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a) the critical number x= N/A ,b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

what is critical number?

The term "critical number" can have different meanings depending on the context in which it is used. Here are a few possible definitions:

In the given question,

To find the critical numbers of the function, we need to find where the derivative is either zero or undefined. Let's find the derivative of y with respect to x:

y' = 4/x²

The derivative is undefined at x = 0, but this point is not in the given interval, so we don't have to consider it. The derivative is zero when:

4/x² = 0

This equation has no real solutions, so there are no critical numbers in the interval (0.25, 5).

Since the function y = -4/x is decreasing on the interval (0.25, 5), the absolute maximum will occur at the left endpoint x = 0.25, and the absolute minimum will occur at the right endpoint x = 5. Therefore:

a) the critical number x= N/A

b) the absolute maximum is -16 at x= 5

c) the absolute maximum is -4 at x= 0.25

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Answer:

64%

Step-by-step explanation:

1. First, we must know that the fraction 48/75 represents that out of 75 total fish, 48 of them were trout.

2. Now, let's divide 48 by 75:

3. Lastly, to convert it into a percentage, we must multiply 0.64 by 100:

Therefore, the answer is 64%.

Answer: - 21/16 = 15/16 (simplified)

= - 1.3125 convert decimal to fraction

= - 13125/10000

= - 21/16 = 15/16  (simplified)

Part a: The four layers can be stacked up to 1,000.

Part b: Most common value of x in this population $0 gift .

Part c: P(x ≥ 25) = 0.30.

Part d: P(x > 0) = 0.60

Part a: It is also anticipated that the students will donate nothing, or around 1000 x 0.40 = 400 of both.

To donors 10, about 1000 x 0.30 = 300.

1000 x 0.25 = 250 donors who gave $25, and 1000 x 0.05 = 50 donors who gave $50.

Its frequencies would approximate the likelihood but not exactly.

The four layers can be stacked up to 1,000.

Part b:

A $0 gift is the population's key value of x in point b, and 40% of students make this choice.

Part c: P(x ≥ 25)

P(x ≥ 25) = 0.25 + 0.05

P(x ≥ 25) = 0.30

Part d: P(x > 0)

P(x > 0) = 1 - P(x = 0)

P(x > 0) = 1 - 0.40

P(x > 0) =0.60

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Answer:

The answer to the questions is

a)1

b)60°

Step-by-step explanation:

tan 45°=1

sin‐¹(√3/2)=60°

The values of the given trigonometric expression are:

(a) tan 45° = 1

(b) \(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Use the concept of trigonometric identity defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

(a) The given trigonometric ratio is,

tan 45°

Since we know that,

In the trigonometric ratio table for the measure 45°,

The value of tangent is 1.

Hence,

tan 45° = 1

For the given trigonometric exprssion,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2})\)

Since we know that,

Sin 60° = √3/2

Therefore,

\(\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ\)

Hence,

The value of the given expression is 60°.

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a. To calculate the present value of investment A at a discount rate of 21 percent, we need to find the present value of each cash flow and then sum them up. The present value of each cash flow can be calculated using the formula PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

Using the given cash flows and the discount rate of 21 percent, we have:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4 + 11,000 / (1 + 0.21)^5 + 11,000 / (1 + 0.21)^6

Calculating this expression will give us the present value of investment A.

b. Similarly, to calculate the present value of investment B, we use the same formula and substitute the cash flows for investment B:

PV = 11,000 / (1 + 0.21)^1 + 11,000 / (1 + 0.21)^2 + 11,000 / (1 + 0.21)^3 + 11,000 / (1 + 0.21)^4

c. For investment C, we use the formula with the cash flows for investment C:

PV = 16,000 / (1 + 0.21)^1 + 48,000 / (1 + 0.21)^2

Calculating these expressions will give us the present values of investments B and C, respectively.

The present values of investments A, B, and C are $37,461.97, $29,930.99, and $48,003.16 respectively.

To calculate the present value of the cash flows from every investment, we use the present value of annuity formula: PV = C * [(1 - (1 + r)^-n ) / r], where PV is the present value, C is the constant cash flow per period, r is the discount rate, and n is the number of periods.

(a) Investment A: C = $11,000, r = 21% or 0.21, n = 6 years. PV = $11,000 * [(1 - (1 + 0.21)^-6) / 0.21] = $37,461.97.

(b) Investment B: C = $11,000, r = 21% or 0.21, n = 4 years. PV = $11,000 * [(1 - (1 + 0.21)^-4) / 0.21] = $29,930.99.

(c) Investment C has 2 cash flows: $16,000 at end of year 1 and $48,000 at end of year 3. We calculate their present value separately and sum those up. PV = $16,000 / (1 + 0.21)^1 + $48,000 / (1 + 0.21)^3 = $13,223.14 + $34,780.02 = $48,003.16.

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Answer:

The answer is 4x^2y^4y^3 simplified to 4x^2y^7

Step-by-step explanation:

Answer:

I'd say you could but 11 lattes

Step-by-step explanation:

First of all I worked out the complete price of the latte which is $4.45*1.1825. Then I took away from the $60 I have to spend the price of the scone plus the sales tax and tip ($2*1.1825).

That leaves you with about 11 lattes plus some change... I think... Sorry this is my first answer here. Hopefully it helps...

Answer:

It’s b UwU even though someone helped you but still

Step-by-step explanation:

Answer:

202

Step-by-step explanation:

Did it on Edu.

Answer:

The answer is 202.

Step-by-step explanation:

Steps to solve:

1/2hb = d²

~Divide 1/2h to both sides

b = 2d²/h

Best of Luck!

Answer:

92

Step-by-step explanation:

Add 95, 90, and 83 all together

add 92 to that total

divide by 4

Answer:

110, 130, 140

Step-by-step explanation:

The x-values are the elements of the domain.

Answer:

3/4 would represent the shaded in parts of the circle

Step-by-step explanation:

I cannot give you an accurate answer seeing as you did not give much detail

Answer:

12

Step-by-step explanation:

the other numbers are way too high that line is shorter than my little sister

Answer:

I believe 12, but do not take my word for it. It seems unsolvable bc there is no height, but 12 seems to be the most accurate.

Step-by-step explanation

So,

Here we have the following inequalities:

We're going to solve each inequality and then notice which could be the solution set.

Let's begin with:

Now, what we have to do is to graph both solution sets and find the intersection between them:

As you can notice, both solution sets intersect at the interval (9,12).

So, the solution set is (9,12), which is: 9

If you have to graph it, put:

Which is 9

Answer:

2^12

Step-by-step explanation:

answer is in photo above

Answer:

B F and A

Step-by-step explanation:

Answer:

D is the answer to the problem

Answer:

Simplifying 9m + -3 + -7m = 0

Reorder the terms: -3 + 9m + -7m = 0

Combine like terms: 9m + -7m = 2m -3 + 2m = 0 Solving -3 + 2m = 0

Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right.

Add '3' to each side of the equation. -3 + 3 + 2m = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2m = 0 + 3 2m = 0 + 3 Combine like terms: 0 + 3 = 3 2m = 3

Divide each side by '2'. m = 1.5

Step-by-step explanation:

Hope this helps :)

Answer:

a

Step-by-step explanation:

the perimeter (P) of a square is the sum of the 4 congruent sides.

the area of a square is calculated as

area = s² ( s is the length of a side )

here area is 36 , then

s² = 36 ( take square root of both sides )

s = \(\sqrt{36}\) = 6

then

P = 4s = 4 × 6 = 24 cm

Answer:1 19/21

Step-by-step explanation:

Answer

\(a=0\), \(b=2\)

\(g_1(x)=\frac{5x}{2}\),  \(g_2(x)=7-x\)

Step-by-step explanation:

Given that

\(\int \int Df(x,y)dA=\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy+\int_5^7\int_0^{7-y} f(x,y)dxdy\; \cdots (i)\)

For the term  \(\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy\).

Limits for \(x\) is from \(x=0\) to \(x=\frac {2y}{5}\) and for \(y\) is from \(y=0\) to \(y=5\)  and the region \(D\), for this double integration is the shaded region as shown in graph 1.

Now, reverse the order of integration, first integrate with respect to \(y\) then with respect to \(x\) . So, the limits of \(y\) become from \(y=\frac{5x}{2}\) to \(y=5\) and limits of \(x\) become from \(x=0\) to \(x=2\) as shown in graph 2.

So, on reversing the order of integration, this double integration can be written as

\(\int_0 ^5\int _0 ^ {\frac {2y}{5}} f(x,y)dxdy=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx\; \cdots (ii)\)

Similarly, for the other term  \(\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy\).

Limits for \(x\) is from \(x=0\) to \(x=7-y\) and limits for \(y\) is from \(y=5\) to \(y=7\)  and the region \(D\), for this double integration is the shaded region as shown in graph 3.

Now, reverse the order of integration, first integrate with respect to \(y\) then with respect to \(x\) . So, the limits of \(y\) become from \(y=5\) to \(y=7-x\) and limits of \(x\) become from \(x=0\) to \(x=2\) as shown in graph 4.

So, on reversing the order of integration, this double integration can be written as

\(\int_5 ^7\int _0 ^ {7-y} f(x,y)dxdy=\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\;\cdots (iii)\)

Hence, from equations \((i)\), \((ii)\) and \((iii)\) , on reversing the order of integration, the required expression is

\(\int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^5 f(x,y)dydx+\int_0 ^2\int _5 ^ {7-x} f(x,y)dydx\)

\(\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\left(\int _ {\frac {5x}{2}}^5 f(x,y)+\int _5 ^ {7-x} f(x,y)\right)dydx\)

\(\Rightarrow \int \int Df(x,y)dA=\int_0 ^2\int _ {\frac {5x}{2}}^{7-x} f(x,y)dydx\; \cdots (iv)\)

Now, compare the RHS of the equation \((iv)\) with

\(\int_a^b\int_{g_1(x)}^{g_2(x)} f(x,y)dydx\)

We have,

\(a=0, b=2, g_1(x)=\frac{5x}{2}\) and \(g_2(x)=7-x\).

The required values are,

\(a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x\)

Double integral is mainly used to find the surface area of a 2d figure, and it is denoted using ‘ ∫∫’. We can easily find the area of a rectangular region by double integration.

Given function is,

\(\int \int_Df(x,y)dA=\int_{0}^{5}\int_{0}^{2y}f(x,y)dxdy+\int_{5}^{7}\int_{0}^{7-y}f(x,y)dxdy\)

We can write the double integral as a single term by reversing the order as,

\(\int_{a}^{b}\int_{g_1(x)}^{g_2(x)}f(x,y)dydx=\int_{0}^{2}\int_{\frac{5x}{2}}^{7-x}f(x,y)dydx)\)

The region D is attached below.

Hence, we get the values,

\(a=0\\b=2\\g_1(x)=\frac{5x}{2} \\g_2(x)=7-x\)

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From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.

Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

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Answer:

\(x=\frac{\pi }{4}\)

Step-by-step explanation:

csc(2x) = 2

is also the same as

sin(2x) = 1/2

so we have to solve for sin(x)=1/2

\(x=\frac{\pi }{2}\)

but we want to sin(2x) = 1/2 so we make it.

\(\\2x=\frac{\pi }{2} \\x=\frac{\pi }{4}\)

Answer:

The answer is Add 2x to both sides of the equation

Step-by-step explanation:

Answer: "The pyramid and the cone have the same volume despite their different shapes."

Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:

"The pyramid and the cone have the same volume despite their different shapes."

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The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right 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.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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