Graph the following equation: y = -4x + 2​

Answer:

11.2

Step-by-step explanation:

multiply 1.6 by 7 since that's how many days there are in a week

Answer:

11.2

Step-by-step explanation:

you collect 1.6 packs of chile peppers a day there is 7 days in a week 1.6x7=11.2

hope it helps.

Answer:

- \(\frac{2}{3}\) x

Step-by-step explanation:

Given

\(\frac{4x-8x^2}{12x-6}\) ← factorise numerator and denominator

= \(\frac{4x(1-2x)}{6(2x-1)}\) ← factor out - 1 from (1 - 2x) on numerator

= \(\frac{-4x(2x-1)}{6(2x-1)}\) ← cancel the common factor (2x - 1)

= \(\frac{-4x}{6}\) ← cancel 4 and 6 by 2

= - \(\frac{2}{3}\) x

Simplifying the expression will give us: \(\frac{4x-8x^2}{12x-6} = \frac{-2x}{3}\)

Given the expression, \(\frac{4x-8x^2}{12x-6}\), we are required to simplify the expression as follows:

Step 1: Factorize the denominator and the numerator.

\(\frac{4x-8x^2}{12x-6}\\\\=\frac{(1 - 2x)4x}{(2x - 1)6}\)

Step 2: Rewrite the fraction by factoring out -1 from the numerator.

\(=\frac{(2x - 1)-4x}{(2x - 1)6}\)

Step 3: Divide the numerator and denominator by (2x - 1) respectively.

\(=\frac{-4x}{6}\)

Step 4: Divide the numerator and denominator by 2 respectively.

\(=\frac{-2x}{3}\)

Therefore, simplifying the expression will give us: \(\frac{4x-8x^2}{12x-6} = \frac{-2x}{3}\)

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The total length of the beads on one braid is 8.11 centimeters

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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(a) The number of five-digit integers divisible by 5 can be calculated by finding the number of multiples of 5 within the given range.

To determine the count of multiples, we need to find the first and last multiples of 5 within the range. The first multiple of 5 greater than or equal to 10,000 is 10,000 itself. The last multiple of 5 less than or equal to 99,999 is 99,995. Thus, the range contains 99,995 - 10,000 + 1 = 89,996 integers. To calculate the count of five-digit integers divisible by 5, we divide this range count by 5: 89,996 ÷ 5 = 17,999. Therefore, there are 17,999 five-digit integers divisible by 5.

(b) To determine the probability of randomly selecting a five-digit integer that is divisible by 5, we need to calculate the ratio of the number of five-digit integers divisible by 5 to the total number of five-digit integers. The total count of five-digit integers can be calculated by finding the range count from 10,000 to 99,999: 99,999 - 10,000 + 1 = 90,000. Therefore, the probability can be calculated as (17,999 ÷ 90,000) × 100% = 19.999%, which can be approximated as 20%. Hence, the probability that a randomly chosen five-digit integer is divisible by 5 is 20%.

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The mean of this probability distribution is 1.55.

To find the mean of a probability distribution, we need to multiply each possible value by its corresponding probability, and then add up these products. So, the mean is:

mean = (0)(0.19) + (1)(0.37) + (2)(0.16) + (3)(0.26) + (4)(0.02)
    = 0 + 0.37 + 0.32 + 0.78 + 0.08
    = 1.55

Therefore, the mean of this probability distribution is 1.55.

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(a) You are approximately 11.79 meters East (-x) of the town center and 2.98 meters South (-y) of the town center.

(b) You are approximately 13.00 meters away from the center of town at an angle of -67.38°.

(c) You are approximately 57.45 meters away from the center of town at an angle of 3° North of East.

(d) You walked approximately 45.28 meters away from the center of town in a direction of 33° North of West (-x).

(a) Given:

Distance from the center of town = 14.2 meters

Angle North of East = 190°

(i) To find how far East (+x) of the town center you are, we can use trigonometry. The horizontal component (East) is given by:

Distance East = Distance from center * cos(Angle)

Distance East = 14.2 * cos(190°) ≈ -11.79 meters

(ii) To find how far North (+y) of the town center you are, we can use trigonometry. The vertical component (North) is given by:

Distance North = Distance from center * sin(Angle)

Distance North = 14.2 * sin(190°) ≈ -2.98 meters

Therefore, you are approximately 11.79 meters East (-x) of the town center and 2.98 meters South (-y) of the town center.

(b) Given:

Distance North (+y) of the center = 12.00 meters

Distance East (+x) of the center = -5.00 meters

(i) To find the distance from the center of town, we can use the Pythagorean theorem:

Distance from center = √((Distance North)² + (Distance East)²)

Distance from center = √((12.00)² + (-5.00)²) ≈ 13.00 meters

(ii) To find the angle, we can use trigonometry. The angle is given by:

Angle = atan(Distance North / Distance East)

Angle = atan(12.00 / -5.00) ≈ -67.38°

Therefore, you are approximately 13.00 meters away from the center of town at an angle of -67.38°.

(c) Given:

Distance from the center of town = 44.0 meters

Angle North of East = 23°

Distance walked = 30.0 meters

Angle of walking North of East = 160°

(i) To find the new distance from the center of town, we can use the Law of Cosines:

New distance from center = √((Distance from center)² + (Distance walked)² - 2 * Distance from center * Distance walked * cos(Angle of walking))

New distance from center = √((44.0)² + (30.0)² - 2 * 44.0 * 30.0 * cos(160°)) ≈ 57.45 meters

(ii) To find the new angle, we can use the Law of Sines:

New angle = Angle + Angle of walking - 180°

New angle = 23° + 160° - 180° ≈ 3°

Therefore, you are approximately 57.45 meters away from the center of town at an angle of 3° North of East.

(d) Given:

Distance from the center of town = 22.0 meters

Angle North of East = 123°

Distance walked = 40.0 meters

Direction = West (-x)

(i) To find the new distance from the center of town, we can use the Pythagorean theorem:

New distance from center = √((Distance from center)² + (Distance walked)²)

New distance from center = √((22.0)² + (40.0)²) ≈ 45.28 meters

(ii) To find the new direction, we can subtract the angle of walking from the original angle:

New angle = Angle - 90°

New angle = 123° - 90° ≈ 33°

Therefore, you walked approximately 45.28 meters away from the center of town in a direction of 33° North of West (-x).

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The product of the complex numbers is -3 + 29i

Let the complex numbers be

Their difference M - N = x + iy - (a + ib) = x - a + i(y - b)

Their sum M + N = x + iy + (a + ib) = x + a + i(y + b)

Since the sum of two complex numbers is 7 + 8i, we have that

M + N = x + a + i(y + b) = 7 + 8i

⇒x + a = 7  (1) and y + b = 8 (2)

Also, the difference of the numbers is 1 - 2i, we have that

M - N = x - a + i(y - b) = 1 - 2i

⇒ x - a = 1 (3) and y - b = -2 (4)

Adding equations (1) and (2), we have

x + a = 7

+

x - a = 1

2x = 8

x = 8/2

x = 4

Substituting x = 4 into equation (1), we have

x - a = 1

4 - a = 1

a = 4 - 1

a = 3

Adding equations (2) and (4), we have

y + b = 8

+

y - b = -2

2y = 6

y = 6/2

y = 3

Substituting y = 3 into equation (2), we have

y + b = 8

3 + b = 8

b = 8 - 3

b = 5

So,

So, their product M × N = (4 + 3i)(3 + 5i)

= 4 × 3 + 4 × 5i + 3 × 3i + 3i × 5i

= 12 + 20i + 9i - 15

= 12 - 15 + 20i + 9i

= -3 + 29i

So, the product of the complex numbers is -3 + 29i

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Sin x = 2sin (x/2)cos (x/2) = 2(sin (x/2))/(cos (x/2)). This fraction is in its simplest form.

Fraction is a mathematical concept that represents a part of a whole or a ratio between two numbers. It is expressed as a numerator (top number) over a denominator (bottom number). A fraction is a way to express a number that is not whole, such as 1/2, which is one half, or 3/4, which is three quarters. Fractions are used in many areas of mathematics, including basic arithmetic, algebra and geometry.

The expression sin x can be rewritten in simplest terms as a fraction using the trigonometric identity sin x = 2sin(x/2)cos(x/2).

Therefore, sin x = 2sin (x/2)cos (x/2) = 2(sin (x/2))/(cos (x/2)). This fraction is in its simplest form.

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Answer:

discontinuous

Step-by-step explanation

The required number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
The number line is typically drawn from left to right to show all of the possible solutions that make the inequality true.

The inequality may involve a variable x, and the number line would represent all possible values of x that satisfy the inequality. The solutions could be, for example, all values of x greater than 3, in which case the number line would start at 3 and extend to the right to represent all values of x greater than 3. Alternatively, the solutions could be all values of x less than or equal to -2, in which case the number line would start at -2 and extend to the left to represent all values of x less than or equal to -2.

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Answer:

34 and 30

Step-by-step explanation:

8 times 3 = 34

and 34-4=30

divide 8 by 2 and you'll get 4

so, 34-4=30

Answer:

the answer is if we don't act the beauty of nature may disappear

Step-by-step explanation:

This is so because nature is fragile and needs to be taken care of properly thus this poem portrays various ways we are endangering nature and it's beautiful aesthetic features

Answer:

2x + 7y and 7g + 3h

Step-by-step explanation:

(a)

3x + 5y - x + 2y ← collect like terms

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

= 2x + 7y

(b)

3g + 5h + 4g - 2h ← collect like terms

= (3g + 4g) + (5h - 2h)

= 7g + 3h

Answer:

A) 2x + 7y

B) 7g + 3h

Step-by-step explanation:

A)   3x + 5y - x +2y =  

      3x - x = 2x

      5y + 2y = 7y                ans:   2x + 7y

B)   3g + 5h +4g - 2h =

     3g + 4g = 7g

     5h - 2h  = 3h                ans:   7g + 3h

Answer:

The number y decreased by 12.

Step-by-step explanation:

Answer

the answer is b y decreased by 12

Step-by-step explanation:

that is what y-12 is

As X and Y are two numerical variables. Because they are independent so there is no relationship between the two variables other than the linear relationship described by the regression equation. The correct answer is B. III only, that is  X and Yare independent.

When performing a regression analysis involving two numerical variables, we assume that X and Y are independent, meaning that the value of one variable does not depend on the value of the other variable. However, we do not assume that the variances of X and Y are equal or that the variation around the line of regression is the same for each X value. These assumptions are not necessary for performing a regression analysis. Violation of this assumption can lead to spurious results and incorrect inferences. So, the correct option in  B. III only.

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To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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Answer:  Lottie saved 330 pounds.

Step-by-step explanation:

Lottie's amount can be represented by the expression   x + 76  and Kai's amount is unknown so we will also represent by x.

We know that the combination of their savings will be 584 pounds so we will add the expression and set them equal 584.  

x + (x + 76) = 584   Now solve for x

2x + 76 = 584      

      -76     -76

2x = 508

x= 254  

If x was Kai's amount then Kai save 254 pounds.

Lottie saved 76 more that Kai

254 + 76 = 330

Lottie also save 330 pounds

Answer:

The area of the shaded region is 240 ft.

Step-by-step explanation:

Area Formula: A = L * H

First, find the area of the WHOLE shape. (300 = 25 * 12)

Next, find the area of the WHITE section. (60 = 5 * 12)

Lastly, subtract the area of the entire shape to the area of the white section. (300 - 60 = 240)

Your final answer should be 240 ft. Hope this helps! :D

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

The first derivative of G(r) is (3/2).
The second derivative of G(r) is (-3/4)/√(r³).

To find the first derivative of G(r), we use the power rule of differentiation:

G'(r) = (1/2)r(-1/2) + 5(1/2)r(-1/2)

Simplifying, we get:

G'(r) = (1/2)(1 + 5)√(r)/√(r)

G'(r) = (3/2)√(r)/√(r)

G'(r) = (3/2)

To find the second derivative, we differentiate G'(r) using the power rule again:

G''(r) = (-1/4)r(-3/2) + 5(-1/4)r(-3/2)

Simplifying, we get:

G''(r) = (-3/4)r(-3/2)

G''(r) = (-3/4)/√(r^3)

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Given that a circle with radius 20 has a corresponding angle of 305°.

To find the coordinates of a point on the circle, we use the formula:`(r cos (θ), r sin (θ))`Here, `r = 20` and `θ = 305°`.

Substituting the values of `r` and `θ` in the formula, we get:`(20 cos (305°), 20 sin (305°))`

Using the values of trigonometric ratios, we can write:cos(305°) = cos(360° - 305°) = cos(55°) ≈ -0.5736sin(305°) = sin(360° - 305°) = sin(55°) ≈ 0.8192

Hence, the coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`.

The coordinates of a point on a circle with radius 20 corresponding to an angle of 305° are approximately `(-11.47, 16.38)`

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The row numbers along the left side of the worksheet are 1, 2, 4, 5, 6. We can observe that there is a missing number in the sequence, specifically the number 3. Therefore, based on the pattern, we can deduce that row 3 is missing from the worksheet.

Based on the given information, the row numbers along the left side of the worksheet are 1, 2, 4, 5, 6, with a missing number in the sequence, which is the number 3.

The presence of the numbers 1, 2, 4, 5, and 6 indicates that rows corresponding to those numbers exist in the worksheet. However, there is no row with the number 3 mentioned in the sequence. Thus, we can conclude that row 3 is missing from the worksheet.

It is important to note that the missing row could be intentional or accidental, but based on the given information, we can deduce that there is a discontinuity in the row numbering, specifically the absence of row 3.

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If there are implicit costs of production, economic profit will be lower than accounting profit.

Implicit costs refer to the opportunity costs of using resources in a particular production process. These costs are not explicitly recorded in accounting statements but represent the value of alternative uses of resources. When implicit costs exist, economic profit will be lower than accounting profit. Accounting profit is calculated by subtracting only explicit costs, such as wages, rent, and materials, from total revenue.

On the other hand, economic profit takes into account both explicit and implicit costs. Implicit costs represent the foregone opportunities or benefits that could have been obtained if resources were used in alternative ways. Since accounting profit does not consider these opportunity costs, it is generally higher than economic profit. Economic profit reflects the true economic performance of a business by considering all costs, both explicit and implicit.

Therefore, if there are implicit costs of production, economic profit will be lower than accounting profit.

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A: accounting profit will exceed economic profit.

Implicit costs of production refer to the opportunity cost of using resources that a firm already owns rather than selling them in the market. These costs are not reflected in accounting records but are included in economic analysis. Accounting profit is calculated by subtracting only explicit costs from total revenue, while economic profit is calculated by subtracting both explicit and implicit costs from total revenue. Since accounting profit does not include implicit costs, it will always be higher than economic profit. In some cases, economic profit may even be negative, indicating that a firm is better off not producing anything at all. Thus, option A is the correct answer. Option B is incorrect because economic profit can be positive or negative. Option C is incorrect because economic profit is always lower than accounting profit. Option D is incorrect because accounting profit can be positive or negative. Option E is incorrect because economic profit and accounting profit are not always equal.

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Answer:

Length = \(57.5\ \text{inches}\)

Width = \(18\ \text{inches}\)

Step-by-step explanation:

The scale of the toy train is \(\dfrac{2}{9}\)

So, the dimensions of the toy train is \(\dfrac{2}{9}\) times the actual dimensions of the train.

The dimensions of actual train is \(\dfrac{1}{\frac{2}{9}}=\frac{9}{2}\) times the toy train's dimensions.

Length

\(15\times \dfrac{9}{2}=57.5\ \text{inches}\)

Width

\(4\times \dfrac{9}{2}=18\ \text{inches}\)

The length of the railroad car on the long island railroad is 57.5 inches.

The width of the railroad car on the long island railroad is 18 inches.

Using compound interest, it is found that:

a) $1,270.70 will be in the account after 6 years.

b) It will take 17.53 years for the $1000 to double.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

In this problem, the parameters are given as follows:

\(A(0) = 1000, r = 0.04, n = 12\)

Item a:

Over 6 years, that is t = 6, thus:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(t) = 1000\left(1 + \frac{0.04}{12}\right)^{12 \times 6}\)

\(A(t) = 1270.7\)

$1,270.70 will be in the account after 6 years.

Item b:

This is t for which A(t) = 2P = 2000, hence:

\(2000 = 1000\left(1 + \frac{0.04}{12}\right)^{12t}\)

\((1.0033)^{12t} = 2\)

\(\log{(1.0033)^{12t}} = \log{2}\)

\(12\log{(1.0033)} = \log{2}\)

\(t = \frac{\log{2}}{12\log{1.0033}}\)

\(t = 17.53\)

It will take 17.53 years for the $1000 to double.

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The population of the town in 60 years will be approximately 7,776 people.

Since the population grows at a rate proportional to the population present, we can use the exponential growth formula:

\(P(t) = P0 * e^{kt}\)

where P0 is the initial population, t is the time elapsed in years, k is the proportionality constant, and e is Euler's number (approximately 2.71828).

From the problem, we know that the population increased by 25% in 10 years. This means that:

P(10) = P0 * 1.25

Substituting the given values, we have:

\(P0 * e^{k*10} = P0 * 1.25\)

Simplifying and solving for k, we get:

k = ln(1.25)/10

Using this value of k, we can find the population after 60 years:

\(P(60) = P0 * e^{k*60}\)

Substituting the given values and the value of k we just calculated, we have:

\(P(60) = 500 * e^{ln(1.25)/10 * 60}\)

Simplifying and rounding to the nearest person, we get:

P(60) ≈ 7,776 people

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Answer:

87

Step-by-step explanation:

common difference = d  = 2

an = a1 + (n-1)*d

a43 = 3 + 42*2  = 87