HELP!! Prove that cos²A + cos²B + cos²C = 2 + sinAsinBsinC​

Answer:

I think its true although Im not sure

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

The time necessary for p dollars to double when it is invested at interest rate r compounded annually is given by the formula:

t = (ln 2) / (r ln (1 + r))

When compounded monthly, the formula becomes:

t = (ln 2) / (12 r ln (1 + r/12))

When compounded daily, the formula becomes:

t = (ln 2) / (365 r ln (1 + r/365))

When compounded continuously, the formula becomes:

t = ln 2 / (r)

Note that ln is the natural logarithm function.

To use these formulas, you need to know the value of the interest rate r. For example, if r is 5%, then:

When compounded annually, t = (ln 2) / (0.05 ln 1.05) = 13.86 years
When compounded monthly, t = (ln 2) / (12 x 0.05 ln 1.0041) = 14.21 years
When compounded daily, t = (ln 2) / (365 x 0.05 ln 1.000137) = 14.27 years
When compounded continuously, t = ln 2 / (0.05) = 13.86 years

Therefore, the time necessary for p dollars to double depends on the interest rate and the frequency of compounding. Generally, the more frequently the interest is compounded, the shorter the time necessary for p dollars to double.

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The probability that none of the employees in the sample work at the plant in hawai is 0.0112

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

PH= 20/60 = 1/3

P(T) = 2/3

It is hypergeometric distribution

P(X=k)={\frac {{\binom {K}{k}}{\binom {N-K}{n-k}}}{\binom {N}{n}}},

where

N = 60

K = 20 for Hawai; 40 for Texas

n = 10

P(X=0) = 0.0112

Hence The probability that none of the employees in the sample work at the plant in hawai is 0.0112

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Answer:

Yes

Step-by-step explanation:

Both quadrilaterals have two triangles. The triangles that coordinate with the triangles in the other quadrilateral are proven congruent by AAS and AA. That makes the quadrilaterals congruent.

Based on the provided information, the ownership costs for a scraper include the purchase cost of $162,000 (including tires), salvage value of $32,400, and repair costs at 120% of depreciation, while the operating costs consist of fuel cost at $3.90 per gallon with a consumption rate of 0.06 gallons per horsepower per hour, power utilization at 85%, and a use factor of 66.67%, with additional expenses for air filter changes every 200 hours.

In order to determine the ownership and operating costs for a scraper, several pieces of information need to be considered.

Ownership Costs:

Purchase Cost:

The scraper's purchase cost is $162,000, which includes the cost of tires.

Salvage Value:

The estimated salvage value of the scraper is $32,400.

Useful Life:

The scraper has a useful life of 6 years, with an expected usage of 1,400 hours per year.

Tire Life:

The tires of the scraper have a lifespan of 3,500 hours.

Repair Costs:

Repairs to the equipment are estimated to be 120% of the depreciation.

Air Filter:

The air filter needs to be changed every 200 hours and costs $17.00 per change.

Operating Costs:

Fuel Cost:

The fuel cost is $3.90 per gallon, and the scraper's fuel consumption rate is 0.06 gallons per horsepower per hour.

Power Utilization:

The scraper's power utilization, or operating factor, is 85%, meaning it operates 85% of the time.

Use Factor:

The scraper is used for 40 minutes per hour, which is approximately 66.67% of the time.

Rental Costs:

To determine the rental costs of a telescoping forklift, it is necessary to contact a local equipment rental company to obtain the monthly rental rate and information about what costs are included in the rental and what costs the renter must cover additionally.

Supplier Information:

By visiting or contacting a local equipment supplier, one can gather more information about ownership and operation costs specific to the equipment, including any additional costs, maintenance requirements, and available warranties.

In summary, the ownership costs of the scraper include the purchase cost, salvage value, useful life, tire life, repair costs, and air filter expenses, while the operating costs encompass fuel costs, power utilization, and use factor.

The rental costs and additional expenses for a telescoping forklift can be obtained from a local equipment rental company, and more detailed information can be obtained from a local equipment supplier.

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Answer: 8, 754.72

Step-by-step explanation:

Take the present value of the car, then add 22%. The car had only been owned for a year, so the value only depreciated 22%.

Hope this helps! :)

Answer:

r can be 0.5

Step-by-step explanation:

Here, we want to get a possible value of r

From the question, the value of r is between 0 and 3

Mathematically, we know that in degrees pi is the same as 180 degrees

In a case where we have r = 1/2

we have it that;

cos(pi/2) = 2 cos (pi/2)

Since pi/2 is 90 and cos 90 is zero; then we have it that the two sides of the equation is the same and r can be 1/2

It is an illustration of theoretical probability.

Theoretical probability establishes the probability of certain events occurring.

The ratio of the entire number of conceivable possibilities to the intended outcome is known as theoretical probability.

In this case, the intended consequence is earning a 2, which is only one of the six potential possibilities. The possibility of receiving a 2 is.

Observance determines empirical probability. Nothing about the observing of the specified episode is indicated in the question, hence it is not an empirical probability.

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Answer:

Hamburger:  $3.75 each

Soda:  $1.25 each

Step-by-step explanation:

(cost of 2 hamburgers) + (cost of 1 soda) = (total expenditure of $8.75).

Letting s represent the cost of a soda and h the cost of a hamburger in terms of the cost of a soda results in the system

h = s + $2.50

2h + 1s = $8.75

Use the substitution method.  In the second equation replace h with s + $2.50:

2(s + $2.50) + 1s = $8.75, or

2s + $5.00 + 1s = $8.75

Then 3s = $3.75, and s = $1.25.  A soda costs $1.25.

Since h = s + $2.50, we learn that a hamburger costs $1.25 + $2.50, or $3.75.

Hamburger:  $3.75 each

Soda:  $1.25 each

Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

Answer:

2 dollars

72 dollars

Step-by-step explanation:

im not completely sure

Answer:

Arianna paid $2.75 for each photo coaster. If she purchased three dozen photo coasters, how much did she spend? $99.00

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

.......................

The goal of maximizing sustainable yield is to find the optimum population size and yield that can be sustained over time. In this case, given the information provided, the optimum population size and yield is 8,750 fish and 750 fish per year respectively.

The first step in finding the optimum population size and yield is to calculate the maximum sustainable yield (MSY) using the equation MSY = 0.5 x R. In this case, R = 10,500 fish, and thus MSY = 0.5 x 10,500 = 5,250 fish. This is the number of fish that can be harvested each year without over-harvesting the population and depleting its resources.
However, the current population size of 3,250 fish is below the MSY, indicating that the population size is already being over-harvested. Therefore, to increase the sustainable yield and maximize it, the population size must be increased.

The optimum population size to maximize the sustainable yield is calculated using the equation:
Optimum Population Size = MSY + (1 - harvest rate) x (current population size - MSY).
In this case, the harvest rate is 1300/10,500 = 0.124. Therefore, the optimum population size is 8,750 fish.
Once the optimum population size is known, the yield can be determined by subtracting the current population size from the optimum population size. In this case, the optimum yield is 8,750 - 3,250 = 5,500 fish. However, since the harvest rate is uniformly distributed throughout the year, the sustainable yield is 750 fish per year (5,500/7.5).

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Answer:

Step-by-step explanation:

A person who never dreams will never be able to reach anywhere. Thus, dreams stand to be the driving forces behind success. It keeps you moving ahead, without which you would have led a life of a corpse. Consequently, dreaming isn’t just enough! You ought to put your hard work, determination, dedication, too, in reaching the goal. These three elements are essential to help you achieve all that you have craved for! Hard work has no substitute, and there is no shortcut either! Besides, consistency plays a vital role in deciding your success. Distractions are sure to interrupt your path, but it is essential to understand that you must never get carried away by them. Therefore, only if you have a clear vision, you will be able to reach the destination. Last but not the least, it is important to understand that in order to achieve something, you need to have faith in yourself. Keep that belief upon yourself and only then will you be able to fetch success.

Step-by-step explanation:

2² * 3 * 5 = 4 * 3 * 5 = 60.

3² * 5² = 9 * 25 = 225.

Answer:

A) 60

B) 225

Step-by-step explanation:

A) The factorization of a number is finding the factors that, when multiplied together, form the original number. As an example, one instance of the factorization of 24 would be 6 and 4, since 6 × 4 = 24.

The prime factorization of a number is finding the factors of a number and restricting them to only include primes, which are numbers with no other factors except themselves and 1.

Hence, all you have to do for A) is to multiply all the factors together, which is \(2^{2} \cdot 3 \cdot 5\), which equates to 60.

B) Since this three-digit number has 5 as a prime factor, it has to end in a 5 or 0. This narrows our search hugely.

Accounting for the fact it has a 3 as a prime factor, the number has 3 × 5 = 15 as a factor. This yet again narrows our search hugely.

Finally, to find the square number, there is actually a really simple way of doing this; simply square 15 to get 225. We can confirm this is a square number because we squared 15 to get that number; hence, 225 is an answer.

Hope this helped!

Simultaneous equation is a finite set of equations for which common solutions are soughtThe equivalent expression is 5x + 7y = 37

A finite set of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Given the simultaneous equation below:

-2x - y = -4

7x + 8y = 41

In order to compress the equation into 1, we need to add the equation or subtract the equation

On adding, we will have:

(-2x + 7x) + (-y + 8y) = -4 + 41

5x + 7y = 37

Hence the equivalent expression is 5x + 7y = 37

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Answer:

A. 12.5 cups of coffee

B. 6.96 cups of milk

Those are the only ones I have the brain power to do so..........

Hope this helped!!!

Answer:

(4)

Step-by-step explanation:

you times the thing by the thing and then go boom because 3 x 4 - 2 = 10 ez ez gg

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Answer:

Step-by-step explanation:

∠b  & ∠g  are consecutive exterior angles

∠e & ∠c are alternate interior angles.

∠b and ∠f are corresponding angles.

∠h and ∠c are supplementary angles.

Option D) is correct. The equation representing the above sequence is   f(x) = f(x-1) - 6.

According to the question we have been the sequence

                             2, -4, -10, -16,.......

Here,  a₁ = 2                        a₃ = -10

        a₂ = -4                        a₄ = -16

Thus, difference between the first two terms is:

         d = a₂ - a₁

            = -4 - 2 = -6

Similarly difference between the second third term is :

            d = a₃ - a₂ = -10 - (-4) = -10 + 4 = -6

We will see that the difference between the terms is constant that is

                    d = -6

We know that ,   aₙ = aₙ₋₁ + d

putting the value of d in the above formula we get

     aₙ = aₙ₋₁ + (-6)

     aₙ = aₙ₋₁ -6

Also can be written as :

  f(x) = f(x-1) - 6

That is option D) is correct. The equation representing the above sequence is   f(x) = f(x-1) - 6.

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Answer:

Good luck with math this year. Study hard for tests

Step-by-step explanation:

See the image.

Answer: 32.75

Step-by-step explanation:

So you can break this trapezoid into two parts: a square and a triangle. the square has an area of 25 square feet. For the triangle, we can just use 3.1 (the base) * 5 (the height)/2 because the triangle is just a half of a rectangle, so we can just treat it as a normal rectangle, but them divide by two at the end. so 3.1*5/2 = 7.75 square feet, and 25 + 7.75 square feet = 32.75 square feet

Answer:

4,365,421,006

4,000,000,000  

300,000,000  

60,000,000  

5,000,000  

400,000  

20,000  

1,000  

0  

0  

6

Explanation:

You're basically going from each number starting from left to right and naming out their placements.

Answer:

x1=\(\frac{-1-13}{3}\), x2=\(\frac{-1+13}{3}\)

Step-by-step explanation:

Answer:

∠D = 56°

∠D = 180° - (35° + 89°) = 56°