write the equations after translating the graph of y = | 1/2 x -2 | + 3 one unit to the right

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer:

3 pie, 2√10, and √90

Step-by-step explanation:

3 times pie is 9.472525 or smth, √10 is 3. 45672 times 2, and √90 is like 9

The amount of money Kadeesha have in her account after 11 years is $1059.3.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = \(A=P(1+\frac{r}{100})^{nt}\)

Given that, principal=$900, rate of interest=1.5% and time period =11 years.

Now, amount =900(1+1.5/100)¹¹

= 900(1+0.015)¹¹

= 900(1.015)¹¹

= 900×1.177

= $1059.3

Therefore, the amount of money Kadeesha have in her account after 11 years is $1059.3.

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The appropriate test to examine the relationship between the number of steps taken and HR in a group of 1000 athletes depends on the type of data and the research question.

If the number of steps and HR are both measured on a continuous scale and the research question is to examine the strength and direction of the relationship between the two variables, then the appropriate test would be Pearson's correlation coefficient.

If either the number of steps or HR is measured on a continuous scale and the other variable is measured on an ordinal scale, then the appropriate test would be Spearman's correlation coefficient.

However, if the research question is to predict HR based on the number of steps taken, and there are other variables that may influence the relationship, then multiple regression analysis would be the appropriate test.

Chi-Square test is used to examine the association between two categorical variables. It is not appropriate for examining the relationship between a continuous and categorical variable.

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Answer:

yes

Step-by-step explanation:

hyp^2=3.9^2=15.21

1.5^2 +3.6^2=15.21

since hpy^2=sum of square of legs

it can be sides of a rt triangle...

A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² =  8 (y - 3)

Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The focus

F (h, k + p) = (-5,-1)

h = -5

k + p = -1

P in this problem, is the midpoint between the focus and the directrix

P = (-1 - 7) / 2 = -4

p = -4

the vertex

v(h, k)

h = -5

k + p = -1, k = 3

v(h, k) = v(-5, 3)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -5)² =  4 * 2 (y - 3)

(x + 5)² =  8 (y - 3)

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Answer: Value of B= 75  Basketball cards

Step-by-step explanation:

STEP 1

let number of cards Steve has be =a

let number of cards Claire has be =b

STEP 2

Steve has a= 84 basketball cards

Claire has 7 times less than Steve = 84 /7 = 12=b

STEP 3

if Claire buys 63 more cards

The present value of card Clare now has = 12 +63 = 75 basket ball cards=b

The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

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The rule that describes the function is (c) Output = (0.5)(Input) + 1.5

The points on the coordinate plane are given as

(negative 1, 1), (1, 2), (3, 3), (5, 4)

Express as numbers

So, we have

(-1, 1), (1, 2), (3, 3), (5, 4)

Divide the input values by 2

So, we have

0.5(Input) => (-1/2, 1), (1/2, 2), (3/2, 3), (5/2, 4)

Add 1.5 to the input values

So, we have

0.5(Input) + 1.5 => (1, 1), (2, 2), (3, 3), (4, 4)

So, we have

Output = 0.5(Input) + 1.5

Hence, the equation is (c)Output = 0.5(Input) + 1.5

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The 5-number summary are:

Th box plot suggests that the values in the dataset are close to the median and there are no extreme outliers.

To know 5-number summary, we will sort the data in ascending order:

\(0.598, 0.751, 0.752, 0.766, 0.771, 0.820\)

The 5-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3) and maximum.

To create a box plot, we represent these values on a number line. We draw a box between Q1 and Q3, with a vertical line at the median. Then, we extend lines (whiskers) from the box to the minimum and maximum values.

0.598 0.752 0.766 0.771 0.820

|---------|---------|---------|---------|

|-------------------|

Median

The variability of the data around the median. The data exhibits relatively low variability around the median. The range between the first quartile (Q1) and third quartile (Q3) is narrow, indicating that the middle 50% of the data is tightly grouped together.

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Answer:

$1,680

Step-by-step explanation:

i think it is right because 12,000 at 2 percent=280 then 280×7= 1,680

To hide the last two rows in a table view in Swift and set their row heights to 0, you can modify the table view's delegate method `heightForRowAt` for the respective rows.

In Swift, you can achieve this by implementing the UITableViewDelegate protocol's method `heightForRowAt`. Inside this method, you can check if the indexPath corresponds to the last two rows (in this case, rows 9 and 10). If it does, you can return a row height of 0 to hide them from the view. Here's an example of how you can write this logic:

```swift

func tableView(_ tableView: UITableView, heightForRowAt indexPath: IndexPath) -> CGFloat {

   let numberOfRows = tableView.numberOfRows(inSection: indexPath.section)

   if indexPath.row == numberOfRows - 2 || indexPath.row == numberOfRows - 1 {

       return 0

   }

   return UITableView.automaticDimension

}

```

In the above code, `tableView(_:heightForRowAt:)` is the delegate method that returns the height of each row. We use the `numberOfRows(inSection:)` method to get the total number of rows in the table view's section. If the current `indexPath.row` is equal to `numberOfRows - 2` or `numberOfRows - 1`, we return a height of 0 to hide those rows. Otherwise, we return `UITableView.automaticDimension` to maintain the default row height for other rows.

By implementing this logic in the `heightForRowAt` method, the last two rows in the table view will be effectively hidden from the view by setting their row heights to 0.

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A simple random sample of steel canisters has been taken, and you have the mean wall thickness and standard deviation in millimeters. To determine if it is appropriate to perform a hypothesis test about the population mean, consider the following factors:

1. Randomness: The sample has been taken using a simple random sampling method, which helps ensure that each canister has an equal chance of being selected. This is a crucial factor for conducting a hypothesis test.

2. Sample size: Although the sample size is not mentioned, a large sample size (usually 30 or more) is preferred for hypothesis testing. The larger the sample size, the more accurate the results of the test will be in representing the entire population.

3. Normality: Hypothesis tests about the population mean often rely on the assumption that the data follows a normal distribution. With a large sample size, the Central Limit Theorem suggests that the sampling distribution of the mean will be approximately normally distributed, even if the population itself is not.

4. Known standard deviation: You have the standard deviation for the sample, which is necessary for conducting the hypothesis test.

Given the information provided, it seems appropriate to perform a hypothesis test about the population mean for the wall thickness of steel canisters, provided the sample size is large enough.

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Answer:

Yes

Step-by-step explanation:

The given length of sides are \(5\) feet, \(6\) feet, and \(9\) feet.

For these sides to form a triangular truss, the sum of any two sides must be greater than the third side.

Here, \(5+6=11\) which is greater than \(9\), the third side.

Similarly, \(6+9=15\) which is greater than \(5\), and \(5+9= 14\) which is greater than \(6\).

So, this satisfies the conditions to the three sides to form a triangle.

Hence, yes, the triangular truss can be made by the given three sides.

Answer:

h

Step-by-step explanation:

Step-by-step explanation:

they weigh 11 pounds and 4 ounce

As per the concept of unitary method, Together, Isaac and Isaiah weigh 182 ounces.

To determine the total weight of the twins in ounces, we first need to convert their weights to a common unit. Since the weight of Isaac is given in both pounds and ounces, we can easily calculate his weight solely in ounces. One pound is equivalent to 16 ounces. So, Isaac's weight in ounces would be:

Weight of Isaac in ounces = (6 pounds * 16 ounces/pound) + 2 ounces

Weight of Isaac in ounces = 96 ounces + 2 ounces

Weight of Isaac in ounces = 98 ounces

Next, we calculate the weight of Isaiah in ounces. Similarly, we convert his weight to ounces by multiplying the number of pounds by 16 and then adding the remaining ounces:

Weight of Isaiah in ounces = (5 pounds * 16 ounces/pound) + 4 ounces

Weight of Isaiah in ounces = 80 ounces + 4 ounces

Weight of Isaiah in ounces = 84 ounces

Finally, we add the weights of Isaac and Isaiah together to get their combined weight:

Total weight of Isaac and Isaiah = Weight of Isaac in ounces + Weight of Isaiah in ounces

Total weight of Isaac and Isaiah = 98 ounces + 84 ounces

Total weight of Isaac and Isaiah = 182 ounces

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The maximum height of the projectile is 56.53 meters.

The height of a projectile at time t is represented by the function h (t)= −4.9 t² +18t + 40, where h(t) is the height in meters and t is the time in seconds.

This is a quadratic function of the form h(t) = at² + bt + c, where a = -4.9, b = 18, and c = 40.

To find the maximum height of the projectile, we need to find the vertex of the parabolic graph of the function h(t).

The vertex of the parabola is at the point (t, h(t)) where t = -b/2a. Substituting the values of a and b, we get t = -18/(2(-4.9)) = 1.8367 seconds.

To find the maximum height, we need to substitute t = 1.8367 seconds into the function h(t). h(1.8367) = -4.9(1.8367)^2 + 18(1.8367) + 40 = 56.53 meters.

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Answer:

see explanation

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (y, - x ) , thus

C)- 8, - 4 ) → C'(- 4, 8 )

D(0, - 4 ) → D'(- 4, 0 )

E(- 8, - 9 ) → E'(- 9, 8 )

Answer:

Reflection, then rotation

Step-by-step explanation:

The first triangle is flipped to the second position and then rotated to the thrid position.

The angle of attack α at zero lift is equal to the zero-lift angle of attack α₀. To provide a specific value, we would need more information about the airfoil being used, such as its camber or profile.

Using thin airfoil theory, we can calculate the angle of attack α when the lift coefficient (Cl) is equal to zero. In thin airfoil theory, the lift coefficient is given by the formula:

Cl = 2π(α - α₀)

Where α₀ is the zero-lift angle of attack. To find α when Cl = 0, we can rearrange the formula:

0 = 2π(α - α₀)

Now, divide both sides by 2π:

0 = α - α₀

Finally, add α₀ to both sides:

α = α₀

So, the angle of attack α at zero lift is equal to the zero-lift angle of attack α₀. To provide a specific value, we would need more information about the airfoil being used, such as its camber or profile.

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The volume of the sphere with a diameter of 13.6 miles is approximately 1663.17 cubic miles.

To find the volume of a sphere, we need to use the formula:
V = (4/3)πr³

where V is the volume, π is the constant pi, and r is the radius of the sphere.

But in this problem, we are given the diameter of the sphere, which is 13.6 miles.

We can use this information to find the radius by dividing the diameter by 2:
r = d/2 = 13.6/2 = 6.8 miles

Now we can substitute this value of r into the formula for the volume:
V = (4/3)πr³
V = (4/3)π(6.8)³
V = (4/3)π(314.432)
V = 1663.17 cubic miles (rounded to the nearest tenth)

Therefore, the volume of the sphere with a diameter of 13.6 miles is approximately 1663.17 cubic miles.

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3.45 to 5.71 is the correct interpretation of 90%confidence interval

Explaining, rephrasing, or otherwise demonstrating your own understanding of something is the act of interpretation. An interpreter is a person who interprets from one language into another for the purpose of explaining what is being said to a non-native speaker. To interpret something, you must first comprehend the music, writing, language, or idea in question before offering your interpretation. Although a machine may generate enormous amounts of data, it will still require your interpretation for people to understand it.

With 90% certainty, we project that between 3.45 and 5.71 percent of the population actually shop at their neighborhood mall.

To calculate the confidence interval, we must find p′, q′. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then α = 1 – CL = 1 – 0.95 = 0.05 ( α 2 ) ( α 2 ) = 0.025.

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Complete Question is -

Stephanie wants tO estimate the proportion of people who shop at the local mall, random survey of indivlduals finds a 90% confidence interval to be (3.45, 71). Whar the correct interpretation of the 90% confidence Interval? Select the correct answer below: We estimate with %0% confidence that the sample proportion of people who shop at the mall Is between 3,45 and 5.71. We estimate that %% ofthe tlme survey Is taken; the proportion of peop who shop at the mall will be between } A5 and $.71, We estimate wlth %; confidence that the true population proportion of people who shop at the local mall Is between 3AS and 5,71

Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

Therefore the mass of the element is given by:

If the initial mass is 760 g and the final mass is 15 g, we have:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

Element X take 32.6 minutes to decay to 87 grams.

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

Given that;

Element X decays radioactively with a half life of 15 minutes.

And, there are 400 grams of Element X.

Now, By the given information, we can formulate;

⇒ \(y = x (0.5)^{t/h}\)

Substitute all the values we get;

⇒ 400 = 87 × \((0.5)^{t/15}\)

⇒ 400 / 87 =  \((0.5)^{t/15}\)

⇒ 4.6 =  \((0.5)^{t/15}\)

Take log both side,

⇒ ln 4.6 = t/15 (ln 0.5)

⇒ 1.52 = t/15 x 0.7

⇒ t = 32.6 minutes

Thus, Element X take 32.6 minutes to decay to 87 grams.

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Using 3 different methods, we can find that YZ = 25m

Method 1:

For a given triangle rectangle with a known angle θ and a hypotenuse H, we can write the trigonometric relations -

sin(θ) = (opposite side)/Hypotenuse

cos(θ) = (adjacent side)/Hypotenuse

tan(θ) = (opposite side)/(adjacent side)

Now, in the given image we can see that:

θ = 30°

H = 50m

XY = adjacent side

YZ = opposite side.

We want to find YZ, so with the known things, we can use the first relation:

sin(30°) = YZ/50m

YZ = sin(30°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 2:

We know that the sum of the measure of all the internal angles of a triangle is always equal to 180°.

In a right-angled triangle, we have an angle equal to 90°.

Then we can write -

Z + 90° + 30° = 180°

Z = 180° - 90° - 30°

Z = 60°

From this angle, the side YZ is the adjacent side, then we can use the second trigonometric relation:

cos (60°) = YZ/50m

YZ = cos(60°) * 50m

YZ = 1/2 *50m

YZ = 25m

Method 3:

With the same angle of 60° we could find side XY, the opposite side as follows:

sin(60°) = XY/50m

XY = sin(60°) * 50m

XY = √3/2 *50m

XY = 25m

Now that we know one of the sides, we can use the last trigonometric relation-

tan(60°) = XY/YZ

tan(60°) = 43.3m/YZ

YZ =  43.3m/tan(60°)

YZ = 25m

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The complete question is -

Describe three ways to determine the measure of segment YZ.

Triangle XYZ is shown. Angle XYZ is a right angle and angle ZXY is 30 degrees. The length of hypotenuse XZ is 50 meters.

C. Yes, both member variables and methods are inherited by a subclass.

In object-oriented programming, a subclass inherits both the member variables and methods from its superclass. This means that the subclass can access and use the same member variables and methods as the superclass.

Inheritance allows the subclass to extend or modify the behavior of the superclass by adding new variables and methods or overriding the existing ones. This is a key feature of object-oriented programming, as it allows for code reuse and facilitates the creation of hierarchies and relationships between classes.

Therefore, the correct answer is C: Yes, both member variables and methods are inherited by a subclass, allowing it to extend or modify the behavior of the superclass.

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Answer:

725 x0.05=36.25

Step-by-step explanation:

when finding percentage move the decimal over two places, making 5 0.05

Answer:

(-1,0)

Step-by-step explanation:

Look to see which points have the same x value (in this case -1)