solve the equation for exact solutions in the interval (0-360). use an algebraic method
(cot(theta) - square root of 3) (square root of 2)sin(theta)+1) = 0
solution set=?

Part a: The expression that represents the area of the rectangle is A = (3x + 5)(6x + 11). To calculate the area, we must multiply the two sides of the rectangle together. The length of the rectangle is 3x + 5 units and the width of the rectangle is 6x + 11 units. Therefore, the area is (3x + 5)(6x + 11).

Part b: The degree of the expression obtained in part a is 2 and the classification is a binomial.

Part c: The closure property for polynomials states that the result of combining two polynomials is also a polynomial. In part a, we combined two polynomials, 3x + 5 and 6x + 11, to form the expression (3x + 5)(6x + 11). This expression is also a polynomial, demonstrating the closure property for polynomials. The closure property for polynomials allows us to combine two polynomials and still have a polynomial as the result. This is important in mathematics because it allows us to simplify equations and solve problems more quickly and efficiently.

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Answer: there is no solution

Step-by-step explanation: 1/4z — 13 is not the same as 1/4 + 13

Say z = 1 that would simplify as -12 3/4 = 13 1/4 they are not the same so there is no solution

\(k \begin{bmatrix} 2&3\\5&6 \end{bmatrix}~~ = ~~ \begin{bmatrix} 6&9\\15&18 \end{bmatrix}\implies \begin{bmatrix} 2k&3k\\5k&6k \end{bmatrix}~~ = ~~ \begin{bmatrix} 6&9\\15&18 \end{bmatrix} \\\\\\ 2k=6\implies k=\cfrac{6}{2}\implies k=3\)

In the sequence of file folders, the number of yellow folders increases by 2 at each step. We can model this pattern using a linear function, where the number of yellow folders Y(n) at step n can be represented as Y(n) = 2n.

By observing the sequence of file folders, we can identify a pattern that the number of yellow folders increases by 2 at each step. This means that for each step n, the number of yellow folders Y(n) can be obtained by multiplying the step number n by 2.

Therefore, we can model the relationship between the step number and the number of yellow folders using a linear function. The function Y(n) = 2n represents this pattern, where Y(n) denotes the number of yellow folders at step n.

For example, at step 1, we have Y(1) = 2(1) = 2 yellow folders. At step 2, we have Y(2) = 2(2) = 4 yellow folders, and so on.

This linear model accurately captures the pattern observed in the sequence of file folders, where the number of yellow folders increases by 2 at each step.

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Answer:

B.(x-y)(x+y)

Step-by-step explanation:

The factor of x² - y² can be represented by,

A.(x - y)²

INCORRECT:

Translated to (x - y)(x - y) as the exponent says it multiplied by it self

(x - y)(x - y) = x²- 2xy + y² which doesn't match

B.(x-y)(x+y)

Correct!

x times x =  x²

-y times y = -y²

x² - y²

C.(x+y)(x+y)

INCORRECT

x times x =  x²

y times y = y²

x² + y² which doesn't match as y positive here

D.2(x - y)

INCORRECT

distribute 2 so 2x - 2y which isn't the original

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The value of the expression, [9(10 - 2)] ÷ [2 + (5 × 2)], found using PEMDAS order of operations is 6

A mathematical expression is a mathematical statement which consists of two or more numbers or variables that are linked by mathematical operators.

The possible expression in the question is presented as follows;

[9(10 - 2)] ÷ [2 + (5 × 2)]

The above expression can be evaluated using the order of operations convention, which is a set of rules used in mathematics and computer programming, that indicates the procedure which comes first when evaluating a mathematical expression.

The rules can be memorized using mnemonics like PEMDAS that represents;

PEMDAS indicates that operations within a parentheses is to be performed first, before exponents, which comes before multiplication, followed by division then addition before subtraction.

The convention aims to remove ambiguity, such that the expression 1 + 2 × 3 = 1 + (2 × 3)

To evaluate the given expression, we therefore have;

[9(10 - 2)] ÷ [2 + (5 × 2)]

Performing operations within the parentheses gives;

[9(10 - 2)] ÷ [2 + (5 × 2)] = [9(8)] ÷ [2 + (10)]

[9(8)] ÷ [2 + (10)] = [9×8] ÷ [2 + 10]

[9×8] ÷ [2 + 10] = 72 ÷ 12

There are no exponents, (E), or further multiplication, (M), outside the parentheses, therefore performing the, division, (D) gives;

\(\displaystyle{ 72 \div 12 = \frac{72}{12} =6}\)

The value of the expression is therefore;

[9(10 - 2)] ÷ [2 + (5 × 2)] = 6

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I Hope it is correct

Step-by-step explanation:

The total number of sodas in the fridge is:

6 + 4 + 5 + 9 + 7 + 3 + 6 = 40

The number of NuGrapes or ginger ales is:

7 (NuGrapes) + 6 (Canada Dry ginger ales) = 13

The probability of selecting a NuGrape or a ginger ale is the number of favorable outcomes (selecting a NuGrape or a ginger ale) divided by the total number of possible outcomes (selecting any soda):

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 13 / 40

Probability = 0.325

So, the probability of selecting a NuGrape or a ginger ale is 0.325 or 32.5%.

Answer:

t = 6.15 seconds

Step-by-step explanation:

A ball is thrown upward with an initial velocity of 35 meters per second from a cliff that is 30 meters high. The height of the ball is given by the quadratic equation h=-4.9t^2+35t+30 where h is in meters and t in the time in seconds since the ball was thrown, find the time it takes the ball to hit the ground. Round you answer to the nearest tenth of a second.

-----------------

h(t) =-4.9t^2+35t+30

----

When the ball hits the ground its height is zero.

So, solve -4.9t^2+35t+30 = 0

Use the quadratic formula:

t = [-35 +- sqrt(35^2-4*-4.9*30)]/(2(-4.9))

----

t = [-35 +- sqrt(637)]/(-9.8)

---

To get a positive solution:

t = [-35-25.24]/(-9.8)

t = 6.15 seconds

========================

Answer:

The ball hits the ground when h(t) (the height) is equal to 0.

0=-4.9t^2+30t

0=t(-4.9t+30)

t=0 and t=6.1224…

So, the ball hits the ground when it is thrown (0 seconds) and after about 6.1224 seconds.

:)

The equation that can be used to determine the amount of dirt on the floor after 6 passes is 20 x 0.750^6 ≈ 3.56 oz.

The equation that can be used to determine the amount of dirt left after 6 passes is an exponential equation. Exponential equations have the form:

Amount of dirt left = p(1 - r)^n

Where:

20(1 - 0.25)^6

20(0.75^6) = 3.56 oz

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Rounding up to the nearest integer, we get a sample size of 1068. Therefore, the answer is 1068.

To find the required sample size, we need to use the formula for the margin of error of a proportion:

Margin of error = z*sqrt(p(1-p)/n)

where z is the z-score for the desired level of confidence, p is the estimated proportion, and n is the sample size.

Since we want the confidence interval to have a width of 0.06, the margin of error should be 0.03. Also, since the scientists believe that about half of all people with the blood disorder will benefit from the drug, we can estimate p as 0.5. Finally, we can use a z-score of 1.96 for a 95% confidence interval.

Substituting these values into the formula, we get:

0.03 = 1.96sqrt(0.5(1-0.5)/n)

Solving for n, we get:

n = (1.96/0.03)^20.5(1-0.5) = 1067.11

Rounding up to the nearest integer, we get a sample size of 1068. Therefore, the answer is 1068.

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Answer: 20.1

Step-by-step explanation: Based on triangle sum theorem all angles add up to 180. 3x-11+6x-10+x=180

Combine like terms. 10x-21=180

Add 21 to both sides. 10x=201

Divide by 10 on both sides. X=20.1

The merger profitable is c ≤ 2.5. The value of c that makes the price decrease is c > 0.

1) Value for c such that the merger becomes profitable:

To calculate the value of c that makes the merger profitable, we must follow the following steps:

First, let's calculate the total output of the industry, which is:

Q = q1 + q2 + q3 + q4

Second, we must determine the total cost of production (TC) of each firm, which is:

TC = C*q,

where C is the marginal cost of each firm.

Third, we must determine the total cost of production of the industry, which is:

TC = C*(q1 + q2 + q3 + q4)

Fourth, we must determine the total revenue of the industry, which is:

TR = P*Q, where P = 10 - Q

Then, we can calculate the profit (Π) of each firm, which is given by:

Π = TR - TC

And, finally, we can calculate the total profit (Π) of the industry, which is given by:

Π = TR - TC * 4, where 4 is the number of firms in the industry.

Now, let's substitute the expressions we found for TR and TC into the equation for Π:

Π = (10 - Q)*Q - C*(q1 + q2 + q3 + q4) * 4

Π = (10 - (q1 + q2 + q3 + q4))*(q1 + q2 + q3 + q4) - C*(q1 + q2 + q3 + q4) * 4

Π = (10 - Q)*(Q) - C*Q * 4

Π = 10Q - Q² - 4CQ

Now, we must differentiate Π with respect to Q and equate it to zero to find the value of Q that maximizes profit:

Π' = 10 - 2Q - 4C = 0

Π' = 10 - 2(Q) - 4(C)

= 0Q

= 5 - 2C

The value of c that makes the merger profitable is c ≤ 2.5.

To verify that this is true, we can substitute this value of Q into the equation for Π and check if it is positive:

Π = 10Q - Q² - 4CQ

Π = 10(5 - 2C) - (5 - 2C)² - 4C(5 - 2C)

Π = 50 - 20C - (25 - 20C + 4C²) - 20C + 8C²

Π = 3C² - 30C + 25

Π = 3(C - 2.5)² - 3.75

Since Π is positive for c ≤ 2.5, the merger is profitable for c ≤ 2.5.2) Value for c such that the price decreases post-merger:

To calculate the value of c that makes the price decrease after the merger, we must follow the following steps:

First, let's calculate the output of each firm before the merger, which is given by:

q = (10 - C - q)/3, where q is the output of each firm.

Second, let's calculate the total output of the industry before the merger, which is given by:

Q = 4q

Third, let's calculate the price before the merger, which is given by:

P = 10 - Q

Substituting Q and q into this equation, we get:

P = 10 - 4q

Since the firms have the same marginal cost, their output levels are the same.

Thus, after the merger, the new output level of the merged firm is Q' = 4Q/2 = 2Q, and the price is given by:

P' = 10 - Q'

To find the value of c that makes the price decrease, we must compare P and P':

P = 10 - 4c/3

P' = 10 - 8c/3

To find the value of c that makes P' < P, we must solve the inequality:

P' < P

P' - P < 0-8c/3 + 4c/3 < 0-4c/3 < 0c > 0

Thus, the value of c that makes the price decrease is c > 0.

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Step-by-step explanation:

x-3/4=5 1/6

(4x-3)/4=31/6

(4x-3)/2=31/3

12x-9=62

12x=71

X=71/12

a)f(x)=2x-10 = y = 2    b) g(x) = 2x^2-3 = y = 4

Answer:

2 5/12

Step-by-step explanation:

You put it so that the denominators are the same so in this case I used 12 as the denominator and used the rule for each. Next I subtracted 3 9/12 minus 1 4/12 and got 2 5/12

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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In response to the question, we may say that  As a result, the angle of trigonometry inclination of the ramp is 4 degrees, to the closest degree.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. Consequently, studying geometry entails learning about the characteristics of all geometric forms.

The ratio of an angle's opposing side (such as the rise of a ramp) to its adjacent side is known as the tangent (the length of the ramp).

Angle's tangent is equal to its opposite and adjacent sides.

In this instance, the ramp's opposite side represents its 3/4-foot rise, and the ramp's adjacent side is its 12-foot length.

Angle's tangent is equal to 3/4 / 12 (or 0.0625).

We may take the inverse tangent (or arctangent) of this number to determine the angle itself.

Amount = arctan (0.0625)

Calculating the answer, we obtain:

Angle is 3.58 9 degrees.

When we convert this to degrees, we get:

a 4 degree angle

As a result, the angle of inclination of the ramp is 4 degrees, to the closest degree.

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Answer:

1- c:25

2-cant help

3- A:2,8

4-cant help

To obtain a sample of 500 sales invoices from the given population of 5,000 invoices separated into four strata, you can use stratified random sampling.

In stratified random sampling, we divide the population into different groups or strata based on certain characteristics. The goal is to ensure that each stratum is represented in the sample proportionally to its size in the population.
In this case, we have four strata with different numbers of invoices. To calculate the sample size for each stratum, we use the formula:
Sample size for a stratum = (Size of the stratum / Total size of the population) x Desired sample size
For stratum 1: (50 / 5,000) x 500 = 5
For stratum 2: (500 / 5,000) x 500 = 50
For stratum 3: (1,000 / 5,000) x 500 = 100
For stratum 4: (3,450 / 5,000) x 500 = 345
Therefore, the sample size for each stratum is 5, 50, 100, and 345 invoices, respectively.

By selecting invoices randomly within each stratum according to their proportional sample size, you will have a representative sample of 500 invoices from the population.

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The debt-equity ratio is  0.726 : 1 or 72.64%

Debt is the product of debt ratio and total equity

Debt = debt ratio × total equity

We have been given that

Asset turnover = 1.84

Profit margin = 5.1%

Return on equity of 16.2 percent

Let we have to assume that sales are $100.

Therefore net Income = 100×0.051 = 5.1

Total Assets = 100/0.84

Total Assets = 54.35

⇒ 0.162 = 5.1 / Total equity

⇒ Total Equity = 5.1 / 0.162

⇒ Total Equity = 31.48

Total assets = Total debt + Total equity

⇒ 54.35 = Total debt + 31.48

⇒ Total debt = 54.35 - 31.48

⇒ Total debt = 22.87

The debt-equity ratio = 22.87 / 31.48

The debt-equity ratio = 0.72649 : 1 or 72.649%

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The probability that it will rain on exactly one of the five days is approximately 0.395 .

To find the probability that it will rain on exactly one of the five days, we can use the binomial probability formula.

The probability of rain on any given day is 1/4, and we want to find the probability of rain on exactly one day out of the five.

Using the binomial probability formula, the probability of rain on exactly one day can be calculated as follows:

P(X = 1) = C(5, 1) * (1/4)^1 * (3/4)^4

where C(5, 1) represents the number of ways to choose one day out of the five.

C(5, 1) = 5! / (1! * (5-1)!) = 5

Plugging in the values, we have:

P(X = 1) = 5 * (1/4)^1 * (3/4)^4

Calculating this expression gives us approximately 0.395 .

Therefore, the probability that it will rain on exactly one of the five days they are there is approximately 0.395 , rounded to the nearest thousandth.

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Step-by-step explanation:

b)

make it braintliest please

Answer:

490,000 grams

Step-by-step explanation:

To convert from kilograms to grams - multiply the number of kilograms by 1000. (there are 1000 grams in a kilogram)

\(490 * 1000 = 490,000\)

Answer:

490000

Step-by-step explanation:

1 kg : 1000 gram

So,

490 kilograms : 490 ×1000 grams

: 490000 grams

Answer: x>2.7

Step-by-step explanation:

Answer:

153 units²

Step-by-step explanation:

Area of a Parallelogram: L x W (same as a rectangle)

L x W = A

17 x 9 = A

A = 153

The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.

Using ratio to solve, find the ratio of candle length to the time taken to burn down

let

4 1/2 : 9 = 4 1/4 : x

9/2 ÷ 9 = 17/4 ÷ x

9/2 × 1/9 = 17/4 × 1/x

1/2 = 17/4x

1 × 4x = 2 × 17

4x = 34

x = 34/4

x = 8.5 hours

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Answer:

c 89+42x+42y

Step-by-step explanation:

On day 1 :

First Machine= 89 stickers

Second Machine= none

On day 2 :

First Machine= ? stickers ( if in 1min = 42stickers

x min=?

( x min/1 min × 42stickers)

=42x stickers.

Second Machine=?stickers ( if in 1min = 42stickers

y min=?

( y min/1 min × 42stickers)

=42y stickers.

Total = 89 + 42x + 42y

Answer:

3!*7+12-2=

(3*2*1)*7+12-2=

6*7+12-2=

42+12-2=

54-2=

52