2.
12
Bo
5
13
xº
Which measures shown in the triangle are
equivalent to ? (MGSE9-12.G.SRT.6)
5
13
A. sin a Only
B. cos ß Only
C. sin a and cos B
D. sin ß and cos a

Answer:

16.9265381881

Step-by-step explanation:

Tangent = Opposite/Adjacent.

Thus, tan62 = x/9 --> tan62 = 1.88072646535, multiply by 9 to get x, 1.88072646535* 9 = 16.9265381881

After approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

The value of shares t years after their floatation on the stock market, is modelled by V = 10e0.09t

The initial value of shares = V when t = 0. So, putting t = 0 in V = 10e0.09t,

we get

V = 10e0.09 × 0= 10e0 = 10 × 1 = 10 million dollars.

The values after 5 years, 10 years and 12 years, respectively are:

For t = 5, V = 10e0.09 × 5 ≈ 19.65 million dollarsFor t = 10, V = 10e0.09 × 10 ≈ 38.43 million dollarsFor t = 12, V = 10e0.09 × 12 ≈ 47.43 million dollars

The total revenue (TR) in t years' time is modelled as TR = 10e−0.19t (in million dollars)

The current revenue is the total revenue when t = 0.

So, putting t = 0 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 0= 10e0= 10 million dollars

Revenue in 5 years' time is TR when t = 5.

So, putting t = 5 in TR = 10e−0.19t, we get

TR = 10e−0.19 × 5≈ 4.35 million dollars

To find when the revenue of this firm is going to drop to $1 million, we need to solve the equation TR = 1.

Substituting TR = 1 in TR = 10e−0.19t, we get1 = 10e−0.19t⟹ e−0.19t= 0.1

Taking natural logarithm on both sides, we get−0.19t = ln 0.1 = −2.303

Therefore, t = 2.303 ÷ 0.19 ≈ 12.13 years.

So, after approximately 12.13 years, the revenue of this firm is going to drop to $1 million.

Know more about revenue:

https://brainly.com/question/27325673

#SPJ11

Given :

Jaylen earns the same amount of money each month.

His telephone bill is 1/20 of his monthly earnings, and he pays a total of $840 each year for his telephone service.

To Find :

How much does Jaylen earn each month, in dollars.

Solution :

Monthly payment of telephone bill is :

\(M = \$ \dfrac{840}{12}\\\\M = \$70\)

Let, his monthly salary is A.

So,

\(M = \dfrac{A}{20}\\\\A = 20\times M\\\\A = 20 \times 70\\\\A = \$1400\)

Therefore, Jaylen monthly income is $1400.

Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

Answer:

Step-by-step explanation:

The cylindrical coordinates for point :

(a) (5, −5, 1) is  (√50, 3π/4, 1)

(b) (−4, −4sqrt(3), 1) is (8, 4π/3, 1)

To change from rectangular to cylindrical coordinates (with r ≥ 0 and 0 ≤ θ ≤ 2π), we'll convert the given points (a) and (b) using the following equations:

r = √(x² + y²)
θ = arctan(y/x) (adjusting for the correct quadrant)
z = z

(a) (5, -5, 1)
Step 1: Calculate r
r = √(5² + (-5)²) = √(25 + 25) = √50

Step 2: Calculate θ
θ = arctan((-5)/5) = arctan(-1)
Since we're in the third quadrant, θ = π + arctan(-1) = π + (-π/4) = 3π/4

Step 3: z remains the same
z = 1

So, the cylindrical coordinates for point (a) are (r, θ, z) = (√50, 3π/4, 1).

(b) (-4, -4√3, 1)
Step 1: Calculate r
r = √((-4)² + (-4√3)²) = √(16 + 48) = √64 = 8

Step 2: Calculate θ
θ = arctan((-4√3)/(-4)) = arctan(√3)
Since we're in the third quadrant, θ = π + arctan(√3) = π + (π/3) = 4π/3

Step 3: z remains the same
z = 1

So, the cylindrical coordinates for point (b) are (r, θ, z) = (8, 4π/3, 1).

Learn more about : Coordinates - https://brainly.com/question/31499714

#SPJ11

Answer:

192.5 kg

Step-by-step explanation:

220-12.5%=220*(100-12.5)/100=220*0.875= 192.5 kg

Answer:

Step-by-step explanation: IONK BUT I LIKE YOUR PFP

The person's total salary over the first 6 years is $231,750.

To determine the person's total salary over the first 6 years, we need to calculate the sum of the salary for each year.

Given information:

- Initial salary: $34,000

- Annual raise: $1,850

- Number of years: 6

To calculate the total salary, we can use the arithmetic progression formula:

[ S = frac{n}{2} left(2a + (n - 1)dright) ]

Where:

- ( S ) is the sum of the salaries

- ( n ) is the number of terms (years)

- ( a ) is the first term (initial salary)

- ( d ) is the common difference (annual raise)

Substituting the given values, we have:

[ S = frac{6}{2} left(2(34000) + (6 - 1)(1850)right) ]

Simplifying the expression:

[ S = 3 left( 68000 + 5 times 1850 right) ]

[ S = 3 left( 68000 + 9250 right) ]

[ S = 3 times 77250 ]

[ S = 231750 ]

Therefore, the person's total salary over the first 6 years is $231,750.

Learn more about arithmetic progression from :

https://brainly.com/question/6561461

#SPJ11

The expression 24 - 2x is suitable for the length of the garden as it accounts for the width and represents the remaining length of fencing available for the garden.

To enclose a rectangular garden, three sides need to be fenced, while one side is already adjacent to Mr. Picasso's house. The remaining three sides will consist of two equal lengths for the width and one length for the length of the garden.

Since the total length of fencing available is 24 ft, the width requires two equal sides, each of length x ft, which amounts to 2x ft. Subtracting this width from the total length of fencing gives us 24 - 2x ft, which represents the remaining length available for the length of the garden.

Therefore, 24 - 2x is an appropriate expression for the length of the garden as it takes into account the already utilized length for the width and represents the remaining length available for the garden's length.

Learn more about Rectangular area click here :brainly.com/question/29298005

#SPJ11

The equation that shows the relationship between the chicken's age, and its weight is y = 1 + 2x

The given parameters in the question are:

Initial weight = 1 ounce

Additional weight each week = 2

The equation that shows the relationship in the variables is represented as

y = Initial weight + Additional weight each week * x

Substitute the known values in the above equation, so, we have the following representation

y = 1 + 2 * x

Evaluate

y = 1 + 2x

Hence, the equation  is y = 1 + 2x

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

The students can be selected in 4060 ways.

Given that there are 30 students in a class we need to find that in how many ways one can select 3 students from the class.

Using the concept of combination,

ⁿCₓ = n! / x! (n-x)!

So,

³⁰C₃ = 30! / 3! (30-3)!

= 30! / 3! × 27!

= 4060

Hence the students can be selected in 4060 ways.

Learn more about combination, click;

https://brainly.com/question/31586670

#SPJ1

your going fail?! ill help itis 6

Step-by-step explanation:

The work done in pushing the package can be calculated by multiplying the force applied to the package by the distance it is pushed. The force exerted is 42 pounds at an angle of 10° with the horizontal, and the distance is 20 feet.

To determine the horizontal component of the force, we can use trigonometry. The horizontal force is given by the formula force * cosine(angle). In this case, the horizontal force is 42 pounds * cos(10°), which is approximately 41.91 pounds. Therefore, the work done is the product of the horizontal force and the distance, which is 41.91 pounds * 20 feet, equal to approximately 838.2 foot-pounds. Rounded to the nearest whole number, the work done is 838 foot-pounds.

In summary, the work done in pushing the package a distance of 20 feet with a force of 42 pounds at an angle of 10° with the horizontal is approximately 838 foot-pounds. This value is obtained by calculating the horizontal component of the force using trigonometry, is approximately 41.91 pounds, and then multiplying it by the distance. The rounded answer is 838 foot-pounds.

Learn more about horizontal  click here:

brainly.com/question/29019854

#SPJ11

To find the length of the third side of the triangular birthday card, Sarah can use the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

In other words, 4 + 9 > x, so 4 + 9 > x is the inequality that is true.

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the third side. This means that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This theorem is useful for determining the possible lengths of the sides of a triangle, as well as for proving that a set of three lengths cannot form a triangle.

Learn more about the Triangle Inequality Theorem:

https://brainly.com/question/1163433

#SPJ4

So the order from left to right would be: Mode, Median, Mean.

In a positively skewed distribution, the mean is typically larger than the median, and the median is larger than the mode.

This can be illustrated in the following way:

Mean: The mean is affected by extreme values in the tail of the distribution, and will be pulled in the direction of the skew. Therefore, in a positively skewed distribution, the mean will be to the right of the median.

Median: The median is the value that separates the lower 50% of the data from the upper 50% of the data. In a positively skewed distribution, the tail of the distribution is on the right-hand side, which means that the median will be closer to the left-hand side than the mean.

Mode: The mode is the most frequent value in the distribution. In a positively skewed distribution, the mode will be the smallest value, located at the left-hand side of the distribution, while the mean and median will be to the right of it.

To know more about positively skewed distribution,

https://brainly.com/question/12320081

#SPJ11

Answer:

x=67.5

Step-by-step explanation:

The interior angles of a triangle add up to 180. therefore

45+x+x=180

2x=135

x=67.5

Answer:

x=67.5

Step-by-step explanation:

180-45=135

135/2

67.5

Answer:One way of knowing the correct answers, we substitute the ordered pairs to the function and see whether it would make the function true.

3x – 4y = 21

A. (−3, 3)

3(-3) – 4(3) = 21

-21 = 21 ---------------> not equal

B. (−1, −6)

3(-1) – 4(-6) = 21

21 = 21 ---------------> equal

C. (7, 0)

3(7) – 4(0) = 21

21 = 21 ---------------> equal

D. (11, 3)

3(11) – 4(3) = 21

21 = 21 ---------------> equal

To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.

(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402

(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256

Adding the two decimal numbers together gives us:

131402 + 256 = 131658

To convert this decimal number back to hexadecimal form, we can use the repeated division method.

131658 / 16 = 8228 remainder 10 (A)

8228 / 16 = 514 remainders 4 (4)

514 / 16 = 32 remainder 2 (2)

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.

To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.

131402 x 256 = 33559552

Converting this decimal number to hexadecimal form gives us:

33559552 / 16 = 2097472 remainder 0

2097472 / 16 = 131092 remainder 0

131092 / 16 = 8193 remainder 4 (4)

8193 / 16 = 512 remainders 1 (1)

512 / 16 = 32 remainder 0

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.

For more questions like numbers (20cba)16, visit the link below:

https://brainly.com/question/9713995

#SPJ11

Answer:

the question is uncompltre

Step-by-step explanation:

The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

Learn more about profit at: brainly.com/question/15699405

#SPJ11

The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = \(0.001x^2 + 3x + 1800\)

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =\(0.001(1500)^2 + 3(1500) + 1800 = $4800\)

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

Learn more about maximum profit

https://brainly.com/question/29248429

#SPJ4

The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Learn more about significant figures here

https://brainly.com/question/30169

#SPJ11

Based on the information, we can infer that the second plan is the best for the bicycle company because it will cost less and will earn more.

To identify the best alternative for the bicycle company, we must take into account the information on the cost of design and construction of the bicycles and the cost of labor and production.

In accordance with the above, we can infer that in alternative one the design and construction of the bicycle would be more expensive than alternative two. However, the production of each bicycle would be less.

Therefore, the best alternative would be option two because it requires less initial research and the product will cost more, so it would have a higher retail value, so the investment could be recovered much faster. .

Learn more about financial analysis in: https://brainly.com/question/14234253

#SPJ1

Hello!

The slope of a line is found using the following formula:

\(m=\frac{y2-y1}{x2-x1}\)

\(m=\frac{9-5}{-2-2}\)

\(m=\frac{4}{-4}\\m=-1\)

So the slope is -1.

Hope this helps!

#HaveAnAmazingDay

\(GraceRosalia\)

The data in the accompanying table of 36 diamonds includes the price (in dollars), the weight (in carats), and the clarity grade of the diamonds. The diamonds have clarity grade either VS1 or VVS1. VVS1 diamonds are nearly flawless; VS1 have more visible (but still small) flaws. The results of the two-sample t-test to compare the prices of VS1 and VVS1 diamonds are as follows: Sample statistic, Two-sample t-statistic, P-value, Interpretation.

Sample statistic: The difference between the sample means of the two groups is x₁ - x₂ = -56.78 (rounded to two decimal places).

Two-sample t-statistic: The calculated t-value is -2.301 (rounded to three decimal places).

P-value: The p-value associated with the t-statistic is 0.0300 (rounded to four decimal places).

Interpretation: Based on the p-value, which is less than the commonly used significance level of 0.05, we can conclude that there is statistically significant evidence to suggest that there is a difference in prices between VS1 and VVS1 diamonds.

The negative value of the sample statistic indicates that, on average, VS1 diamonds have lower prices compared to VVS1 diamonds. This aligns with the definitions of the categories, as VVS1 diamonds are considered to have a higher clarity grade and are expected to command higher prices.

To learn more about carats refer here:

https://brainly.com/question/16782628#

#SPJ11

Answer:

1.22 is greater

Step-by-step explanation:

everything after the decimal point is still the same as if it was a regular number. It's like comparing 22 and 02.

You can do 1.22-1.02 without getting a negative number

But when you do 1.02-1.22 the answer is -0.2.

I hope I could help!

To find the probability that a plant chosen at random will be between and cm tall, we need to use the normal distribution formula. We know that the mean height of the plant is cm and the standard deviation is cm.

First, we need to standardize the values of and by subtracting the mean and dividing by the standard deviation:

Z1 = ( - ) / = ( - ) /
Z2 = ( - ) / = ( - ) /

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two Z-values. This area represents the probability that a plant chosen at random will have a height between and cm.

Alternatively, we can use the normal distribution function on a calculator or software to find the probability directly. The formula for the normal distribution function is:

P( < X < ) = 1/2[erf(( - )/sqrt(2)) - erf(( - )/sqrt(2))]

where erf is the error function.

Using either method, we can find that the probability that a plant chosen at random will be between and cm tall is approximately %.

Learn more about normal distribution function here: brainly.com/question/30637875

#SPJ11

Answer:

38

Step-by-step explanation:

No. of yellow envelopes she has

= 6-2

= 4

No. of green envelopes she has

= 7×4

= 28

Total number of envelopes she has

= 6+4+28

= 38

Answer:

Sry don't know it lol. Stop answering my questions if you don't know it I want people that know the answer