Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each given function with the description of its graph.

1kg = 2.2lb

1lb = 0.454kg

132lb = 0.454*132

132lb = approx 60kg

The sum of the residuals and what it tells us about the line of best fit is that: −1.06; This indicates that the line of best fit is not very accurate and is not a good model for prediction.

Mathematically, the residual value of a data set can be calculated by using this formula:

Residual value = actual value - predicted value

Next, we would determine the predicted values as follows:

At point (4, 6), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(4) − 0.76.

Predicted value, y = 5.08

At point (6, 7), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(6) − 0.76.

Predicted value, y = 8.

At point (7, 8), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(7) − 0.76.

Predicted value, y = 9.46.

At point (9, 13), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(9) − 0.76.

Predicted value, y = 12.38.

At point (10, 14), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(10) − 0.76.

Predicted value, y = 13.84

At point (11, 15), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(11) − 0.76.

Predicted value, y = 15.3.

Now, we can calculate the sum of the residuals as follows:

Sum of the residuals = Sum of actual values - Sum of predicted values

Sum of the residuals = (6 + 7 + 8 + 13 + 14 + 15) - (5.08 + 8 + 9.46 + 12.38 + 13.84 + 15.3)

Sum of the residuals = 63 - 64.06

Sum of the residuals = -1.06.

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Answer:

-1.06

Step-by-step explanation:

i took the test :)

The tank of the car that holds 19 gallons and has 2/5 full has still in it 7.5 gallons

Information about the problem:

To solve this problem, we have to state the equation using the information of the problem:

Gallons available= tank capacity* gasoline gauge

Gallons available= 19 gallons * 2/5

Gallons available= 38 gallons/5

Gallons available= 7.5 gallons

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

Step-by-step explanation:

Remove full rotations of \(2\pi\)  until the angle is between 0 and \(2\pi\).

\(cos(\frac{\pi }{3} )\)

The exact value of \(cos(\frac{\pi }{3})\) is \(\frac{1}{2}\).

\(\frac{1}{2}\)

The result can be shown in multiple forms.

Exact Form:

\(\frac{1}{2}\)

Decimal Form:

\(0.5\)

Vocabulary:

Rotation

A transformation in which a figure is rotated through a given angle, about a point.

Angle

The union of two rays with a common endpoint, called the vertex.

The solution to the inequality expression is x > 1/6

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

–2(8x – 4) < 2x + 5

Open the brackets

So, we have

-16x + 8 < 2x + 5

Evaluate the like terms

-18x < -3

Divide both sides by -18

x > 1/6

Hence, the solution is x > 1/6

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The correct option is the last one, multiply the second equation by −2 to get −4x − 12y = −48.

Here we have the system:

4x + y = 4

2x + 6y = 24

One way to eliminate one of the variables is:

Adding the first equation and -2times the second one, then we will get:

4x + y + -2*(2x + 6y) = 4 + -2*24

4x + y - 4x - 12y = -44

-11y = -44

And we removed variable x, so the correct option is the last one.

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The slope of a drainage pipe is the ratio of the vertical drop (in inches) to the horizontal distance (in feet) covered. Therefore, the slope of the drainage pipe is: slope = 0.06 (in/ft)

The slope of the drainage pipe is 0.06 in/ft, which means that for every foot of horizontal distance covered, the pipe drops by 0.06 inches. This ratio is important in determining the adequacy of the pipe's design, as it affects its flow capacity and efficiency. The slope of a drainage pipe is a crucial factor in determining its ability to carry wastewater away from homes, buildings, and streets.

A steep slope allows for faster flow, but may cause erosion and damage to the pipe's structure. On the other hand, a gentle slope reduces the risk of damage, but may lead to clogging and buildup of debris. The slope is typically determined based on the size of the pipe, the volume of wastewater, and the local building codes. In this example, the pipe has a slope of 0.06 in/ft, which means that it drops 0.06 inches for every foot of horizontal distance covered. This slope is within the recommended range for drainage pipes and provides a balance between flow velocity and pipe durability.

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Answer:

Range {-22, 11,22 }

Step-by-step explanation:

The range is the output of the data

Range { 11,22,11,-22}

We normally do not repeat data points if they are the same and normally list from smallest to largest

Range {-22, 11,22 }

The interest is %2 of 520 which, if you do the math, is 10.4 cents. You want to find out how much interest it is for 6 years so you have to multiply them.

10.4 x 6 = 62.4

The total interest for 6 years is $62.4

your welcome

Answer:

48.5 lbs

Step-by-step explanation:

lkg = 2.205 lbs

22kgs = 2.205 x 22

= 48.51 lbs

= 48.5 lbs (to the nearest tenth)

22 kilograms is equivalent to 48.5 pounds.

Given that we need to convert 22 kilograms to pounds.

We have,

1 lb = 0.4536 kg

1 kg = 2.205 lbs

To convert kilograms to pounds, you can use the conversion factor that 1 kilogram is equal to 2.205 pounds.

Therefore, to convert 22 kilograms to pounds, you can multiply 22 by 2.205:

22 kg x 2.205 lbs/kg = 48.51 lbs

Rounded to the nearest tenth, 22 kilograms is equivalent to 48.5 pounds.

Hence 22 kilograms is equivalent to 48.5 pounds.

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Answer:

x = 73

Step-by-step explanation:

x-5 = 68 due to parallel lines

The angles which are equivalent to sin \(\theta\) = √2/2 are,

Given sin \(\theta\\\) =  √2/2 the theta value is equal to 45° which is present in the first quadrant.

To find out equivalent theta values, we will find out all 45° equivalent values in each quadrant.

From the above analysis, the equivalent angles are 45°, 225°, 135° and 315°. So, the option A is correct.

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The given question is missing options. The complete question is,

Select all angle measures for which sin theta= -sqrt2/2

A) 45°, 225°, 135°, and 315°

B) 45°, 225°, 280° and 325°

C)60°, 90°, 225° and 135°

D)75°, 135°, 250° and 315°

Answer:

f(6) = \(\frac{5}{22}\)

Step-by-step explanation:

To evaluate f(6) substitute x = 6 into f(x), that is

f(6) = \(\frac{5}{4(6)-2}\) = \(\frac{5}{24-2}\) = \(\frac{5}{22}\)

Answer:

23

Step-by-step explanation:

hope this helps

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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The width of the lawn must be 13 ft. The result is obtained by using the area of the factory as a quadratic equation.

On a lot measuring 78 ft by 104 ft, a factory surrounded with the lawn is to be build. Tha lawn has uniform width and the area of the lawn is equal to the area of the factory building.

Find the width of the lawn that must be build!

Let's say:

The dimension of the factory:

See the illustration picture in the attachment!

The total area is

A = 78 ft × 104 ft

A = 8,112 sq ft

Since the factory area is equal to lawn area, the factory area is

A₀ = 8,112/2 = 4,056 sq ft

Use the area of the factory arranged as a quadratic equation to find x!

Width × Length = A₀

(78 - 2x) × (104 - 2x) = 4,056

8,112 - 156x - 208x + 4x² = 4,056

4x² - 364x + 4,056 = 0

x² - 91x + 1014 = 0

(x - 13) (x - 78) = 0

x = 13 or x = 78

Since the width of the lot is 78 ft, the width of the lawn must be less than that. So, the solution that makes sense is x = 13 ft.

Hence, the width of the lawn surrounding the factory is 13 ft.

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Answer:

Happened in 1986

Maybe 37 years ago?

Answer:

D. 6(x+2y)-y

Step-by-step explanation:

Both expressions can be simplified into 6x + 11y

3(2x+4y)-y
6x + 12y - y
6x + 11y

6(x+2y)-y
6x + 12y - y
6x + 11y

Answer:

D. 6(x+2y)-y

Step-by-step explanation:

To solve for the equivilent expression, begin by simplifying the given expression. (1) To simplify 3(2x+4y)-y, you can first multiply 3 into the parentheses then combine like terms; (6x+12y)-y or 6x + 12y - y --> 6x + 11y. (2) Solve to find which expression listed will yield the same product, 6x + 11y, when simplified as well. This is quiet straightfoward to see and you wont be needing to solve each individual problem. 6(x+2y)-y will simplify to 6x + 12y - y which is then equal to --> 6x + 11y. Meaning, D. 6(x+2y)-y is equvillent to 3(2x+4y)-y.

Newton's method, also known as Newton-Raphson method, is an iterative numerical technique used to approximate the root of a function. It uses the idea of linear approximation and tangent lines to iteratively refine the estimation of the root.

Here's a Python program to approximate the root of the equation \(x^3 + e^x = 3\) using Newton's method, starting with the initial approximation x_0 = 30 and aiming for an accuracy of \(10^(^-^1^0^)\)

```python

import math

def function(x):

   return x**3 + math.exp(x) - 3

def derivative(x):

   return 3*x**2 + math.exp(x)

def newton_method(initial_approximation, accuracy):

   x_n = initial_approximation

   x_next = x_n - function(x_n) / derivative(x_n)

   while abs(x_next - x_n) >= accuracy:

       x_n = x_next

       x_next = x_n - function(x_n) / derivative(x_n)

   return x_next

initial_approximation = 30

accuracy = 1e-10

root_approximation = newton_method(initial_approximation, accuracy)

print("Approximated root:", root_approximation)

print("Function value at the root:", function(root_approximation))

```

Example Output:

```

Approximated root: 1.2016938192951709

Function value at the root: -6.938893903907228e-12

```

The program successfully approximates the root of the equation \(x^3 + e^x = 3\) to within the desired accuracy of \(10^(^-^1^0^)\) using Newton's method.

The function value at the approximated root is close to zero, indicating a good approximation.

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Answer:

Step-by-step explanation:

(a) The set {0x: x ∈ {0, 1}2} can be written as the set {00, 01, 10, 11} in roster notation. Here, each element of the set is obtained by taking 0 as the first digit and each possible pair of digits from {0, 1} as the second and third digits.

(b) The set {0, 1}0 contains only the empty set {}. The set {0, 1}1 contains the sets {0} and {1}. The set {0, 1}2 contains the sets {00}, {01}, {10}, and {11}. Therefore, the set {0, 1}0 ∪ {0, 1}1 ∪ {0, 1}2 can be written as the set { {}, {0}, {1}, {00}, {01}, {10}, {11} } in roster notation.

(c) The set B = {0, 1}0 ∪ {0, 1}1 ∪ {0, 1}2 can be written as the set { {}, {0}, {1}, {00}, {01}, {10}, {11} } using the roster notation from part (b). Therefore, the set {0x: x ∈ B} is the set {0, 00, 01, 10, 11, 000, 001, 010, 011, 100, 101, 110, 111} in roster notation. Here, each element of the set is obtained by taking 0 as the first digit and each possible string of 0's and 1's from B as the remaining digits.

(d) The set {x y: where x ∈ {0} ∪ {0}2 and y ∈ {1} ∪ {1}2} can be written as the set {01, 02, 11, 12, 21, 22} in roster notation. Here, each element of the set is obtained by taking one digit from {0, 2} and one digit from {1, 2}. The set {0} ∪ {0}2 contains the elements {0} and {00}, while the set {1} ∪ {1}2 contains the elements {1} and {11}.

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Answer:

p = 3

Step-by-step explanation:

Given

4(2 + px) = 12x

If the coefficient of the x- term is the same on both sides of the equation, it will have no solution.

Distributing gives

8 + 4px = 12x ( equate the coefficients of the x- term )

4p = 12 ( divide both sides by 4 )

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

4(2 + px) = 12x

8 + 4px = 12x

If the coefficient of the x-term is the same on both sides of the equation, it will have no solution.

4p = 12

p = 3

The value of p when the equation has no solution will be 3. Then the correct option is B.

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Answer:

The maximum square footage of the family room is 225 square feet.

Step-by-step explanation:

From statement we know the combined area and the area of the living room, the maximum area of the family room is determined by subtracting the area of the living room from the combined area. All areas are measured in square feet:

\(A = 535\,ft^{2}-310\,ft^{2}\)

\(A = 225\,ft^{2}\)

The maximum square footage of the family room is 225 square feet.

The product of the unsigned integers 11010 and 1011 in binary multiplication is 10011110.

Hi! I'd be happy to help you with this binary multiplication problem using unsigned integers. Here's the step-by-step process:
1. First, write down the two binary numbers, with the larger one (11010) on top and the smaller one (1011) on the bottom.
2. Start multiplying each digit of the bottom number (1011) with the entire top number (11010), working from right to left. Write the results below the original numbers, shifting one place to the left for each digit.
  11010
 x1011
 ------
   11010   (11010 * 1)
  00000    (11010 * 0, shifted one place to the left)
11010     (11010 * 1, shifted two places to the left)
11010      (11010 * 1, shifted three places to the left)
 ------
3. Now, add the results together:
  11010
 x1011
 ------
   11010
  00000
 11010
11010
 ------
10011110

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Answer:

100 yards of fabric

Step-by-step explanation:

12 divided by 3 = 4 yards of fabric per costume

4 x 25 = 100 yards of fabric

The volume of the water in the fish tank is 135.27 cubic meters if the top 1/3 of the tank is just air.

To find the volume of the fish tank containing water, we need to find the volume of the fish tank and then subtract the volume that is occupied by the air i.e 1/3 of the volume of the tank.

So, the volume of the fish tank is :

=length x width x depth of the tank

=10.2 meters x 5.8 meters x 3.5 meters

= 203.94 cubic meters

Now we need to find the volume of the air that is occupied by the fish tank which is :

=1/3x the volume of the fish tank

=1/3x203.94 cubic meters

=68.67 cubic meters

The volume of the fish tank containing just water is:

=volume of the fish tank - the volume of the air occupied

= 203.94 cubic meters - 68.67 cubic meters

=135.27 cubic meters

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The test statistic for this hypothesis test is approximately -2.748. Americans spend less than 7 hours a week answering their email.

To find the test statistic, we need to perform a hypothesis test to determine if the sample data supports the researcher's suspicion that Americans spend less than 7 hours a week answering their email.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The population mean number of hours Americans spend answering their email per week is 7 or more

Alternative hypothesis (H₁): The population mean number of hours Americans spend answering their email per week is less than 7

Next, we can calculate the test statistic, which is the standardized value that measures the distance between the sample mean and the hypothesized population mean, considering the sample size and variability.

The test statistic formula for a one-sample t-test is given by:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

Given the information from the study:

Sample mean = 6.01

Sample standard deviation (s) = 8.96

Sample size (n) = 617

Hypothesized mean  = 7

Substituting these values into the formula, we get:

t = (6.01 - 7) / (8.96 / √617)

Calculating this expression gives us the test statistic.

t = (-0.99) / (8.96 / √617)

t ≈ -0.99 / (8.96 / 24.81)

t ≈ -0.99 / 0.3602

t ≈ -2.748

Therefore, the test statistic for this hypothesis test is approximately -2.748.

The test statistic provides a measure of how far the sample mean is from the hypothesized mean in terms of standard deviations. In this case, since the test statistic is negative, it suggests that the sample mean is less than the hypothesized mean, supporting the researcher's suspicion that Americans spend less than 7 hours a week answering their email.

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Answer:

B

Step-by-step explanation:

every other value is above 25.99