for each situation, described given a linear model, is there a correlation. if so is there a causal correctaion

The answers to the statements that have been made here are:

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

(B) 60°

Step-by-step explanation:

The total sum of angles in a triangle is 180°. Since you already know the first 2 angles, you can find the last angle C.

C = 180° - 50° - 70°

  = 60°

Answer:

What angel are you aking for?

Step-by-step explanation:

Answer:

6(2 + 7)

Step-by-step explanation:

I hope this helps!

The exact value of x is √1156 and it follows the Pythagorean triple

From the question, we have the following parameters that can be used in our computation:

Legs of the right triangle = 16 and 30

Using the pythagoras theorem, we have

Hypotenuse^2 = the sum of the squares of the other lengths

So, we have

x^2 = 16^2 + 30^2

When evaluated, we have

x^2 = 1156

This gives

x = √1156

Hence, the exact value is √1156

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Answer:

\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)

Answer:

\(x = -5 \pm \sqrt{26}\)

Step-by-step explanation:

\(x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}\)

Answer:

A

If you go to desmos and plug in these points you can check.

Hello!

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

6x(x + 1) = 0

6x = 0                 x + 1 = 0

x = 0                   x = -1

Answer:

The calculated value t = 3.032 >  1.9904 at 5% level of significance

Step-by-step explanation:

Step(i):-

Given mean of the population 'μ'=75 feet

Given mean of the sample(x⁻) = 77

Given standard deviation of the sample(S) = 5.9

Given sample size 'n' =80

Step(ii):-

Test statistic

              \(t=\frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

             \(t=\frac{77-75}{\frac{5.9}{\sqrt{80} } }\)

            t = 3.032

Degrees of freedom ν=n-1 = 80-1 =79

tabulated value = 1.9904 at 5% level of significance

The calculated value t = 3.032

Final answer:-

The calculated value t = 3.032 >  1.9904 at 5% level of significance

Answer:

The speed in miles per hour

Step-by-step explanation:

Distance = (speed)(time)

We already have time, t, so 65 must represent the speed (which is in miles per hour).

Given the angle = 24

the complementary angles have a sum of 90

The complemantry angle of 24 will be = 90 - 24 = 66

so, cot 24 = tan 66

So, the answer will be tan 66

The surface area of the triangular prism will be 540 square inches. Then the correct option is D.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle. Then the surface area of the triangular prism will be given as,

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The surface area of the triangular prism is given as,

SA = (5 x 12) + (5 + 12 + 13) x 16

SA = 60 + 30 x 16

SA = 60 + 480

SA = 540 square inches

The surface area of the triangular prism will be 540 square inches. Then the correct option is D.

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The study is classified as an observational study, and the problem is given as follows:

A.

This is a convenience sample with voluntary​ response, which has a high chance of leading to bias.

Experiments are studies in which there are two groups, with different features, and then the effect of a feature is studied.

For an observational study, there are no changes, just a question is asked, as is the case for this problem.

Convenience samples lead to bias as many people that share characteristics can answer.

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There were approximately 6056 no votes.

Let's assume the number of yes votes is represented by the variable "5x," where x is a positive constant.

Similarly, the number of no votes can be represented by "8x" since the ratio of yes votes to no votes is 5 to 8.

The total number of votes is given as 9854, so we can set up the following equation:

\(5x + 8x = 9854\)

Combining like terms, we have:

\(13x = 9854\)

To solve for x, we divide both sides of the equation by 13:

\(x = \frac{9854 }{13}\)

\(x \approx 757.23\)

Since x represents a positive constant, we round it to the nearest whole number, giving us x = 757.

Now, we can find the number of no votes by multiplying x by the ratio of no votes:

No votes \(= 8x\)

\(= 8 \times 757\)

\(= 6056\)

Therefore, there were approximately 6056 no votes.

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An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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Key features for the graph given in the problem will be-:Vertex (-1, -5), Axis of symmetry=> (x = -1), y-intercept (0,-3), Minimum=> (y=-5), Domain=> (All Real), Range=>( y >= -5)

Refering to the graph given in the problem(refer image attached).The key features of the graph can be given as:

The graph has an upward-opening form, an axis of symmetry at x = -1, a y-intercept at (0, -3), a minimum point at y = -5 (which is also the vertex), and it spans all real numbers on the x-axis (domain) while being larger than or equal to -5 on the y-axis (range).

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Answer:

x=3 y=1 i it's the answer❤

To determine how many trees the lot must sell each season to break even, a system of equations should be written and solved.The cost of operating the Christmas tree lot is $1200 per season. It pays an average of $15 per tree sold, and the average selling price of each tree is $45. Let's assume that the number of trees sold is t. Then we can write two equations to represent the situation:

Revenue = Selling Price * Number of Trees SoldCost = Operating Cost + Pay Per Tree SoldBased on the information given in the problem statement, we can write the following equations:Revenue = 45tCost = 1200 + 15tTo break even, revenue must equal cost. Therefore, we can set the two equations equal to each other and solve for t:45t = 1200 + 15t30t = 1200t = 40The Christmas tree lot must sell 40 trees each season to break even. This means that the revenue generated from selling the 40 trees would be equal to the cost of operating the lot plus the pay per tree sold.

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Answer:

9.71 in decimal form

Step-by-step explanation:

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

Required probability = 2 / 11

Step-by-step explanation:

Sample space of 5 person = 11!

One woman one man arrangement = 2!

Arrangement without woman = 10!

Required probability = [2!][10!] / [11!]

Required probability = 2 / 11

The probability that the parents will be standing next to each​ other is 2/11

Probability is the likelihood or chance that an event will occur.

Given a woman, man and their four children, if their parents will be standing next to each other, that makes it 5 people. The sample space for 5 people is 11!

Pr(parents standing next to each other) =  2!10!/11!

Pr(parents standing next to each other) = 2*10!/11*10!

Pr(parents standing next to each other) = 2/11

Therefore the probability that the parents will be standing next to each​ other is 2/11

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

≈0.3875.

Step-by-step explanation:

1) the rule:

f(x₀+Δx)≈f(x₀)+d[f(x₀)]=f(x₀)+f'(x₀)*Δx;

2) f(x)=sqrt(x) and x₀=0.16, then

f(x₀)=0.4; f'(x₀)=1/(2sqrt(x₀))=1/0.8=1.25;

Δx=0.15-0.16=-0.01;

3) finally,

\(\sqrt{0.15}=\sqrt{0.16}-1.25*0.01=0.4-0.0125=0.3875.\)

Answer:

400

Step-by-step explanation:

The manufacturer spends $5 to make each widget and sells them for $8.  This means that each widget gives him a profit of $3.

8 - 5 = 3

You need to figure out how many widgets it will take for the manufacturer to make up for the costs each month ($1200).

3x = 1200

(3x)/3 = 1200/3

x = 400

The manufacturer needs to sell 400 widgets.

Answer:

Step-by-step explanation:

He sells them 8 dollars and uses 5 dollars worth of material.

His profit is 8 - 5 = 3 dollars.

He has to sell enough to overcome the 1200 dollars.

1200 / 3 = 400

He breaks even after selling 400 widgets.

Answer:$2.36

Step-by-step explanation:

2.95 x .8 = 2.36