Examine the steps below. Between which two lines was a mistake made?

A.
between line 1 and line 2
B.
between line 2 and line 3
C.
between line 3 and line 4
D.
between line 4 and line 5

The resulting function is given as follows:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

The parent function in the context of this problem is given as follows:

[tex]y = e^{-2x}[/tex]

When the function is vertically compressed by a factor of 3, we have that it is divided by three on the range, hence:

[tex]y = \frac{e^{-2x}}{3}[/tex]

When the function is reflected across the x-axis, we multiply by -1 on the domain, hence:

[tex]y = \frac{e^{2x}}{3}[/tex], as -2x x -1 = 2x.

When it is shifted down two units, we subtract by two on the range, hence:

[tex]y = \frac{e^{2x}}{3} - 2[/tex]

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The equation of circle whose center is at (4,-7) and radius is "5 units", is (b) (x − 4)² + (x + 7)² = 25.

We know that the equation of a circle which have center at the coordinate (h, k) and has a radius as "r" is represented by the formula ⇒ (x - h)² + (y - k)² = r²,

In this case, the center of the circle is situated at the coordinate (4, -7) and the radius is 5.

So, we substitute these values into the "circle-equation" to get;

⇒ (x - 4)² + (y + 7)² = 5²,

⇒ (x - 4)² + (y + 7)² = 25,

Therefore, the correct option is (b): (x − 4)² + (y + 7)² = 25.

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The given question is incomplete, the complete question is

A circle is centered at (4, −7) and has a radius of 5. Which of the following is the equation of this circle?

(a) (x − 4)² + (x + 7)² = 5,

(b) (x − 4)² + (x + 7)² = 25,

(c) (x + 4)² + (x − 7)² = 5,

(d) (x + 4)² + (x − 7)² = 25.

Thus, radius of the smaller cylinder is found as the 0.08 cm, for the given ratio of surface areas.

A cylinder's surface area provides information on how much space is present on the whole surface of the cylinder. If you were to use wrapping paper to wrap a can of Pringles as a birthday gift, then amount required would be equal towards the surface area of a Pringles can.

Let the surface area of smaller cylinder be s.

Let the  surface area of larger cylinder be S.

ratios of surface area:

s/S = 4 / 25

Radius of larger cylinder = 0.5 cm.

As,both cylinders are similar height will be same.

The formula for the surface area = 2*π*r*h

Put the values in ratio:

2*π*r*h / 2*π*R*h = 4 / 25

r / 0.5 = 4/25

cross multiplying:

r = 0.5*4 / 25

r = 0.08

Thus, radius of the smaller cylinder is found as the 0.08 cm.

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Answer:Answer and Explanation: An algebraic expression for the phrase '6 more than the product of 8 and n' is '8n + 6.

Step-by-step explanation:

The probability that he passes Math and does not pass Physics is given as follows:

0.28 = 28%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probabilities for each event is given as follows:

The events are independent, hence the probability that he passes Math and does not pass Physics is given by the multiplication of the probabilities of each event, as follows:

0.7 x 0.4 = 0.28 = 28%.

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The surface area of the triangular pyramid is 147.6 cm².

The surface area of a three-dimensional object is the total area of all its faces.

To calculate the surface area of the triangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

Family: exponential functions

Step-by-step explanation:

The given function is:

[tex]y = 3*2^x - 6[/tex]

It is in the form of exponential function:

[tex]y = a*b^x + c[/tex]

where "a", "b", and "c" are constants.

The parent function of an exponential function is:

[tex]y = b^x[/tex]

where "b" is the base of the exponential function. In this case, the parent function would be:

The given function is a member of the family of exponential functions with base 2 and with a vertical shift of -6 units and a vertical stretch by a factor of 3.

Answer:

Exponential function family with base 2.

[tex]\textsf{Parent function:} \quad y=2^x[/tex]

Step-by-step explanation:

The given equation is in the form of an exponential function with a vertical stretch and vertical shift.

The standard form of this type of exponential function is:

[tex]y=ab^x+c[/tex]

where:

If |a| > 1 then it is a vertical stretch, and if 0 < |a| < 1 it is a vertical "compression".

The parent function of this type of exponential function is y = bˣ, where b is the base.

Given function:

[tex]y=3 \cdot 2^x-6[/tex]

Therefore, the parent function of the given function is:

[tex]\boxed{f(x)=2^x}[/tex]

The given function is a vertical stretch by a factor of 3, followed by a vertical shift downwards by 6 units, from the parent exponential function with base 2.

Hence, the family of functions that this equation belongs to is the exponential function family with base 2, and the parent function is [tex]y = 2^x[/tex].

The situation that requires a square root operation is calculating the height of a cylinder given the area of the base. third option

It should be noted that the operation that needs square root among the given option lies on the selected option above, this is because from the formular we can see that there is square of r which is r^2

However thegeometry  fiqure of the volume of a cylinder can be calculated using this formular V = πr^2h

height of a cylinder can be calculated using the formular V/ πr2.

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Answer:$578.81

Step-by-step explanation:

✨magic✨

The year in which  the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.

The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.

To derive the number of year,

140 = 2.86t + 112

Subtracting 112 from both sides gives:

28 = 2.86t

Dividing both sides by 2.86 gives:

t ≈ 9.79 years

See attached graph.

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There are 25% chance of 5 more people in the party.

Hence option (a) is correct.

Relative frequency = (number of times of occurrence of an event )/ (number of trials)

For the given table

relative frequency for 1 people = 0.05 = 5%

relative frequency for 2 people = 0.46 = 46%

relative frequency for 3 people = 0.18 = 18%

relative frequency for 4 people = 0.22 = 22%

relative frequency for 5 people = 0.06 = 6%

relative frequency for 6 people = 0.03 = 3%

Since relative frequency for 1 people is 5%

Therefore,

Relative frequency for 5 people is = 5x5%

                                                         = 25 %

Hence,

Relative frequency of 5 more people 25%.

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The equation of the circle in this problem is given as follows:

x² + y² = 90000

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The center for this problem is given as follows:

(0,0).

The radius is given as follows:

300 ft.

Hence the equation is of:

x² + y² = 90000

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The solution to the equation 2,401 = 7⁶⁻²ˣ is x ≈ 1.4076.

In mathematics, a logarithm is the inverse operation to exponentiation. Given a base b and a positive number y, the logarithm of y with respect to the base b is the exponent to which b must be raised to yield y. In other words, if x is the logarithm of y with respect to base b, then bˣ = y.

We can begin solving this equation by isolating the exponential term on one side of the equation and taking the logarithm of both sides.

2,401 = 7⁶⁻²ˣ

Taking the logarithm base 7 of both sides:

log₇(2,401) = log₇(7⁶⁻²ˣ )

Using the property of logarithms that states that log base a (aᵇ) = b, we can simplify the right-hand side of the equation:

log₇(2,401) = (6-2x)log₇(7)

Since log₇(7) = 1, we can further simplify:

log₇(2,401) = 6-2x

-2x = log₇(2,401) - 6

x = (6 - log₇(2,401))/2

Using a calculator, we find:

x ≈ 1.4076

Therefore, the solution to the equation 2,401 = 7⁶⁻²ˣ  is x ≈ 1.4076.

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Answer:

1/8

Step-by-step explanation:

The absolute value of positive numbers (decimals, fractions, etc.) is the same number. The absolute value of negative numbers (decimals, fractions, etc.) is the same, but positive.

What is Absolute value?

Absolute value is a set of lines that if any number is placed in it, the number would be positive

Absolute signs: | |

Examples:

|-6|= 6 (Absolute value of -6 is 6)

|9|=9 (Absolute value of 9  is 9) (Because 9 is already positive)

Your Question

Since 1/8 is already positive, the absolute value of it would just be 1/8

Please feel free to ask questions

The polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6 is f(x) = x³ - x² - 30x.

To find a polynomial function of degree 3 with leading coefficient 1 and zeros at -5, 0, and 6, we start by using the factor theorem. This theorem tells us that if a polynomial function has a zero at some value c, then it is divisible by the linear factor (x - c).

Therefore, the polynomial with zeros at -5, 0, and 6 can be written as:

f(x) = a(x + 5)(x - 0)(x - 6)

where a is a constant coefficient that we need to determine. Since the leading coefficient of the polynomial is 1, we set a = 1.

Multiplying out the factors, we get:

f(x) = (x + 5)(x)(x - 6)

= x³ - x² - 30x

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Therefore , the solution of the given problem of area comes out to be the trapezium has a surface area of 39 square centimetres.

Calculating how much space would be needed for fully covering its exterior will reveal its overall dimensions. The surrounding environment is considered while selecting a comparable product with a rectangular shape. The surface area of anything determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal shapes determines how much water it can contain.

Here,

We can use the formula for a trapezoid's area if we assume that the shape is a trapezoid with parallel sides that are 9 cm and 4 cm and a height of 6 cm.

=> A = (a + b)h/2

where h is the height, and a and b are the lengths of the parallel sides.

When we enter the values we have, we obtain:

=> A = (9 + 4)(6)/2

=> A = 13(3)

=> A = 39

Consequently, the trapezium has a surface area of 39 square centimetres.

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Answer:

Perimeter of rhombus = 4(9.7) = 38.8 cm

Area of rhombus = 4(1/2)(6.2)(7.4)

= 91.76 cm^2

Answer:

a. 3x = 23-2

3x = 21

x = 21÷3

x = 7

b. 5x - 2 = 4

5x = 4+2

5x = 6

x = 6÷5

x = 1.2

c. 3x = 23-2

3x = 21

x = 21÷3

x = 7

d. 7 = 2x+0.5x

7 = 2.5

x = 2.5÷7

x = 2.8

Answer:

I'm sorry, but there is no feature for this in this game.  But, there is a grid and a sizing tool.  You'll just have to make an educated guess based on the size of your character and your character's stage of life (baby, toddler, kid, teen, adult).  Hope I helped!  I once had the same question, but just did this.  I think each big grid square maybe is 3-5 ft?

The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)

Given data ,

To find the intersection points of the two functions, we can set them equal to each other and solve for x:

x² - 6x + 9 = -x² + 17

Bringing all the terms to one side:

2x² - 6x - 8 = 0

Dividing by 2:

x² - 3x - 4 = 0

We can factor this quadratic equation as:

(x - 4)(x + 1) = 0

So the solutions are:

x = 4 or x = -1

To find the corresponding values of y, we can substitute each value of x into either of the original equations

y = x² - 6x + 9

When x = 4:

y = 4² - 6(4) + 9 = 1

So one intersection point is (4, 1).

When x = -1:

y = (-1)² - 6(-1) + 9 = 16

So the other intersection point is (-1, 16).

Hence , the two functions intersect at the points (4, 1) and (-1, 16)

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The surface area of the rectangular prism is 2200 square mm

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

Dimensions = 5 mm by 40 mm by 20 mm

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 40 + 5 * 20 + 40 * 20)

Evaluate

Area = 2200

Hence, the area is 2200 square mm

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Answer:

14:10

Step-by-step explanation:

We are given that the total train journey from Reading to Worle is the same for all trains

For the first train the time taken = 13:45 - 12:05

13:45
   -
12:05
--------
1 : 40
--------

So total travel time = 1 hour 40 minutes

For the third train time taken
15:05  -  13:25

15:05 = 14:05 + 0:60 since there are 60 minutes in an hour (we carry 60 from the hours part)

14:05 + 0:60 = 14:65

15:05 - 13:25 =

14:65
   -
13:25
---------
1 : 40 or 1 hour 40 minutes same as train #1

We want to find the arrival time of train #2 at Worle

Departure time of train #2 from Reading = 12:30

Time of travel = 1 hour 40 minutes

Arrival time = 12:30 + 1:40

12:30 time
   +
 1: 40  hours
----------
13:70   time
------------------
Since there are 60 minutes in 1 hour, to convert 13:70 to proper time units
subtract 60 from 70 to get the minute part of time and add 1 to 13 to get the hour part of time

13:70 = 14:10

Therefore the time that goes into the gap = 14:10

Verify

If the second train leaves Reading at 12:30 and arrives at Worle at 14:10, then time taken =

14:10 - 12:30 = 13:70 - 12:30 = 1:40 = 1 hour 40 minutes

Hope that helps and please don't hesitate to ask more questions if you have not fully understood my explanation

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

There are two distinct y values satisfying the given equation.

First, we rewrite the equation as |y-3| = 5 - x² + 8x - 18. Then, we express |y-3| as two cases: y-3 and -(y-3).

Case 1: y - 3 = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 16.

Case 2: -(y - 3) = 5 - x² + 8x - 18

Solving for y, we get y = x² - 8x + 10.

Both parabolic equations yield distinct y values for any x in the set of integers (Z). Thus, there are two distinct y values satisfying the given equation.

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Answer:

last choice:  2b²/a³

Step-by-step explanation:

2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³

Answer:

It is 50x or 50*x or 50(x).

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

According to the information, Sandra charges $2.25 for each necklace. So the correct option would be A.

To find the answer to this problem we must identify the information that the function raises. In this case we must replace the n by a number (in this case it will be 5) to find the value of P as shown below:

Once we identify how much 5 necklaces are worth, we divide that value by 5 to find the unit value.

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We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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