Compare the functions f(x) = x5 and g(x) = 5x by graphing both functions in several viewing rectangles. find all points of intersection of the graphs correct to one decimal place. (enter your answers as a comma-separated list. round any decimal answers to one decimal place.)

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=3x^{2}-5[/tex] -----> quadratic equation of a vertical parabola open upward

Find the inverse function

Exchange variables x for y and y for x

[tex]x=3y^{2}-5[/tex]

Isolate the variable y

[tex]3y^{2}=x+5[/tex]  -----> inverse function (horizontal parabola open to the right)

or

[tex]y=(+/-)\sqrt{\frac{x+5}{3}}[/tex]

using a graphing tool

see the attached figure

The graph of function and it's inverse of the graph is shown in image.

We have to given that,

To graph the function y = 3x² - 5 and it's inverse.

Here, The equation is,

y = 3x² - 5

So, We can find it's inverse as,

y = 3x² - 5

y + 5 = 3x²

(y + 5) / 3 = x²

x² = (y + 5)/3

x = √(y + 5)/3

Hence, the inverse of function is,

f ⁻¹ (x) = √ (x + 5)/3

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Answer:

Option C

Step-by-step explanation:

In the given right angle triangle

Hypotenuse = 4.5 cm

Height = 2.5 cm

and base = g cm.

Pythagoras theorem says

(hypotenuse)² = (base)² + (height)²

So by putting the values in the formula

(4.5)² + (2.5)² + g²

Option C is the answer.

Answer:

5.4? I don't really know I'm just going off other answers but clearing it up,,,hope it help :')

Step-by-step explanation:

Answer:  Option 'B' is correct.

Step-by-step explanation:

Since we have given that

We need to express a point in the three-dimensional coordinate plane.

As we know that In 3- dimensional plane, there are 3 axes;

One for x-axis (say  length)

One for y- axis (say breadth)

One for z-axis (say height)

So, the proper notation would be (x,y,z).

Hence, Option 'B' is correct.

Transmutation is the process of changing the substance, tangible or not, from one form to the other. It means the transformation of one element in the periodic table into another by one or a series of nuclear decays or reactions. One type of transmutation is nuclear transmutation. Nuclear transmutation is the conversion of one chemical element or isotope into another though nuclear reactions or nuclear decay. Second type of transmutation is artificial transmutation. Artificial transmutation occur in machinery that uses nough energy to cause changes in the nuclear structure of the elements.

Engineers test the weld strength of pipe welds in nuclear power plants to ensure they meet safety specifications. Tensile strength and pressure tolerance are key factors tested to maintain plant safety and functionality. Regulatory standards, like those from the NRC, guide acceptable performance levels for power plant components.

To ensure the safety and functionality of the nuclear power plant's infrastructure, engineers conduct tests on components such as pipe welds. These tests involve assessing weld strength, which is the force required to break a weld, and must meet specific specifications for the plant to operate safely. If not, the structural integrity of the power plant could be compromised, potentially leading to failures in electrical generation or even safety hazards.

The tensile strength of a material is a critical factor in this scenario. It is defined as the force per unit area (measured in Newtons per square meter or Pascals) needed to cause failure of the material by pulling it apart. This strength needs to be tested to prevent issues like the SS Schenectady ship's cracking under stress, which can have catastrophic consequences.

Regulatory standards, such as those set by the Nuclear Regulatory Commission (NRC), often determine the acceptable levels of component performance, including valves and tubing, within a power plant. These standards may change over time in response to new findings or incidents, reflecting the evolving understanding of material properties and failure risks under operational conditions.

In statistical terms, such tests might involve a hypothesis test to determine if the pressure tolerances of two valve types differ significantly, or if the structural components meet the required strength, safety, and operational standards.

Answer:

The standard normal table gives areas under the curve to the left of z-scores.

Find the probability in the standard normal table that a value is to the left of 1.9.

Find the probability in the standard normal table that a value is to the left of 0.4.

Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.

Step-by-step explanation:

edge2020

In order to find the probability associated with the shaded area under the curve using the standard normal table, you should subtract the probability of a value left of 0.4 from the probability of a value left of 1.9.

We are trying to find the probability of the area between 1.9 and 0.4 so the first thing to do is to find the probability that a value is to the left of 1.9 from the Standard normal table.

After this is done, you then find the probability that the value is left of 0.4.

To find the probability of the middle area, subtract the value to the left of 0.4 from that of the value left of 1.9

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Starting at vertex V going until vertex S, we make our calculations.

VR = 14

Rx = x

therefore, xS = VR – Rx

xS = 14 – x                           ---> 1

Now starting at vertex V going left to vertex S, we make our next set of calculations. Assuming x is on VR but nearer R

VR  = 14 - x

at UV = 15 – (14 – x)

at UV = 1 + x

at TU = 7 – (1 + x)

at TU = 6 – x

at ST = 9 – (6 – x)

at ST = 3 + x                        ---> 2

Equate 1 and 2:

14 – x = 3 + x

2 x = 11

x = 5.5

To find the value of x in the circumscribed pentagon RSTUV with given sides, we set up an equation based on the sum of the lengths of the opposite sides. After solving the equation, we determined that x is 25.

Pentagon RSTUV and the Value of x

Given that pentagon RSTUV is circumscribed about a circle, we need to find the value of x,

where RS = 6, ST = 9, TU = 7, UV = 15, and VR = 14.

For a polygon circumscribed about a circle, the sum of the lengths of the pairs of opposite sides must be equal. Therefore, we can set up the equation:

RS + TU + x = ST + UV + VR

Substituting the given values:

6 + 7 + x = 9 + 15 + 14

Simplifying the right-hand side:

Thus, the value of x is 25.

Answer:

The answer is B

Step-by-step explanation:

1 degree = 0.0174533 radians

85* 0.0174533 = 1.4835305 radians

Round answer as needed

Answer:

17pi/36 (PLATO answer)

Step-by-step explanation:

Final answer:

To find the number that is 24% of 25, you multiply 0.24 by 25, which equals 6.

Explanation:

To find what number a is 24% of 25, we can set up an equation using the concept that a percent is a way of expressing a fractional amount of something.

We know that 24% means 24 out of 100, which can be written as the fraction 24/100 or 0.24 in decimal form.

To translate the question into an equation, we write:

a = 0.24 × 25

Next, we calculate the value of a by multiplying 0.24 (the decimal form of 24%) by 25. This gives us:

a = 6

Therefore, the number a, i.e., 24% of 25 is 6.

Since pi is equivalent to 3.14 and means 180°, therefore 1.75 which is about half of pi should be at almost 90°. The cos of a 90° angle which is located on the y axis should be zero, therefore cos 1.75 must be near zero. However in this case it is near one, clearly his calculator is in degree mode that is why he got an erroneous answer.

What Sam can do to get the correct answer would be to convert his calculator into radian mode or convert the given 1.75 rad into degrees:

θ = 1.75 rad (180° / π rad)

θ = 100.2676

cos 100.2676 = -0.1782   which is now correct since it is nearer to zero

The mean number of overtime hours worked is 3.4 with a standard deviation of approximately 1.4 hours, which corresponds to option D.

The correct answer for the given probability distribution of overtime hours worked per employee in one week is D. An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.

To find the mean (μ) of the probability distribution, we multiply each possible value by its corresponding probability and then sum all these products. The mean of this distribution is given as 3.4, which is found by summing up the product of each value of overtime hours and its corresponding probability:

μ = (0 * 0.026) + (1 * 0.072) + (2 * 0.154) + (3 * 0.303) + (4 * 0.215) + (5 * 0.164) + (6 * 0.066) = 3.4

The variance (σ2) is calculated by taking each value's deviation from the mean, squaring it, multiplying by the probability, and summing all these values. The variance for this distribution is given as 2.0:

σ2 = Σ [(x - μ)2 * P(x)] = 2.0

And the standard deviation (σ) is simply the square root of the variance:

σ = √σ2 = 1.4

The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.

The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.

Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.

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Answer: B or 0 < t < 5/4

Step-by-step explanation:

I got it wrong from the other answers and found out that this was the right one.