Answer the following questions in order to sketch the curve F(x) = 1/x^2 – 9
a. Domain b. Intercepts c. Symmetry d. Asymptotes e. Intervals of increase or decrease f. Local maximum or minimum values g. Concavity and points of inflection h. Sketch the curve!

Answer:

Max is 9 feet above Brett.

Step-by-step explanation:

If you subtract how far Max is below the surface to how far Brett is below the surface you find the difference of how much more above Brett Max is.

This would be the mathematical process:

34-25=9

Max is 9 feet above Brett.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

Given that Brett is 34 feet below the surface and Max is 25 feet below the surface.

Max is more than twice as deep below the surface as Brett,

Thus we can determine this difference by subtracting Max's depth from Brett's.

The mathematical solution would be as follows:

⇒ 34 - 25

⇒ 9

Hence, Max is 9 feet above Brett.

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If the reserve ratio is equal to the reserve requirement, excess reserves would be zero.

To understand this concept, let's define a few terms:

Reserve Ratio: The reserve ratio is the percentage of customer deposits that banks are required to hold as reserves. It is set by the central bank and serves as a safeguard to ensure that banks have enough funds to meet withdrawal demands from depositors.

Reserve Requirement: The reserve requirement is the actual amount of reserves that banks are required to hold based on the reserve ratio. It is calculated as a percentage of customer deposits.

Excess Reserves: Excess reserves are the funds that banks hold in addition to the required reserves. These reserves are not mandated by the reserve requirement but are voluntarily held by banks as a buffer to cover unexpected deposit outflows or to meet lending needs.

Now, if the reserve ratio is equal to the reserve requirement, it means that banks are fulfilling their reserve obligations precisely. In other words, they are holding the exact amount of reserves required by the central bank based on the reserve ratio. In this scenario, there are no excess reserves because banks are not holding any additional funds beyond the required reserves.

This situation can occur when banks have a carefully balanced approach to managing their reserves, ensuring compliance with regulatory requirements while avoiding holding excessive funds that could be used for lending or investment purposes. It signifies that banks are operating efficiently within the regulatory framework and utilizing their resources effectively to meet the demands of depositors and borrowers.

Therefore, If the reserve ratio is equal to the reserve requirement, excess reserves would be zero.

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Answer:

w = √(10^2 - 6^2) = √(100 - 36) = √64 = 8

x/8 = 8/6, so x = 32/3 = 10 2/3

y = √(8^2 + (32/3)^2) = √(64 + (1,024/9))

= (√(576 + 1,024))/3 = (√1,600)/3 = 40/3

= 13 1/3

z = 6 + 32/3 = 18/3 + 32/3 = 50/3 = 16 2/3

The value of x, y, and w are 6, 10, and 8.

We have,

There are three triangles in the figure.

Applying the Pythagorean theorem on one triangle,

10² = 6² + w²

100 = 36 + w²

w² = 100 - 36

w² = 64

w = 8

Now,

We consider two similar triangles.

The ratio of corresponding sides is equal.

so,

10/W = y/w

10/8 = y/8

y = 10

Now,

Applying the Pythagorean theorem on one triangle,

y² = w² + x²

10² = 8² + x²

100 = 64 + x²

x² = 100 -64

x² = 36

x = 6

Thus,

The value of x, y, and w are 6, 10, and 8.

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Answer:

340

Step-by-step explanation:

1/4 = .25

85 / .25 = 340

85 goes into 1/4 340 times

hope this helps

plz mark brainliest :)

Answer:

340

Step-by-step explanation:

85 ÷ 1/4 =

85/1 ÷ 1/4 =

85/1 • 4/1 =

340/1 = 340

If z = log(y) where z is a random variable following the standard normal distribution, \(e(y) = exp(1/2).\)

To compute e(y), we'll need to use the properties of the standard normal distribution, logarithms, and expectations.

First, recall that z is a standard normal random variable, which means it follows the normal distribution with mean μ = 0 and standard deviation σ = 1.

Next, we are given that z = log(y). To find e(y), we need to find the expected value of Y. We can do this by transforming the random variable z into Y using the exponential function. Since z = log(y), we have y = exp(z), where exp denotes the exponential function.

Now, we need to compute the expected value e(y). Using the properties of expectations, we have:

\(e(y) = e(exp(z))\)

Since z is a standard normal random variable, we know the probability density function (pdf) of z is given by:

\(f(z) = (1/sqrt(2π)) * exp(-z^2/2)\)

To compute e(y), we integrate the product of y and its pdf with respect to z:

\(e(y) = ∫[exp(z) * (1/sqrt(2π)) * exp(-z^2/2)] dz,\)from -∞ to ∞

This integral can be evaluated using a known result called the moment generating function (MGF) of the standard normal distribution:

\(E(exp(tz)) = exp(μt + (σ^2 * t^2)/2)\)

For our case, μ = 0, σ = 1, and t = 1, so the MGF becomes:

\(e(y) = e(exp(z)) = exp((0 * 1) + (1^2 * 1^2)/2) = exp(1/2)\)

Thus, the expected value of Y is:

\(e(y) = exp(1/2).\)

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Answer:

1.45%+4.2%= 5.65%

100%->650

5.65%-> 36.725

650- 36.725 - 10 = 603.275

~ 603. 27

hence answer is b

Correct Answer: $603.27

Answer: The results are likely valid because a large number of tires produced during the week were part of the sample.

The results are likely valid because each tire sampled was part of the population of tires that week.

Step-by-step explanation: 400 tires per day and 8 hours per day would be 50 tires per hour  so like one per minute

For dimensions of x =10 and y=5 for the base and height that will make the tank weight as little as possible.

Here we are given the information of a square-based, open-top, rectangular steel holding tank, so here the tank is in the shape of a cuboid and we know  the formula  for :

volume = x*y*z, as  here it is a square base, so the volume will be

volume =  x²*y, where x and y are the dimension of the base and height

So for the  given reason,  

=>x²*y =  500

=> y = 500/x²

Again, the surface area formula  will be

S=x²+4xy, substituting the value of  y in this question

=>S=x²+4x(500/x²)

=>S=x²+2000/x

Differentiating the above formula with respect to x, we get

=>2x-2000/x²=0

=>2x³= 2000

=>x³= 1000

=>x =10

so the substituting the x values of x in  the equation y , we get

y = 500/x²

=>y = 5

so the dimensions are x= 10 and y=5

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The number of books Sophia and her brother read is 32 and 8 respectively.

Given that,

The total number of books = 40 books

The number of books Sophia read = 4[The number of books Sophia's brother read]

Assuming that the number of books Sophia's brother read = a

So, the number of books Sophia read = 4a

Thus,

a + 4a = 40

Solving the equation further, we get:

5a = 40

a = 8

The number of books Sophia's brother read = 8 books

Hence, the number of books Sophia read = 32 books

Therefore, The number of books Sophia and her brother read is 32 and 8 respectively.

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Answer:

Step-by-step explanation:

\((-1)^{n} = -1 , if \ n \ is \ a \ odd \ integer\\\\\\\\(-1)^{2003} =-1 \\\\(\dfrac{-3}{4)}^{2}=\dfrac{3}{4}, \ as \ 2 \ is \ even \ number.\\\\(\dfrac{2}{3})^{3}*(\dfrac{-3}{4})^{2}*(-1)^{2003}=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{4^{2}}*(-1)\\\\\\=\dfrac{2^{3}}{3^{3}}*\dfrac{3^{2}}{2^{4}}*(-1)\\\\\\=\dfrac{-1}{3^{3-2}*2^{4-3}}\\\\\\=\dfrac{-1}{3^{1}*2^{1}}\\\\=\dfrac{-1}{6}\)

\((\dfrac{2}{5})^{2}*(\dfrac{-5}{12})^{3}=\dfrac{2^{2}}{5^{2}}*\dfrac{(-5)^{3}}{(2^{2}*3)^{3}}\\\\\\=\dfrac{2^{2}}{5^{2}}*\dfrac{- 5^{3}}{2^{6}*3^{3}}\\\\\\= -\dfrac{5^{3-2}}{2^{6-2}*3^{3}}\\\\\\= -\dfrac{5}{2^{4}3^{3}}\\\\= -\dfrac{5}{16*3}\\\\\\= \dfrac{-5}{48}\)\(HINT: \dfrac{a^{m}}{a^{n}}=a^{m-n}, m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}}, n >m\\\\\\(a^{m})^{n}=a^{m*n}\)

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

option C.

The ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is determined as follows;

The four points include;

A = (1, 2)

B = (2, - 3)

C = (-2, - 2)

D = (-3,  1)

The  ordered pair that can be plotted together with these four points, must fall withing these coordinates. Going by this condition we can see that the only option that meet this criteria is;

(2, - 1)

Thus, the ordered pair that can be plotted together with these four points, so that the resulting graph still represents a function is (2, -1).

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The probability that the person likes ice cream and the coin shows heads is 0.93 * 0.5 = 0.465, or 46.5%.

To find the probability that a person likes ice cream and the coin shows heads, we can multiply the probabilities of these two independent events.

Given that the probability of a random person liking ice cream is 0.93, and assuming the coin is fair, the probability of the coin showing heads is 0.5.

Therefore, the probability that the person likes ice cream and the coin shows heads is 0.93 * 0.5 = 0.465, or 46.5%.

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Answer: 225 cm^3

Step-by-step explanation:

Volume = Length * Width *Height

Volume= 5cm*5cm*9cm

Volume= 225 cm^3

Answer: 225 cm

Step-by-step explanation:

Length x width x height

5x5x9

5x5 = 25

25x9 = 225

Answer 225

Answer:

its <2 im pretty sure

Step-by-step explanation:

the explicit particular solution to the initial value problem is:

y = -19/4 * (1/3)e³ˣ + 19/12

To find an explicit particular solution of the initial value problem dy/dx = \(19e^{(3x-4y)\) y(0) = 0, we can use separation of variables.

First, let's rewrite the differential equation as:

dy/\(e^{4y\) = 19e³ˣdx

Now, we integrate both sides with respect to their respective variables:

∫(1/\(e^{4y\))dy = ∫(19e³ˣ)dx

To integrate the left side, we can make a substitution u = \(e^{4y\), then du = -4e\(e^{4y\)dy:

∫(1/u)(-du/4) = ∫(19e³ˣ)dx

-1/4 ∫(1/u)du = 19 ∫(e³ˣ)dx

-1/4 ln|u| = 19 ∫(e³ˣ)dx

-1/4 ln|\(e^{4y\)| = 19 ∫(e³ˣ)dx

-1/4 (-4y) = 19 ∫(e³ˣ)dx

y = -19/4 ∫(e³ˣ)dx

To find the particular solution, we need to evaluate the integral on the right side. The integral of e³ˣ can be found easily:

y = -19/4 * (1/3)e³ˣ + C

Now, we can apply the initial condition y(0) = 0 to find the value of the constant C:

0 = -19/4 * (1/3)e³⁽⁰⁾ + C

0 = -19/4 * (1/3) + C

C = 19/12

Therefore, the explicit particular solution to the initial value problem is:

y = -19/4 * (1/3)e³ˣ + 19/12

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Based on the definition of a line of symmetry, we can conclude that: "the line is not a line of symmetry, because the two parts are not an exact match when the rectangle is folded over the line."

A line of symmetry is like a mirror that splits a shape into two parts that look exactly the same. If you fold a shape in half along a line and both sides look exactly the same, that line is called a line of symmetry.

Thus, from the image shown with the rectangle given, we can conclude that: "the line is not a line of symmetry, because the two parts are not an exact match when the rectangle is folded over the line."

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Answer:

49×66+49×34 = 49× (66+34)

Answer:

49×66+49×34 = 49× (66+34)

Step-by-step explanation:

Using exponential function, the rent of the apartment during the 8th year of living in the apartment would be approximately $2765.5.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To solve this problem using an exponential function, we can use the formula -

\(y = a \times (1 + r)^t\)

where -

y is the final value we want to find (in this case, the rent in the 8th year)

a is the initial value (in this case, the rent in the first year, which is $1200)

r is the growth rate per period (in this case, 11% per year, or 0.11)

t is the number of periods (in this case, 8 years)

Plugging in the values in the equation, we get -

\(y = 1200 \times (1 + 0.11)^8\)

y = 1200 × 2.30453777

y = 2765.44532

Rounding to the nearest tenth, we get -

y ≈ $2765.5

Therefore, the rent of the apartment value is obtained as $2765.5.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The figure showing the construction is given below.

Steps for the construction of a circle through three points not on a straight line are as follows:

1. To create two lines, connect the points.

2. Create the line's perpendicular bisector.

3. Create the opposite line's perpendicular bisector.

4. The circle's center is where they intersect.

5. Draw your circle by placing the compass on the center point and adjusting its length to reach any point.

What happens if the points are parallel?

The circle traveling through all three points will have an infinite radius if the three points are collinear, or all situated on a straight line. Therefore, a practical circle cannot traverse three collinear locations. The two radii would be parallel and would never come together at a center if you tried the construction. We may claim that they do cross mathematically but at infinity.

Hence, after following the steps we obtain the circle.

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Answer:

6120

Step-by-step explanation:

i)

15/100 × 7200

=1080 ( the amount of discount based on the marked prize )

ii) 7200-1080=6120

Answer:

4, 5, 6

Step-by-step explanation:

x>3.75

If the triangle has sides with lengths of 49 cm, 68 cm, and 92 cm , then the triangle is not a Right Triangle .

If the Triangle is a right triangle , then the sides of the triangle should satisfy the Pythagoras Theorem which states that the sum of the square of two smaller sides is equal to square of longest side(hypotnuse) .

that means ⇒ (Hypotnuse)² = (Perpendicular)² + (Base)² ;

Substituting the longest value as 92 and other values as 49 and 68 ,

we get ;

⇒ 92² = 49² + 68² ;

⇒ 8464 = 2401 + 4624 ;

⇒ 8464 ≠ 7025 .

the sides 49 cm, 68 cm, and 92 cm do not satisfy Pythagoras theorem ,

Therefore , the side lengths do not form a Right Triangle .

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The length of one side of the box, in meters, is 0.138 meters.

The density of water is approximately 1000 kg/m^3 or 1 g/cm^3. If a cubic box is filled with 2650 g of water, we can find the volume of the box and then find one side length.

Volume = Mass / Density = 2650 g/(1 g/cm^3) = 2650 cm^3

Since the box is cubic, one side length is the cube root of the volume.

Side length = (Volume)^(1/3) = (2650 cm^3)^(1/3) = 13.8 cm

To convert cm to meters, divide by 100:

Side length = 13.8 cm/100 cm/m = 0.138 m

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Answer: A) 4

Explanation:

For any 30-60-90 triangle, the short leg is half as long as the hypotenuse.

The short leg is opposite the smallest angle (30 degrees), so we see that

x = 8/2 = 4.

The correct answer is E, 9.

4•9=36.

36+14=50.

The angles have to equal 180 so.

130+(50)=180 which is correct.

Answer:

h = 9km

Step-by-step explanation:

area of a trapezoid= ½ x (a+b) x h

117 = (2+2+11 +11) / 2 x h

h = 117 / 26÷2

h = 9km

The polynomial with degree 4, zeros 2+4i and 4 with multiplicity 2, and real coefficients can be represented as f(x) = a(x - (2+4i))(x - (2-4i))(x - 4)^2, where a is the leading coefficient.

To form a polynomial with the given degree and zeros, we can use the fact that complex zeros occur in conjugate pairs. The zero 2+4i implies that 2-4i is also a zero. Additionally, the zero 4 has a multiplicity of 2, which means it appears twice as a zero.

Therefore, the polynomial can be expressed as f(x) = a(x - (2+4i))(x - (2-4i))(x - 4)(x - 4).

Now, let's simplify the polynomial. To multiply the complex conjugates, we use the difference of squares formula: (a - b)(a + b) = a^2 - b^2.

Expanding the first two factors, we have:

(x - (2+4i))(x - (2-4i)) = (x - 2 - 4i)(x - 2 + 4i)

                           = (x - 2)^2 - (4i)^2

                           = (x - 2)^2 - 16i^2

                           = (x - 2)^2 + 16

Expanding the remaining factors, we have:

(x - 4)(x - 4) = (x - 4)^2

Combining all the factors, the polynomial becomes:

f(x) = a(x - 2)^2(x - 2)^2(x - 4)^2 + 16(x - 2)^2.

Finally, we can rewrite the polynomial in a simplified form:

f(x) = a(x - 2)^4(x - 4)^2 + 16(x - 2)^2.

In this expression, a represents the leading coefficient of the polynomial.

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Answer:

-17

Step-by-step explanation:

-21-c

Let c = -4

-21 - -4

Subtracting a negative is like adding

-21 +4

-17

Answer:

-17

Step-by-step explanation:

- 21 - c

Put c as -4.

- 21 - (-4)

The negative signs cancel.

- 21 + 4

Add both the terms.

= -17

The value of test statistic is  -1.14

Define Standard error.

The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).

Null Hypothesis

P = 0.54

Alternate Hypothesis

P < 0.54

For 0.05 level , the value of Z = 1.645

Decision rule ,

reject null Hypothesis if test statistic Z < -1.645

sample size (n) = 200

sample success (x) = 100

Standard error SE = √(p * (1 - p) / n

                         = √0.54 * (1 - 0.54) / 200

Standard error SE= 0.0352

Sample proportion (р)  = x/n

                               = 100 / 200 ⇒ 0.5

test statistic  Z = (р - P) / SE

                         = (0.5 - 0.54) / 0.0352

test statistic  Z = -1.136 or -1.14

Therefore, the value of test statistic is  -1.14

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