Domain of the function showed in the graph?

The amplitude of the wave is 4 units,

The period of the wave is π.

The period and amplitude of the wave is calculated as follows;

The amplitude of a wave is the maximum displacement of the wave, while the period of a wave is the time taken for the wave to make one complete cycle.

From the given wave graph, the amplitude of the wave is 4 units, because it is the maximum displacement of the wave.

The period of the wave is calculated as follows;

points of one complete cycle = π/2 and 3π/2

period = 3π/2 - π/2 = π

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The pressure exerted by the cube on the countertop is 23060 Pa.

We are given that;

Side of cube=30cm

Now,

The force is equal to the weight of the cube, which is the product of its mass and the acceleration due to gravity. To find the mass, you need to multiply the volume and the density of iron. The volume of a cube is the cube of its side, and the density of iron is about 7870 kg/m^3. The acceleration due to gravity is about 9.8 m/s^2. Therefore:

F = mass * gravity F = (volume * density) * gravity F = ((side)^3 * density) * gravity F = ((0.3 m)^3 * 7870 kg/m^3) * 9.8 m/s^2 F = 2075.4 N

The area is equal to the area of one face of the cube, which is the square of its side. Therefore:

A = (side)^2 A = (0.3 m)^2 A = 0.09 m^2

Now that you have the force and the area, you can plug them into the formula for pressure:

P = F / A P = 2075.4 N / 0.09 m^2 P = 23060 Pa

Therefore, by algebra the answer will be 23060 Pa.

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The complete question is;

If an iron cube of 30 cm side is resting on a countertop, what pressure does it exert?

Answer:

Its D 1/221

Step-by-step explanation:

The scale factor of the dilation is: 3/2

Dilation is a transformation of an object which changes its size. if the dilated image is larger then it is called enlargement. If the dilated image is smaller it is called reduction.

If the dilation has the origin as the center of dilation, we can find points on the image formed by dilation by multiplying the coordinates of the original geometric object like triangle multiplying by the scale factor. For scale factor k, the transformation of the dilation is written as :  (x, y) → (k x, k y).

The scale factor ,k  = coordinate of image / coordinate of original

Given that Triangle ABC is dilated to create triangle A’B’C’ using point O as the center of dilation as shown in the figure

A is two units away from O and A' is 1 unit away from O. You add 1 + 2 to get the total distance and divide that number by 2 to get the scale factor. 3/2

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Answer:

x <  4

the 1st number line should be used.

Step-by-step explanation:

3/4(x + 8) > 1/2(2x + 10)

(2)(3)(x + 8) > (4)(1)(2x + 10)

6x + 48 > 8x + 40

6x - 6x + 48 - 40 > 8x - 6x + 40 - 40

8 > 2x

x < 8/2

x < 4

Answer:

Step-by-step explanation:

The probability that a randomly chosen musician is a singer is

To find the probability that a randomly chosen musician is a singer, we need to divide the number of singers by the total number of musicians.

Probability of choosing a singer = Number of singers / Total number of musicians

probability of choosing a singer = 35 / 82

simplifying this fraction, we find that the probability is approximately:

probability of choosing a singer ≈ 0.4268

Therefore, the probability that a randomly chosen musician is a singer is 35/82 or approximately 0.4268.

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Answer:

-----------------------

Probability of drawing a green marble is:

Since marbles are replaced the probability of a second green is same, 1/2.

So the probability of two green marbles is:

The probability of drawing two green marbles in a row is, 1/4

We have to given that,

In a bag with 20 marbles, 10 marbles are white and 10 are green. They are all mixed up.

Since, Each time a marble is pulled from the bag, the color is recorded and the marble is put back into the bag.

Hence, The probability of drawing a green marble on any one draw is,

= 10/20

= 1/2

Thus, The probability of drawing two green marbles in a row is,

= 1/2 x 1/2

= 1/4

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Answer:

Step-by-step explanation:

are 2 similar triangles, we solve with a proportion between the corresponding sides, see the figure below

4 : a = 3 : 4

a = 4 × 4 : 3

a = 16 : 3

a = 5.333...

or a = 5 1/3 (your answer)

The area of a rectangle is calculated by multiplying its length by its width. In this case, the rectangle is 3 inches by 5 inches. Therefore, the area of the rectangle is:

Area = Length × Width

Area = 3 inches × 5 inches

Area = 15 square inches

So, the area of the rectangle is 15 square inches.

Answer:

15 inches

Step-by-step explanation:

We can use the formula Length times Width to find the Area. In this case the Length and Width are 3 inches and 5 inches. 3 times 5 is 15, so that is the answer.

The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

We know the following:

Cylinder volume: V₁ = π r² h

Ball (sphere) volume: V₂ =4/3 π r³

where:

V - volume

r - radius of base of cylinder and diameter of ball

h - height of cylinder.

Here, We have,

D = 16 cm ⇒ r = 16 ÷ 2 = 8

π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:

h = 3 × r = 3 × 16 cm = 48 cm

r = 8 cm

So,

V₁ = π r² h

V₁ = 3.14 × (8 cm)² × 48 cm

V₁ = 9,646.1 cm³

Thus, The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

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Answer:

-6x^3 + 5x^2 + 13x - 20

Step-by-step explanation:

The solution -2 * 15/2 to the expression is -15

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

-2 * 15/2

The above expression is a mathematical expression

And it can be solved as follows

Using the above as a guide, we have the following:

-2 * 15/2 = -1 * 15/1

So, we have

-2 * 15/2 = -1 * 15

Evaluate

-2 * 15/2 = -15

Hence, the solution to the expression is -15

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Answer:

In continuous exponential growth, the size of a population can be modeled by the formula:

P = P0 * e^(rt)

where:

P = final amount (1982 bacteria in this case)

P0 = initial amount (1900 bacteria in this case)

r = growth rate (the variable we're trying to find)

t = time (1.5 hours in this case)

First, let's isolate the variable r in the equation:

1982 = 1900 * e^(1.5r)

Dividing both sides by 1900 gives:

1982 / 1900 = e^(1.5r)

Taking the natural logarithm (ln) of both sides (since the natural logarithm is the inverse of the exponential function) gives:

ln(1982 / 1900) = 1.5r

Now, solve for r:

r = ln(1982 / 1900) / 1.5

Using a calculator to evaluate this, we get:

r ≈ 0.0224

Therefore, the hourly growth rate is approximately 0.0224 or about 2.24% per hour. This means the bacteria population is growing at a rate of about 2.24% every hour.

The index in the radical is,

⇒ 7

We have to given that,

The expression is,

⇒ [tex]\sqrt[7]{3^{4} }[/tex]

Since, We know that,

The index of a radical indicates the degree of the root, such as the square root has index 2 or the cube root has index 3.

Here, the radical symbol has a small 7 in the corner, which implies that the index is 7.

Therefore, the expression  [tex]\sqrt[7]{3^{4} }[/tex] represents the seventh root of 34.

Thus, The index in the radical is,

⇒ 7

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a.) The two of the graphs given above that displays the same data is graph I and II.

b.) The third graph which is III doesn't match with others because the years where not represented.

A bar chart is defined as a type of data representation that involves the use of rectangular bars that compares two different variables.

In graph I (a bar chart), the county voter turnout was plotted against the various years it was carried out which is the same with the second graph.

But the third graph is different from the first two graphs because the years where removed and a new variable was introduced.

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Answer:

  (b)  3 units

Step-by-step explanation:

You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.

The dilation factor multiplies every length.

If OB is 3/4, then OB' is 4(3/4) = 3.

The length of OB' is 3 units.

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The quadratic parent function, f(x) = x², represents the most basic form of a quadratic function.

f(x) = x² is called the "parent" or "standard" form because it serves as a template or starting point for other quadratic functions.

In this function, x represents the input or independent variable, and f(x) represents the output or dependent variable.

The function takes any real number as an input, squares it, and produces the corresponding output.

By modifying the quadratic parent function with additional terms or coefficients, we can create different variations of quadratic functions that result in shifts, stretches, or compressions of the parabola, as well as changes in its orientation or vertex position.

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The y-intercept of the equation for the line of best fit would increase while the magnitude of the slope would decrease, if only the data from 2010 to 2016 are considered. Also, there would be a positive correlation because as the independent variable increases, the dependent variable increases.

In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible.

By critically observing the scatter plot using the data from 2010 to 2016, we can logically deduce that the y-intercept of the equation for the line of best fit would increase while the magnitude of the slope for the line of best fit would decrease.  

Additionally, there would be a positive correlation from 2010 to 2016 because as the independent variable on the x-axis increases, the dependent variable on the y-axis increases simultaneously.

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The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum of angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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The graph of Melinda's model for the height of the Ferris wheel using the transformation of y = sin(x) indicates;

The amplitude = 35 feet

The midline is the line; y = 43

The period = 120 seconds

The frequency = 1/120 s

Phase shift = 90°

A transformation of a function is the translation, resizing, rotation, or reflection of a parent function.

The parent function which Melinda transforms to model her height on the Ferris wheel is; y = sin(x)

The peak of the height on the graph = (60, 78)

The trough of the graph = (0, 8), (120, 8)

The amplitude, a = (Peak y-value - Trough y-value)/2 = (78 - 8)/2 = 35

The period = 2·π/b = The distance between two troughs = 120 - 0 = 120

Therefore; 120 = 2·π/b

b = π/60

The y-coordinates of the midline of the graph, D = 8 + a = 8 + 35 = 43

The sine function is; y = a·sin(b·x + c) + d

The coordinates of the trough and peak points, (0, 8), (60, 78), indicates that the phase shift of the midline from the y-axis to the graph is; c = (60 - 0)/2 = 30

However, Δx = 60 is equivalent to a rotation of 180°

Therefore, Δx = 30 is equivalent to a rotation of 90°

90°  = π/2

Therefore, the phase shift = π/2 = 90°

The equation for the Ferris wheel is therefore;

Please find attached the graph of the function showing the amplitude, midline, period, vertical shift and phase shift created with MS Excel

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Answer:

66-26 = 40

Step-by-step explanation:

u = 40 degrees

Fr tho. I'm over here as a freshman answering sophmore-junior year college questions with ease.

The inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

Let's denote the distance between Jim and the car as "d" (in feet), and the time elapsed after Jim spots the car as "t" (in seconds).

Given that no car travels faster than 90 feet/second on this road, we can establish the following relationship between distance, time, and speed:

d ≤ 90t

However, Jim has a camera that allows him to see up to 1,080 feet in either direction.

This means that the distance between Jim and the car should be within the range of the camera's visibility, which is 1,080 feet.

Therefore, the inequality representing the possible distances between the car and Jim for any period of time after he spots it is:

-1,080 ≤ d ≤ 1,080

Combining both inequalities, we have:

-1,080 ≤ d ≤ 1,080 and d ≤ 90t

Hence the inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

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If you apply the changes below to the absolute value parent function, f(x) = |x|, the equation of the new function is option  A. g(x) = |x – 4| + 6

The mathematical function f(x) = |x|, commonly referred to as the absolute value parent function, yields the numerical value of a provided input in an absolute sense.

from the question,

[tex]f(x)= /x/[/tex]

as well as the fact that  It shifted 4 units to the right end 6 units up.

So, we see that:

(0) 4 units to the right

(b) 6 units up

Hence, Equation f(x)= /x/ is one that have moved the vertex of the parabola 4 units to the right as well as 6 units up.

So,

[tex]f(x) = a(x-h)^{2} + k\\\\f(x) = /x/[/tex]

So by moving right it implies one is adding 4 h= 4 and going up implies adding for example. k = 6

So:

[tex]f(x)= |x|\\\\g(x) = /x-4/ + 6[/tex]

So, based on the equation above, the transformation that is correct is option (A).

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See full text below

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 4 units to the right.Shift 6 units up.

A. g(x) = |x – 4| + 6

B. g(x) = |x – 6| + 4

C. g(x) = |x + 6| + 4

D. g(x) = |x + 4| + 6

The sum of the infinite geometric sequence is 3 3/4

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

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

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Answer: x=26 degrees. These angles are complementary angles, meaning they add up to 90 degrees. if you do 90-64, you get 26 degrees.

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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There were no fewer than 1 fruit snacks in the bag.

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

x + 3 >= 4

Subtract 3 from both sides of the inequality

So, we have the following representation

x + 3 - 3 >= 4 - 3

When the like terms are evaluated, we have

x >= 1

This means that that were at least 1 fruit snack in the bag.

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