Show how to find the sine, cos, and tangent of 30° given that cos60°=1/2.

Step-by-step explanation:

distinct ways !

STATICS and STATICS are 2 different ways to arrange them. have you noticed the difference ?

no, of course not. I only exchanged the 2 S. the same problem with the 2 T.

while they are different permutations, their arrangements are not distinctly different. to us observers they look the same.

so, for the 7 letters, 7! is not the full answer.

these 7! permutations include all the ones, where we only change the S and the T with each other.

we need to eliminate those. we do this by dividing by the S permutations (2! = 2) and the T permutations (again, 2! = 2).

so, the answer is

7! / (2×2) = 5040 / 4 = 1260

the 7 letters can be arranged in 1260 distinctly different ways.

Please find attached the graph of the residual plot created with MS Excel

A residual plot is the plot of the vertical distances between the data points and the regression line.

The residuals can be obtained by the equation;

r = y - y₀

The residuals are calculated using the above formula for the residuals and presented in a tabular format as follows;

x    [tex]{}[/tex]    y              [tex]\hat{y}[/tex]                 r

10 [tex]{}[/tex]    4.472      4.73            0.258

24[tex]{}[/tex]    6.928      6.312         -0.616

53 [tex]{}[/tex]   10.296     9.589        -0.707

46  [tex]{}[/tex]  9.592      8.798        -0.794

5    [tex]{}[/tex]  3.162        4.165         1.003

78    [tex]{}[/tex]12.49        12.414        -0.076

100   [tex]{}[/tex]14.142      14.9            0.758

84 [tex]{}[/tex]   12.962      13.092       0.13

The residual plot can be graphed using the data points for the x-values, x, and the residuals, r, as follows;

x; 10         [tex]{}[/tex]       24        53        46              5              78        100            84

r; 0.258     [tex]{}[/tex]  -0.616    -0.707    -0.794      1.003     -0.076     0.758       0.13

Please find attached the graph of the residuals, the residual plot created with MS Excel

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The given statement is true i.e. 4 € (3,4,5}.

What are Sets and Subsets?

A set is a mathematical representation of a group of diverse items. A set has elements or members, which can be any type of mathematical object, including numbers, symbols, lines, points in space, other geometric structures, variables, or even other sets.

When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A.

Here, (3,4,5} has open ended bracket on 3 which implies it does not contain 3 .

Similarly, (3,4,5} has closed bracket on 5 which implies it contains 5.

Since, we have to check whether 4 belongs to the set or not,

4 belongs to the given set because it is a part of given set which is in the mid hence, we don't need to check bracket here.

Hence, 4 € (3,4,5} and the given statement is true.

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y' = (y-3)(y+3)exp(y)

This differential equation has equilibrium solutions at y=0 and y=3, and y' is positive for -inf < y < 0 and 3 < y < inf and negative for 0 < y < 3.

1. Set y′ = 0 to get the equilibrium solutions

y′ = 0 → y = 0 and y = 3

2. Find the sign of y′

y′ = (y-3)(y+3)exp(y)

For y < 0, y′ is positive

For 0 < y < 3, y′ is negative

For y > 3, y′ is positive

This differential equation has two equilibrium solutions at y=0 and y=3, meaning the value of y does not change when the equation is applied.

To determine the sign of the equation, we can look at the equation y′ = (y-3)(y+3)exp(y). For y < 0, y′ is positive. This means that when y is less than 0, the equation increases in value. For 0 < y < 3, y′ is negative. This means that when y is in between 0 and 3, the equation decreases in value. And for y > 3, y′ is positive. This means that when y is more than 3, the equation increases in value.

Overall, the equation behaves as expected: it increases when y is less than 0 and more than 3, and decreases when y is between 0 and 3. This is what we would expect in order for the equation to have the equilibrium solutions at y=0 and y=3.

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The probability of drawing two blue cards is 0.09.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

given:

Green cards = 5

Blue card=3

Red card= 2

So, the probability of getting blue card at first time

= 3/ 10

Now, the probability of getting blue card at second time

= 3/10

Thus, the probability of drawing two blue cards

= 3/10 x 3/10

= 9/100

= 0.09

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The density functions of U1, U2 and U3 can be calculated as fU1(u) = 2(2 - (u+1)), 0 < u < 1, 0, elsewhere; fU2(u) = 4/u2, 0 < u < 1, 0, elsewhere; and fU3(u) = 2/√u, 0 < u < 1, 0, elsewhere.

The method of transformation is used to find the density functions of U1, U2 and U3 when given the probability density function of a random variable Y. The equation for the transformation of a random variable Y to U is U = g(Y), where g is a function of Y. To find the density functions of U1, U2 and U3, we need to first calculate the derivatives of U1, U2 and U3 with respect to Y, which are given by dU1/dY = 2, dU2/dY = -1/2 and dU3/dY = 2Y. Then, the density functions of U1, U2 and U3 can be calculated using the formula fU(u) = fY(g-1(u)) * |dg-1/du|, where fU(u) and fY(y) denote the density functions of U and Y, respectively, and g-1 is the inverse of g. For U1, U2 and U3, g-1(u) is y = (u+1)/2, y = 2/u and y = √u, respectively. Therefore, the density functions of U1, U2 and U3 can be calculated as fU1(u) = 2(2 - (u+1)), 0 < u < 1, 0, elsewhere; fU2(u) = 4/u2, 0 < u < 1, 0, elsewhere; and fU3(u) = 2/√u, 0 < u < 1, 0, elsewhere.

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A central angle in a circle measures 52 degrees. 13° is the measure of an inscribed angle that intercepts the same arc.

An arc's inscribed angle is the angle that it occupies at any given point on the circle. The angle created when two chords cross on a circle's interior is known as a "inscribed angle" in geometry. The angle formed at a specific location on the circle by two specified points on the circle can also be used to define it. Two chords of the circle that share an endpoint define an inscribed angle in the same way.

Half of the size of the central angle that corresponds with the intercepted arc makes up the size of an inscribed angle. An inscribed angle's measurement is equal to half of its intercepted arc's measurement.

Thus, central angle = 52°

so, intercepted arc = 26°

hence, inscribed angle = 13°

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No, there isn't a week when they have the exact same amount of money, however at week 7, Diego has $45 and Lin has $44.

Answer:

x = - 2 , x = 2 are the input values

Step-by-step explanation:

g(x) = 4 , means y has the value of 4 and we want to find the values of x corresponding to this.

locate y = 4 on the y- axis , then a horizontal line through this point , intersects the graph at (- 2, 4 ) and (2, 4 )

thus when g(x) = 4 , the input values are x = - 2 and x = 2

The better buy is 10 tickets for $1.00.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Polk Elementary School was putting on its annual fall carnival.

The school was selling 10 tickets for $1.00 or 2 tickets for $0.254.

That means,

A). 10 tickets for $1.00 or

B).  2 tickets for $0.254.

So, 10 tickets for $1.3

Therefore, option A is a better choice.

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Answer:

y= -3+5

its the same thing

Step-by-step explanation:

The best choice for the man and his spouse is that they should upgrade to the new policy because the current policy costs $1,044 for nine months, which is significantly less than the upgrade which costs $2,619 for nine months. That is option A.

A health insurance is defined as the amount of money deducted from a salary account which is used for health care services of the individual when accumulated over time.

The man and his spouse are expectant and they believe that the money for prenatal care and delivery would be from the health insurance.

Therefore, they should upgrade to the health insurance that pays $291 per month so as to accumulate an amount such as $2,619 which is approximately $3000.

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Complete question:

Analyze the following situation and determine which decision would be the best decision to make. Explain your answer. A man and his spouse are expecting a baby. Their current health insurance costs $116 per month, but doesn't cover prenatal care or delivery. They can upgrade to a policy that will cover their prenatal care and delivery, but their new premium will be $291 per month. The cost of prenatal care and delivery is approximately $3000. Select the correct choice below and fill in any answer boxes within your choice.

O A. They should upgrade to the new policy because the current policy costs $ for nine months, which is significantly less than the upgrade which costs $ for nine months.

OB. They should keep their current policy because it costs $ for nine months, which is significantly less than the upgrade which costs $ for nine months.

Answer:

- 3 26/55

Step-by-step explanation:

There are 12 students that know all of the language .

Given : Total U = 80

Let A be the set of students  that know English

A = 50

Let A be the set of students  that know French

B = 55

Let A be the set of students  that know German

C =46

Since , 7 students know none of the language

Therefore , |A?B?C| = 7

Also ,

|A∩B| = 37

|B∩C| =28

|C∩A| = 25

Now ,

U - (A∪B∪C) = (A?B?C)

80 - (A∪B∪C) = 7

(A∪B∪C) = 73

Number of students that know all three languages

(A∪B∪C) = A + B + C - [(A∩B) + (B∩C) + (A∩C)] + (A∩B∩C)

73 = 50 + 55 + 46 - 37 -28 -25 + (A∩B∩C)

Therefore , (A∩B∩C) = 12

Hence , there are 12 students that know all of the language .

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The domains of the composite function (f/g)(4) and (f + g)(4) for f(x) = x² + 2x - 3 and g(x) = x² - 9 are equal to 3 and 28 respectively.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domains of the function (f/g)(4) and (f + g)(4) as follows:

(f/g) = (x² + 2x - 3)/(x² - 9)

by factorization of the right hand side;

(f/g) = (x - 1)(x + 3)/(x - 3)(x + 3)

(f/g) = (x - 1)/(x - 3)

(f/g)(4) = (4 - 1)/(4 - 3)

(f/g)(4) = 3

(f + g) = x² + 2x - 3 + x² - 9

(f + g) = 2x² + 2x - 12 {simplify like terms}

(f + g)(4) = 2(4)² + 2(4) - 12

(f + g)(4) = 28

Therefore, the domains of the composite function (f/g)(4) and (f + g)(4) for f(x) = x² + 2x - 3 and g(x) = x² - 9 are equal to 3 and 28 respectively.

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Answer: First one is -11

Second one is 0

Step-by-step explanation:

Answer:

not possible

Step-by-step explanation:

it's not equal to zero, and the answer ends up with imaginary number

The order of the values from the least to the greatest is:

To order the values, it would be best to convert them to decimals or whole numbers to better see how they relate with each other.

The value of 8 tens means:

= 8 x 10

= 80

The value of 8 x 1 / 100 comes to :

= 8 x 1 / 100

= 8 / 100

= 0.08

The value of 0. 88 is already in decimals.

The largest number therefore, is 8 tens. Then 0. 88 follows as it is greater than 0. 08.

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Without doing any calculations, the values of m, x_{0} and y_{0} in the point-slope form include the following:

M = 6

x_{0} = -1

y_{0} = 9.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₀ = m(x - x₀)

Where:

From the information provided above, we have the following slope and data points on the line:

Initial point on the x-axis, x₀ = -1.

Initial point on the y-axis, y₀ = 9.

Slope, m = 6.

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Insurance is a financial service that allows a: C. consumer to share liability with a company.

In Economics, an insurance company can be defined as a business organization (company or firm) that is established to collect premium from all of the insured for losses which may or may not occur, so they can easily use this cash to compensate or indemnify for losses (liabilities) incurred by those having high risk.

In this context, we can reasonably infer and logically deduce that an insurance simply refers to a financial service that is designed and developed to avail a consumer an opportunity or ability to share his or her liabilities with a business organization (company or firm).

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Answer:

C - consumer to share liability with a company.

Step-by-step explanation:

Edge 2023

So the correct answer is $6,645, or option D. If just a portion of that sum was spent on print advertising.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. A division in mathematics is the process of dividing a specified amount into equal pieces. For example, we can split a group of 20 people into four groups of five people each, or five groups of four people each, and so on.

Here,

If half of the $13,290 was spent on print advertising, then $13,290 / 2 = $6,645 was spent on print advertising.

Therefore, $13,290 - $6,645 = $6,645 was spent on TV advertising.

So, the answer is $6,645, or option D If of that amount was spent on print advertising.

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lmk is anything is unclear. This would also work with cosine but it would have to be set up a little differently.

Methods for receiving the most recent hazardous weather information and current updates directly from your local Weather Forecast Office (WFO) include all  except C. NWSChat, phone calls, phone alerts

Simply put, a weather prediction is a scientific projection of the coming weather. The most important meteorological variables are used to express the state of the atmosphere at any particular time as the weather condition. Significant weather factors that are expected vary by location.

It is possible to predict the weather by employing technology and scientific understanding to make weather observations. This process is known as weather forecasting. In other words, it allows for the early prediction of events like cloud cover, rain, snow, wind speed, and temperature.

Therefore, option C is correct.

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Answer:

see below

Step-by-step explanation:

every year goes up 16%, so

250 * (1+16%)^8 = 819.6

Answer:

9x^2+4-12x+21x^2+x-10

30x^2-11x-6

Step-by-step explanation:

please make me as brainlest

Therefore , the solution of the given problem of equation comes out to be Matias operated with the number 760.

A straightforward regression graph is created using the equation y=mx+b. B is the slope, and m is the y-intercept. Even though the portion before it consists of separate sections, it is frequently described as just a "simple algorithm combining many variables". Two factors make up bivariate linear equations. There are no solutions known for application issues involving linear equations.

Here,

When Matias moved the decimal point in 7.6 two places to the left, he essentially divided 7.6 by 100, which is equivalent to dividing by 10 raised to the power of 2.

So, if we let x be the number Matias operated with, we can set up the equation:

x ÷ 10² = 7.6

Simplifying:

x ÷ 100 = 7.6

Multiplying both sides by 100:

x = 760

Therefore, Matias operated with the number 760.

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The ratio of chocolate bars More Preferred: (9 chocolate bars, 3 glasses of milk); Equally Preferred: (6 chocolate bars, 3 glasses of milk); Less Preferred: (3 chocolate bars, 2 glasses of milk) and (9 chocolate bars, 2 glasses of milk).

The ratio of chocolate bars to glasses of milk that Isabel consumes is 3-to-1. This means that whenever she has 3 chocolate bars, she also has 1 glass of milk. Currently, Isabel has 6 chocolate bars and 2 glasses of milk. The bundles listed above are compared to Isabel's current consumption. Out of the five bundles, the one with 9 chocolate bars and 3 glasses of milk is more preferred than what Isabel currently has because it has more of the ratio than Isabel's current consumption. The bundle with 6 chocolate bars and 3 glasses of milk is equally preferred because it holds the same ratio as Isabel's current consumption. The bundles with 3 chocolate bars and 2 glasses of milk and 9 chocolate bars and 2 glasses of milk are less preferred because they both have less of the ratio than Isabel's current consumption.

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Answer:

Step-by-step explanation:

Given a sawtooth, a parabola, and a logistic function, you want to identify the graphs that represent their derivatives.

The "zigzag" sawtooth function has constant positive slope alternating with constant negative slope. This is shown in derivative graph (c).

The slope of the parabola changes smoothly from positive to negative, going through zero in the middle. This is shown in derivative graph (a).

The slope of the logistic curve is positive everywhere, with a higher rate of change in the middle. This is shown in derivative graph (b).

If David uses 4 GB over the limit, then he has used a total of 6 + 4 = 10 GB of data in that month. Since his plan includes 6 GB of data, he has exceeded the limit by 4 GB.

For the extra 4 GB of data, he will be charged an additional $10 per GB, so his total extra charge will be $10 x 4 = $40.

Therefore, in a month where David used 4 GB over the limit, he would have to pay $30 (the base cost of the plan) plus $40 (the extra charge for the additional data), for a total of $70.

If David went over the limit by x GB, then his total data usage for the month would be 6 + x GB. He would then be charged $10 for each GB over the limit, so his extra charge would be $10 x x.

Therefore, in a month where David went over the limit by x GB, he would have to pay $30 (the base cost of the plan) plus $10x (the extra charge for the additional data), for a total of $30 + $10x.

The null hypothesis is that the percentage of Americans who start the day with cereal for breakfast is 80%. The alternative hypothesis is that the percentage is less than 80%.

Let p be the true proportion of Americans who start the day with cereal. The sample proportion is 70/100 = 0.7. The standard error is √(p(1-p)/n) = √(0.8(0.2)/100) = 0.04.

The test statistic is (0.7 - 0.8) / 0.04 = -2.5. From the standard normal distribution table, the p-value for a one-tailed test with a test statistic of -2.5 is 0.0062.

Since the p-value (0.0062) is less than the significance level (0.05), we reject the null hypothesis. There is evidence to support the claim that the percentage of Americans who start the day with cereal for breakfast is less than 80%.