The equation y=ax^2 describes a parabola. If the value of a is positive, which way does the parabola open?
A.Up
B.Right
C.Left
D.Down

The correct answer for the transformation will be:

translation up π/4

vertical stretch by 2

translation right π/4

The parent function of g(x) is y = sin(x), and g(x) is obtained from the parent function by performing the following transformations:

Translation: The argument of sin(x) is shifted by π/4 units to the left, which results in a horizontal translation to the right by π/4 units.

Vertical stretch: The amplitude of the sine function is multiplied by 2, which results in a vertical stretch by a factor of 2.

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The procedure described, where participants are assigned into groups through a coin flip to ensure equal probability, is called random assignment.

Random assignment is a fundamental technique in experimental research. It is used to minimize potential biases and ensure that participants have an equal chance of being assigned to different groups. In this case, the two groups are Group 1 and Group 2 of the independent variable.

By using a coin flip, a randomization process is employed where the outcome (heads or tails) determines the group assignment. This random assignment helps to control for confounding variables and distribute their potential effects evenly across the groups.

It increases the likelihood that any observed differences between the groups are due to the manipulation of the independent variable rather than pre-existing differences among participants.

Random assignment is crucial in experimental design as it enhances the internal validity of the study. It allows researchers to make causal inferences and draw conclusions about the effects of the independent variable on the dependent variable.

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Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

The perimeter of the cross section formed is 44.22 in.

The area of the cross section formed is 72.44 in.²

From the question, we are to determine the perimeter and area of the cross section formed by the cut

As indicated in the diagram,

If the wood is cut along the indicated diagonal, the cross section formed is a rectangle whose length will be the length of the diagonal and its width will be 4 in.

Now, we will calculate the length of the diagonal,

Let the diagonal be d

Then, we can write that

d² = 2² + 18²

d² = 4 + 324

d² = 328

d = 18.11 in.

Thus,

The length of the rectangular cross-section is 18.11 in.

Now, using the formula for calculating the perimeter of a rectangle

P = 2(l +w)

Where P is the perimeter

l is the length

and w is the width

For the rectangular cross-section

l = 18.11 in.

w = 4 in.

Putting the parameters into the formula,

P = 2(18.11 + 4)

P = 2(22.11)

P = 44.22 in.

∴ The perimeter of the cross section formed is 44.22 in.

For the area of the cross section

Using the formula for calculating the area of a rectangle,

A = l × w

∴ Area of the cross section formed = 18.11 × 4

Area of the cross section formed = 72.44 in.²

Hence, the area of the cross section formed is 72.44 in.²

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Red Circle:

First find the diameter

We can do that by counting the squares

Diameter:4

The radius is half of the diameter

4/2=2

Radius of the Red Circles:2

Blue Circle:

Diameter: 2

2/2=1

Radius of the Blue Circle:1

First second thrid

I believe it's the 2nd one

the x-value of the point where the function has a relative extrema is x = 81, and the value of the relative extrema is -6561.

To find the x-values of all points where the function has any relative extrema and the value(s) of any relative extrema for the function f(x) = x^2 - 162x, follow these steps:

Find the first derivative of the function. The derivative of a function tells us the slope at a given point and can be used to determine extrema.
f'(x) = d/dx (x^2 - 162x)
f'(x) = 2x - 162
Set the first derivative equal to zero and solve for x. This will give us the critical points where extrema may occur.
2x - 162 = 0
2x = 162
x = 81
Check the second derivative to determine if the critical point is a relative extrema. If the second derivative is positive, it is a relative minimum, and if it is negative, it is a relative maximum.
f''(x) = d/dx (2x - 162)
f''(x) = 2
Since the second derivative is positive, the critical point x = 81 is a relative minimum.
Find the value of the function at the critical point to determine the value of the relative extrema.
f(81) = (81)^2 - 162(81)
f(81) = 6561 - 13122
f(81) = -6561

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Answer:

-2x-24/6

pass the x susbtrating divided it by 6

The minimum amount of money Camille could have is 0 dollars if she doesn't buy anything, and the maximum amount of money she could have is 166 dollars if she buys the maximum quantity of each item.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

We are given that;

The prices of different items at a garage sale: pants, shirts, shorts, and belts.  

Camille can buy up to 5 shirts.

Now,

If Camille buys 5 shirts, she would spend 5 * 6 = 30 dollars on shirts. Since she can buy up to 5 shirts, she may spend less than 30 dollars if she buys fewer shirts.

She can buy up to 10 pants, which would cost her 10 * 8 = 80 dollars.

She can buy up to 5 shorts, which would cost her 5 * 4 = 20 dollars.

She can buy up to 12 belts, which would cost her 12 * 3 = 36 dollars.

30 + 80 + 20 + 36 = 166 dollars

Therefore, by the  maxima and minima the answer will be 166 dollars if she buys the maximum quantity of each item.

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Answer:

X = 6y-2 is the easier substitution for another equation because all you have to do is just plug in the equation into the value of x.

Answer:

1260 degrees

Step-by-step explanation:

Answer:

  396 cm

Step-by-step explanation:

You want the distance traveled by a wheel of radius 21 cm in 3 revolutions.

The circumference of the wheel is ...

  C = 2πr

  C = 2π(21 cm) = 42π cm

In 3 revolutions of the wheel, it travels 3 times that distance, or ...

  3(42π cm) = 126π cm ≈ 396 cm

The distance traveled is about 396 cm.

__

Additional comment

The value shown is rounded to the nearest centimeter. The attachment shows the value to higher precision, for the usual approximations of pi.

<95141404393>

Depreciation is the accountant's estimate of the cost of a capital asset used in the production process, which is allocated over its useful life based on the benefits it generates.

Depreciation is a concept in accounting that recognizes the gradual reduction in value or usefulness of a capital asset over time. When a company purchases a capital asset, such as machinery, equipment, or vehicles, it incurs a cost that is expected to be spread over the asset's useful life. This cost is allocated as an expense called depreciation. The purpose of depreciation is to match the cost of the asset with the benefits it produces during its useful life. The estimation of depreciation involves considering factors like the initial cost of the asset, its expected useful life, and its residual value (the estimated value at the end of its useful life). By spreading the cost of the asset over its useful life, depreciation helps in accurately reflecting the consumption of the asset's value in the production process and provides a more accurate representation of the company's financial performance.

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Answer:

10

Step-by-step explanation:

14+14+18+18+22=86

6*16=96

96-86=10

Step-by-step explanation:

✧ \( \underline{ \underline{ \large{ \tt{S \: O \: L \: U \: T \: I \: O \: N}}} }: \)

Let the age of a person who entered the room be ' x '.

✧ \( \underline{ \underline{ \large{ \tt{G \: I \: V \: E \: N \: \: D \: A\: T \: A } }}} : \)

n ( number of observation ) = 6

\( \sum\) x = 14 + 14 + 18 + 18 + 22 + x = 86 + x

Mean = 16

☯ \( \boxed{ \large \tt{Mean \: = \frac{ \sum \: x}{n} }}\)

~Plug the values :

⇢ \( \large{ \tt{16 = \frac{86 + x}{6}}} \)

~Apply cross product property :

⇢ \( \large{ \tt{86 + x = 16 \times 6}}\)

⇢ \( \large{ \tt{86 + x = 96}}\)

Move 86 to right hand side and change it's sign

⇢ \( \large{ \tt{x = 96 - 86}}\)

⇢ \( \boxed{ \large{ \tt{x = 10}}}\)

\( \large{ \boxed{ \boxed{ \underline{ \large{ \tt{Our \: Final \: Answer : \underline{10}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♪

⋆ Let me know if you have any questions regarding my answer ⋆

\( \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}\) !! ✎

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The value of the height of the building is,

⇒ 247.5 feet

We have to given that;

A model of a building is 27.5 inches tall.

And, The scale of the model is 1 inch : 9 feet.

Since, A model of a building is 27.5 inches tall.

And, Scale is,

1 inch : 9 feet

Hence, The value of the height of the building is,

⇒ 27.5 x 9

⇒ 247.5 feet

Thus, The value of the height of the building is,

⇒ 247.5 feet

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HY OLA SUN TEFONO ME QVLOE AHRAC JU PSTICIORQ ME QUITASTUE MIS UNTPOS PER LAO RESPUSTA ES QU HEEEAYFRUS RALPH LIBRTA UVS AA A 8NTAVOS0 CE

Answer:

is a parallelogram and ab is produced to x such that ab=bx as shown in figure. show that dx and bc bisect eachother at o.

Answer:

its c

Step-by-step explanation:

because i said

Answer:

c is the correct option

Step-by-step explanation:

Answer: Choice C

\(\displaystyle g(x) = \left(\frac{1}{2}\right)5^{x+3}-2\)

=====================================================

Explanation:

The 1/2 out front handles the vertical compression by 1/2. For example, if two points are vertically spaced by 10 units, then their new vertical distance is now (1/2)*10 = 5 units.

The x+3 in the exponent means "shift 3 units to the left". Effectively what's going on is that the old input x is now x+3, ie 3 units larger than before. This shifts the xy axis itself 3 units to the right. If we held the curve fixed in place while the xy axis moved like this, then it gives the illusion the curve is moving 3 units to the left.

Then finally the -2 at the very end shifts the curve down 2 units. This is because whatever the y coordinate is, we subtract 2 from it to do this vertical shifting. For example, the point (0,62.5) shifts 2 units down to (0,60.5)

The value of f is 2 in the given equation.

An equation is a mathematical statement which is formed when two algebraic expressions are equated using an equal sign.

The given equation is

2 +1.25 f = 10 -2.75f

It has to be solved for f

1.25f + 2.75 f = 10 - 2

4 f = 8

f = 2

Therefore , The value of f is 2.

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The value that is part of the solution to the trigonometric inequality on the first lap of the trigonometric circle are given as follows:

x = 2pi/3.

The trigonometric inequality in this problem is defined as follows:

sec(2x) < -1.

The secant of an angle is defined as follows:

sec(x) = 1/cos(x).

Hence:

sec(2x) = 1/cos(2x).

Thus:

sec(2x) < -1.

1/cos(2x) < -1

1 < -cos(2x)

cos(2x) < -1

2x < arccos(-1)

x < arccos(-1)/2

x < 90º.

Meaning that the answer is composed by the angles x for which 2x is either on the second quadrant or in the third quadrant, in which the cosine is negative.

The values are given as follows:

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Answer:

∡3 & ∡6 are same side interior angle.

∡4 & ∡6 are alternate interior angles.

∡2 & ∡8 are vertical angles.

∡1  & ∡5 are corresponding angles (because they are in the same spot).

∡1  & ∡3 are vertical angles (because they are the opposite angle of each other).

∡1 & ∡2 are supplementary angles (because they add up to 180°).

We can answer the two questions by relying on our knowledge of how to solve equations, showing how both strategies are efficient, and finding x.

a. Both strategies will work and lead to the same solution. It's just a matter of personal preference which one to use. However, subtracting 7 from both sides may be more efficient in this case because it eliminates the need for an extra step of adding 5 to both sides.

b. TStarting with 7 = 3x - 5, we can add 5 to both sides to get:

7 + 5 = 3x - 5 + 5

12 = 3x

12/3 = 3x/3

4 = x

To solve an equation, you need to find the value of the variable that makes the equation true. The following steps can be used to solve most equations:

It's important to remember that whatever you do to one side of the equation, you must also do to the other side to maintain the equality. Additionally, if the equation has parentheses, use the distributive property to simplify the expression inside the parentheses.

Some equations may have special cases, such as quadratic equations or equations with absolute values. These types of equations may require additional steps and methods to solve.

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The angle pairs by parallel lines cut by a transversal are corresponding angles, interior/exterior angles etc.

Many angle pairs are created when a transversal crosses a pair of parallel lines. They consist of the following:

Corresponding angles: The positions on either side of the transversal and on the opposing sides of the parallel lines are referred to as corresponding angles. If the parallel lines are sliced by the transversal, then the corresponding angles are congruent and have the same measure.

Interior angles: These are a pair of angles that are inside parallel lines and on the opposing sides of the transversal. If the transversal cuts the parallel lines, alternate inner angles are equivalent.

External angles: These are a pair of angles that are outside the parallel lines and on the opposing sides of the transversal. If the transversal cuts the parallel lines, then alternate exterior angles are congruent.

Vertical angles: These are opposite-to-each pairs of angles created by the junction of two lines. By definition, these are the angles that are congruent, which means having the same measure.

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Answer:

13. \(12.88m\)

14. \(10ft\)

Step-by-step explanation:

To calculate the circumference, use the following formula, where \(d\) is the diameter:

\(C = \pi d\\C = 3.14159 * 4.1 = 12.88m\)

To find the arc length, use the following formula, where \(r\) is radius and \(\theta\) is the angle in radians:

\(s = r\theta\)

Before you plug in any values, convert the angle from degrees to radians using the following formula, where x is the angle in degrees:

\(\theta = \frac{x}{180}\pi\\\theta = \frac{144}{180}\pi\\\theta \approx 2.5\)

Now plug in your values:

\(s = 4 \cdot 2.5\\s = 10ft\)

Answer:

It would require 40 teaspoons

Step-by-step explanation:

Given that;

A cookie recipe requires 3 teaspoons of baking soda for 36 cookies

The amount of teaspoons of baking soda required per cookie is;

r = 3/36 teaspoons per cookie

So, for 480 cookies i would require;

N = r × 480 cookies

Substituting r, we have;

N = 3/36 teaspoons per cookie × 480 cookies

N = 40 teaspoons

It would require 40 teaspoons

Answer: 361

Step-by-step explanation:

Answer:

They'll need to see 12 movies together before they pay the same amount.

Let the number of movies be x

Based on the question given, the equation for Jaycie will be:

= 27 + (6 × x)

= 27 + 6x

The equation for Clarie will be:

= 8.25 × x

= 8.25x

Then, the equation to solve the question will be:

27 + 6x = 8.25x

Collect like terms

27 = 8.25x - 6x

2.25x = 27

x = 27/2.25

x = 12

They will see 12 movies together.

Answer:

First, we need to calculate the daily interest rate on the credit card. We can do this by dividing the annual percentage rate (APR) by the number of days in a year:

Daily interest rate = APR / 365

Daily interest rate = 0.2445 / 365

Daily interest rate = 0.00067 or 0.067%

Next, we can calculate the interest that will accrue over the course of one month, which is approximately 30 days:

Interest = Balance * Daily interest rate * Number of days

Interest = $1,359 * 0.00067 * 30

Interest = $27.42

Adding the interest to the outstanding balance, we get:

Balance after one month = $1,359 + $27.42

Balance after one month = $1,386.42

Therefore, the balance on the credit card after one month will be approximately $1,386.42.

The best equation that approximates the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is \(p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })\) .

Given:

Probability of children who live in households with incomes that are classified at a particular income level,p = 22/100 = 0.22

Number of children in a simple random sample,n = 300

Probability of children who do not live in households with incomes that are classified at a particular income level, q = 1-p = 0.78

The probability of children in the sample living in households that are classified at a particular income level,p₁ = 27/100 = 0.27

Now, we know

\(p(z > \frac{p_{1} -p}{\frac{\sqrt{p.q} }{n} } )\)

So,

\(p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })\)

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