Compare each pair of expressions using >, <, or =.
.-32
. |-32|
5 -5
15
___|15|
. |5|_____|-5|
2-17
▾
2 ____ |-17|
. |-27|_____|-45|
.-27______-45

The rate of change is 4/1

Answer:

x^1/4 + 8x^1/4 + 12

Step-by-step explanation:

Using the FOIL method, we get x^1/4 + 8x^1/4 + 12

The value of k that satisfies the given condition is approximately 0.4041.

In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:

C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵

where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.

So, we have the equation:

k⁵ * C(5,k) = -672

We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:

k⁵ * C(5,5-k) = -672

Expanding C(5,5-k), we get:

k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672

Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.

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The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53

Given that, we have

∠2 = 29°

(a)

Angles 2 and 4 are vertical angles

So, we have

∠4 = 29°

(b) and (c)

We have

∠3 = (3x - 8)°

Angles 3 and 4 are angles on a straight line

So, we have the equation to be

3x - 8 + 29 = 180

Solving for x, we have

3x = 159

Divide by 3

x = 53

This means that the equation is 3x = 159 and the value of x is 53

In this section, we have the following side lengths

Lengths = 6, 8 and 10

This means that

Side lengths = 6 and 8

Hypotenuse = 10

Next, we create the right angle using the given lengths of the legs and the hypotenuse

Here, we have

R = 13

r = 8

The exact area is calculated as

A = π(R² - r²)

So, we have

A = π(13² - 8²)

Evaluate

A = 105π

For the approximate area, we have

A = 105 * 22/7

A = 330

This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters

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Answer:

do it by yourself what you do while teacher is teaching

The coordinates of each point after the quadrilateral MNPQ is translated 2 units right and 5 units down are:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

To calculate the coordinates, we shall assume that the coordinates of the points of the quadrilateral MNPQ are:

M = (x1, y1)

N = (x2, y2)

P = (x3, y3)

Q = (x4, y4)

Next, we translate the quadrilateral 2 units right and 5 units down by adding 2 to the x-coordinate and subtracting 5 from the y-coordinate of each point.

The new coordinates of the points after the translation will be:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

Therefore, the coordinates of each point after the quadrilateral is translated 2 units right and 5 units down are:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

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Question completion:

Although part of your question is missing, you might be referring to the below question:

What are the coordinates of each point after quadrilateral MNPQ is translated 2 units right and 5 units down?

This statement describes the relationship between symmetries and rotations

This statement describes a relation between two symmetry operations, denoted by [tex]s_i[/tex] and [tex]s_j[/tex], and a rotation operation denoted by [tex]r_{i-j}[/tex]. The notation [tex]"s_i \circ s_i"[/tex] and [tex]"s_j \circ s_i"[/tex] denotes the composition of these operations, which means applying one operation after the other.

The statement says that [tex]s_i[/tex] and [tex]s_j[/tex] are both symmetries, and that they have a specific relationship with each other: when [tex]s_i[/tex] is composed with itself, it gives the identity operation (denoted by 1), and when [tex]s_j[/tex] is composed with [tex]s_i[/tex], it also gives the identity operation.

Then the statement concludes that this relationship implies that [tex]s_j[/tex] can be obtained by first applying [tex]s_i[/tex] and then applying a rotation operation [tex]r_{i-j}[/tex], and that [tex]s_i[/tex] can be obtained by first applying a rotation operation [tex]r_{i-j}[/tex] and then applying [tex]s_j[/tex].

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The standard deviation for the given distribution is 8.739 using either the direct method or the shortcut method.

Standard deviation is defined as a measure of how spread out numbers are. It is also referred to as the square root of the Variance, and then the Variance is the average of the squared differences from the Mean.

To calculate the standard deviation for the given distribution, we will utilize either the direct method or the shortcut method.

Direct method:

Calculate the mean wage (F) for the distribution:

Mean = (20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10

Mean = 34

Calculate the differences between each wage and the mean wage:

20 - 34 = -14

22 - 34 = -12

27 - 34 = -7

30 - 34 = -4

31 - 34 = -3

32 - 34 = -2

35 - 34 = 1

45 - 34 = 11

40 - 34 = 6

48 - 34 = 14

Square each of the differences:

(-14)² = 196

(-12)² = 144

(-7)² = 49

(-4)² = 16

(-3)² = 9

(-2)² = 4

1² = 1

11² = 121

6² = 36

14² = 196

Add up the squared differences: 196 + 144 + 49 + 16 + 9 + 4 + 1 + 121 + 36 + 196 = 756

Divide the sum of the squared differences by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

√75.6 = 8.739

Shortcut method:

The mean wage (F) for the distribution:

(20 + 22 + 27 + 30 + 31 + 32 + 35 + 45 + 40 + 48)/10 = 34

The sum of the squares of the differences between each wage and the mean wage:

(20 - 34)² + (22 - 34)² + (27 - 34)² + (30 - 34)² + (31 - 34)² + (32 - 34)² + (35 - 34)² + (45 - 34)² + (40 - 34)² + (48 - 34)² = 756

Divide the sum by the number of workers: 756/10 = 75.6

Take the square root of the result to get the standard deviation:

Standard deviation = √75.6 = 8.739

Therefore,

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Complete question is:

Calculate standard deviation for the following

distribution by direct and shortcut method.

Assume mean as 32.

Serial No. of Workers

1

2

3

4

5

6

7

8

9

10

Wage (F)

20

22

27

30

31

32

35

45

40

48

The missing side measure is equal to: A. 14.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given parameters into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

4/5.6 = 10/x

4x = 56

x = 56/4

x = 14

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

1.235 kg

Step-by-step explanation:

Let's assume that each packet of flour and salt weighs the same.

When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.

Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.

Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:

19 kg - 9.12 kg = 9.88 kg

Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:

9.88 kg ÷ 8 = 1.235 kg

Therefore, each packet of salt weighs approximately 1.235 kg.

The height of the square pyramid is 35.5 in.

From the given figure we can see that the figure is a pyramid.

The base of the pyramid is a square.

The each side of base square i = 24.8 in.

The slant height is = 37.6 in.

So the right angle formed in between prism has hypotenuse = 37.6 in.

one of the rest two sides = 24.8/2 = 12.4 in.

So another side is the height of the pyramid. Let that side be = x in.

By Pythagoras Theorem we get,

(12.4)² + x² = (37.6)²

153.76 + x² = 1413.76

x² = 1413.76 - 153.76

x² = 1260

x = 35.5 (rounding off to nearest tenth and neglecting the negative value obtained from square root as length cannot be negative.)

Hence the height of the square pyramid is 35.5 in.

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Answer:

Step-by-step explanation:

This problem can be solved using the binomial distribution, which gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

Let p be the probability that a single ibuprofen tablet has a defect, which is given as 15% or 0.15. Then, the probability that a single ibuprofen tablet does not have a defect is 1 - p = 0.85.

The acceptance sampling plan requires that at most one tablet does not meet the required specifications out of 29 tablets. This means that the shipment will be accepted if there are 0 or 1 defective tablets in the sample of 29.

The probability of getting exactly k defective tablets in a sample of n tablets is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) = n! / (k! * (n - k)!) is the number of ways to choose k defective tablets out of n, and ! denotes the factorial function.

To find the probability that the whole shipment will be accepted, we need to find the probability that there are 0 or 1 defective tablets in the sample of 29:

P(0 or 1 defects) = P(0 defects) + P(1 defect)

= (29 choose 0) * 0.15^0 * 0.85^29 + (29 choose 1) * 0.15^1 * 0.85^28

≈ 0.1098

Therefore, the probability that the whole shipment will be accepted is approximately 0.1098 or 10.98%

Answer:

A ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.

Step-by-step explanation:

Let's use variables to represent the cost of each dinner. Let's say that the cost of a ribeye steak dinner is "r" and the cost of a grilled salmon dinner is "s".

From the first day's sales, we know:

From the second day's sales, we know:

We now have two equations with two variables, which we can solve using elimination or substitution.

Let's use elimination. If we multiply the first equation by 15 and the second equation by 11, we can eliminate the "r" variable:

Subtracting the second equation from the first, we get:

Dividing both sides by 133, we get:

So a grilled salmon dinner costs $14.04.

We can substitute this value back into one of the original equations to solve for "r". Let's use the first equation:

So a ribeye steak dinner costs $32.23.

Therefore, a ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.

Answer:

First, you distribute the 3 into the brackets,

3(x - 2) + 5x

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

=3x - 6 + 5x

Adding the like terms, 3x and 5x, gives you

=8x - 6

Step-by-step explanation:

The solution of the matrix is [tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]

A matrix is a rectangular array of numbers arranged in rows and columns. The size of a matrix is given by its dimensions, which indicate the number of rows and columns in the matrix. In this question, both matrices G and F have 4 rows and 5 columns, so we say that they are 4x5 matrices.

Scalar multiplication is performed by multiplying each element of a matrix by a scalar, which is simply a number.

Now, to find the value of 4G + 2F, we need to perform scalar multiplication on each matrix and then add the results. We get:

[tex]4G = 4 * \begin{bmatrix}8 &-5 &-8& -2 &-10 \\-6& -7 &1 &9 &2 \\4& 6 &3 &7 &5 \\-4&-3 &0 &-10 & -9\end{bmatrix}\\= \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 & -36\end{bmatrix}[/tex]

[tex]2F = 2 * \begin{bmatrix}1 &8 &-2& -5 &9 \\-9& 10 &6 &-3 &0 \\4& 5 &-4 &3 &7 \\2&-10 &-6 &-1 & -8\end{bmatrix}= \begin{bmatrix}2 &16 &-4& -10 &18 \\-18& 20 &12 &-6 &0\\8& 10 &-8 &6 &14 \\4&-20 &-12 &-2 & -16\end{bmatrix}[/tex]

Now, we can perform matrix addition on 4G and 2F to get:

[tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]

Therefore, the value of 4G + 2F is the 4x5 matrix given above.

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Answer:

5.5.5.5.5.5.5.5.5 in exponential notation is 5^9

7.7.7.7.7.7.7.7.7.7.7.7.7.7 in exponential notation is 7^13

Therefore, (5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7) in exponential notation is:

5^9 * 7^13

The slope of a line parallel to this line is 6/7.

The slope of a line perpendicular to this line is -7/6.

In Mathematics and Geometry, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

Slope, m₁ = Slope, m₂

Based on the information provided about this line, we have the following equation in standard form;

6x - 7y = 4

By making y the subject of formula, we have:

7y = 6x - 4

y = 6x/7 - 4

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

6/7 × m₂ = -1

6m₂ = -7

Slope, m₂ = -7/6

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The required equation of line is y = 2x

A straight line's equation is y=mx+c, where m denotes the gradient and c denotes the height at which the line crosses the y-intercept, also known as the y-axis.

Given points:

(1,2) and (2,4)

then

[tex]Slope of line = \frac{4-2}{2-1}= 2[/tex]

then

y-2 = 2(x-1)

y = 2x - 2 + 2

y = 2x

Thus, required equation of line is y = 2x

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The calculated value of the area of the real room is 10.67 cm²

From the question, we have the following parameters that can be used in our computation:

In the drawing, 3cm represents 4cm

This means that

Scale factor = 4/3

Also, we have the dimension of the scale drawing to be

Dimension = 3cm by 2 cm

So, the area of the bedroom in the scale is

Area = 3cm * 2cm

For the actual room, we have

Area = 3cm * 2cm * (4/3)²

Evaluate the exponent

Area = 3cm * 2cm * (16/9)

Evaluate the products

Area = 10.67 cm²

This means that the real area is 10.67 cm²

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Answer:

Step-by-step explanation:

We are given a figure, consisting of a right triangle with a circle cut out of it.

To Calculate : area of the shaded region below,

First Let's find the Area of the right triangle:

Area(triangle) = 1/2 × Base × Height

= 1/2 × 56 × 56

= 1/2 × 3136

= 3136/2

= 1568 m².

Now, We are diameter of the circle = 20 m

Radius of the circle = 20/2 = 10 m

Acc. to question we have to use 3.14 as an

approximation for pi.

Area (circle) = 3.14 × 10 × 10

Area (circle) = 3.14 × 100

Area (circle) = 314 m²

Area of shaded region = Area of triangle - Area of circle =

= 1568 m² - 314 m²

= 1.254 square meters

Therefore, The approximate area of the shaded region is 1.254 square meters.

Option (a) is the required answer.

Answer:

( -6, 6)

Step-by-step explanation:

The appropriate diagram to illustrate the cube is given.

A cube is a three-dimensional shape featureing six equal square faces, with its edges and vertices being of congruent length. It counts as one of the five platonic solids distinguished by all of its features having matching sizes.

The cube can be perceived as a special instance of a rectangular parallelepiped where all six are perfectly square in shape. In order to calculate the volume of such an ordinary cube, the number of its edge needs to be multiplied by itself thrice (V = a³).

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Answer:

Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum

Answer:

1 over 16 is not the same as 16.

1 over 16 is a fraction, which means that it represents a part of a whole. It can be written as 1/16, which means one part out of a total of sixteen equal parts.

On the other hand, 16 is a whole number, which represents a quantity of sixteen units.

So, 1/16 is not equal to 16.

Step-by-step explanation:

The woman's gross income, adjusted income and taxable income are:

The gross income to the woman is:

= Wages + interest

= 33, 900 + 2, 600

= $ 36, 500

The adjusted gross income :

= Gross income - Retirement plan contribution

= 36, 500 - 3, 600

= $ 32, 900

The taxable income ;

= AGI - Personal exemption - Deductions

= 32, 900 - 3, 500 - 5, 440

= $ 23, 960

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Answer:

The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Step-by-step explanation:

To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.

2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.

The slope of this line is 1/2.

Since we want a line parallel to this line, the slope of the new line will also be 1/2.

Next, we can use the point-slope form of a line to write the equation of the new line.

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get:

y - 3 = (1/2)(x - (-4))

Simplifying, we get:

y - 3 = (1/2)x + 2

Adding 3 to both sides, we get the final equation in slope-intercept form:

y = (1/2)x + 5

Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Kyle has $306 in his account so, right answer is Option D.

Let Kyle's money = x

Hayden's money = y

Jeremy's money = z

Given that Kyle has three times as much money in his savings account as  Hayden.

x = 3y   .....Eqn 1

Hayden has twice as much money in his savings account  as Jeremy.

z = 2y  ..... Eqn 2

Now Combined Kyle, Hayden, and Jeremy have a total of  $612.

x+y+z=612   .....Eqn 3

Putting value of x and z from Eqn 1 and 2 in Eqn 3

6y = 612

y = 106

Putting in Eqn 1;

x = 306

Thus, Kyle has $306 in his account.

The right answer is Option D.

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