For problems 9 and 10, identify the type of graph and then sketch the graph of the given polar equation using the technique for that type of graph. 9. r = 4cos 8 Type of graph: 90° 75° 165 180 150 1

The exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

To find the exact value of tan(2arcsin(x)), we start by considering the definition of arcsin. Let θ = arcsin(x), where |x| ≤ 1. From the definition, we have sin(θ) = x.

Using the double angle identity for tangent, we have tan(2θ) = 2tan(θ) / (1 - tan²(θ)). Substituting θ = arcsin(x), we obtain tan(2arcsin(x)) = 2tan(arcsin(x)) / (1 - tan²(arcsin(x))).

Since sin(θ) = x, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find cos(θ). Taking the square root of both sides, we have cos(θ) = √(1 - sin²(θ)) = √(1 - x²).

Now, we can determine the value of tan(arcsin(x)) using the definition of tangent. We know that tan(θ) = sin(θ) / cos(θ). Substituting sin(θ) = x and cos(θ) = √(1 - x²), we get tan(arcsin(x)) = x / √(1 - x²).

Finally, substituting this value into the expression for tan(2arcsin(x)), we obtain tan(2arcsin(x)) = 2x / (1 - x²).

Therefore, the exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

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Answer:

b = $2.40

d = $5.70

Step-by-step explanation:

d = hot dog and b = hot dog buns

Equations:

2d + 5b = $23.40

3d + 2b = $21.90

-------------------------------subtract these two equations

-d + 3b = $1.50

3b - $1.50 = d

Substitute:

3d + 2b = $21.90

3(3b - $1.50) + 2b = $21.90

9b - $4.50 + 2= $21.90

11b = 26.40

b =  $2.40

Substitute again but this time with b:

3d + 2b = $21.90

3d + 2($2.40) = $21.90

3d + $4.80 = $21.90

3d = $21.90

d = $5.70

Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.

Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.

the complete question is :

Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

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Answer:

no solutions

Step-by-step explanation:

7x-3(x-1)=2(2x+3)

7x-3x+3=4x+6

4x+3=4x+6

3=6

no solutions

Answer:

No solution

Step-by-step explanation:

Answer:

1. Numerator: 8                2. Numerator: 1

Denominator: 8                    Denominator: 6

Fraction: 8/8                        Fraction: 1/6

Step-by-step explanation:

A numerator is the top part of a fraction, and in this case is represented by the shaded parts. for example, question 2 has 1 out of the 6 parts shaded, this would make 1 the top number.

A denominator is the bottom part of the fraction and is represented by how many parts of there in all. for example, question 2 has 6 parts in all, this would make 6 the bottom number.

Answer:

3.9 percent

Step-by-step explanation:

gfdsryuvcnkijnvcddxxcccvhjurddcccz

Answer:

First one is C the next one is D

Step-by-step explanation:

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:

look in explanation

Step-by-step explanation:

what is the probability of the ball hitting u in dodge ball in pe

what is the ratio of your computer to everyone else's in comp science

how much of your essay did you finish (in a fraction)

how many people are there in psychology class for every notebook?

From the information provided, the warehouse space has 8000 sq ft of showroom and workshop. One hal o this would be used which translates to 4000 sq ft. The warehouse has a height of 20 ft.

The cubic vloume of the warehouse is given as follows;

The dimensions for each rim is given as

The volume of each rim therefore is;

To determine how many rims would fit into half of the warehouse,

If you must have exactly 4 cans in a rim, then

Answer:

3/6 or 1/2 scoop

Step-by-step explanation:

Answer:

1 1/2 more

Step-by-step explanation:

If you convert 5/6 to a 3rd it would be 2.5/3

2.5 - 1= 1.5.

1.5 as a fraction is 1 1/2.

Hope this helps!:)

-Amelia

Answer:

11

Step-by-step explanation:

5+6=11

Answer:

3

Step-by-step explanation:

got it on edge

Answer:

Step-by-step explanation:

a

The chi-square test of independence is typically used to analyze the relationship between two variables when both variables are nominal, the two variables have been measured on different individuals and the observations on each variable are within-subjects in nature. The answer is  D. all of the above

The chi-square test of independence is a statistical test that is used to determine if there is a significant association between two categorical variables. It is commonly used when both variables are nominal, meaning they consist of categories or groups rather than numerical values.

When conducting the chi-square test of independence, the data is typically collected by measuring the two variables on different individuals or units.

For example, researchers may collect data on the gender (nominal variable) and political affiliation (nominal variable) of different individuals and analyze whether there is a relationship between the two variables.

The test examines the observed frequencies of the different categories in a contingency table and compares them to the expected frequencies under the assumption of independence. If the observed and expected frequencies significantly differ, it suggests that there is an association between the two variables.

Therefore, the chi-square test of independence is applicable when both variables are nominal and the data is collected on different individuals. This allows researchers to investigate the relationship between the variables and determine if they are associated or independent.

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Answer:

Step-by-step explanation:

\(\frac{a^{3}.b^4.5^4}{b^2.5}\\ = a^3.b^2.5^3\\= 125a^3b^2\)

\( { {a}^{3} } \times {b}^{2} \times 125\)

When dividing variables with exponents, subtract the bottom exponent from the top. since there is no "a" in the denominator, we would leave it as is. The "b" at the top (numerator) has an exponent of 4, and the one in the bottom (denominator) has an exponent of 2, so we would do 4 - 2, which equals 2, so the exponent on b would be 2. Then, the exponent for 5 in the numerator is 4, and in the denominator, it's 1 (any number that with no visible exponent has an exponent of 1). 4 - 1 is 3, and 5^3 is 125.

Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.

A candy box is made from a piece of a cardboard that measures 43 × 23 inches.

Let squares of equal size will be cut out of each corner with the measure of x inches.  

Therefore, measures of each side of the candy box will become

Length = (43 - 2x)

Width   = (23 - 2x)

Height  = x

Now we have to calculate the value of x for which volume of the box should be maximum.

Volume (V) = Length×Width×Height

 =>V = (43 -2x)×(23 - 2x)×(x)

 =>V= [(43)×(23) - 46x - 86x + 4x²]×x

 =>V= [989 - 132x + 4x²]×x

 =>V= 4x³- 132x² + 989x

Now we find the derivative of V and equate it to 0

\(\frac{dV}{dx}\)= \(12x^{2} -264x+989\)=0

Now we get values of x by quadratic formula

x=(264±\(\sqrt{264^{2}-4.12.989 }\) )/24

=>x=(264±\(\sqrt{69696-47472}\))/24

=>x=(264+√22224)/24, and x=(264-√22224)/24

=>x=(264+149.07)/24 and x=(264-149.07)/24

=>x=17.212                  and x=4.79

Now we test it by second derivative test for the maximum volume.

\(\frac{d^{n}V }{dx}\)=24x-264

For x = 17.212

\(\frac{d^{n}V }{dx}\)=(24×17.212)-264=413.088-264=149.088

This value is > 0 so volume will be minimum.

For x = 4.79

\(\frac{d^{n}V }{dx}\)=(24×4.79)-264= -149.04

-149.04 < 0, so volume of the box will be maximum.

Therefore, for x = 4.79 inches volume of the box will be maximum.

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(Complete Question) is

A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from  each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum​ volume?

The value of the expression when n equals -8 is 61

Algebraic expressions are expressions made up of variables, constants and factors.

They also consist of mathematical operations sch as addition, subtraction, multiplication, division, etc

From the information given, we have;

h(n) = n²-3

For h(-8), we substitute the value do n as -8

h(-8) = (-8)^2 - 3

Find the square

h(-8) = 64 - 3

h(-8) = 61

Thus, the value of the expression when n equals -8 is 61

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Answer: cool

Step-by-step explanation:

Answer: ok

Step-by-step explanation: ok

\(\sqrt{169}<\sqrt{184}<\sqrt{196}\\\\\sqrt{13^2}<\sqrt{184}<\sqrt{14^2}\\\\13<\sqrt{184}<14\\\\\text{Answer}:\text{C}\)

The statement that is NOT equivalent to the others is option c. "P(0) = r."

In the context of polynomials, a factor of a polynomial is a term or expression that divides evenly into the polynomial. So, if (x - r) is a factor of P(x), it means that when P(x) is divided by (x - r), the remainder is zero. This is equivalent to saying that r is a zero or root of the polynomial P(x). In other words, if r is a zero of P(x), then P(r) = 0.

Option c, on the other hand, states that P(0) = r. This means that when x is equal to zero, the value of the polynomial P(x) is equal to r. This statement does not provide any information about whether (x - r) is a factor of P(x) or if r is a zero of P(x). It simply relates the value of the polynomial at x = 0 to the constant value r.

To summarize, options a, b, and d are equivalent because they all refer to the fact that r is a zero of the polynomial P(x), while option c does not provide the same information and is therefore not equivalent to the others.

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168 grams of the trace element will be collected by owen.

First, we need to calculate the volume of the container by using the formula for the volume of a cylinder: volume = pi * radius^2 * height. Plugging in the given values, we get: volume = 3.14 * 6.7^2 * 13.3 = 1733.29 cm^3

Then we can use the given proportion of 0.097 grams of the trace element per cubic centimeter of water to estimate the amount of trace element in the sample. Multiplying the volume of the container by the proportion of trace element in the water gives us: 1733.29 cm^3 * 0.097 g/cm^3 = 167.86 g

Thus, Owen has collected approximately 168 grams of the trace element. Rounding to the nearest tenth, the final answer is 168.0 grams.

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Answer:

5 5/9

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

Plug it into your calculator and you get -0.5

Answer:

\(\huge\boxed{\sf x = 10}\)

Step-by-step explanation:

Hypotenuse = x

Base = 4

Perpendicular = \(\sqrt{84}\)

Using Pythagoras Theorem:

\(\sf H^2 = P^2 + B^2\\\\ x^2 = (\sqrt{84} )^2 + (4)^2\\\\x^2 = 84 + 16\\\\x^2 = 100\\\\Taking \ sq \ root \ on \ both \ sides\\\\x = 10\\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

1) 100 degrees F

2) 50 degrees F

Step-by-step explanation:

its just simple subtraction

Answer:

The equation of the line is;

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

Substituting the values of the slope and coordinates;

Therefore, the equation of the line is;

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

The Gini index corresponding to the Lorenz curve L(x) = x¹² is 0.6. 35% of the total income is received by approximately 18.42% of the population.

The Lorenz curve represents the cumulative distribution of income across a population, while the Gini index measures income inequality. To calculate the Gini index, we need to find the area between the Lorenz curve and the line of perfect equality, which is represented by the diagonal line connecting the origin to the point (1, 1).

In the given Lorenz curve L(x) = x¹², we can integrate the curve from 0 to 1 to find the area between the curve and the line of perfect equality. By performing the integration, we get the Gini index value of 0.6. This indicates a moderate level of income inequality.

To determine the percentage of the population that receives 35% of the total income, we analyze the Lorenz curve. The x-axis represents the cumulative population percentage, while the y-axis represents the cumulative income percentage.

We locate the point on the Lorenz curve corresponding to 35% of the total income on the y-axis. From this point, we move horizontally to the Lorenz curve and then vertically downwards to the x-axis.

The corresponding population percentage is approximately 18.42%.

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To find the values of cosθ and sinθ for an angle of 154°, we can use the trigonometric identities and a calculator. Hence, the values of cosθ and sinθ for an angle of 154° are approximately -0.988 and 0.154, respectively.

1. cosθ:

cosθ = cos(154°)

Using a calculator, we find cos(154°) ≈ -0.988.

Therefore, cosθ ≈ -0.988 (rounded to the nearest hundredth).

2. sinθ:

sinθ = sin(154°)

Using a calculator, we find sin(154°) ≈ 0.154.

Therefore, sinθ ≈ 0.154 (rounded to the nearest hundredth).

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Answer:B

Step-by-step explanation:

Answer:

RA ≈ 43.42; m∠D ≈ 67°; m∠R ≈ 23°