The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?

Exactly one-year later,

(a) Mean of the ages will be 13 years and 3 months.

(b) Range of the ages will be same 2 years and 7 months.

Part (a) : To find the mean of the ages of the same group of students exactly one year later, we add one year to each student's age and find the new mean.

New mean is : 12 years and 3 months + 1 year = 13 years and 3 months;

So the mean of the ages of the same group of students exactly one year later is 13 years and 3 months.

Part (b) : The range of their ages would still be 2 years and 7 months because we are adding the same amount to all of their ages, the difference between the youngest and oldest member of the group would remain the same.

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Answer:

O True

Step-by-step explanation:

Unit rate of essays/minute:

40 minutes / 5 essays = 8 essays/minute

256 essays / 32 minutes = 8 essays/minute

The unit rates are equal.

Answer: O True

Answer:

x = 3.5

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:

[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]

Next, isolate the variable, x. First, subtract 7 from both sides of the equation:

[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]

Finally, divide 2 from both sides of the equation:

[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]

x = 3.5 is your answer.

~

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Answer:

[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]

Step-by-step explanation:

To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.

We can do this by first combining the constants on the right-hand side of the equation:

[tex]2x+15-8=14[/tex]

[tex]2x+7=14[/tex]

Next, we can isolate x by subtracting 7 from both sides of the equation:

[tex]2x=7[/tex]

Finally, we can solve for x by dividing both sides of the equation by 2:

[tex]x=\frac{7}{2}[/tex]

Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].

Answer:

1/3

Step-by-step explanation:

There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.

5/15 is 5 out of 15. 5/15 simplifies to 1/3.

Answer:

Step-by-step explanation:

However many decimals you move to get 1 after the first number that is not 0 is what goes in the exponent.  Negative version because to get to a decimal you move in the negative direction.

.1  =  1.0 x [tex]10^{-1}[/tex]

.01 = 1.0 x [tex]10^{-2}[/tex]

.001 = 1.0 x [tex]10^{-3}[/tex]

.000001  =,1.0 x [tex]10^{-6}[/tex]

_________________________________

_________________________________

Answer:

$6,840

Step-by-step explanation:

The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).

The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:

T = 2π√(l/g)

where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).

Substituting l = 1 m, we get

T = 2π√(1/9.81)

T ≈ 2.006 s.

In one day, there are

24 hours x 60 minutes/hour x 60 seconds/minute

= 86,400 seconds.

The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes

86,400/2

= 43,200 back-and-forth swings in one day.

The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is

2 x 12 degrees

= 24 degrees

= 0.419 radians.

Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is

1 meter x 0.419

= 0.419 meters.

Multiplying by the number of swings in one day, we get:

0.419 meters/swing x 43,200 swings/day

= 18,115.2 meters/day.

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The surface area of the rectangular prism is 210 in²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The surface area of a rectangular prism is the sum of each area for the surface.

Hence:

Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²

The surface area of the prism is 210 in²

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Step-by-step explanation:

Here is a graph from Desmos....you should be able to see where the function is > 0

According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.

To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:

According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.

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The area needed for the green region is 40 square feet.

To do so, we can take the area of the whole green area, and then remove the areas of the two holes.

Remember that the area of any rectangle is the product of the two dimensions.

For the green one:

A = 4ft*12ft = 48 ft²

Removing the two areas for the holes we have:

a1 = 3ft*2ft = 6ft²

a2 = 1ft*2ft = 2ft²

Remove that:

green area=  48 ft² - 6ft² - 2t² = 40ft²

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The equation of the quadratic function g whose graph is shown above is g(x) = -(x + 4)² - 4

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex and other points, we can determine the value of a as follows:

g(x) = a(x - h)² + k

-13 = a(-7 + 4)² - 4

-13 = a(-3)² - 4

-13 + 4 = 9a

-9 = 9a

a = -1.

Therefore, the required quadratic function is given by:

g(x) = a(x - h)² + k

g(x) = y = -(x + 4)² - 4

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Answer:

70.4%

Step-by-step explanation:

Assuming the test is the only graded assignment, and the remaining 80% of her grade is still at 73%, we can calculate Kayla's new overall grade as follows:

New overall grade = (0.80 x 73) + (0.20 x 60)

New overall grade = 58.4 + 12

New overall grade = 70.4

Therefore, Kayla's new overall grade is 70.4%

Answer:

70.4% or a C-.

Step-by-step explanation:

To calculate Kayla's new grade after taking the test, you need to first find out what percentage of her overall grade the test is worth. If the test is worth 20% of her grade, then the remaining 80% of her grade is based on other factors, such as homework, quizzes, and other tests.

To calculate Kayla's new grade, you can use the following formula:

New grade = (Current grade x Weight of current assignments) + (Grade on test x Weight of test)

Plugging in the numbers given in the problem, we get:

New grade = (0.73 x 0.80) + (0.60 x 0.20)

New grade = 0.584 + 0.12

New grade = 0.704

Therefore, Kayla's new grade after taking the test would be approximately 70.4%, or a C-.

The graphs are:

1) not one-to-one

2) one-to-one

3) not one-to-one

A graph represents an one-to-one function only if.

We can't draw a vertical line that touches the graph twice or more.

We can't draw an horizontal line that touches the graph twice or more.

For example, for the first graph, we can see that there are horizontal lines like y = -5 that touch the graph two times.

Similarly forthe third graph, the line y = 0 touches two points-

So these two are not one-to-one.,

For the remaining graph, the middle one, no line touches the graph more than once, so it is one-to-one.

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Answer:

x = 23°

Step-by-step explanation:

We Know

The 67° angle + the x must be equal to 90°

Find the x.

Let's solve

67° + x = 90°

x = 23°

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

For the frequencies to be the same, we need to find values of n and m such that:

n = m

Solving for n and m, we get:

n = m = 2

So both functions complete two cycles in the interval [0, 2π).

We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:

2sin2x = sin x

2sin2x - sin x = 0

sin x (2sin x - 1) = 0

sin x = 0 or 2sin x - 1 = 0

sin x = 0 when x is an integer multiple of π.

2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.

Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.

The correct answer is:

x = 0°, 30°, 150°, 180°

This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.

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Answer:

  (3, 9) and (3, -7)

Step-by-step explanation:

You want the end points of the latus rectum for the parabola defined by ...

 (y -1)² = 16(x +1)

Compare the given equation to the form ...

  (y -k)² = 4p(x -h)

we see that (h, k) = (-1, 1) and p = 16/4 = 4. The ordered pair (h, k) is the vertex of the parabola. The scale factor 'p' gives the distance from the vertex to the focus (and from the directrix to the focus). Larger 'p' values result in a "flatter" parabola.

Since the squared term is a y-term, and the value of 'p' is positive, we know the parabola opens to the right. The end points of the latus rectum are ...

  (h+p, k±2p) = (-1+4, 1±2·4) = (3, 9) and (3, -7)

__

Additional comment

If the roles of x and y are interchanged (the parabola opens up or down), then the end points of the latus rectum are (h±2p, k+p).

On a graph of the parabola, the end points of the latus rectum lie on lines through the vertex with slope ±2 (parabola opens in x-direction), or with slope ±1/2 (parabola opens in y-direction).

The ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.

To determine if the ball reaches a height of 40 meters, we can substitute h(t) = 40 into the equation and solve for t.

40 = -2t² + 4t + 27

Rearranging the terms, we get:

2t² - 4t - 13 = 0

We can solve for t using the quadratic formula:

t = [4 ± √(4² - 4(2)(-13))]/(2(2))

t = [4 ± √(176)]/4

t ≈ 3.38 or t ≈ -0.88

Since time cannot be negative, we can discard the negative solution. Therefore, the ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.

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Answer: y = -4

Step-by-step explanation:

Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.

This means the equation of the line is:

       y = -4

See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.

The maximum voltage produced by the system is 12 volts.

The function given is:

[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]

To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.

Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.

First, calculate the value of the argument:

360 * 60 * 6.3 + 79 = 136080 + 79 = 136159

Now, substitute this value back into the sine function:

sin(136159)

The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:

136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22

Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.

Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.

So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:

Maximum voltage = 12 * 1 = 12 volts.

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Answer:

3√3 ft or 5.20 ft

Step-by-step explanation:

The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.

x = L × √3

x = 3 × √3

x = 3 × 1.7

x = 5.20 ft

To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.

For the 7 oz bag, the price per ounce is:

1.10 / 7 = 0.1571

For the 9 oz bag, the price per ounce is:

1.46 / 9 = 0.1622

Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.

The value of x in the function f(x) = (1/3)^x - 2 such that f(x) = 7 is -2

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

f(x) = (1/3)^x - 2

When the value of f(x) is 7, we have

(1/3)^x - 2 = 7

So, we have

(1/3)^x = 9

Take the log of both sides

x = log(9)/log(1/3)

Evaluate

x = -2

Hence, the value of x is -2

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The measure of angle B is given as follows:

m < B = 49.2º.

Two angles are said to be complementary angles when the sum of their measures is of 90º.

The measures are given as follows:

As the angles are complementary, the value of x is obtained as follows:

x + 21 + 4x - 30 = 90

5x - 9 = 90

5x = 99

x = 19.8.

Hence the measure of angle B is obtained as follows:

m < B = 4 x 19.8 - 30

m < B = 49.2º.

The measures are given as follows:

The angles are complementary, and it asks for the measure of angle B.

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Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

Probability refers to the chance or likelihood that an expected event occurs out of many possible events.

Probability lies between 0 and 1, depending on the degree of certainty.

Mean = 300

Standard deviation = 30

Range = 300 to 390

Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.

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Answer:

v=12

Step-by-step explanation:

9/v = 6/8

9 = 6v/8

72= 6v

v= 12

Answer:

v = 12

Step-by-step explanation:

Now we have to,

→ Find the required value of v.

Given proportion,

→ (9/v) = (6/8)

Then the value of v will be,

→ (9/v) = (6/8)

→ 9 × 8 = 6 × v

→ 72 = 6v

→ 6v = 72

→ v = 72/6

→ [ v = 12 ]

Hence, the value of v is 12.

Answer:

X = 6

Y = 17

Step-by-step explanation:

The points GHIJ for a cyclic quadrilateral.

The sum of opposite angles of a cyclic quadrilateral is 180°

So

     ∠J + ∠H = 180°

⇒   6y + 78° = 180°

⇒   6y = 180° - 78°

⇒   6y = 102°

⇒   y = 102°/6

⇒   y = 17°

Similarly for angle x

     ∠I + ∠G = 180°

⇒   16x + 14x = 180°

⇒   30x = 180°

⇒   x = 180°/30

⇒   x = 6°

Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is  4 : 20 which is 1: 5

Therefore, 4 of the next 20 horses that come to board should you expect to be white horses