A manager at a local manufacturing company has been monitoring the output of one of the machines used to manufacture chromium shells. Past data indicate that if the machine is functioning properly, the length of the shells produced by this machine can be modeled as being normally distributed with a mean of 118 centimeters and a standard deviation of 6.3 centimeters. Suppose 10 shells produced by this machine are randomly selected. What is the probability that the average length of these 10 shells will be between 116 and 120 centimeters when the machine is operating "properly?"

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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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

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

See the attached pictures for the answers.

➷ tanR = 20/29

tanR = 0.689655

The correct option would be 0.6897

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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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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

I got your answer right my guy X=12

Answer:

4.24

Step-by-step explanation:

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

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).

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:

its b . 24.5

Step-by-step explanation:

Answer:

24.5

Step-by-step explanation:

Two sides are 3 by 2 = 2 x 3 x 2 = 12 square m.

Two sides are 17 by 2 = 2 x 17 x 2 = 68 square m.

Two sides are 17 by 3 = 2 x 17 x 3 = 102 square m.

Total = 12 + 68 + 102 = 182 m²

Answer:

114m 2

Step-by-step explanation:

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:

  c. 30.9 °C; 32.9 °C

Step-by-step explanation:

Put the given numbers into the given formula and do the arithmetic.

(a) The temperature of sample 1 is ...

  y = (100 -24)e^(-0.12·20) + 24 ≈ 30.9

___

(b) The temperature of sample 2 is ...

  y = (100 -4)e^(-0.12·10) +4 ≈ 32.9

Hey nice job up there. Well thought out answer.

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:

-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

Answer:

A) F or G = {5, 6, 7, 8, 9, 10, 11, 12}; B) P(F or G) = 8/12 = 0.667

Step-by-step explanation:

The outcomes in event F are 5, 6, 7, 8 and 9.  The outcomes in event G are 9, 10, 11 and 12.  This means that the event F or G, containing all elements of both events, will be

{5, 6, 7, 8, 9, 10, 11, 12}.  Note that we do not count 9 twice; it only appears in the sample space once.  There are 8 elements out of 12 total in the sample space; this means the probability is 8/12 = 0.667.

Using the addition rule, we begin with P(F).  There are 5 elements in this event; this makes P(F) = 5/12.  

For P(G), there are 4 elements in G; this makes P(G) = 4/12.

To add them, we add P(F) and P(G) but then must take out the element counted twice; this gives us

5/12+4/12-1/12 = 9/12-1/12 = 8/12 = 0.667.

We have that

From the question we are told

a)

Generally

The P(F or G) by counting the number of outcomes in F or G is

F&G={5, 6, 7, 8, 9, 10, 11, 12}

b)

P(F or G) using the general addition rule

[tex]P(FG)=\frac{N_f}{N_g}\\\\P(FG)=\frac{8}{12}[/tex]

[tex]P(FG)=0.667[/tex]

c)

Generally Using addition Rue to attain P(F or G) we have

For P(F or G)

[tex]P(F or G)=PF+PG-P(F+G)[/tex]

[tex]P(F or G)=5/12+4/12-(1/12)\\\\ P(F or G)=5/12+1/4\\\\ P(F or G)=\frac{8}{12}[/tex]

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Answer:

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

Step-by-step explanation:

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]

233÷11=21.18

for a total of 22 pieces of wood

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:

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:

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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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

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

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: [tex]\frac{1}{4}=2^{(-2)}[/tex]

Step-by-step explanation:

You know that an expression written is logarithmic form is:

[tex]x=log_b(y)[/tex]

And an expression equivalent to the expression above that is written in exponential form is:

[tex]y=b^x[/tex]

Therefore, keeping the information above on mind, you have that an equivalent exponential equation for [tex]log_{2}(\frac{1}{4}) =-2[/tex] , is the shown below:

[tex]\frac{1}{4}=2^{(-2)}[/tex]

Answer:

[tex]\frac{1}{4} =2^{-2}[/tex]

Step-by-step explanation:

We are given the following expression and we are to write an equivalent exponential equation for it:

[tex] log_2 (\frac { 1 } { 4 } ) = - 2 [/tex]

We know that the standard form of a logarithmic expression is given by:

[tex] y = log_a ( x ) [/tex]

which is equivalent to the exponential form [tex] x = a ^ y [/tex].

Therefore, for the given expression, the equivalent exponential equation will be:

[tex] \frac { 1 } { 4 } = 2 ^ { - 2 } [/tex]

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

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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Answer:

13

Step-by-step explanation:

The 4 consecutive odd numbers that have a sum of 40 are 13, 11, 9, 7. 13 is the greatest of these numbers.

Hope this helps