An empty swimming pool needs to be filled to the top.

Answer:

  (c)  The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

Step-by-step explanation:

You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).

The inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...

  f(a) = b

then the graph of f(x) contains the ordered pair (a, b).

The inverse function will have the ordered pair (b, a). That is,

  f⁻¹(b) = a

If an ordered pair (x-intercept) of the inverse function is ...

  (P, 0)

Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.

The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).

__

Additional comment

The graphs of the two functions are mirror images of each other across the line y=x.

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Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.

For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:

150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms

Therefore, 150 pounds is approximately equal to 68.0388 kilograms.

In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.

It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.

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The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

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Step-by-step explanation:

tossing 2 coins at the same time, or one coin twice is the same scenario.

anyway, a probability is always the ratio

desired cases / all possible cases

when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :

head head

head tails

tail head

tail tails

how many of these 4 possible cases show at least one head ?

3 : head-head, head-tails, tails-head

so the probability to get at least one head is

3/4 = 0.75

formally calculated we would get this by saying either

this is NOT 2 times tail.

the probability of 2 times tails is

1/2 × 1/2 = 1/4 = 0.25

the probability for NOT 2 times tails is then

1 - 0.25 = 0.75

or by saying

this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.

the probability of heads on the first and tails on the other coin is

1/2 × 1/2 = 1/4

the probability of tails on the first and heads on the other coin is

1/2 × 1/2 = 1/4

the probability of heads on both coins is

1/2 × 1/2 = 1/4

so, the total probability of all 3 cases is

1/4 + 1/4 + 1/4 = 3/4 = 0.75

you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.

Answer:

7 cm.

Step-by-step explanation:

Area of the 2 bases = total area - area of curved surface

= 408 - 100 = 308cm^2.

So the area of 1 base = 154 cm^2.

If radius of the base  = r:

pi r^2 = 154

r^2 = 154/pi

r =  sqrt (154/pi)

r = 7.0014 cm

Answer:

Obtuse angle

Step-by-step explanation:

Your angle equals 180, so it would be a Obtuse angle

Answer:

68%

Step-by-step explanation:

17/25=0.68

If we turn 0.68 into a percent it would be 68%

The translation transformation part of the rule that transforms circle A into circle B is; ((x + 2), (y + 3))

A translation transformation is a geometric transformation that involves moving an object in a straight line, without rotating or dilating the object.

The coordinates of the centers of the circle indicates the translation rule, used to transform the circles.

The coordinate of center of circle A is; (-1, -1)

The coordinates of the center of circle B is; (1, 2)

Therefore, we get;

The difference in the x and y values of the circles are;

Difference in the x-values = 1 - (-1) = 2

Difference in the y-values = 2 - (-1) = 3

The translation transformation part of the transformation that produces circle B from circle A is; ((x + 2), (y + 3))

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Step-by-step explanation:

To find the greatest common factor (GCF) of 8, 16, and 40, we can determine the largest number that evenly divides all three of them.

Let's first find the prime factorization of each number:

- 8 = 2 * 2 * 2

- 16 = 2 * 2 * 2 * 2

- 40 = 2 * 2 * 2 * 5

Now, let's identify the common factors by finding the minimum exponent for each prime factor:

- 2 is a common factor with an exponent of 2 (appearing twice in the prime factorization of 8 and 16).

- 5 is not a common factor since it appears only in the prime factorization of 40.

The GCF is obtained by multiplying the common factors with their respective minimum exponents:

GCF = 2^2 = 4

Therefore, the greatest common factor of 8, 16, and 40 is 4.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

x = 6

Step-by-step explanation:

This is a bit of a tricky equation, and it's what we call an exponential equation since it involves some exponents. The way we begin to solve these kinds of problems is make the base on each side of the equals sign the same. On one side, we have 9 as our base, and on the other side, we have 3 as our base. 9 = 3², so we can rewrite our equation as shown below:

(3²)⁴ˣ⁻¹⁰ = 3⁵ˣ⁻²

From there, we can use the exponent rule (xᵃ)ᵇ = xᵃᵇ to simplify the left side of the equation.

3²⁽⁴ˣ⁻¹⁰⁾ = 3⁵ˣ⁻²

3⁸ˣ⁻²⁰ = 3⁵ˣ⁻²

Since our bases are now the same, we can take just the exponents and turn it into a new equation as shown below:

8x - 20 = 5x - 2

Hopefully at this point, this problem becomes easy for you, but I'll show how I solved this new equation below in case it doesn't make sense.

8x - 20 = 5x - 2

8x - 20 - 5x = 5x - 2 - 5x

3x - 20 = -2

3x - 20 + 20 = -2 + 20

3x = 18

3x/3 = 18/3

x = 6

Hopefully that's helpful! Let me know if you need more help. :)

9514 1404 393

Answer:

  240

Step-by-step explanation:

Your calculator can tell you the answer.

__

If you're doing this by hand, it can be convenient to combine the multipliers of 48:

  (2 5/7)·48 +(2 2/7)·48 = (2 5/7 +2 2/7)·48 = ((2+2) +(5/7+2/7))·48

  = (4 +7/7)·48 = 5·48 = 240

Answer:

1. The first theorem used is that vertical angles are congruent.

2. The next theorem used is that adjacent angles in a parallelogram are supplementary.

3. The definition of supplementary angles is then used for angle formed by intersecting  lines.

4. The theorem on vertical angles is used again.

5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

  1.6 N/kg

Step-by-step explanation:

The units of gravitational field strength are newtons per kilogram. The joule is a derived unit equivalent to a newton·meter.

Then the field strength is ...

  newtons/kg = (1.2 N·m)/((1 m)(0.75 kg)) = 1.6 N/kg

Answer:

B

Step-by-step explanation:

Here, we want to use the empirical rule to find the percentage.

The first thing we will do here is to find the z-score

Mathematically;

z-score = (x -mean)/SD

from the question, x = 95, mean = 110

and SD = 15

So z-score will be ;

(95-110)/15 = -15/15 = -1

So the probability we want to calculate is;

P(z < -1)

In terms of the empirical rule, we want to find the proportion of the scores which is less than 1 standard deviation of the mean.

According to the empirical rule, the proportion which is less than 1 standard deviation below the mean is 15.866% and the closest answer to this is 16% which is option B

By definition, the empirical rule is basically used in finding the proportion of values in this case scores which are at a certain standard deviation value below or above the mean. Below the mean are represented as negatives while above the mean are represented as positives.

There are 12 lowercase words of length 8 in which each distinct letter appears exactly twice.

To form a lowercase word of length 8 in which each distinct letter appears exactly twice, we can choose 4 distinct letters from the English alphabet and then arrange them in pairs in the word. The number of ways to choose 4 distinct letters from 26 is:

C(26, 4) = 26! / (4! * 22!) = 14,950

Once we have chosen 4 distinct letters, we can arrange them in pairs in the word in the following way:

Therefore, the total number of such words is:

4 * 3 * 1 = 12

Thus, there are 12 lowercase words of length 8 in which each distinct letter appears exactly twice. Here are all the possible words:

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Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

The simplified boolean expression for F5 is F5 = P OR (NOT R). In this expression, P represents one boolean variable, and (NOT R) represents the negation of another boolean variable R. The OR operator combines the two variables, resulting in the final boolean expression F5.

To simplify the boolean expression F5 = (P AND Q) OR (R AND NOT P), we can apply Boolean algebra rules to reduce it to its simplest form.

Step 1: Apply De Morgan's laws

NOT (R AND NOT P) can be simplified as (NOT R) OR P.

Step 2: Distributive property

F5 = (P AND Q) OR ((NOT R) OR P)

Step 3: Apply associative property

F5 = (P AND Q) OR (P OR (NOT R))

Step 4: Apply absorption law

F5 = P OR (P OR (NOT R))

Step 5: Apply idempotent law

F5 = P OR (NOT R)

By simplifying the expression, we have reduced it to its simplest form while preserving its logical meaning. The simplified expression can be used to analyze and evaluate logical circuits or systems where the variables P and R are used.

Remember, boolean algebra allows us to manipulate and simplify complex logical expressions by applying various rules and properties. These simplifications help in understanding and analyzing logical operations in digital systems and circuits.

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The question probable may be:

Consider the boolean variables P, Q, and R. Determine the boolean expression for the variable F5 using the given variables:

F5 = (P AND Q) OR (R AND NOT P)

Using the boolean variables P, Q, and R, can you simplify the expression F5 to its simplest form by applying Boolean algebra rules?

The length of the towel bar is 9.5 inches.

Length is used to measure distance, In the International System of Quantities, a quantity with the distance dimension is referred to as length. The majority of measurement systems select a base unit for length from which all other units are derived. The metre serves as the International System of Units' fundamental unit of length.

Suppose, the length of the towel bar is x inches

The distance from each end of the towel bar to the end of the door is 9

inches. So, the total width of the door will be:[(x+(9*2)]=(x+18) inches

Given that, the width of the door is 27 inches 27.5 So, the equation will be.

x+18=27.5

x=27.5-18=9.5

Thus, the length of the towel bar will be 9.5 inches.

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Answer: C. 13.86

Step-by-step explanation:

The end behavior of the function is as x tends to infinity, f(x) tends to zero. It is power function.

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function given is determine the end behavior of the graph.

Given that function has a vertical asymptote at x = -5 and x = 3 , a point discontinuity at x = 2.

The end behavior of f(x) goes to 0 as x goes to negative infinity and f(x) goes to 0 as x goes to positive infinity.

The domain is (-inf, -5)U(-5, 2)U(2, 3) U (3,inf).

Hence, we can conclude that the end behavior of the function is as x tends to infinity, f(x) tends to zero.

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Answer:

7 weeks

Step-by-step explanation:

Answer:

7 weeks

Step-by-step explanation:

Answer:

421.4 miles

Step-by-step explanation:

Numner of miles= ($270.79-$17.95)/86 cents

= $252.84/$0.60

=421.4 miles

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Answer:

Step-by-step explanation:

Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;

M(X, Y) = (x₁+x₂/2, y₁+y₂/2)

X = x₁+x₂/2 and  Y = y₁+y₂/2

From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5

Substituting the given parameters into the formula, we can get the value of a and b as shown;

3 = b+1+2a/2

6 = 2a+b+1

2a+b = 5 ............... 1

Similarly, for the Y coordinate;

5 = a+2+3b+3/2

10 =  a+2+3b+3

a+3b = 10-2-3

a+3b = 5 ........ 2

Solving equation 1 and 2 simulatneously using elimination method

2a+b = 5 ............... 1 * 1

a+3b = 5 ........ 2 * 2

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

2a+b = 5 ...........3

2a +6b = 10.......... 4

subtract 3 from 4

b - 6b = 5-10

-5b = -5

b = -5/-5

b = 1

substitute b =1 into equation 2 to get a;

a + 3b = 5

a + 3(1) = 5

a = 5-3

a = 2

From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2

Answer:

To determine the value of​ a, set up and solve a system of equations in two variables. The value of a is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

15.75m + 850 ≤ 598