I need help with #4 asap plsss

The simplified expression cos(2θ)/\(tan^2\) θ is equal to -1. None of the options provided (a, b, c, d, e) is the correct answer.

The expression cos(2θ)/\(tan^2\)θ can be simplified using trigonometric identities.

We'll start by expressing cos(2θ) and \(tan^2\)θin terms of sine and cosine. cos(2θ) = \(cos^2\)θ -\(sin^2\)θ

\(tan^2\)θ = \(sin^2\)θ/\(cos^2\)θ

Now, substituting these values back into the expression,

we have: cos(2θ)/\(tan^2\)θ = (\(cos^2\)θ - \(sin^2\)θ) / (\(sin^2\)θ / \(cos^2\)θ)

To simplify the expression,

we can multiply the numerator and denominator by

\(cos^2\)θ:= (\(cos^2\)θ - \(sin^2\)θ) × (\(cos^2\)θ / \(sin^2\)θ)

Expanding the numerator:

= (\(cos^2\)θ × \(cos^2\)θ - \(sin^2\)θ × \(cos^2\)θ) / \(sin^2\)θ

= (\(cos^4\)θ - \(sin^2\)θ × \(cos^2\)θ) / \(sin^2\)θ

Using the Pythagorean identity \(sin^2\)θ = 1 - \(cos^2\)θ :  

=(\(cos^4\)θ - (1 - \(cos^2\)θ) × \(cos^2\)θ) / (1 - \(cos^2\)θ)

= (2\(cos^4\)θ - \(cos^2\)θ) / (1 - \(cos^2\)θ).

At this point, we can rewrite the expression as:

2\(cos^2\)θ - 1 / (1 - \(cos^2\)θ)

Recognizing that : \(cos^2\)θ = 1 - \(sin^2\)θ

= 2(1 - \(sin^2\)θ) - 1 / (1 - (1 - \(sin^2\)θ))

= 2 - 2\(sin^2\)θ - 1 / (\(sin^2\)θ)

= 1 - 2\(sin^2\)θ / \(sin^2\)θ

= 1 - 2= -1

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Answer:

\(f(x) = \frac{x+5}{2} - 3\)

Step-by-step explanation

Let the unknown number be x

If the function adds 5 to the number, then;

f(x) = x + 5

If it is divide by 2;

f(x) = x+5/2

If it is then subtracted from 3;

\(f(x) = \frac{x+5}{2} - 3\)

Hence the required function will be \(f(x) = \frac{x+5}{2} - 3\)

Answer:

This number is rational because there is a repeating pattern. Following the decimal, there is one 0 then a 2. This process repeats by adding a 0 each time the number 2 is passed.

Step-by-step explanation:

Let the original cost be \( x\).

Profit= $187-x$

The profit is 120%, which means:

$\frac{(187-x)}{x}\times 100 = 120$

Solve to get:

$x=\frac{187\times 5}{11}=85$

The scalar field f such that g = ∇f for g(x) = ||x||x is f = ||x||. The gradient of f, denoted as ∇f, is a vector field that represents the rate of change of f at each point.

To find f, we need to integrate g with respect to x along a path from a reference point to the desired point. The path can be represented as a curve C.

The line integral of g along C is given by ∫g · dr, where dr is the differential displacement vector along C. Since g(x) = ||x||x, we can substitute g into the line integral equation.
∫g · dr = ∫(||x||x) · dr

In this case, we can choose the path C as a straight line from the origin to the point x. This makes the line integral path-independent.

Now, let's calculate the line integral:
∫(||x||x) · dr = ∫(||x||x1 + ||x||x2 + ||x||x3) · (dx1 + dx2 + dx3)

Using the properties of dot product and linearity, we can simplify the expression:
∫(||x||x) · dr = ∫(||x||dx1)x1 + ∫(||x||dx2)x2 + ∫(||x||dx3)x3

Since ||x|| is a constant along the path C, we can take it out of the integral:

∫(||x||dx1)x1 + ∫(||x||dx2)x2 + ∫(||x||dx3)x3 = ||x|| ∫dx1 x1 + ||x|| ∫dx2 x2 + ||x|| ∫dx3 x3

Integrating dx1, dx2, and dx3 gives:
||x||x1 + ||x||x2 + ||x||x3 = g(x)

Comparing this result with g(x) = ||x||x, we see that f = ||x|| satisfies g = ∇f.

Therefore, the scalar field f such that g = ∇f for g(x) = ||x||x is f = ||x||.

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The given curve is y = x³ − 2x and it has to be rotated about the x-axis to find the area of the surface. The formula to find the surface area of a curve obtained by rotating about the x-axis is given by:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
$$Differentiating the curve with respect to x, we get:$$
y = x^3 - 2x
$$$$
\frac{dy}{dx} = 3x^2 - 2$$Now, squaring it, we get:$$
\left(\frac{dy}{dx}\right)^2 = 9x^4 - 12x^2 + 4$$$$
1 + \left(\frac{dy}{dx}\right)^2 = 1 + 9x^4 - 12x^2 + 4$$$$
= 9x^4 - 12x^2 + 5$$Putting the values in the formula, we get:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 12x^2 + 5} dx$$Simplifying it further, we get:$$
A = 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{(3x^2 - 1)^2 + 4} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 6x^2 + 5} dx$$Now, substituting $9x^4 - 6x^2 + 5 = t^2$, we get:$$(18x^3 - 12x)dx = tdt$$$$
(3x^2 - 2)dx = \frac{tdt}{3}$$When $x = -1$, $t = \sqrt{20}$ and when $x = 2$, $t = 5\sqrt{5}$Substituting the values in the formula, we get:$$
A = 2\pi \int_{\sqrt{20}}^{5\sqrt{5}} \frac{t^2}{27} dt$$$$
= \frac{28\pi}{27} \left[ t^3 \right]_{\sqrt{20}}^{5\sqrt{5}}$$$$
= \frac{28\pi}{27} \left[ 125\sqrt{5} - 20\sqrt{20} - 5\sqrt{5} + 2\sqrt{20} \right]$$$$
= \frac{28\pi}{27} \left[ 120\sqrt{5} - 18\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 9\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 18\sqrt{5} \right]$$$$
= \frac{56\pi}{27} \cdot 12\sqrt{5}$$$$
= \boxed{224\sqrt{5}\pi/3}$$Therefore, the area of the surface obtained by rotating the curve $y = x^3 - 2x$ about the x-axis is $\boxed{224\sqrt{5}\pi/3}$.

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The total area of the regions between the curves is 1.134π square units

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

x = ∛y

We have the interval to be

0 ≤ y ≤ 1

The area of the regions between the curves is then calculated using

\(A =2\pi \int\limits^a_b {f(x) * \sqrt{1 + (dy/dx)^2} } \, dx\)

From x = ∛y, we have

y = x³

Differentiate

dy/dx = 3x²

So, the area becomes

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + (3x^2)^2} } \, dx\)

Expand

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + 9x^4 } \, dx\)

Integrate

\(A =2\pi \frac{(9x^4 + 1)^{\frac{3}{2}}}{54}|\limits^1_0\)

Expand

\(A = 2\pi [\frac{(9(1)^4 + 1)^{\frac{3}{2}}}{54} - \frac{(9(0)^4 + 1)^{\frac{3}{2}}}{54}]\)

This gives

A = 2π * 0.5671

Evaluate the products

A = 1.1342π

Approximate

A = 1.134π

Hence, the total area of the regions between the curves is 1.134π square units

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Answer: 1/48

Step-by-step explanation:

Write 2.5/120 as a fraction , then rewrite it as 25/1200 simplify and get 1/48

Hope this helps!

The value of x is 8 and  the measure of the two marked angles is  60°.

When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

we know that ,

10x-20=7x+4   (it is corresponding opposite angle)

3x=24

x=8

the value of x is 8.

the measure of the two marked angles is 10*8-20= 80°-20°= 60°.

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Answer:

sum of five and 3 is divided by n

The expected value of a random variable is the measure of the central location of a random variable.

Expected value can be defined as the weighted average value of a random variable where the weights are the probability of occurrence of each value of the random variable. It is a measure of the central location of a random variable.

It represents the average value of a random variable that is expected to occur after an experiment has been conducted several times.

The formula for the expected value is: E(x) = ∑xP(x), where x represents the different values of the random variable, and P(x) represents the probability of occurrence of each value of the random variable x.

Summary:The expected value of a random variable is the measure of the central location of a random variable. It is the average value of a random variable that is expected to occur after an experiment has been conducted several times. The formula for the expected value is E(x) = ∑xP(x).

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Answer:

Step-by-step explanation:

80 inches = 6 feet and 8 inches

Answer: 120162518920000000

Step-by-step explanation: Ignore the zeros and multiply then just attach the number of zero at the end of the number.

Answer:

47 is the correct answer.

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

divide 473 by 10

473 divided by 10 = 47

Option B : The area of the rhombus is 119 square inches. It's important to note that the units of the sides and height are both in inches, so the units of area will be in square inches.

A rhombus is a four-sided polygon with equal sides and opposite angles that are congruent. To calculate the area of a rhombus, we use the formula (base x height) / 2, where the base is the length of one of its sides, and the height is the perpendicular distance between the base and the opposite side.

The area of a rhombus can be calculated by multiplying its base by its height and then dividing by 2.

In this case, the base of the rhombus is given as 17 inches, and the height is given as 14 inches. We simply substitute these values into the formula and simplify:

Area = (base x height) / 2

Area = (17 x 14) / 2

Area = 238 / 2

Area = 119 square inches

Therefore, the area of the rhombus is 119 square inches.

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A rhombus with a base of 17 inches and a height of 14 inches.

What is the area of the rhombus?

A. 62 in2

B. 119 in2

C. 124 in2

D, 238 in2

Answer:

D

Step-by-step explanation:

15 + 3x = 30

If Barry already made 15 subscriptions then we could remove 15 from 30.

30 - 15 = 15

Now, we have 15 subscriptions needed. We can multiply 3 times 5 that would equal 15.

15 + 15 = 30 subscriptions

Answer:

no sign (not positive or negative)

Step-by-step explanation:

The value of the expression

4.3 ⋅ (-3.2) ⋅ 0

is 0, as the value of any number multiplied by zero is 0.

The number zero is neither positive or negative; hence there is no sign.

The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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Answer:

1406.7 in^3

Explanation:

The volume of a cylinder with radius r and height h is given by

Now in our case h = 7 in, r = 16 /2 = 8 in, and in we use pi = 3.14, the above gives

which gives

Rounded to the nearest tenth this is

Answer:

The formula to calculate volume of a cylinder is given by the product of base area and its height. Volume of a cylinder = πr2h cubic units.

Step-by-step explanation:

To determine the number of gold atoms in the coin, we need to use the molar mass of gold and Avogadro's number. The number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

1. Find the molar mass of gold (Au):

The molar mass of gold is the atomic mass of gold, which can be found on the periodic table. The atomic mass of gold is approximately 197 g/mol.

2. Convert the mass of the coin to moles:

Number of moles = Mass / Molar mass

Number of moles = 3.5 g / 197 g/mol ≈ 0.01777 mol

3. Calculate the number of atoms:

Number of atoms = Number of moles × Avogadro's number

Number of atoms = 0.01777 mol × 6.022 × 10^23 atoms/mol ≈ 1.068 × 10^22 atoms

Therefore, the number of gold atoms in the coin is approximately 1.068 × 10^22 atoms. None of the provided options matches this value.

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On solving the equation 5/3k + 8 = 3, the value of unknown variable k is obtained as -3.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

5/3k + 8 = 3

Solve the equation.

Collect the like terms -

5/3k = 3 - 8

Use the arithmetic operation of subtraction -

5/3k = -5

Use the arithmetic operation of multiplication.

The fraction will reciprocate when shifted to RHS -

k = -5 × 3/5

k = -3

Therefore, the value of k is obtained as -3.

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The numerical length of BD is 20.

We have a Line Segment BD and a point C on it.

We have to determine the numerical length of BD.

A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

According to question, we have -

BD = 5x

BC = 4x

CD = 4

Now,

BD = BC + CD

5x = 4x + 4

x = 4

Therefore - BD = 5x = 5 x 4 = 20

Hence, the numerical length of BD is 40.

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Answer: $52.50

Step-by-step explanation: Divide 28.00 by 8. It would equal $3.50, and that's how much per gallon. Multiply 3.50 by 15. So, the final answer is $52.50.

The total sales in week 20 after the beginning of the advertising campaign was $3297.03

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Her sales in the first week were $86. After starting an online advertising campaign, her sales increased 20% the following week. This expression can be represented in the form of an exponential function:

y = abˣ

Where a is the initial value and b is the multiplication factor

Let y represent the total sales after x weeks. Comparing with the expression:

a = $86, b = 100% + 20% = 1.2. Hence:

y = 86(1.2)ˣ

After 20 weeks:

y = 86(1.2)²⁰ = 3297.03

The total sales was 3297.03

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Answer:

30 is the perimeter i think 2 x 5 = 10 + 2 x 4.5 = 10 x 2 = 20 so 20 + 10 = 30

I think the area is 45, 5 x 4.5 = 22.5 and 2 x 22.5 = 45

Wait for more responses if needed please.

Answer:

A) Yes, m=-3 and b = -3

Step-by-step explanation:

The m is the slope of the line and the b is the y-intercept. We can see that the y-intercept is at -3, so that means D and B are not the answer. This leaves us with A and C. The slope of the line is going down instead of up, meaning that the slope of the line is negative. This means that C is not the answer.

Therefore, the answer is A, m= -3 and b= -3.

Answer to 2a: The mean of Asset A is 0.235  and the variance is 0.0123

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

2a. Mean of Asset A (Expected Value):

The mean of Asset A (E(A)) can be calculated as:

\(\[E(A) = \sum_{i} (x_i \cdot P_i)\]\)

where \(\(x_i\)\) represents the return on Asset A in each state and\(v \(P_i\)\) represents the probability of that state.

Using the given information, we have:

Boom:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Average:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Bust:

\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)

Therefore, the mean of Asset A is\(\(E(A) = 0.235\).\)

2b. Correlation Coefficient of A and C:

The correlation coefficient\((\(\rho\))\)between Asset A and C can be calculated using the formula:

\(\[\rho = \frac{{\text{{Cov}}(A, C)}}{{\sigma_A \cdot \sigma_C}}\]\)

where\(\(\text{{Cov}}(A, C)\)\) represents the covariance between Asset A and C, and \((\sigma_A\)\) and\(\(\sigma_C\)\)represent the standard deviations of Asset A and C, respectively.

Using the given information, we have:

Boom:

\(\(\text{{Cov}}(A, C) = (0.35 - 0.235) \cdot (0.10 - 0.25) = -0.017\)\)

Average:

\(\(\text{{Cov}}(A, C) = (0.20 - 0.235) \cdot (0.15 - 0.25) = -0.005\)\)

Bust:

\(\(\text{{Cov}}(A, C) = (0.05 - 0.235) \cdot (0.35 - 0.25) = -0.017\)\)

Now, we calculate the standard deviations of Assets A and C:

\(\(\sigma_A = \sqrt{{\text{{Var}}(A)}} = \sqrt{0.0123} \approx 0.1108\)\)

\(\(\sigma_C = \sqrt{{\text{{Var}}(C)}} = \sqrt{0.0517} \approx 0.2274\)\)

Finally, we can calculate the correlation coefficient:

Boom:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Average:

\(\(\rho = \frac{{-0.005}}{{0.1108 \cdot 0.2274}} \approx -0.187\)\)

Bust:

\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)

Therefore, the correlation coefficient between Asset A and C is approximately\(\(\rho \approx -0.670\) (Boom), \(\rho \approx -0.187\) (Average), and \(\rho \approx -0.670\) (Bust).\)

Answer to 2a: \(The mean of Asset A is \(0.235\) and the variance is \(0.0123\.\)

Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).

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Answer:

The error was that -10+(-10) does not equal 0.

-10+(-10) = -10-10 = -20

Let me know if this helps!

Answer:

2m-17

Step-by-step explanation:

-20+1/4(8m+12)

-20+2m+3

2m-20+3

2m-17

the answer is -20+ (8m+12/4)