated using the formula: p = 1-N(x; 10, 1). If we assume a defect occurs at 8 grams, then the probability of a defect occurring is 1-N(8; 10, 1) = 0.1587. This means that there is a 15.87% chance of a defect occurring in the production process.

To calculate the expected number of defects, we can use the formula E(x) = μ + (σ * N’(p)), where N’(p) is the inverse normal distribution function and p is the probability of a defect occurring. Using the example above, we can calculate the expected number of defects as 10 + (1 * N’(0.1587)) = 10.24, meaning that we can expect 10.24 defects for every 100 items produced.

In this example, there is a 15.87% chance of a defect occurring in the production process, and we can expect 10.24 defects for every 100 items produced.

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Simplify by combining like terms.

You can rearrange the problem to help you make it easier.

4x + (-2x) - 3 + 5

4x - 2x - 3 + 5

2x + 2

The simplest form is 2x + 2.

Answer:

Step-by-step explanation:

You rearrange the question by bringing the like terms together

[tex]4x + ( - 2x) + 5 - 3[/tex]

[tex]4x + ( - 2x) = 4x - 2x = 2x[/tex]

[tex]5 - 3 = 2[/tex]

Elementary row operations to find system of equation solutions in row echelon or reduced row echelon form.

We first write the augmented matrix [A|B] by combining the coefficients of the variables and the constants on the right side of the equations:

x + y + 6z | 8

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0.

Here are the steps to perform Gauss-Jordan row reduction on the augmented matrix [A|B]:

Step 1: Divide the first row by x + y + 6z to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

1/3 x - 1/3 y + 2/3 z | 2

1/2 x | -z | 0

Step 2: Subtract the first row multiplied by 1/3 from the second row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

1/2 x | -z | 0

Step 3: Subtract the first row multiplied by 1/2 from the third row to eliminate x:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 - 2/3 y + 5/3 z | 4/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 4: Divide the second row by -2/3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | -z + 3z/x + y + 6z | 3/x + y + 6z

Step 5: Subtract the second row multiplied by 5/2 from the third row to eliminate y:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 3z | -15/2

Step 6: Divide the third row by 3 to get 1 as the leading coefficient:

1 y/x + y + 6z 6z/x + y + 6z | 8/x + y + 6z

0 1 5/2 | -2/3

0 | 1 | -5

Thus, the reduced row echelon.

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a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2).

b) The joint density function for X and Y is given by: f(x,y) = 1/2 for 0 < x < y < 2.

c) The marginal probability density for Y is given by: fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.

d) The conditional probability density of X, conditional on Y = y, is given by: fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2.

This only exists for 0 < y < 2.

a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2). This is because the lengths of the two pieces of the ruler must be non-negative and must add up to 2.

b) The joint density function for X and Y is given by:

f(x,y) = 1/2 for 0 < x < y < 2.

c) The marginal probability density for Y is given by:

fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.

d) The conditional probability density of X, conditional on Y = y, is given by:

fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2. This only exists for 0 < y < 2.

Note: The factor of 1/2 in the joint density function accounts for the uniform distribution of the two breaks on the ruler, while the factor of 2 in the conditional density function accounts for the change of variables from the joint density to the conditional density.

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Answer:

The two alarm clocks will ring together again at 2:54 p.m

The correct answer is d. 260 tacos and 156 burritos and Dina gained 260 tacos and 156 burritos.

If each person specializes in the production of the good in which they have a comparative advantage and trade 260 tacos for 156 burritos, this means that both individuals benefit from trade as they can consume more of both goods than they would have without trade. Arturo specializes in producing tacos, which he trades for burritos produced by Dina. Similarly, Dina specializes in producing burritos, which she trades for tacos produced by Arturo. As a result, both individuals gain from trade, and the combined total of tacos and burritos remains the same after trade as before. In this case, both Arturo and Dina would end up with 260 tacos and 156 burritos each, which is the outcome of trade.

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The stem and leaf plot shown above indicates that the range is 33.

The difference between the greatest number in a data set and the lowest number in the same set is referred to as the data set's range.

The stem and leaf plot shown above shows that the maximum number is 50 and the lowest number is 17.

As a result, the range is:

= 50 - 17

= 33

Therefore, we may say that the data set's range is 33.

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Using either shell method, the volume of the solid generated by revolving the region bounded by y = [tex]x^{3}[/tex] and y = 0 around the lines x = 2 (a), x = 0 (b), and x = 9 (c) can be determined to be 8π, 0, and 54π, respectively.

To solve this problem using the disk method, we first need to determine the area of the region bounded by the two equations. This can be done by integrating y = [tex]x^{3}[/tex] from x = 0 to x = 2, which gives us A = 8/4 = 2. We then need to determine the radius of the disk, which is the distance from the line of rotation to the point of intersection of the two equations.

For (a), this is the distance from x = 2 to y = 2, which is 2. For (b), this is the distance from x = 0 to y = 0, which is 0. For (c), this is the distance from x = 9 to y = 27, which is 27/3. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:

(a) V = π(2)2 × 2 = 8π

(b) V = π(0)2 × 2 = 0

(c) V = π(27/3)2 × 2 = 54π

To solve this problem using the shell method, we first need to determine the limits of integration, which is the same as for the disk method. We then need to determine the radius of the shell, which is the distance from the line of rotation to the point of intersection of the two equations.

This is the same as for the disk method. We can now use the formula for the volume of a solid generated by revolving a region around a line to calculate the volume for each of the three lines:

(a) V = 2π ∫(2) ([tex]x^{3}[/tex]) dx = 8π

(b) V = 2π ∫(0) ([tex]x^{3}[/tex]) dx = 0

(c) V = 2π ∫(27/3) ([tex]x^{3}[/tex]) dx = 54π

The disk and shell methods are two methods used to find the volume of a solid generated by revolving a region bounded by the graphs of two equations around a given line.

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The distance covered by the bicycle is 0.2 miles.

A bicycle is traveling at 19 miles per hour. The number of feet the bicycle will cover in 30 seconds can be calculated as follows:

Therefore,

speed = distance / time

Hence, let's find the distance covered by the bicycle using the data given:

speed = 19 miles per hour

time = 30 seconds = 0.00833333 hours

Therefore,

distance covered = speed × time

distance covered = 19 × 0.00833333

distance covered = 0.15833327

distance covered = 0.2 miles

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The set of vectors is linearly dependent, and the linear combination equals the zero vector.

To determine whether a set of vectors is linearly independent or linearly dependent, we can use the following method:

1. Write the vectors as columns in a matrix.

2. Perform row reduction on the matrix to obtain an echelon form.

3. Check if the last non-zero row in the echelon form has leading entry 1, which indicates that the vectors are linearly independent.

4. If there is a row of all zeros in the echelon form, excluding the last row, then the vectors are linearly dependent, and we can find a nontrivial linear combination that equals the zero vector by looking at the non-trivial coefficients in that row.

The last non-zero row in the echelon form has leading entry 6, which is not 1, indicating that the set of vectors is linearly dependent.

To find a nontrivial linear combination that equals the zero vector, we can look at the row in the echelon form that has a non-trivial coefficient. In this case, the second row has coefficients 6 and -2, so a nontrivial linear combination that equals the zero vector is:

6 * V2 - 2 * V3 = |0 0 0|

So, the set of vectors is linearly dependent, and the above linear combination equals the zero vector.

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The answer is Six

for Y-intercept, x is equal to zero therefore y is equal to six

Answer:

-2/5

Explanation:

The equation is written in slope-intercept form, aka y = mx + b, where m is the slope and b is the y-intercept.

In slope intercept, the slope is always the number that comes before x.

In other words, it is the coefficient of x.

For this equation, the coefficient of x is -2/5. Hence -2/5 is the slope.

As for the y-intercept, that is a constant in the equation.

For this equation, the constant is 6. Hence, the y intercept is 6.

The missing value in the expression is 6x²

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, (-4x²+ 6x + 3) + (8x + 5+ ?) = 2x² + 14x + 8 we need to find the missing value in the expression,

(-4x²+ 6x + 3) + (8x + 5+ ?) = 2x² + 14x + 8

-4x²+ 6x + 3 + 8x + 5+ ? = 2x² + 14x + 8

-4x²+14x+8+? = 2x² + 14x + 8

14x-14x+8x-8x+? = 2x² + 4x²

? = 6x²

Hence, the missing value in the expression is 6x²

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The equation for the sphere is [tex](x-5)^2 + (y-1)^2 + (z-4)^2 = r^2[/tex] , that passes through the point (5, 1, 4) and is tangent to all three coordinate planes.

A sphere centered at the point (x0, y0, z0) with a radius of r can be represented by the equation [tex](x-x0)^2 + (y-y0)^2 + (z-z0)^2 = r^2.[/tex]

Therefore, a sphere that passes through the point (5, 1, 4) and is tangent to all three coordinate planes can be represented by substituting the values of x0, y0, and z0: [tex](x-5)^2 + (y-1)^2 + (z-4)^2 = r^2[/tex], where r is the radius of the sphere and is equal to the distance from the center of the sphere to the tangent point on the coordinate plane.

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The fact that multiple number of models of abnormality exist is caused by cultural and social values, cognitive bias, biological factors and limited research. Therefore, the answer is B. Cognitive bias.

The fact that multiple number of models of abnormality exist is caused by a variety of factors. Cultural and social values play a key role in influencing how mental health is viewed and understood. Biological factors, such as genetic predispositions and changes in the brain, can also contribute to psychological distress. Limited research on the subject has led to many different models of abnormality being developed, each with its own unique set of criteria for diagnosing mental health disorders. However, cognitive bias, or the tendency to think of certain behaviors and thoughts as abnormal, is not a major cause of the existence of multiple models of abnormality.

the complete question is :

according to the text, the fact that multiple models of abnormality exist is caused by all of these except:

A. Cultural and social values

B. Cognitive bias

C. Biological factors

D. Limited research

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The mean, median and the mode of the given sets of data above would be = 3.3, 4.3, and 4.5 respectively.

A mode is the value in a data set that appeared the most when compared with others.

The mode of this data set = 4.5. This is because it appeared twice.

The median of the data set is the value that is at the middle after being arranged.

The median of the data set = 3.1,3.2,4.3,4.5,4.5 = 4.3

The mean of the data set = 3.1+3.2+4.3+4.5+4.5/6

= 19.6/6

= 3.3

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The given triangles are not similar.

Similar triangles are those triangles which has the same shape but different size.

The length of corresponding sides are proportional and the corresponding angles are equal in similar triangles.

Looking at the figure, points A, B and C in triangle ABC corresponds to points G, H and J.

If the triangles are similar,

AB / GH = BC / HJ = AC / GJ

AB / GH = 10/20 = 1/2

BC / HJ = 6/16 = 3/8

AC / GJ = 12/25

Sides are not proportional. So they are not similar.

Hence the given triangles are not similar.

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a) The numeric values of each function at x = 3 are given as follows:

b) The division is given as follows: f(3)/g(3) = 5.

c) The domain of f(x)/g(x) is given as all real values except x = -7, as the function g(x), which is the denominator of the division, assumes a value of 0 at x = -7.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Hence the numeric values are found replacing the lone instance of x by 3 in each function, as follows:

Hence the division is given as follows:

(f/g)(3) = f(3)/g(3) = 50/10 = 5.

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Answer:

Step-by-step explanation:

oi gooot

Answer:100

Step-by-step explanation:

40+40 =80 +20=100

The solution is Option A.

The value of the equation is g ( x - 3 ) = √ ( x - 12 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as g ( x )

Now , the value of g ( x ) is

Substituting the values in the equation , we get

g ( x ) = √ ( x - 9 )    be equation (1)

On simplifying the equation , we get

when the value of x is x - 3 , we get

g ( x - 3 ) = √ ( x - 3 ) - 9

On further simplification , we get

g ( x - 3 ) = √ ( x - 3 - 9 )

g ( x - 3 ) = √ ( x - 12 )

Hence , the equation is g ( x - 3 ) = √ ( x - 12 )

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The required inverse function of the given function f(x) = x + 2/3 is h(x) = 3x - 2. Option C is correct.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given expression,
f(x) = x + 2/3

Put f(x) = y
y = x + 2/3

Now, isolate x
x = 3y - 2

Put x = h(x) and y = x
h(x) = 3x - 2

Thus, the required inverse function of the given function f(x) = x + 2/3 is h(x) = 3x - 2. Option C is correct.

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