Let f(x)=100 / −10+e^−0.1x .

What is f(−11) ?


Enter your answer, rounded to the nearest tenth, in the box

Answer:

3.7  liters

Step-by-step explanation:

The required amount of water in each bottle is 0.5 gallon.

Given that,
2.5 gallons of water are poured into 5 equally sized bottles, how much water is in each bottle is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Total volume = 2.5 gallon,
Number of bottle = 5,
Gallon per bottle = 2.5 / 5 = 0.5 gallon per bottle

Thus, the required amount of water in each bottle is 0.5 gallons.

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The area of the ellipse [tex]E[/tex] is given by

[tex]\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy[/tex]

To use Green's theorem, which says

[tex]\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

([tex]\partial E[/tex] denotes the boundary of [tex]E[/tex]), we want to find [tex]M(x,y)[/tex] and [tex]L(x,y)[/tex] such that

[tex]\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]

and then we would simply compute the line integral. As the hint suggests, we can pick

[tex]\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]

The line integral is then

[tex]\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy[/tex]

We parameterize the boundary by

[tex]\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the integral is

[tex]\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt[/tex]

[tex]=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi[/tex]

###

Notice that [tex]x^{2/3}+y^{2/3}=4^{2/3}[/tex] kind of resembles the equation for a circle with radius 4, [tex]x^2+y^2=4^2[/tex]. We can change coordinates to what you might call "pseudo-polar":

[tex]\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}[/tex]

which gives

[tex]x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}[/tex]

as needed. Then with [tex]0\le t\le2\pi[/tex], we compute the area via Green's theorem using the same setup as before:

[tex]\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt[/tex]

[tex]=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt[/tex]

[tex]=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt[/tex]

[tex]=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt[/tex]

[tex]=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt[/tex]

[tex]=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi[/tex]

The areas of the ellipse and curve interior can be calculated using Green's Theorem and the respective parametrizations, x(t) = 5cos(t) and x(t) = 4cos3(t), followed by integrating.

To compute the area inside the ellipse using Green's Theorem, we use the fact that the area can be written as ∬ dxdy = 1/2 ∫ d(−y dx+x dy). Using the hint, x(t) = 5cos(t), we parametrize the ellipse and integrate over the boundary to compute the area.

Similarly, for the parametrization of the curve x2/3 + y2/3 = 42/3, we could use the hint x(t) = 4cos3(t), which is a cube root form representation. After this, compute the area of the interior using the proper integration methods.

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Answer:

[tex]Cos (\frac{\pi}{3})[/tex]

Step-by-step explanation:

To get the angle in the first quadrant, we need to subtract 2π from the angle given as many times we need UNTIL we get an angle that is between 0 degree and 90 degree (1st quadrant).

Let's start by subtracting 2π from the angle given:

[tex]\frac{7\pi}{3}-2\pi\\=\frac{7\pi -2\pi(3)}{3}\\=\frac{7\pi - 6\pi}{3}\\=\frac{\pi}{3}[/tex]

This angle is in the 1st quadrant, so we don't need to subtract 2π anymore. Thus we can write:

[tex]Cos(\frac{7\pi}{3})=Cos(\frac{\pi}{3})[/tex]

Answer:

(1.5, 1.5)

Step-by-step explanation:

To solve the system of equations, use elimination, substitution, or graphing to find the solution. The solution is the point (x,y) where they intersect.

Graph 2x + 12y = 21 and 2x + 2y = 6.

See attached picture.

The solution is (1.5, 1.5).

Final answer:

To find the inverse function of a given function, interchange x and F(x) and solve for x. The steps involve replacing F(x) with y, interchanging x and y, and then solving for y.

Explanation:

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and F(x) and solve for x. Step by step:

Replace F(x) with y: y = (8 - 2x)²

Interchange x and y: x = (8 - 2y)²

Solve the resulting equation for y: y = 4 - √(x) / 2

The function F(x) = (8 - 2x)² does not have an inverse function because it's not one-to-one. Instead, for all x, the inverse is a constant function [tex]\( F^{-1}(x) = 4 \)[/tex].

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and y and then solve for y. So, let's start by writing y instead of F(x):

y = (8 - 2x)²

Now, our goal is to solve this equation for x. First, we'll expand the expression:

y = (8 - 2x)(8 - 2x)

y = 64 - 16x - 16x + 4x²

y = 4x² - 32x + 64

Now, to find the inverse, we switch x and y and solve for y :

x = 4y² - 32y + 64

This is a quadratic equation in terms of y, so we need to solve it. To do that, we can use the quadratic formula:

[tex]\[ y = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where a = 4, b = -32, and c = 64. Plugging in these values:

[tex]\[ y = \frac{{32 \pm \sqrt{{(-32)^2 - 4(4)(64)}}}}{{2(4)}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{{1024 - 1024}}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{0}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm 0}}{{8}} \][/tex]

[tex]\[ y = \frac{{32}}{{8}} \][/tex]

y = 4

So, the inverse function of F(x) is [tex]\( F^{-1}(x) = 4 \)[/tex].

This result suggests that the function F(x) is not one-to-one, meaning it doesn't have an inverse that's a function. Instead, it suggests that for every value of x, the function F(x) produces the same output, which is 4. Therefore, F(x) doesn't have a unique inverse function.

Answer:

89

Step-by-step explanation:

86+78+80+99+99+92+86 = 620

620/7 = 88.57142857

And since you requested the nearest whole number the 88 turns into an 89 due to the fact that the tenth place is a 5 (or greater).

Since he has four cuts for each pizza, jason has 8 pizzas

Answer:

f(x) = -|x - 3| + 2.

Step-by-step explanation:

f(x) = |x| is shaped like a V and the vertex is at (0, 0). f(x) = -|x| is  a reflection  in the x-axis so will be an inverted V , opening down. f(x) = - |x - 3|  will be the  -|x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex  to (3, 2)   it will move upwards 2 units.

So it is f(x) = -|x - 3| + 2.

f(x)=-|x-3|+2

Negative before the abs value inverts the graph and it moves right 3 and up 2

Answer:

-2

Step-by-step explanation:

log3 (1/9)

Replace 1/9 with a power of 3

1/9 = 3^-2

log3 (3^-2)

Using the power of power rule  loga (b^c) = c log a(b)

-2 log3(3)

We know that loga(a) =1

-2 (1)

-2

Final answer:

To find the length (c) of a rectangle when the perimeter is 30 inches, we use the formula c = (P - 2w) / 2, with P representing the perimeter and w the width.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that the perimeter (P) is 30 inches, and we are looking to find the formula that shows the length of side c assuming c represents either the length or the width of the rectangle. Let's say c represents the length for this context. Therefore, the formula rearranges to c = (P - 2w) / 2. We use this formula when we know the perimeter and the width (w), and we want to find the length (c).

Why this is so easy

Ok so, 75/5=15

15*7 =105 so the answer is 105 pages

47,448/12=$3954

As, 28/36 rule states that maximum of 28% of your monthly expenditure should be spent on housing finances.

0.28*3954=$1107,12

Answer: $1107.

Answer:

4.24

Step-by-step explanation:

You can use the formula d=sqrt(2a to calculate this with ease.

The equations are classified as follows: 1. 2nd order non-linear differential equation, 2. 2nd order linear differential equation, 3. 3rd order non-linear differential equation, 4. 1st order non-linear differential equation.

The task given is to classify each differential equation into one of several categories: whether the order of the equation is first, second, third, fourth or fifth, and whether or not it is a linear differential equation.

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let's say hight of tree is x.

from figure attached , using trigonometry we can say

tan 37 = x / 26

multiplying by 26 both side

tan 37 × 26 = x/26 × 26

tan 37× 26 = x

putting value of tan 37

x = tan 37 × 26 = 0.7535 × 26

x = 19.592 meters

Answer:

C. Money market

Best regards

Final answer:

Venture capital is money loaned for the purpose of earning a share of the profits in startups or small businesses. Venture capitalists provide funds in exchange for equity in the company.

Explanation:

Venture capital is money loaned for the purpose of earning a share of the profits. It is a form of financing for startups or small businesses that have potential for high growth. Venture capitalists provide funds to these companies in exchange for equity, or ownership stake, in the company.

For example, let's say a student wants to start a tech company but doesn't have the funds to do so. They approach a venture capitalist who believes in their idea and is willing to invest money in their company. In return, the venture capitalist will receive a portion of the company's profits.

So, the correct answer is D. Venture capital.

Answer:

{0.16807, 0.36015, 0.3087, 0.1323, 0.02835, 0.00243}

Step-by-step explanation:

The expansion of (p+q)^n for n = 5 is ...

(p+q)^5 = p^5 +5·p^4·q +10·p^3·q^2 +10·p^2·q^3 +5·p·q^4 +q^5

When the probability p=0.3 and q = 1-p = 0.7 the terms of this series correspond to the probabilities of 5, 4, 3, 2, 1, and 0 favorable outcomes out of 5 trials.

For example, p^5 = 0.3^5 = 0.00243 is the probability of 5 favorable outcomes in 5 trials where the probability of each favorable outcome is 0.3.

___

The attachment shows the calculation of these numbers using a graphing calculator. It lists them in reverse order of the expansion of (p+q)^5 shown above, so that they are the probabilities of 0–5 favorable outcomes in the order 0–5.

Answer:

[tex]f(a^{2})=7(a^{4})-8[/tex]

Step-by-step explanation:

we have

[tex]f(x)=7x^{2}-8[/tex]

we know that

[tex]f(a^{2})[/tex]

Is the value of f(x) for [tex]x=a^{2}[/tex]

so

substitute the value of x in the function

[tex]f(a^{2})=7(a^{2})^{2}-8[/tex]

[tex]f(a^{2})=7(a^{4})-8[/tex]

Answer:

The correct answer option is P (S∩LC) = 0.16.

Step-by-step explanation:

It is known that the probability if someone is a smoker is P(S)=0.29 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.552.

So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.552 = P(S∩LC) / 0.29

P (S∩LC) = 0.552 × 0.29 = 0.16

➷ tanR = 20/29

tanR = 0.689655

The correct option would be 0.6897

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

The value of tan R using trignonometic values is 0.9524.

Tan is used to determine the value of an angle given the opposite side and the adjacent side. Tan R is the opposite side divided by the adjacent side.

Tan = opposite / adjacent

Tan = 20/21

Tan = 0.9524.

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[tex] ln( \sqrt{ex {y}^{2} {z}^{5} } ) \\ = ln{(ex {y}^{2} {z}^{5} ) }^{ \frac{1}{2} } \\ = \frac{1}{2} ln(ex {y}^{2} {z}^{5} ) \\ = \frac{1}{2} ln(e) + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) \\ = \frac{1}{2} + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) [/tex]

Answer:

Answer A  B and D

Step-by-step explanation:

This one requires and eagle eye. You have to be a bit careful with it.

The one you checked (D) is correct. There are a couple more and one is really tricky.

The first one is actually correct.

So is the second one, which I'll show first. Only C is incorrect.

======

B]

ln(e^(1/2) + ln(x^(1/2)) + ln(y^(2/2) + ln(z^(5/2))

1/2 + ln(x^(1/2)) + ln(y) + (5/2) ln(z)

1/2 + 1/2 ln(x) + ln(y) + 5/2 ln(z)

A]

(1/2) * Ln(ex*z) + ln(yz^2)

(1/2)ln(e) + (1/2)ln(x) + (1/2)ln(z) + ln(y) + lnz^2

ln(e) = 1;   ln(z^2) = 2 ln(z)

1/2 + 1/2 ln(x) + 1/2 ln(z) + ln(y) + 2ln(z)

1/2 ln(z) + 2ln(z) = 5/2 ln(z)

So put all this together

1/2 + 1/2 ln(x) + 5/2 ln(z) + ln(y) which is Exactly like B

Answer:

The dependent variable is the total cost "t"

Explanation:

The given equation is:

3n + 10 = t

where n is the number of yards and t is the total cost

We have two variables in this equation, n and t

We know that the total cost "t" will depend on the number of yards of fabric she buys

This means that the total cost will change by changing the number of yards bought

For example:

If she bought 1 yard: t = 10 + 3(1) = $13

If she bought 3 yards: t = 10 + 3(3) = $19

Therefore, the total cost "t" depends on the number of yards which means that "t" is the dependent variable in the equation

Hope this helps :)

See the attached pictures for the answers.

Answer:

The first option i.e a

Step-by-step explanation:

- 2.5 + (-1) = - 2.5 -1 = -3.5

and the arrow indicating towards -3.5 is first option

Answer:

Dina's friend is jealous of Dina's confidence so she wanted to "what up" her :)

Step-by-step explanation:

233÷11=21.18

for a total of 22 pieces of wood

1/6 because 1/3 of 1/2 is 1/6

Answer:

14.04°

Step-by-step explanation:

In this right triangle, we're seeking the measurement of an angle at the base of the triangle and we have the measurements of two of the sides (none are the hypotenuse) : the opposite one of the angle and the adjacent side.

The relationship between the two sides we have the measurement and the angle we are looking for is the tangent:

[tex]tan(\alpha) = \frac{a}{b} = \frac{5}{20} = 0.25[/tex]

To find the angle we do an arctan on 0.25 and we get an angle of 14.04 degrees.

Answer:

14.04

Step-by-step explanation:

i took the test

Answer:A translation then rotation then reflection

Step-by-step explanation:

In the context of the Side-Side-Side (SSS) theorem in geometry, the rigid transformations referred to are typically translation, rotation, and reflection. By strategically applying these transformations, one can map one triangle onto another, thereby demonstrating their congruence according to the SSS theorem.

Rigid transformations in the context of geometry often refer to transformations that preserve the shape and size of geometric figures. The characterization quoted as 'SSS proof' likely refers to the Side-Side-Side congruence theorem in geometry, which states that if the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This congruence can be proven through certain rigid transformations, most commonly, translation, rotation and reflection.

In the case of the SSS proof, one or a combination of these three transformations can be used to map one triangle onto another. For example, you can translate one triangle so that a vertex matches a corresponding vertex on the other triangle. Then rotate the translated triangle if necessary so that one side matches the direction of the corresponding side on another triangle, this is rotation. Finally, if the triangle is flipped relative to the other one, reflect along the appropriate axis to match the final side. Again, this is the most common example and sometimes you may need to combine the transformations.

The inquiry about Einstein's postulate and other references seems unrelated to rigid transformations in Geometry and the SSS proof specifically.

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