a) Write the value of sin for the right-angled triangle below as a fraction.
b) Using your answer to part a), work out the size of angle 0.
Give your answer in degrees to 1 d.p.

Answer:

The answer to this question is 140

Answer: 140

Step-by-step explanation:

1.25 * 112 =140

Because the percent is bigger than 100% your answer will be bigger than the number you started with 112, so 140 makes sense

The answer of the given question based on models are , Model 1 = e⁽⁽ˣ⁻³⁾/²⁾ , Model 2 = (x/3)³ - 4 , Model 3 =  (15x-y)/(y-5) .

An inverse function is a function that undoes the effect of another function. Specifically, if a function f maps an input value x to an output value y, then the inverse function f⁻¹ maps the output value y back to the original input value x. In other words, the inverse function "reverses" the mapping of the original function.

In each of these models, the inverse function f⁻¹(x) represents the input value (x) that would yield a particular output value (y) of the original function f(x).

In Model 1, the inverse function f⁻¹(x) is  e⁽⁽ˣ⁻³⁾/²⁾, which represents the number of hours required to produce a certain amount of fresh water. The inverse function allows us to determine how long it would take to produce a specific amount of fresh water, given the rate of production provided by the original function.

In Model 2, the inverse function f⁻¹(x) is (x/3)³ - 4, which represents the number of units of product A needed to generate a certain amount of profit. The cube root function is used to represent the relationship between the profit and the number of units sold. The inverse function allows us to determine how many units need to be sold to achieve a specific level of profit.

In Model 3, the inverse function f⁻¹(x) is (15x-y)/(y-5), where y represents the number of penguins. This function represents the number of years that have passed since 2012 to achieve a certain population of penguins. The rational function is used to represent the relationship between the population of penguins and the number of years that have passed. The inverse function allows us to determine how many years have passed to achieve a specific population of penguins.

Overall, the inverse function provides a way to determine the input value that corresponds to a particular output value of the original function. This information can be useful in understanding the behavior and relationships between variables in each of these models.

To know more about Function visit:

https://brainly.com/question/10500042

#SPJ1

Answer:

-3/5

decimal form: -0.6

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

have a good day :)

A sample size of at least 29 is necessary to achieve a margin of error of $8 for a 90% confidence interval of the mean daily spending on all holiday spending.

The following equation may be used to calculate a confidence interval's margin of error:

Margin of error = z *  [tex](\frac{standard\: deviation} {\sqrt{(sample\:\: size)} }\:)[/tex]

We want the margin of error to be $8, so we can set up the following equation:

[tex]$8 = 1.645 * (\$26 / \sqrt{(sample\: size))[/tex]

To solve for the sample size, we need to isolate the variable "sample size" on one side of the equation:

[tex]\sqrt{(sample\: size)} = 1.645 * (\$26 / \$8)\\\sqrt{(sample\: size)} = 5.365[/tex]

sample size = [tex](5.365)^2[/tex]

sample size = 28.8

We can round up to the nearest whole number to ensure that the sample size is large enough:

sample size = 29

Margin of error refers to the range of possible values that a statistical result may vary from the actual population parameter. It is a measure of the precision of a survey or poll's results and indicates how much confidence one can have in the results.

When conducting a survey or poll, researchers typically take a sample from a larger population and use statistical techniques to estimate the parameters of interest, such as the mean or proportion. The margin of error is then calculated based on the sample size, level of confidence, and the variability of the data. It's important to consider the margin of error when interpreting survey results to avoid making incorrect conclusions or assumptions.

To learn more about Margin of error visit here:

brainly.com/question/10501147

#SPJ4

The constant phase associated with the complex number represented by the radial line with polar coordinates (|z|, θ) = (√(2)/2, 135°) is found out being 135°.

The constant phase associated with the complex number represented by the radial line with polar coordinates (|z|, θ) = (√(2)/2, 135°) is 135°.

To see why, we can first express the complex number in rectangular form:

z = (√(2)/2) x exp(i x 135°) = (√(2)/2) x cos(135°) + (√(2)/2) x i x sin(135°) = (-1 + i) / √(2)

The angle θ associated with this complex number can be found using the arctangent function:

θ = arctan(Im(z) / Re(z)) = arctan((√(2)/2) / (-√(2)/2)) = -45°

However, since we want the angle measured from the positive real axis, we need to add 180° to get:

θ = -45° + 180° = 135°

Therefore, the constant phase associated with the complex number represented by the radial line with polar coordinates (|z|, θ) = (√(2)/2, 135°) is 135°.

Learn more about polar coordinates :

https://brainly.com/question/16970032

#SPJ4

Answer:

  C = 18°

Step-by-step explanation:

You want the value of angle C in the given figure.

The angle marked X in the attachment is an exterior angle to the left triangle. As such, its measure is the sum of the remote interior angles, marked 30° and 51°.

  X = 30° +51° = 81°

The angle marked X is one of two congruent base angles of the isosceles triangle on the right. That means ...

  C = 180° -2X = 180° -2(81°)

  C = 18°

The value of C is 18°.

it would take 7.5 gallons of paint to cover 2000 square feet of surface.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

The proportion that can be used to find the number of gallons of paint needed to cover 2000 square feet of surface is:

3 gallons : 800 square feet = x gallons : 2000 square feet

where x is the number of gallons of paint needed to cover 2000 square feet of surface.

Simplifying the proportion, we can cross-multiply to get:

3 * 2000 = 800 * x

Solving for x, we get:

x = (3 * 2000) / 800 = 7.5 gallons

Therefore, it would take 7.5 gallons of paint to cover 2000 square feet of surface.

Learn more about equations, by the following link

brainly.com/question/2972832

#SPJ4

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing with an alpha value of 0.01.

If you are testing the null hypothesis with an alpha value of 0.05, the critical value will be smaller than if you were testing the alpha value of 0.01. This is because a smaller alpha value means a more stringent test of significance, which requires stronger evidence to reject the null hypothesis.

Therefore, the critical value is larger for a smaller alpha value to reflect the higher level of evidence required for rejection. Conversely, a larger alpha value allows for a less stringent test of significance, requiring weaker evidence to reject the null hypothesis, which results in a smaller critical value.

Know more about the alpha value

https://brainly.com/question/30639544

#SPJ11

The probability of getting a blue marble and coin tails up is 540 / 2500.

Given that, Victoria is having a bag of three colored marbles and 50 coins in a bag,

Blue marbles = 18

Green = 20

Yellow = 12

Head up Coin = 20

Tails up coins = 30

So, P(E) = favorable outcomes / total number of outcomes

P(A and B) = P(A) × P(B)

P(A) = Getting a blue marble = 18/50

P(B) = Getting a coin inn which tail is upside = 30 / 50

P(A and B) = 18/50 x 30/50 = 540/2500

Hence, the probability of getting a blue marble and coin tails up is 540 / 2500.

Learn more about probability, click;

https://brainly.com/question/30034780

#SPJ1

The system of equations that describes the number of wizards and necromancers in the village is: w + n = 30 n = w + 6.

Let's denote the number of wizards as 'w' and the number of necromancers as 'n'.

From the problem, we know that there are a total of 30 magical people in the village. Therefore, our first equation is simply: w + n = 30. Additionally, we're told that there are six more necromancers than wizards. This means that:

n = w + 6.

We can substitute this second equation into the first to get: w + (w + 6) = 30. Simplifying this equation gives us: 2w + 6 = 30

This is as far as we can simplify the equations without solving for 'w' and 'n'. These equations can be used to determine the values of 'w' and 'n' by solving the system of equations using algebraic methods.

Learn more about equation here:

https://brainly.com/question/29657988

#SPJ4

Answer:

Step-by-step explanation:

To make each table identical, we need to find the greatest common divisor (GCD) of 8 and 12, which will give us the maximum number of people that can be seated at each table.

We can find the GCD using the Euclidean algorithm:

12 = 8 × 1 + 4

8 = 4 × 2 + 0

Since the remainder is 0, the GCD of 8 and 12 is 4.

Therefore, the event planner can set up tables with 4 people at each table (2 adults and 2 children).

There are a total of 20 people (8 adults + 12 children), so the number of tables needed is:

20 ÷ 4 = 5

Thus, the greatest number of tables the planner can set up is 5.

We know that the circumference C of a circle is related to its diameter d by the formula:

C = πd

We are given that the circumference of the circle is approximately 7,459 miles. Substituting this into the formula above and solving for the diameter d, we get:

d = C/π

d = 7,459/3.14

d ≈ 2375.477707

Rounding to the nearest hundredths place, the diameter is approximately 2375.48 miles.

Therefore, the answer to fill in the blank is 2375.48miles.

Answer:

2374,27 miles

Step-by-step explanation:

diameter of circle = circumference/3.14

d = 7359 / 3.14 = 2374.27 miles

Answer:

$632.58

Step-by-step explanation:

It is given that Derek is paid a 6.5% commission (or 0.065 in decimals) on every appliance sold. It is also given that Derek sold $9,732.00 in total.

To solve, multiply the total sold with the commission percentage to find total amount of commission:

commission percentage x total sold = total amount of commission

Plug in the corresponding numbers to the corresponding variables. Let the variable, t, stand for the total amount of commissions:

0.065 x 9732 = t

t = 632.58

Derek's total commission is $632.58

~

Learn more about percentages, here:

https://brainly.com/question/1878521

Answer: 1:5

Step-by-step explanation:

If you convert that to a ratio, that is 2:10 = 1:5.

The US government gave settlers 160 acres of land in the Great Plains under the Homestead Act of 1862, allowing them to build a house and cultivate crops.

The Homestead Act of 1862 was signed into law by President Abraham Lincoln, which offered settlers the opportunity to claim up to 160 acres of land in the western United States. To be eligible for the land, settlers had to be at least 21 years old, the head of the household, and have lived on the land for at least five years.

They also had to cultivate the land and build a house on it. This act was intended to encourage settlement in the western territories and to promote agriculture in the area. The Great Plains were a prime location for the Homestead Act because the land was relatively flat and had fertile soil, which was suitable for farming.

By the end of the 19th century, over 600,000 claims had been made under the Homestead Act, and millions of acres of land were transferred from government ownership to private ownership.

For more questions like Government click the link below:

https://brainly.com/question/371257

#SPJ11

The distance which the dog ran is equal to 75 meters.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Since this dog ran from one corner to the diagonally opposite corner, we can determine the distance which the dog ran by applying Pythagorean's theorem as follows;

x² + y² = z²

45² + 60² = z²

z² = 2,025 + 3600

z² = 5,625

z = √5,625

z = 75 meters.

Read more on Pythagorean theorem here: brainly.com/question/15430861

#SPJ1

Answer:

The answer to your problem is about, 156 weeks

Step-by-step explanation:

We can first divide it by 7.

We need to divide it by 7 because there is 7 days in a week which is:

1,095 ÷ 7 = 156.428571429.

Rounded; 156 weeks

Thus the answer to your problem is, 156 weeks

Answer:  B

Step-by-step explanation:

Player 1 = 4/7 = .57

Player 2 = 5/8  = .625

Player 3 = 3/6 = .5

a, not true P1 is  not> than P2

b.  is true P2>P1

c.  not true P3 is not > than P1

d. not true P3 is not > than P2

The requried cost is $8995 when the two companies charge the same for transporting 20 tons of sugar.

To estimate the amount of sugar for which the two companies charge the same,

4995 + 200.50x = 6500 + 125.25x

Simplifying and solving for x, we get:

74.75x = 1505

x = 20

Therefore, the two companies charge the same when transporting 20 tons of sugar. To estimate the cost at this point, we can substitute x=20 into either equation:

For the first company:

cost = 4995 + 200.50(20) = $8995

For the second company:

cost = 6500 + 125.25(20) = $8995

Learn more about the equation model here:

https://brainly.com/question/16107051

#SPJ1

The equivalent expression is -4m + 10n + 10

It is important to know that algebraic expressions are described as expressions that are composed of terms, variables, constants, factors and coefficient of variables.

These algebraic expressions are also made up of mathematical operations.

These operations includes;

Note that equivalent expressions have the same solution, we have;

−(4m - 0-  2n - 5. 5)

expand the bracket, we have

-(4m - 10n - 10)

remove the parentheses

-4m + 10n + 10

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ4

If the lawn measures 6m by 5. 2m, the area of the lawn is 31.2 square meters.

To find the area of the lawn, we simply need to multiply the length by the width. In this case, we have a rectangular lawn that measures 6m by 5.2m.

Area = length x width

Area = 6m x 5.2m

Area = 31.2 square meters

It's important to note that when calculating area, the units are squared, which means we are multiplying two lengths together. In this case, we multiplied meters by meters to get square meters. This is because area is a two-dimensional measurement, whereas length and width are one-dimensional measurements.

To learn more about area click on,

https://brainly.com/question/12187609

#SPJ4

Function 2 has the larger maximum at (2, 5).

Hence the correct option is (C).

Given the first function is,

Function 1: f(x) = x² + 8x - 15

Differentiating the function with respect to 'x' we get,

f'(x) = 2x + 8

f''(x) = 2

Now, f'(x) = 0 gives

2x + 8 = 0

2x = -8

x = -8/2

x = -4

At x = -4 the value of f''(-4) = 2 > 0

So there is minimum at x = -4.

Second function is:

Function 2: f(x) = -x² + 4x + 1

Differentiating the function with respect to 'x' we get,

f'(x) = -2x + 4

f''(x) = -2

Now, f'(x) = 0 gives

-2x + 4 = 0

2x = 4

x = 4/2

x = 2

At x =2 the value of f''(2) = -2 < 0

So at x = 2 the function has maximum value.

max f(x) = f(2) = - 2² + 4*2 + 1 = - 4 + 8 + 1 = 5

So function 2 has the larger maximum at (2, 5).

Hence the correct option is (C).

To know more about functions here

https://brainly.com/question/28376218

#SPJ1

The weighted average is 1.

Weighted average is a statistical term used to describe a average calculated by giving different weights to different elements in a set of values.

The weighted average of the numbers -1 and 5 with two thirds of the weight on the first number and one third on the second number is 0.67.

The formula for a weighted average is:

(Weight1 * Value1) + (Weight2 * Value2) / (Weight1 + Weight2)

Where Weight1 is the weight for the first value (-1), Value1 is the first value (-1), Weight2 is the weight for the second value (5), and Value2 is the second value (5).

In this case, Weight1 = 2/3, Weight2 = 1/3, Value1 = -1, and Value2 = 5. Plugging these values into the formula, we get:

(2/3 * -1) + (1/3 * 5) / (2/3 + 1/3) = (-2/3 + 5/3) / 1 = 3/3 = 1

Hence, the weighted average is 1.

To learn more about weighted average, Visit

brainly.com/question/28507971

#SPJ1

The linear equation modeling the given relationship is y = 150 + 200x, where y is the fees and x is the time in hours.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given that,

Registration fee for a new client = $150

There is also a fees of $200 per hour.

If x represents the hours, then the additional fees for x hours is 200x.

Total fees, y = 150 + 200x

If x = 0 hours, then y = $150

If x = 1 hour, y = 150 + (200 × 1) = $350

If x = 3 hours, y = 150 + (200 × 3) = $750

If x = 4 hours, y = 150 + (200 × 4) = $950

If x = 7 hours, y = 150 + (200 × 7) = $1550

Hence the linear equation modeling the situation is  y = 150 + 200x.

If x = 0, 1, 3, 4 and 7, the values of y are 150, 350, 750, 950 and 1550.

Learn more about Linear Equations here :

brainly.com/question/19770987

#SPJ1

complete question:

Kevin runs a legal services company. He charges a registration fee of $150 when a new client is registered. He will then meet with the client to discuss their legal needs and bills they $200 per hour. Write an linear equation that models this relationship.

Fill in the table using the linear equation that models this relationship

x y

0

1

3

4

7

Last year, because finish times were greater last year, on average, as compared to this year. Therefore, the correct option is D.

We can see that finish time A is larger (by 2 seconds) than finish time B, so we can assume that the mean for year A will be larger than the mean for year B.

On the other table, we can see that last year the average was larger (16.2 s compared with 14.7 s this year).

Then we can assume that Finish Time A was recorded last year, just because the mean of last year was larger.

Therefore, the correct option is D.

To learn more about an average visit:

https://brainly.com/question/11195029.

#SPJ1

"Your question is incomplete, probably the complete question/missing part is:"

The first table shows the measures of variability for finish times of 30 runners in the 100-meter dash. Calista’s finish times are recorded in the second table. She cannot tell which number is for which year. Based on the data table, when did Calista likely record Finish Time A? Explain.

A. This year, because finish times were less this year, on average, as compared to last year.

B. Last year, because finish times were less last year, on average, as compared to this year.

C. This year, because finish times were greater this year, on average, as compared to last year.

D. Last year, because finish times were greater last year, on average, as compared to this year.

Answer:2

Step-by-step explanation:

12/6=2

There are 924 possible outcomes 6-person lineups that can be formed from a volleyball roster of 12 players, assuming every player can play any position.

To answer your question, we can use the combination formula which is nCr = n!/(r!(n-r)!), where n is the total number of players in the roster and r is the number of players we want to choose for the lineup. In this case, we want to choose 6 players for the lineup out of 12 players in the roster. So, the formula becomes 12C6 = 12!/(6!(12-6)!) = 924. Therefore, there are 924 possible 6-person lineups that can be formed from the volleyball roster of 12 players, assuming every player can play any position.

To form a 6-person lineup from a 12-player volleyball roster, you can use the concept of combinations. Combinations are used to find the number of ways to choose items from a larger set without considering the order of the items. In this case, you need to choose 6 players from a set of 12. The formula for combinations is:

C(n, k) = n! / (k!(n-k)!)

where C(n, k) is the number of combinations, n is the total number of items, k is the number of items to choose, and ! denotes the factorial of a number. Plugging in the values for your question:

C(12, 6) = 12! / (6!(12-6)!)

C(12, 6) = 12! / (6!6!)

C(12, 6) = 924

So, there are 924 possible outcomes 6-person lineups that can be formed from a volleyball roster of 12 players, assuming every player can play any position.

To learn more about possible outcomes, click here:

brainly.com/question/27292589

#SPJ11