Explain the characteristics that determine whether a function is invertible. Present an algebraic example and a graphic one that justifies your argument. Situation 2: and present the Domain and Range Find the inverse for the function f(x) = - for both f(x) as for f-¹(x). x + 3

Answer:

Parabola

Step-by-step explanation:

Answer:

Step-by-step explanation: Xmin:

-10

Xmax:

10

Ymin:

-10

Ymax:

10

The number of different combination may a new car would have is 10 ways.

What is a combination in mathematics?

The combination is defined as "an arrangement of objects in which the order in which the objects are chosen is unimportant." The combination means "selection of things," where the order is irrelevant.

Given that there are 10 different options.

We have to choose one car.

So total number of combinations = \(^{10}C_1\)

                                                       = 10!/(9!)(1!)

                                                       = 10 ways

Hence, the number of different combination may a new car would have is 10 ways.

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In 10 ways the combination of a new car can be installed as followed by the rules of Permutation combination.

what is Permutation combination ?

Putting things or numbers in order is the definition of a permutation. Combinations are a method of choosing elements such as numbers or objects from a collection or set of elements without regard to the elements' order.

Solution:

Given that the car are 10 different options.

We have to choose one car.

So total number of combinations = 10C1

                                                      = 10!/(9!)

                                                      = 10 ways

Therefore, In 10 ways the combination of a new car can be installed.

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9514 1404 393

Answer:

  4

Step-by-step explanation:

∛64 = ∛(4³) = 4

_____

The real root when the root index is odd will have the same sign as the value whose root it is. 64 is positive, so the real cube root will be positive.

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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No, the first 5 people to arrive at a town meeting is not a random sample of the town's residents.

A random sample is a subset of a population that is selected in a way that gives each member of the population an equal chance of being selected. In this case, the first 5 people to arrive may not be representative of the entire population, as they may not have been selected randomly, and their arrival at the meeting may have been influenced by factors such as their proximity to the meeting place, their level of interest in the topic, or their schedule. A more structured method of selection, such as random digit dialing or door-to-door visits, would be necessary to obtain a random sample of the town's residents.

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Answer: y=3x-2

Step-by-step explanation

(-8)-(7)/ (-2)- (3) = -15/ -5= 3

y=3x+b

f(-2)= -8

y= 3x+ b

-8= 3(-2)+b

-8=-6+b

add 6 on both sides

b=-2

y=3x-2

Answer: x+5x+4x=40

Step-by-step explanation:

Answer:

d = 12cm

Step-by-step explanation:

d=2r = 2·6 = 12cm

Maths keeps one mentally active. The circumference = 2*(pi)*r = 6 cm. Therefore r, the radius = 6 *7/(2*22) = 42/44 = 0.954 cm.

Answer:

12

Step-by-step explanation:

It's double the radius.

The rule for independent samples with equal variance is that the quotient of their variances falls between 0.5 and 2 is the correct answer.

The statement that summarizes a general rule about independent samples with equal variance is: "When the variance of one sample is divided by the variance of the other sample, the quotient is between 0.5 and 2."

This statement reflects the common assumption made in statistical analysis that when dealing with independent samples, the variances of the two samples are approximately equal. This assumption allows for certain statistical tests, such as t-tests, to be applied to compare the means of the samples.

If the quotient of dividing one sample's variance by the other sample's variance falls within the range of 0.5 to 2, it suggests that the variances are not significantly different from each other. This assumption of equal variance simplifies the statistical analysis and allows for more reliable and accurate comparisons between the samples.

It's important to note that this assumption may not always hold true, and there are statistical techniques available to handle cases where the assumption of equal variance is violated.

Therefore, as a general rule, assuming equal variance between independent samples within the range of 0.5 to 2 is a common practice in statistical analysis.  

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A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.

In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

let's solve :

Answer:

From greatest to least: AB, AC, BC

After doing a hypothesis test the conclusion is reject \(H_0\) .

Given:

tom is a big green bay packers and aaron rodgers fan. he claims that aaron rodger's average number of touchdowns per game is 2.45. dave (a hardcore bears fan) believes that tom might be inflating rodgers's statistics. from his debut until november 18, 2019, aaron rodgers has played 175 games! dave does not want to look at all of them. he randomly selects 52 games that rodgers played and finds the sample average number of touchdowns to be 1.942 with a standard deviation of 1.42.

here n = 52

σ = 1.42

x = 1.942

μ = 2.45

z = x - μ / σ/√n

= 1.942 - 2.45 / 1.42/√52

= -2.58

p value = 0.0049

\(H_0:mean = 2.45\)

\(H_a:mean < 2.45\)

Rejection rule:Reject \(H_0\) if p value < 0.05

Conclusion Reject \(H_0\)

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Answer:

31.8°

Step-by-step explanation:

sin x = 39/74

x = arcsin(39/74), which is about 31.8°.

The left-hand limit and right-hand limit are not equal, the limit of f(x) as x approaches 0 does not exist. So the correct answer is (D).

To find the limit of f(x) = 3x^3 + 2x^2 as x approaches 5, we can simply plug in 5 for x and evaluate the expression:

f(5) = 3(5)^3 + 2(5)^2 = 375 + 50 = 425

Therefore, the limit of f(x) as x approaches 5 is 425. So the correct answer is (A).

To evaluate the limit of f(x) where f(x) = {-x^2 + 1, x < 0; + 4x - 3, x > 0; -x, x = 0}, we need to find the left-hand limit and right-hand limit separately and then check if they are equal.

Left-hand limit:

lim x→0- {-x^2 + 1} = -0^2 + 1 = 1

Right-hand limit:

lim x→0+ {4x - 3} = 4(0) - 3 = -3

Since the left-hand limit and right-hand limit are not equal, the limit of f(x) as x approaches 0 does not exist. So the correct answer is (D).

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Answer:

A. no solution

Step-by-step explanation:

y = 3x + 9

y = 3x - 4

Let's solve this.

We can see that both equations equal y, so we can set them equal to each other.

3x + 9 = 3x - 4

Combine like terms.

[add 4 to both sides]

3x + 13 = 3x

[subtract 3x from both sides]

13 = 0

This statement is not true; therefore, there is no solution.

If we look at the graph below, we can see the lines are parallel. Parallel lines will never intersect and have no solution in a system of equations.

Hope this helps!

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

840

Step-by-step explanation:

7000×2×6 ÷ 100. since it is 2%

= 840

Answer:

(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:

a² = 7 cm²

b² = 17 cm²

c² = 10 cm²

We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.

We can rearrange the equations above to solve for a, b, and c:

a = √7 cm ≈ 2.65 cm

b = √17 cm ≈ 4.12 cm

c = √10 cm ≈ 3.16 cm

Now, we can check whether the Pythagorean theorem holds:

c² = a² + b²

(√10 cm)² = (√7 cm)² + (√17 cm)²

10 cm = 7 cm + 17 cm

This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

a. The probability that \(X^2 + Y^2 < 1\) is 0.25. b. The probability that \(2X - Y > 0\) is 0.5. c. The probability that \(X + Y < 2\) is 0.75.

a. To find \(P(X^2 + Y^2 < 1)\), we integrate the joint probability density function (pdf) over the region where \(X^2 + Y^2 < 1\). This calculation results in a probability of 0.25, indicating that 25% of the area under the joint pdf falls within this region.

b. For \(P(2X - Y > 0)\), we integrate the joint pdf over the region where \(2X - Y > 0\). The result is a probability of 0.5, indicating that 50% of the area under the joint pdf satisfies this condition.

c. To calculate \(P(X + Y < 2)\), we integrate the joint pdf over the region where \(X + Y < 2\). This yields a probability of 0.75, indicating that 75% of the area under the joint pdf lies within this region.

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Answer:

X = 1/2

Step-by-step explanation:

JK = NO

4x + 24 = 26

4x = 2

x = 1/2

31.25 g on the 5th day

no it will never by empty because even when it gets down to one singular piece of sugar you would technically just cut it in half, then that in half, yes it would get impossible, that's why you wouldn't actually do it, but if you typed it into a calculator it would just keep getting a smaller and smaller decimal.

Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

  -32 -2 ?? -2

  -34 < -2 . . . . . . not greater than

Answer:

y=2x-3

Step-by-step explanation:

Answer:

Option (B) 0.00076

Step-by-step explanation:

Surface area of a sphere = 4πr²

Volume of a sphere = 4π/3 (r³)

Surface area : Volume = 4πr² : 4π/3 (r³)

                                      = r² : 1/3 (r³)

                                      = 3 r² : r³

                                      = 3/r

                                      = 3/3960

                          (AFTER SIMPLIFICATION)

                                      = 0.00076

Hence the answer is option (B) 0.00076

Hope my answer help you ✌️

The correct option is B) 0.00076. The surface-area-to-volume ratio is 0.00076.

To find the approximate surface-area-to-volume ratio of the Earth with a radius of approximately 3,960 miles, we will use the following formulas:

Surface area (A) of a sphere: A = 4πr²
Volume (V) of a sphere: V = (4/3)πr³

Step 1: Calculate the surface area:
A = 4π(3,960)² ≈ 197,392,088 square miles

Step 2: Calculate the volume:
V = (4/3)π(3,960)³ ≈ 260,625,332,197 cubic miles

Step 3: Calculate the surface-area-to-volume ratio (A/V):
A/V ≈ 197,392,088 / 260,625,332,197 ≈ 0.000757

The best answer from the choices provided is B. 0.00076.

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Less than 1 is the eccentricity of an infinitely long ellipse.

The ratio of the focus's distance from the ellipse's centre and the ellipse's distance from one of its ends is called the eccentricity of an ellipse.

It is easy to understand how circular an ellipse is in relation to a circle when we assume its eccentricity. It also estimates the ovalness of the ellipse, and eccentricity close to 1 directs to the high degree of ovalness.

The eccentricity of an ellipse is always < 1, i.e. e < 1. The formula of the eccentricity of an ellipse is as follows:

Eccentricity = Distance from Focus/Distance from Directrix

Which can be written as

=> e = c/a.    

Where

e = Eccentricity of the ellipse

c = Distance of the focus from the centre of the ellipse

a = Distance of the endpoint of an ellipse from its centre

As we know, the eccentricity of an ellipse is always less than 1, So we can conclude that the eccentricity of an infinitely long ellipse is less than 1.

Therefore, less than 1 is the eccentricity of an infinitely long ellipse.

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Answer:

[11000, 11600]

Step-by-step explanation:

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A square has an area of 15 square feet. Two ways of expressing its side length are given below:Solution 1.

We know that the area of a square is given by the formula:

A = a2 where a is the side length of the square.Since we are given the area of the square as 15 square feet, we can set up the equation as:

15 = a2 To find the value of a, we take the square root of both sides. Therefore, a = sqrt(15) feet.So one way of expressing the side length of the square is a = sqrt(15) feet.

Solution 2: We know that a square has all its sides equal. Therefore, if we can find the square root of the area, it will give us the length of one side of the square. Since the area of the square is 15 square feet, the length of one side is sqrt(15) feet. Alternatively, we can also express the side length using decimal approximation. We have:

sqrt(15) = 3.87 (approx.)Therefore, the side length of the square is either

a = sqrt(15) feet or

a = 3.87 feet (approx.).

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