Intro to Trig Functions
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P
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Here is the unit circle with a point P at (1, 0). Find the coordinates of P after the circle rotates
the given amount counterclockwise around its center.
of a full rotation
of a full rotation
of a full rotation
Auto saved at: 13:34:30
(-1, 0)
(-1/,
(-1,4³) or about (-0.5, 0.87)
✓³) or about (-0.5, -0.87)
!!!

Answer:

The partial derivatives are,

w.r.t x

\(\partial z/ \partial x = 1/x\)

And , w.r.t y

\(\partial z/ \partial y= -1/y\)

Step-by-step explanation:

z = In (x/y).

Calculating both partial derivatives (with respect to x and y)

Wrt x,

wrt x, we get,

\(z = In (x/y).\\\partial/ \partial x[z]=\partial/ \partial x[ln(x/y)]\\\partial z/ \partial x = 1/(x/y)(\partial/ \partial x[x/y])\\\partial z/ \partial x = y/(x)(1/y)\\\partial z/ \partial x = 1/x\)

Now,

wrt y,

we get,

\(z = In (x/y).\\\partial / \partial y[z]=\partial / \partial y[ln(x/y)]\\\partial z/ \partial y =(1/(x/y)) \partial/ \partial y [x/y]\\\partial z/ \partial y = y/x(-1)(x)(1/y^2)\\\partial z/ \partial y= -1/y\)

So, we have found both first partial derivatives.

The percentage of the total bagels made on Saturday, that the leftover bagels were, was 25 %

The bakery sold 60 bagels and this was only 3 / 5 of the total bagels made. This means that the total bagels made was:

= 60 ÷ 3 / 5

= 60 x 5 / 3

= 300 / 3

= 100 bagels

If 25 bagels were leftover on that Saturday then their percentage was:

= Number of bagels leftover / Number of bagels made

= 25 / 100

= 25 %

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Answer:

3.76EE13 is 3.76 * 10^13

Step-by-step explanation:

Here, we are to express what is written on the calculator in scientific notation.

Mathematically, that would be

3.76 * 10^13

The terms EE13 represent 10^13

Using an exponential function, it is found that you allowance will be worth $1,531.84 in 1 and 2/3 years.

An increasing exponential function is modeled by:

\(A(t) = A(0)(1 + r)^t\)

In which:

For this problem, the parameters are given as follows:

A(0) = 190, r = 0.11.

1 and 2/3 years is equivalent to 12 + 2/3 x 12 = 20 months, hence the value of the allowance is given by:

\(A(t) = A(0)(1 + r)^t\)

A(20) = 190(1.11)^20

A(20) = $1,531.84.

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Answer:

21%

Step-by-step explanation:

Out of the 25 + 9 + 12 + 21 + 12 + 21 = 100 total rolls, 6 came up 21 times so the percentage is 21/100 = 21%.

The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. What is multiple linear regression? Multiple linear regression is a regression method where the response variable is dependent on more than one independent variable. Multiple linear regression is an extension of linear regression, where one response variable is dependent on one independent variable. It helps to determine the nature of the relationship between dependent variables and independent variables in the form of linear equations. It is used to find out the relationship between variables and make predictions based on that relationship. Assumptions of multiple linear regression1. Linearity, It is assumed that the relationship between the independent variables and dependent variables is linear. This implies that as the value of the independent variable changes, the change in the dependent variable is constant.2. Independence, There should be independence among the observations. This implies that there should not be any relationship between the residuals of the observations.3. Homoscedasticity implies that the variance of residuals should remain constant across all levels of the independent variable.4. Multicollinearity, It is the condition where the independent variables are highly correlated with each other. If there is perfect collinearity, it will not be possible to obtain the estimates of regression coefficients.5. Normality, The residuals should follow a normal distribution with mean zero and constant variance. The residuals should be normally distributed and centered on zero. The assumptions that are true for multiple linear regression are: The independent variables are not correlated. The residuals are normally distributed. The relationship between dependent and independent variables is linear. The assumption which is not true for multiple linear regression is that there will be a multi-collinearity effect. Hence, the correct option is D) There will be a multi-collinearity effect.

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Answer:

7/25 is a fraction

Step-by-step explanation:

7/25 is a fraction and 7/25 in decimal form is 0.28

To turn into decimal 7 divide by 25 =0.28

[RevyBreeze]

Answer:

7/25 supposed to be a fraction

Step-by-step explanation:

its decimal form is 0.28

Step-by-step explanation:

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables and c is the constant term. The other different forms to find and represent the equation of a line are slope-intercept form, point-slope form, two-point form, intercept form, and normal form.

The number of water specimen is 304.

What is standard deviation?

The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

What is margin of error?

The margin of Error is a statistical expression that is used to determine the percentage point by which the result arrived will differ from the value of the entire population, and it is calculated by dividing the standard deviation of the population by the sample size and lastly multiplying the resultant with the critical factor.

Given,

margin of error = 0.5

Standard deviation = 5.4

To find the total water specimens.

Margin of Error = Z * ơ / √n

For two-sided confidence interva

p' = 1-α/2

α = 1- 0.90

= 0.1

p' = 1-0.1/2

p' = 0.95

The critical z value for cumulative probability of 0.95 is 1.64.

Margin of error = 1.64(5.4/\(\sqrt{n}\))

0.5 = 1.64(5.4/\(\sqrt{n}\))

n = 304

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The probability of the region not flooding the next year is 19/20.

Given that a region is prone to flooding once every 20 years, we can calculate the probability of flooding in any one year as:

Probability of flooding in any one year = 1/20 = 0.05

Since the probability of flooding in any one year is greater than 0, the probability of not flooding in any one year would be:

Probability of not flooding in any one year = 1 - 0.05 = 0.95

Therefore, the probability of not flooding the next year in this region would be 0.95 or 95%.
Hi, I'd be happy to help you with your probability question.

The probability of flooding in the region any one year is 1/20 (once every 20 years). To find the probability of not flooding the next year, we need to find the complement of the probability of flooding.

Step 1: Determine the probability of flooding.
P(Flooding) = 1/20

Step 2: Find the complement probability.
P(Not Flooding) = 1 - P(Flooding)

Step 3: Calculate the probability of not flooding.
P(Not Flooding) = 1 - (1/20) = 19/20

The probability of the region not flooding the next year is 19/20.

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We can approach this problem using the concept of probability and complement rule.

Given that a region is prone to flooding once every 20 years, we can assume that the probability of flooding in any given year is 1/20 or 0.05 (since once in 20 years means once in 20 trials, and the probability of success in any one trial is 1/20).

Now, the probability of not flooding in the next year can be calculated using the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

Therefore, the probability of not flooding in the next year can be calculated as follows:

P(not flooding) = 1 - P(flooding)

P(not flooding) = 1 - 0.05

P(not flooding) = 0.95

So, the probability of not flooding in the next year is 0.95 or 95%. This means that there is a high likelihood that the region will not experience flooding in the next year.

However, it's important to note that the probability of flooding in any given year is still greater than 0, which means that there is always a possibility of flooding occurring, regardless of whether it occurred in the previous year or not.

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Answer:

x=3 y=4

Step-by-step explanation:

5(4)=20

4(3)= 12

20-12=8

4+3=7

An overall loss of number of points is - \(11\frac{13}{35}\) points.

Given that, last week, by Wednesday Hopt LLC's stock had decreased \(5\frac{4}{5}\)   points. By Friday it was down an additional \(5\frac{2}{7}\) points.

Here, \(5\frac{4}{5}\) = 29/5 and \(5\frac{2}{7}\) = 39/7

Since the points decreased on Wednesday and Friday, we get

-29/5 -  39/7

= -203/35 - 195/35

= -398/35

= - \(11\frac{13}{35}\) points

Therefore, an overall loss of number of points is - \(11\frac{13}{35}\) points.

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Answer:

2 and 4 answers

Step-by-step explanation:

\(\frac{xy}{xv} = \frac{yz}{vw} = \frac{zx}{wx}\)

so the second is correct and forth is correct too

- linear pairs are supplementary, meaning they add up to 180°

5x + 9 + 3x + 11 = 180

8x + 20 = 180

8x = 160

x = 20

- now plug in.

angle 1: 5(20) + 9 = 100 + 9 = 109°

angle 2: 3(20) + 11 = 60 + 11 = 71°

Answer:

AB = 2

Step-by-step explanation:

the triangles are similar so that means there is a constant ratio for each side length. so comparing the ratios from the bigger triangle to the smaller triangle,  leaves us with 9/3 and 15/5. if you take those and divide them you get 3 for both of them which is the constant. so then in order to find the length of AB just take the side length of XY (6) and divide it by 3 (the constant ratio) and there you have your answer!

hope this helps.

the required probability is 0.1

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: 3 students study for an hour and total students are 30

Thus P(1 hour) =3/30

                          =0.1

Hence, the required probability is 0.1

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the answer would be C

Step-by-step explanation:

seeing the graph u can see that it moving 2 right and 1 up

The slope of given line from the graph is 2. Therefore, option D is the correct answer.

In the graph, it is given that x-axis represents time (min) and y-axis represents volume(gal).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = Rise/Run

From the graph, the slope is

Slope (m)= 6/3

= 2

The slope of given line from the graph is 2. Therefore, option D is the correct answer.

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The volume of right prism is equal to 464 cubic inches.

Volume of right prisms (V), in cubic inches, is equal to the product of cross area (A), in square inches, and height (h), in inches:

V = A · h

According to figure, cross area is the result of adding the areas of three rectangles. Area formula for rectangles is:

A' = w · l

Where:

First, determine the cross area of the prism:

A = 2 · (3 in) · (7 in) + (4 in)²

A = 42 in² + 16 in²

A = 58 in²

Second, calculate the volume of the right prism:

V = (58 in²) · (8 in)

V = 464 in³

The right prism has a volume of 464 cubic inches.

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Answer:

4

Step-by-step explanation:

2+2 = 4

Answer:

2

Step-by-step explanation:

x²+2xy+y²

Here x² has degree 2

2xy has degree also 2 because x has 1 degree and y has 1 degree so 1+1=2

y² has degree 2

So the highest degree of the expression is 2

Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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The length of the road from the main highway to the western edge of the plot of land is 4 units.

The length of the road from the main highway to the eastern edge of the plot of land is 2√5 units.

A coordinate plane, also known as a Cartesian plane or xy-plane, is a two-dimensional plane formed by two perpendicular lines called the x-axis and the y-axis. The point where the two axes intersect is called the origin, usually denoted by the point (0,0).

To determine the length of the road from the main highway to the western edge of the plot of land, we can calculate the horizontal distance between the two points (0, 3) and (4, 3) using the distance formula:

d = √((4-0)² + (3-3)²)

  = √16

  = 4

To determine the length of the road from the main highway to the eastern edge of the plot of land, we first need to find the point where the road intersects with the eastern edge of the plot. From the graph, we can see that the road intersects with the eastern edge of the plot at the point (4, 5). We can then calculate the distance between (0, 3) and (4, 5) using the distance formula:

d = √((4-0)² + (5-3)²)

  = √(16+4)

  = √20

  = 2√5

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Answer:

1/3 minute per page

Step-by-step explanation:

it takes 10 minutes to read 30 pages right?

So, that means it takes 1 minute to read 3 pages.

Divide by three to get 1/3 Minute to read one page.

Answer:

78.375

Step-by-step explanation:

24 3/8 equals 24.25. 54 1/8 equals 54.125. Since your subtracting from a negative number, you add the two numbers and get 78.375 as your final answer.

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.

An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.

Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).

The given interval is [1, 2]

The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'

The given statement is 'false'.

This is beacuse, an interval consists set of all the real values in between the two values given.

So, according to the definition, there are not only the end values but also many real values in between them.

Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.

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Answer:

The equation of the perpendicular bisector is y =  \(\frac{-1}{2}\) x - 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

∵ A line passes through points (-1, 5) and (-7, -7)

∴ x1 = -1 ad y1 = 5

∴ x2 = -7 and y2 = -7

→ Use the rule of the slope above to find the slope of the line

∵ m = \(\frac{-7-5}{-7--1}\) = \(\frac{-12}{-7+1}\) = \(\frac{-12}{-6}\) = 2

∴ m = 2

→ Reciprocal the value of m and change its sign to find the slope of

  the line perpendicular line

∴ m⊥ = \(\frac{-1}{2}\)

→ Substitute in the form of the equation above

∵ y = \(\frac{-1}{2}\) x + b

∵ The ⊥ line is also the bisector of the given line, find the mid-point

   of the given line because it is also lying on the ⊥ line

∵ M = (\(\frac{-1+-7}{2},\frac{5+-7}{2}\)) =  (\(\frac{-8}{2},\frac{-2}{2}\)) = (-4, -1)

∴ M = (-4, -1)

→ Substitute the coordinates of M in the equation of the ⊥ line above

∵ x = -4 and y = -1

∴ -1 = \(\frac{-1}{2}\) (-4) + b

∴ -1 = 2 + b

→ Subtract 2 from both sides

∴ -3 = b

→ Substitute the value of b in the equation

∴  y =  \(\frac{-1}{2}\) x + -3

∴ y =  \(\frac{-1}{2}\) x - 3

∴ The equation of the perpendicular bisector is y =  \(\frac{-1}{2}\) x - 3

For the simple harmonic motion equation d=2 sin(pi/3t), the period is 6 seconds.

The period of a simple harmonic motion is the time taken for one complete cycle of the motion. In this equation, d represents the displacement or position of the object at time t. The equation is in the form of sin function with the argument (pi/3)t. The general form of the equation for simple harmonic motion is d=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. To determine the period of this motion, we can use the formula T=2π/ω, where T is the period and ω is the angular frequency. In this case, ω=pi/3, so the period is T=2π/(pi/3)=6 seconds (rounded to the nearest second). Therefore, the object completes one full cycle of motion every 6 seconds.

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The number of people in a restaurant is a discrete random variable with possible values ranging from 0 to 100, while the time it takes for a light bulb to burn out is a continuous random variable with values spanning a non-negative real interval.

Let us now explain each sub-question in a detailed way:

(a) The number of people in a restaurant that has a capacity of 100 is a discrete random variable. This is because the possible values of the random variable are countable and distinct. The number of people in the restaurant can only take on whole number values from 0 to 100, inclusive. The values 0, 1, 2, ..., 100 represent the possible occupancy levels of the restaurant.

(b) The time it takes for a light bulb to burn out is a continuous random variable. This is because the possible values of the random variable form a continuous interval. The time it takes for a light bulb to burn out can theoretically range from a fraction of a second to infinity. It can take on any non-negative real value within this range. Therefore, the possible values of this random variable span a continuum rather than a countable set of distinct values.

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The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).

c) The polar representation of a is r_a * e^(i * theta_a), where r_a is the modulus (magnitude) of a and theta_a is the argument (angle) of a.

d) The polar representation of c is r_c * e^(i * theta_c), where r_c is the modulus (magnitude) of c and theta_c is the argument (angle) of c.

e) To find the sum of a and the complex conjugate of c (c*), we add the real parts and imaginary parts separately. The sum is (a + c*) = (2 - 3j) + (-9 + 2j) = (-7 - j).

f) The complex conjugate of a (a*) is obtained by changing the sign of the imaginary part. So, a* = 2 + 3j.

g) The modulus (magnitude) of a, denoted as |a|, is the distance of a from the origin in the complex plane. |a| = sqrt((2^2) + (-3^2)) = sqrt(4 + 9) = sqrt(13).

h) The angle of a, denoted as angle(a), is the angle formed between the positive real axis and the line connecting the origin to a. To find the angle, we can use the arctan function: angle(a) = arctan(-3/2).

i) The angle of c, denoted as angle(c), is the angle formed between the positive real axis and the line connecting the origin to c. To find the angle, we can use the arctan function: angle(c) = arctan(-2/(-9)).

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Answer:

As Jean writes 75,000,000 in scientific notation as 75.

This is INCORRECT!

The correct solution is:

75,000,000 in scientific notation: 7.5 × 10⁷

Step-by-step explanation:

As Jean writes 75,000,000 in scientific notation as 75.

This is INCORRECT!

Here is the correct solution:

Given the number

75,000,000

Let us write the number 75000000 in scientific notation

We know that scientific notation is of the form \(a\times 10^b\) where \(1\le a<10\) and b is an integer.

Move the decimal point to the left to create a new number from 1 up to 10.

\(a=7.5000000\)

Count the number of times you moved the decimal point

b = 7

so

\(=7.5000000\times 10^7\)

Remove the trailing zeros

\(=7.5\times \:10^7\)

Therefore, we conclude that:

75,000,000 in scientific notation: 7.5 × 10⁷