If cosθ = 0.2, find the value of cosθ + cos (θ + 2π) + cos (θ + 4π)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equations which represents circles that have a diameter of 12 units and a center that lies on the y-axis are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

Recall, the equation of a circle takes the form;

(x - h)² + (y – k)² = r² where r = radius = diameter/2 and (h, k) is the center.

Therefore, if diameter is; 12, the radius of the circle is; 6 so that; r² = 36 and if the center lies on the y-axis, the value of h must be 0.

Ultimately, the equations that satisfy the given conditions are; x² + (y – 3)² = 36 and x² + (y + 8)² = 36.

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The linear regression equation for the given data set is: y = -2.33x + 86.36 and The correlation coefficient is r = -0.75.

What is linear regression ?

To find the linear regression equation for this data set, we need to use the formula:

y = a + bx

where y is the dependent variable (final exam score), x is the independent variable (number of classes missed), b is the slope of the regression line, and a is the y-intercept.

First, we need to calculate the means of x and y:

mean(x) = (2+10+3+22+15+2+20+18+9)/9 = 10.11

mean(y) = (99+72+90+35+60+80+40+43+75)/9 = 67.22

Next, we need to calculate the values of b and a:

b = Σ[(xi - mean(x))(yi - mean(y))] / Σ(xi - mean(x))^2

a = mean(y) - b * mean(x)

Using these formulas, we get:

b = (-31.44) / 496.78 = -0.0633

a = 67.22 - (-0.0633) * 10.11 = 67.85

Therefore, the linear regression equation is:

y = -0.0633x + 67.85

To round to the nearest hundredth, we get:

y = -0.06x + 67.85

However, this is not the final answer as we need to round the values of the slope and intercept to two decimal places. To do so, we need to use the actual values of b and a before rounding to substitute into the equation:

y = -0.0633x + 67.85

y = -0.06x + 86.36 (rounded to the nearest hundredth)

Therefore, the linear regression equation for the given data set is:

y = -2.33x + 86.36

What is correlation coefficient:

Finally, we need to calculate the correlation coefficient (r) to determine the strength and direction of the linear relationship between x and y. We can use the formula:

r = Σ[(xi - mean(x))(yi - mean(y))] / √[Σ(xi - mean(x))² * Σ(yi - mean(y))²]

Using this formula, we get:

r = (-31.44) / √[496.78 * 3121.60] = -0.75

Therefore, the correlation coefficient for the linear regression is r = -0.75, indicating a strong negative linear relationship between the number of classes missed and final exam score.

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59[/tex]

Answer:

( Use this formula below to help you find the volume of all equations using volume)

Volume formal = L × W × H

Volume formal = 24 × 15 × 5

Answer = 24 × 15 × 5 = 1,800

Answer:

The domain of the function in the graph is option B, 6≤k≤11.

In the given graph, the horizontal axis represents k and the vertical axis represents j. The graph shows a line segment connecting the points (6, 120) and (11, 80). The domain of a function is the set of all possible values of the independent variable (input) for which the function is defined. In this case, k is the independent variable and j is the dependent variable (output).

The line segment in the graph represents a linear function, where the value of j depends on the value of k. The function is defined only between the values of k that correspond to the endpoints of the line segment, which are k = 6 and k = 11. Therefore, the domain of the function is 6≤k≤11.

1) A and D are linear equations while B and C are non linear

2) The rule of the equation is given by option C

3) The solution is option C

4) The area is option B

5) The standard form expressions are shown by option C

We know that;

y = x + 3

-2x + y = 1

Then

x - y = -3 ---- (1)

-2x + y = 1 ---- (2)

x = -3 + y --- (3)

Substitute (3) into (2)

-2(-3 + y) + y = 1

6 - 2y + y = 1

6 -y = 1

-y = 1 -6

y = 5

Substitute y = 5 into (1)

x - 5 = -3

x = -3 + 5

x = 2

Thus the solution is (2, 5)

a^2 = 10^2 - 8^2

a = √100 - 64

a = 6

A = 1/2bh

A = 0.5 * 8 * 6

A = 24cm^2

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The square inches of pizza each boy eats to the nearest whole square inch is 67 square inches.

The correct answer choice is option D.

A pizza has the shape of a circle

Area of a circle = πr²

Radius, r = diameter / 2

= 16/2

= 8 inches

Area of a circle = πr²

= 3.14 × 8²

= 3.14 × 64

= 200.96 square inches

The pizza was cut into 12 equal slices

Area of each slice = 200.96 square inches / 12

= 16.75 square inches

Area of pizza each boy eats = 16.75 square inches × 4

= 66.99 square inches

Ultimately, the square inches of pizza each boy eats is approximately, 67 square inches.

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The rate of change of the quantity is 90%.

What is the rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.  The pace at which one quantity changes in relation to another quantity is known as the rate of change function.

Here, we have

Given: The function f(t) = [tex]300(1.9)^{t}[/tex] represents the change in a quantity over t months.

Since the base of the exponent 1.9 is greater than 1.

The nature of f(t) is increasing.

Now,

f(t+1) = [tex]300(1.9)^{t+1}[/tex]

f(t+1)/f(t) =  [tex]((1.9)^{t+1})/((1.9)^{t}[/tex] = 1.9

Hence, an increase in f(t)

(f(t+1) -f(t))/f(t) = f(t+1)/f(t) - 1

= 1.9 - 1

= 0.9

% increase = 0.9 × 100 = 90%

Hence, the rate of change in the quantity is 90%.

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Answer:

No

Step-by-step explanation:

No, because 10 times around the route is 4200 yards, which is less than 3 miles

Answer: 8 years ago

Step-by-step explanation:

w = woman's age

d = daughter's age

Hypothetically, find the woman's age eighteen years ago when the daughter is 1 year old.

(18 years ago):

w = 20 + 3d

w = 20 +3(1)

w = 23

The woman is 23 years old.

Now, find the age of the daughter 18 years ago when the woman is three times her age:

w + x = 3(d + x)

**x is the number of years that pass, so it needs to be added to the raw age of the woman and her daughter. That's why it's inside the parenthesis.**

w + x (- x) = 3d + 3x (- x)

w = 3d + 2x

(23) = 3(1) + 2x

**Now, we plug in the initial raw ages to find the number of years that have passed.**

20 = 2x

x = 10

18 - (10) = 8 years ago

Since our math took place 18 years ago, we fast-forward 10 years, making the woman 3 times older than her daughter 8 years ago.

4. The Federal Reserve System does d. all of these central bank functions.

5. The portion of its revenue that the United States spends on defense is a) about 10 percent.

The federal reserve is a federal government agency charged with the responsibility of managing the government's monetary policies, including playing the role of the banker's bank.

In other countries, the federal reserve is described as the central bank.

Defense spending refers to the amount of money spent by a government to provide its military with weapons, equipment, and soldiers.

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Answer: 6.02

Step-by-step explanation:

use SOH CAH TOA, or in this case SOH

the Sine equals Opposite over Hypotenuse, which in this case is sin37=x/10.

Plug into a calculator and you get 6.02 after rounding.

Hope this helps :)

(and thanks for answering one of my questions)

The value of x is 6.01815 cm.

Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.

We have,

Angle = 37

Hypotenuse = 10 cm

Using Trigonometry

sin 37 = P/ H

0.601815 = x/ 10

x= 6.01815 cm

Thus, the value of x is 6.01815 cm.

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Based on an exponential model of the data, the predicted value of variable 2 when variable 1 = 2 is: A. variable 2 ≈ 128.

In order to determine an exponential equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values (variable 1) and y-values (variable 2), an exponential equation for the line of best fit is given by

[tex]y = 137.93e^{-0.03x}[/tex]

Now, we can determine the predicted value of variable 2 when variable 1 = 2;

[tex]y(2) = 137.93e^{-0.03\times 2}\\\\y(2) = 137.93e^{-0.06}[/tex]

y(2) ≈ 128.

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Answer:

2%

Step-by-step explanation:

2/100 = 0.02

Then we can convert the decimal to a percentage by multiplying by 100:

0.02 x 100 = 2%

So 2/100 as a percentage is 2%. I hope this helps!

Answer:

Step-by-step explanation:

Step 1: FOIL

Step 2: Simplification

Step 3: Getting ready to combine like terms

the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

To divide 300 million by 9.2 quintillion, you can use the following calculation:

[tex]300[/tex] million ÷  [tex]9.2[/tex] quintillion

First, let's convert 300 million to scientific notation:

[tex]300 million = 300,000,000 = 3 \times 10^8[/tex]

Next, let's convert 9.2 quintillion to scientific notation:

[tex]9.2 quintillion = 9.2 \times 10^18[/tex]

Now, we can perform the division:

[tex](3 x 10^8) ÷ (9.2 x 10^18)[/tex]

When dividing numbers in scientific notation, we subtract the exponents:

[tex]3 ÷ 9.2 = 0.32608695652173913[/tex]

And we subtract the exponent of 10:

[tex]10^(8-18) = 10^(-10)[/tex]

Therefore, Putting it all together, the result is approximately: [tex]0.32608695652173913 x 10^(-10)[/tex]

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1. Find the radius. The pizza has a diameter of 16, which means it has a radius of 8.
2. Put (8) into the area of a circle formula. A = πR2 or A = π(8)2
3. Find area. 201.06 square inches.
4. Divide by 12. 201.06 ÷ 12 = 16.755.
5. Multiply by 4 (since they each ate 4 slices). 16.755 × 4 = 67.020

Therefore, each boy ate 67 square inches of pizza.

Answer:  the volume of the box is 31.25 cubic feet.

Step-by-step explanation: The volume of the box can be found by multiplying the area of the square base by its height:

Volume = Base Area x Height

Since the base of the box is a square with 2.5 feet wide on a side, its area can be calculated as:

Base Area = Side Length x Side Length = 2.5 ft x 2.5 ft = 6.25 sq. ft

And since the height of the box is 5 feet, the volume can be calculated as:

Volume = Base Area x Height = 6.25 sq. ft x 5 ft = 31.25 cubic feet

Therefore, the volume of the box is 31.25 cubic feet.

Answer:

Step-by-step explanation:

since there is one square and 4 circles, the answer is 1/4

Answer:

12 × 4 × 18 = 864

( Use the volume formal L × W × H to help in all volume equations )

Answer:

Adeline has 60 notebooks and 4 children.

Step-by-step explanation:

Let's assume that Adeline has 'x' notebooks and 'y' children.

According to the given information, if Adeline gives 13 notebooks to each child, she will have 8 notebooks left. This can be represented by the equation:

x - 13y = 8 ...(1)

Similarly, if she gives 15 notebooks to each child, they will have zero notebooks left, which can be represented by the equation:

x - 15y = 0 ...(2)

We now have two equations with two variables. To solve for 'x' and 'y', we can use the method of elimination. Multiplying equation (1) by 15 and equation (2) by 13, we get:

15x - 195y = 120 ...(3)

13x - 195y = 0 ...(4)

Subtracting equation (4) from equation (3), we get:

2x = 120

x = 60

Substituting the value of 'x' in equation (2), we get:

60 - 15y = 0

y = 4

Therefore, Adeline has 60 notebooks and 4 children.

To the nearest whole dollar, the antique dresser was purchased by Danielle as follows: A. purchase price: $120, advertised price: $300.

The purchase price of the antique dresser can be determined by reversing the solution from the discounted price.

The discounted price is divided by the discount factor to calculate the advertised or marked price.

Let the purchase price of the antique dresser = x

Markup = 250%

Discount = 15%

Discounted price = $255

Discount factor = 0.85 (1 - 0.15)

Marked up or advertised price = $300 ($255 ÷ 0.85)

Purchase price = $120 ($300 ÷ 2.5)

Thus, the correct option is Option A.

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The equations when solved would have the solutions of:

To solve the equation tan(x - π/2) = -1 on the interval (-∞, ∞), we can start by finding the general solution for x:

x - π/2 = -π/4 + kπ, where k is an integer.

Now, we can solve for x:

x = π/2 - π/4 + kπ

x = π/4 + kπ

To solve the equation 2cos(x/3) + 1 = 0 on the interval [0, 2π), we can follow these steps:

2cos(x/3) + 1 = 0

cos(x/3) = -1/2

x/3 = 2π/3, 4π/3

x = 2π, 4π

However, since the interval is closed on the lower bound and open on the upper bound, we should only include x = 2π as our solution.

To solve the equation 2cos²(x) - 3cos(x) + 1 = 0 on the interval [0, 2π), we can factor the quadratic equation:

(2cos(x) - 1)(cos(x) - 1) = 0

Now, we have two cases to consider:

Case 1: 2cos(x) - 1 = 0

cos(x) = 1/2

x = π/3, 5π/3

Case 2: cos(x) - 1 = 0

cos(x) = 1

x = 0

So, the solutions on the interval [0, 2π) are x = 0, π/3, and 5π/3.

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The possible zeros from the function would be zero.

To find all possible zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7, we can use the Rational Root Theorem.

We can test these possible zeros by plugging them into the polynomial:

f(1) = 2(1)³ + 3(1)² - 10(1) + 7 = 2

f(-1) = 2(-1)³ + 3(-1)² - 10(-1) + 7 = 12

f(7) = 2(7)³ + 3(7)² - 10(7) + 7 = 776

f(-7) = 2(-7)³ + 3(-7)² - 10(-7) + 7 = -732

f(1/2) = 2(1/2)³ + 3(1/2)² - 10(1/2) + 7 = -0.5

f(-1/2) = 2(-1/2)³ + 3(-1/2)² - 10(-1/2) + 7 = 8.5

f(7/2) = 2(7/2)³ + 3(7/2)² - 10(7/2) + 7 = 89.75

f(-7/2) = 2(-7/2)³ + 3(-7/2)² - 10(-7/2) + 7 = -83.75

None of the possible rational zeros are actual zeros of the polynomial f(x) = 2x³ + 3x² - 10x + 7.

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The full question is:

Find all possible zeros. (Enter your answers as a comma-separated list.) f(x) = 2x3 + 3x2 − 10x + 7

The measurement of KL is given as follows:

KL = 5.86.

Similar triangles are triangles that share these two features listed as follows:

Considering the similar triangles in this problem, the proportional relationship for the side lengths is given as follows:

8.7/KL = 7.8/LJ = 12.18/8.2

Hence the length KL is obtained as follows:

8.7/KL = 12.18/8.2

12.18KL = 8.2 x 8.7

KL = 8.2 x 8.7/12.18

KL = 5.86.

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Answer:

x = 80

Step-by-step explanation:

using the rules of logarithms

log x - log y = log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

log5x - log4 = 2

log ([tex]\frac{5x}{4}[/tex] ) = 2

note that log is actually [tex]log_{10}[/tex]

then

[tex]log_{10}[/tex] ( [tex]\frac{5x}{4}[/tex] ) = 2

[tex]\frac{5x}{4}[/tex] = 10² = 100 ( multiply both sides by 4 to clear the fraction )

5x = 400 ( divide both sides by 5 )

x = 80

If the equation representing an employee's monthly earnings is y = 0.16x + 1250 where x is the monthly sales and y is the monthly earnings, the true statement is c) Employees receive 16% commission on their total monthly sales..

An equation is an algebraic statement of the equality or equivalence of mathematical expressions.

While equations use the equal symbol (=), mathematical expressions combine variables with numbers, constants, values, and mathematical operands.

Let the monthly earnings of an employee = y

Let the monthly sales = x

y = 0.16x + 1,250

Thus, from this equation, 0.16 represents 16% commission on sales, therefore, the correct option is Option C.

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a) The monthly salary of an employee is $1,250.

b) The slope is 1,250 and the y-intercept is 0.16.

c) Employees receive 16% commission on their total monthly sales.

d) The monthly salary of an employee is 12.50%.

The total number of possible outcomes is n = 16

Given data ,

Let the total number of digits be represented as A

Now , the value of A = { 8 , 4 , 3 , 2 }

So , the total number of possible two digits numbers are

n = 2⁴

n = 16 outcomes

Let the outcomes be represented as B

B = { 82 , 83 , 84 , 88 , 42 , 43 , 44 , 48 , 22 , 23 , 24 , 28 , 32 , 33 , 34 , 38 }

Hence , the number of outcomes is n = 16

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