The point P = (12,-9) on the circle x² + y² =2 is also on the terminal side of an angle 0 in standard position. Find sin 0, cos 0, tan, csc 0, sec 0, and cot 0

Answer:

Your answer should be 88

Step-by-step explanation:

The amount of money Gabriela paid for the pair of glasses after the discount is $50.4

Regular price of the pair of glasses= $72

Percentage discount= 30%

Amount Gabriela actually paid= Regular price of the pair of glasses - (Percentage discount of Regular price of the pair of glasses)

= 72 - (30% × 72)

= 72 - (0.3 × 72)

= 72 - 21.6

= $50.4

Therefore, Gabriela paid $50.4 for the pair of glasses after deducting discount.

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Answer:

(3.369, 4.071)

Step-by-step explanation:

Answer:

Timmy has been working at Monster Burger longer than Susie, which explains why he earns more money. Monster Burger employees are given a 50 cent raise each year, so Susie's salary will likely increase over time as she continues to work there.

Step-by-step explanation:

It is possible to determine how long Susie has been working at Monster Burger by using the information given. Since Timmy makes 720 dollars working 40 hours and Susie makes 600 dollars working the same hours, we can calculate their hourly wages:

Timmy's hourly wage: 720 / 40 = 18 dollars

Susie's hourly wage: 600 / 40 = 15 dollars

Since Monster Burger employees are given a 50 cent raise a year, this means that Susie's hourly wage has increased by 50 cents * x years, where x is the number of years Susie has been working there. Thus, we have:

15 + (0.50 * x) = 18

Solving for x, we get:

x = (18 - 15) / 0.50 = 6 years

Therefore, Susie has been working at Monster Burger for 6 years.

Based on the provided lines and angles;

Let's discuss each problem we have:

Problem 2: Parallel lines m and n are cut by transversal l

Statement A: ∠1 = ∠5 is correct because both are corresponding angles and congruent.

Statement B: ∠2 = ∠4 is correct because both are vertical angles and congruent

Statement C: ∠2 = ∠7 is incorrect because ∠7 is the corresponding angle of ∠3 which is the supplementary angle of ∠2

Statement D: ∠3 and ∠6 form a linear pair is correct because both are consecutive interior angles and supplementary

Statement E: ∠4 and ∠5 are supplementary is correct because both are consecutive interior angles.

Problem 3: Parallel lines a and b are cut by transversal c and d

∠1 = 115°

∠8 = 105°

∠5 is adjacent and the supplementary angle of ∠8, then:

∠5 + ∠8 = 180°

∠5 + 105° = 180°

∠5 = 75°

∠11 is the alternate exterior angle of ∠5 and both are congruent, then:

∠11 = ∠5 = 75°

∠16 is the corresponding angle of ∠4 and congruent. ∠4 is the adjacent and supplementary of ∠1, then:

∠16 = ∠4

∠4 + ∠1 = 180°

∠16 + ∠1 = 180°

∠16 + 115° = 180°

∠16 = 65°

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Answer:

D

Step-by-step explanation:

Answer:

So for x sandwiches, the cost would be 10 + 4.5x dollars.

Step-by-step explanation:

The cost for x sandwiches can be calculated by adding the delivery fee to the cost of the sandwiches:

Cost = Delivery fee + Cost of sandwiches

Cost = 10 + 4.5x

The inequality of the statement is x > 16

From the question, we have the following parameters that can be used in our computation:

a city received more than 16 in of snow

In inequality, more than mean >

So, we have the following representation

Snow > 16

Represent the snow with x

So, we have the following representation

x > 16

Hence, the inequality is x > 16

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The mean of 13 words, median of 10 words, and standard deviation of 13.20 words give us an idea of the central tendency and variability of the number of words learned by the seven infants.

(a) Mean: The mean is the average of the values and can be calculated by adding all the values and dividing by the number of values. For the number of words learned by the seven infants, the mean can be calculated as follows:

mean = (10 + 12 + 8 + 0 + 3 + 40 + 18) / 7 = 91 / 7 = 13

So the mean number of words learned by the seven infants is 13 words.

(b) Median: The median is the middle value in a set of values. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

0, 3, 8, 10, 12, 18, 40

The median is 10 words.

(c) Standard Deviation: The standard deviation is a measure of the spread or variability of a set of values.

First, the deviations from the mean are calculated as follows:

10 - 13 = -3

12 - 13 = -1

8 - 13 = -5

0 - 13 = -13

3 - 13 = -10

40 - 13 = 27

18 - 13 = 5

Next, the squared deviations are calculated:

(-3)^2 = 9

(-1)^2 = 1

(-5)^2 = 25

(-13)^2 = 169

(-10)^2 = 100

27^2 = 729

5^2 = 25

The variance is then calculated as the average of the squared deviations, divided by the number of values (n - 1):

variance = (9 + 1 + 25 + 169 + 100 + 729 + 25) / (7 - 1) = 1058 / 6 = 176.33

Finally, the standard deviation is calculated as the square root of the variance:

standard deviation = sqrt(variance) = sqrt(176.33) = 13.20

(d) Explanation: The mean, median, and standard deviation are measures of the central tendency and variability of a set of values. The mean is the average of the values and gives an idea of the typical value.

In this case, The mean tells us that the typical number of words learned by the seven infants is 13 words, the median tells us that half of the infants learned more than 10 words and half of the infants learned less, and the standard deviation tells us that the values are spread out around the mean with a deviation of about 13 words.

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At 38 meters into the pool, the water is 7.6 meters deep. Water depth is the distance in feet between the ocean's surface and bottom, as determined by mean lower low water.

Ocean depth is most frequently and quickly measured using sound. Sonar, which stands for sound navigation and range, is a technique that allows ships to map the topography of the ocean below. The instrument uses sound waves to send to the ocean's bottom and time how long it takes for an echo to come back. The straightforward formula "d/2 = vt" is used to determine the depth "d" because the speed of sound in water is known.

height-1 = 10

height-2 = 38

depth-1=2 m

depth-2 = ?

depth-2 = (height 2* depth 1)/height 1

depth-2 = ( 38*2)/10

depth-2 = 7.6 m

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The given polygons WXYZ and PQRS are similar.

Similar figures are those figures which are having the same shape, but the sizes are different.

Since the shape of similar figures are same, the corresponding angles of the figures will be equal.

And the corresponding sides will be proportional.

From the polygons WXYZ and PQRS, given,

∠X = ∠Q

∠W = ∠P

∠Y = ∠R

∠Z = ∠S

So the figures are similar.

WX / PQ = XY / QR = YZ / RS = WZ / PS

Hence the given figures are similar.

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The statement "generally, parametric estimating requires less information and time than analogous estimating." is False.

Parametric estimating and analogous estimating are two different methods used to estimate the cost of a project or the value of a parameter.

Parametric estimating uses statistical data and mathematical models to make predictions about the cost or value of a project. This method requires specific data and information about the project, such as historical data, vendor quotes, and cost of similar projects.

The advantage of parametric estimating is that it can be more accurate and precise than other methods, but it can also be time-consuming to gather the necessary data and perform the calculations. Analogous estimating, uses information from similar projects to make predictions about the cost or value of a project.

This method requires less data and information than parametric estimating, but it can be less accurate and precise. Analogous estimating is often used as a quick and rough estimate, or when there is not enough data available to use parametric estimating.

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The equation of the graphed line is y = 1/2 x + 6

The general formula for the equation of a graphed line is expressed with the formula;

y = mx + c

Where the parameters are;

From the diagram shown, the values are;

(0, 6) and (2. 7)

The intercept is 6

The slope is expressed as; y₂ - y₁/x₂ - x₁

Substitute the values

Slope, m = 7 - 6/2 - 0

Slope, m = 1/2

Then, the equation is

y = 1/2 x + 6

Hence, the equation is y = 1/2x + 6

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The standard deviation changes as the  three digits 5, 5, and 20 add up to 30 and it would decrease.

Given that,

The three digits 5, 5, and 20 add up to 30 and have a mean of 10 as a result. To calculate the standard deviation, use software. utilize the sample standard deviation function. Give a two-decimal place precision to your response. Assume the data set now included a fourth value, 10, which is equal to the mean.

To find : How would the standard deviation change?

S = √∑(Xi - X)²/n-1

= √ (5-10)² + (5-10)² +(20-10)² / 2

= √ 25+25+ 100 / 2

= √ 75

= 8.66

S = √∑(Xi - X)²/n-1

= √ (5-10)² + (5-10)² +(20-10)² + (10-10)² / 3

= 7.07

So, The standard deviation would drop when the three digits 5, 5, and 20 added up to 30.

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To determine these intervals, one can use the function's critical points, zeros, or other methods, such as testing values or using calculus.

The intervals over which a function is positive, negative, or equal to zero can be determined by analyzing the function's graph. If a function is positive over an interval, its graph is above the x-axis over that interval, meaning that its values are positive. If a function is negative over an interval, its graph is below the x-axis over that interval, meaning that its values are negative. If a function is equal to zero over an interval, its graph passes through the x-axis over that interval, meaning that its values are equal to zero. To determine these intervals, one can use the function's critical points, zeros, or other methods, such as testing values or using calculus.

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The gray squirrel population t years after introduction is P(t) = [tex]340 x 2^(t/9).[/tex]

The formula for the gray squirrel population, p, t years after the introduction of the population is [tex]P(t) = P0 x 2^(t/9)[/tex], where P0 is the initial population. We can use this formula to answer both (a) and (b). For (a), we can substitute t = 0 and P(t) = 680, to solve for P0. This gives us that the initial population of gray squirrels was 340. For (b), we can substitute t = 27 (the number of years since introduction) and P(t) = 680, to solve for P(27). This gives us that the expected population of gray squirrels t years after introduction is 1360. Therefore, the formula for the gray squirrel population t years after introduction is [tex]P(t) = 340 x 2^(t/9)[/tex].

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Step-by-step explanation:

a)

-sin(2x) = cos(2x)

sin(2x) = cos(2x)

2sin(x)cos(x) = cos(2x)

2sin(x)cos(x) = 1 or -1

sin(x) = +/-√(1/2) or sin(x) = 0

x = (2n+1)π/4 or x = nπ

b)

3 tan(x) = 2 sin(2x)

tan(x) = 2/3 sin(2x)

sin(2x) = 3 tan(x)/2

cos^2(x) = (1 - sin^2(x)) = (1 - (3 tan(x)/2)^2)/4

x = nπ/2 + arctan(2√(2)/3) or x = nπ/2 + arctan(-2√(2)/3)

c)

sec(x) cos(3x) = 0

cos(x) = 0 or cos(3x) = 0

x = nπ/2 or x = (3n+1)π/6

d)

1 - cos(x) = 2 - 2sin^2(x)

cos(x) = 2sin^2(x) - 1

2sin^2(x) = cos(x) + 1

sin^2(x) = (cos(x) + 1)/2

sin(x) = +/- √((cos(x) + 1)/2)

e)

4cos^4(x) - 5cos^2(x) + 1 = 0

cos^2(x) = (1 ± √(5))/2

x = arccos(±√((1 + √(5))/2)) or x = arccos(±√((1 - √(5))/2))

Note: n is any integer in the given domain.

The percent decrease of the average gas price from january to February is 7.85%

How to find percent decrease of the average gas price from january to February

Average gas price in January = $4.33 per gallon

Average gas price in February = $3.99 per gallon

Change in average gas price = Average gas price in January - Average gas price in February

= $4.33 - $3.99

= $0.34

Percent decrease in average price = Change in average gas price / Average gas price in January × 100

= $0.34 / $4.33 × 100

= 0.078521939953810 × 100

= 7.85%

In conclusion, the price of gas has decreased at a percentage of 7.85% from January to February.

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complete question

Gas prices averaged $4.33 per gallon in january and $3.99 per gallon in february. what was the percent decrease of the average gas price from january to february?

Step-by-step explanation:

false.

3x + 6x is equivalent to 9x

but not 3x + 6. 6 is a constant added term. not a multiplication factor. so, it cannot be combined with a multiplication factor.

but 3x + 6 = 9x

has one solution, one value of x for which this equation is true :

3x + 6 = 9x

6 = 6x

x = 1

so, for x = 1 (and only for x = 1) this is true. for any other value of x this is false.

therefore, the general equivalent statement is false.

Rounding to four decimal places, the standard divisor is 3.4792.

The standard divisor can be calculated as follows:

Standard Divisor = Total number of schools / Total number of upgrades

Total number of schools = 104 + 33 + 26 + 4 = 167

Total number of upgrades = 48

Standard Divisor = 167 / 48 = 3.4792

Rounding to four decimal places, the standard divisor is 3.4792.

The standard divisor is a term used in resource allocation or distribution problems, where a set number of resources (e.g., funding, personnel, supplies, etc.) has to be divided among a number of recipient entities (e.g., schools, departments, regions, etc.).

The standard divisor is a number that represents the average allocation of resources per recipient entity, calculated as the total amount of resources divided by the number of recipient entities.

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Answer:

Step-by-step explanation:

the total perimeter is 33 so all of the sides are equal to it.

33=3x+13+12

then combine like terms

33=3x+25

subtract from each side

(33)-25=(3x+25)-25

8=3x

divide by 3

x=2  2/3

Answer:

  a.  one solution (x = -8)

Step-by-step explanation:

You want to know how many solutions there are for the equation 2x -48 = 8x.

This is a 2-step linear equation.

Step 1: subtract 2x from both sides.

  -48 = 6x

Step 2: divide by the coefficient of x.

  -48/6 = -8 = x

There is one solution: x = -8.

__

Additional comment

When x terms are on both sides of the equal sign, there will be one solution if their coefficients are different.

If the coefficients are the same, the number of solutions may be 0 or infinite, depending on the constant value(s).

The number of 2/3 parts in the number 4 will be 6.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The number of 2/3 parts in the number 4. Then the expression is given as,

⇒ 4 ÷ (2/3)

⇒ 4 x (3/2)

⇒ 2 x 3

⇒ 6

The number of 2/3 parts in the number 4 will be 6.

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The solution is, Their rate of change is respectively 0.5.

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The slope-intercept form of the equation of a straight line is:

y=mx+c

where, m= rate of change.

From the given equations, the two that have the same rate of change are:

• A. y = 0.5x - 1

• D. t= 0.5n + 1​

Their rate of change is respectively 0.5.

The correct choices are A and D.

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Answer: A teapot.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

7/4 = 14/8 hr

14/8  + 27/8  = (14+27) / 8 = 41/8 = 5  1/8   hr

1 Let's call the two numbers x and y. According to the ratio, x:y = 8:9, so y = (9/8)x. And since their sum is 136, x + y = 136, so we can substitute y = (9/8)x into this equation:

x + (9/8)x = 136

(17/8)x = 136

x = 64

So the two numbers are 64 and 72.

2 Let's call the three numbers x, y, and z. According to the ratio, x:y:z = 3:2:7, so y = (2/3)x and z = (7/3)x. And since their sum is 108, x + y + z = 108, so we can substitute y = (2/3)x and z = (7/3)x into this equation:

x + (2/3)x + (7/3)x = 108

(12/3)x = 108

x = 36

So the three numbers are 36, 24, and 84.

3 Let's call the four numbers a, b, c, and d. According to the ratio, a:b:c:d = 5:6:7:8, so b = (6/5)a, c = (7/5)a, and d = (8/5)a. And since the greatest of these is 24, d = 24, so we can substitute c = (7/5)a and d = (8/5)a into this equation:

a + (6/5)a + (7/5)a + (8/5)a = 24

(27/5)a = 24

a = 24 * 5/27 = 8

So the four numbers are 8, 9.6, 10.4, and 24. And the sum of these numbers is 8 + 9.6 + 10.4 + 24 = 52

4 Let's call the three heirs' land area x, y, and z. Since the eldest heir received three times as much as the youngest child, who received two times as much as the middle child, we can write the equation:

x = 3y and y = 2z

So we can substitute y = 2z into x = 3y to get:

x = 3 * 2z = 6z

And since the middle child received 12 ha of land, we can substitute z = 12 into x = 6z to get:

x = 6 * 12 = 72

So the total area of land they inherited is x + y + z = 72 + 2 * 12 = 96 ha.

5 Let's call the two numbers x and y. According to the ratio, x:y = 4:5, so y = (5/4)x. And since their sum is 108, x + y = 108, so we can substitute y = (5/4)x into this equation:

x + (5/4)x = 108

(9/4)x = 108

x = 36

So the two numbers are 36 and 45.

6 Let's call the three numbers x, y, and z. Then, we have:

x:y:z = 6:7:8

x + y + z = 63

To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:

x = 6t

y = 7t

z = 8t

We can use the second equation to solve for t:

6t + 7t + 8t = 63

21t = 63

t = 3

So, the three numbers are:

x = 6t = 6 * 3 = 18

y = 7t = 7 * 3 = 21

z = 8t = 8 * 3 = 24

7 Let's call the three numbers a, b, and c. Then, we have:

a:b:c = 2:3:5

a = 48 (the least of these)

To find the values of b and c, we can use the first ratio to write b and c as multiples of a:

b = 3a = 3 * 48 = 144

c = 5a = 5 * 48 = 240

8 Let's call the three numbers p, q, and r. Then, we have:

p:q:r = 3:5:7

r = 75 (the greatest of these)

To find the values of p and q, we can use the first ratio to write p and q as multiples of r:

p = 3r/5 = 3 * 75/5 = 45

q = 5r/7 = 5 * 75/7 = 50

9 Let's call the number of male students m and the number of female students f. Then, we have:

m:f = 2:3

m + f = 50

To find the values of m and f, we can use the first ratio to write m and f as multiples of the same number. Let's call that number t:

m = 2t

f = 3t

We can use the second equation to solve for t:

2t + 3t = 50

5t = 50

t = 10

So, the number of male students is:

m = 2t = 2 * 10 = 20

And the number of female students is:

f = 3t = 3 * 10 = 30

10 Let's call the number of stamps that Cherie has x, the number of stamps that Mona has y, and the number of stamps that Kate has z. Then, we have:

x:y:z = 3:4:5

x + y + z = 360

To find the values of x, y, and z, we can use the first ratio to write x, y, and z as multiples of the same number. Let's call that number t:

x = 3t

y = 4t

z = 5t

We can use the second equation to solve for t:

3t + 4t + 5t = 360

12t = 360

t = 30

So, Cherie has:

x = 3t = 3 * 30 = 90 stamps

Mona has:

y = 4t = 4 * 30 = 120 stamps

Kate has:

z = 5t = 5 * 30 = 150 stamps

11 The marbles are divided in the ratio 1:2:2:3, so there are 2 x 2 = 4 times as many yellow and blue marbles as there are red marbles. Therefore, there are 2 + 2 = 4 red marbles. Hence, there are 4 x 2 = 8 yellow and blue marbles. Furthermore, there are 3 times as many green marbles as there are red marbles, meaning there are 3 x 4 = 12 green marbles. Therefore, the total number of yellow and green marbles is 8 + 12 = 20.

12 According to the ratio, there are 6:5:2:3 of fiction to nonfiction to general reference to children's books. So the number of each category can be calculated as follows:

Fiction: 6/16 x 80 = 30 books

Nonfiction: 5/16 x 80 = 25 books

General reference: 2/16 x 80 = 10 books

Children's books: 3/16 x 80 = 15 books

So, there are 15 - 10 = 5 more children's books than general reference books.

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The value of 'x' score in the 7th game is - 47.25.

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

From the given table and concept of weighted average we have,

13.5 = (13.5/2 + 40.5/2 + 67.5/2 + x/1).

13.5 = (6.75 + 20.25 + 33.75 + x).

13.5 = 60.75 + x.

x = - 47.25.

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Answer:

94.5 POINTS

Step-by-step explanation:

because math