What is the Image of the point (1,3) after a counterclockwise rotation of 270 degrees?

Answer:

$3.81

Step-by-step explanation:

$15.25 / 4 = $3.81 You divide the cost of baseballs by the number of baseballs.

Answer:$3.81

Step-by-step explanation:

$15.25/4 = $3.81

Answer:

25%

Step-by-step explanation:

In order to solve this problem we first need to figure out how many students were in the second audition. We calculate this by multiplying the 60 initial students by the 40% that made it to the second audition but in a decimal form which is 0.4 (40 / 100 = 0.4)

60 * 0.4 = 24 students

Now that we know that 24 students made it to the second audition and only 6 made it to the final audition we can divide the number of students in the final audition by those in the second audition to find out the percent of change.

6 / 24 = 0.25 .... multiply by 100 to turn decimal into a percentage.

0.25 * 100 = 25%

We can see now that the percentage of change is 25%

a. the probability that a student in this class passes the course is approximately 1 - 0.0301 = 0.9699 (or 96.99%). b. the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale is approximately 0.9992 (or 99.92%). c. the percentage score required to be in the top 10% of students is approximately 75.24%. d. the student's z-score in statistics (1.875) is higher than their z-score in microeconomics (1.818).

a. To find the probability that a student in the class passes the course (assuming a passing grade is 50%), we need to calculate the area under the normal distribution curve for scores greater than or equal to 50%.

Using Table A or a standard normal distribution calculator, we can find the z-score corresponding to a score of 50% in a normal distribution with a mean of 65% and a standard deviation of 8%.

The z-score can be calculated as:

z = (x - mean) / standard deviation

z = (50 - 65) / 8

z = -1.875

From Table A, the corresponding area (probability) for a z-score of -1.875 is approximately 0.0301.

Therefore, the probability that a student in this class passes the course is approximately 1 - 0.0301 = 0.9699 (or 96.99%).

b. To find the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale, we need to find the corresponding z-score for 3.3.

Since the Queen's University GPA Scale is not explicitly mentioned in the question, we will assume a standard normal distribution with a mean of 0 and a standard deviation of 1.

Using Table A, the area (probability) for a z-score of 3.3 is approximately 0.9992.

Therefore, the probability that a student in this class receives exactly 3.3 Grade Points on the Queen's University GPA Scale is approximately 0.9992 (or 99.92%).

c. To find the percentage score required to be in the top 10% of students, we need to find the z-score corresponding to the area under the normal distribution curve that leaves a probability of 10% in the upper tail.

Using Table A, the z-score corresponding to the top 10% (or 90th percentile) is approximately 1.28.

Now, we can calculate the percentage score using the z-score:

z = (x - mean) / standard deviation

1.28 = (x - 65) / 8

Solving for x, we get:

x - 65 = 1.28 * 8

x - 65 = 10.24

x = 75.24

Therefore, the percentage score required to be in the top 10% of students is approximately 75.24%.

d. To compare the student's performance in the statistics and microeconomics classes, we can use z-scores to standardize the scores relative to their respective class distributions.

For statistics:

z_stats = (x_stats - mean_stats) / standard_deviation_stats

z_stats = (80 - 65) / 8

z_stats = 1.875

For microeconomics:

z_micro = (x_micro - mean_micro) / standard_deviation_micro

z_micro = (80 - 60) / 11

z_micro = 1.818

Comparing the z-scores, we see that the student's z-score in statistics (1.875) is higher than their z-score in microeconomics (1.818).

Since z-scores represent the number of standard deviations above or below the mean, a higher z-score indicates better performance relative to the class. Therefore, the student has performed better in statistics relative to their peers compared to their performance in microeconomics.

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The coordinates of a vector in R² with respect to an orthogonal basis B = {v₁, v₂} can be determined using the formula c₁ = (v₁·X) / ||v₁||² and c₂ = (v₂·X) / ||v₂||², where · denotes the dot product and ||v|| represents the magnitude of vector v.

To find the coordinates of a vector X in R² with respect to an orthogonal basis B = {v₁, v₂}, we use the formula c₁ = (v₁·X) / ||v₁||² and c₂ = (v₂·X) / ||v₂||².

First, we calculate the dot product of v₁ and X, which is given by v₁·X = (v₁x * X₁) + (v₁y * X₂), where v₁x and v₁y are the components of vector v₁ and X₁ and X₂ are the components of vector X. Similarly, we calculate the dot product of v₂ and X, which is v₂·X = (v₂x * X₁) + (v₂y * X₂), where v₂x and v₂y are the components of vector v₂.

Next, we calculate the magnitudes of vectors v₁ and v₂, denoted as ||v₁|| and ||v₂||, respectively. These magnitudes are given by ||v₁|| = √(v₁x² + v₁y²) and ||v₂|| = √(v₂x² + v₂y²).

Finally, we substitute the dot products and magnitudes into the coordinate formulas to obtain c₁ = (v₁·X) / ||v₁||² and c₂ = (v₂·X) / ||v₂||². These formulas give us the coordinates of vector X with respect to the orthogonal basis B.

In conclusion, the coordinates of any vector X in R² with respect to an orthogonal basis B = {v₁, v₂} can be calculated using the formulas c₁ = (v₁·X) / ||v₁||² and c₂ = (v₂·X) / ||v₂||², where v₁ and v₂ are the basis vectors and ||v₁|| and ||v₂|| are their respective magnitudes.

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Answer:

240 houses

Step-by-step explanation:

Given that:

Number of streets = 4

Length of each street = 3/4 miles long

Street is divided into lots with one house built per lot

1 mile = 5289 feets

3/4 miles = (3/4) * 5280 = 3960 feets

Hence, street is 3960 feets long

Since each lot must have at least 65 feet frontage along the street:

Number of lots per street :

Length of street / frontage length

3960 ft / 65 ft = 60.92

Hence, maximum number of lots per street = 60 lots per street

Maximum number of houses in New neighborhoods :

Number of lots per street × number of streets

= 60 × 4

= 240 houses

a) To prove that A + al is similar to B + al, where A and B are similar matrices and "a" is a scalar, we need to show the existence of an invertible matrix Q such that [tex]Q^{-1} (A + al)Q = B + al[/tex].

b) To find (u + 2v, u-v), where u and v are vectors in an inner product space, we can expand the inner product using the distributive property and properties of inner products.

a) To prove that A + al is similar to B + al, we need to find an invertible matrix Q such that [tex]Q^{-1}(A + al)Q = B + al[/tex] . Since A is similar to B, there exists an invertible matrix Q such that [tex]Q^{-1}[/tex]AQ = B. Now, let's consider the expression [tex]Q^{-1}(A + al)Q[/tex].

By applying distributive property and associativity,

we get [tex]Q^{-1}(A + al)Q = Q^{-1} AQ + Q^{-1}alQ = B + al[/tex]. Therefore, we have shown that A + al is similar to B + al.

b) To find (u + 2v, u-v), we can expand the inner product using the distributive property and properties of inner products. The inner product is defined as (u, v) = ||u|| ||v|| cosθ, where θ is the angle between u and v.

Expanding (u + 2v, u-v) using the distributive property,

we get (u, u) + (u, -v) + (2v, u) + (2v, -v).

Using the properties of inner products,

we have (u, -v) = -(u, v) and (2v, -v) = 2(v, -v).

Substituting these values back into the expression,

we get (u + 2v, u-v) = (u, u) - (u, v) + (2v, u) + 2(v, -v).

Given that ||u|| = 2, ||v|| = 3, and (u, v) = -2, we can calculate the individual inner products and substitute the values to obtain the final result.

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Answer:

x=4

Step-by-step explanation:

Problem set up is: 5x-6=14

5x=20

x=4

Answer:

1.6

Step-by-step explanation:

1.6*5=8

8+6=14

Answer:

x = 25

Step-by-step explanation:

m(∠PLM) + m(∠PLK) = 180° [Pair of linear angles are supplementary]

m(∠PLM) + 3x = 180°

m(∠PLM) = 180 - 3x

Similarly, m(∠PMN) + m(∠PML) = 180°

m(∠PML) = 180° - (2x + 72)°

By using the property of a triangle,

Sum of interior angle of a triangle = 180°

m(∠PML) + m(∠PLM) + m(∠LPM) = 180°

180 - (2x + 72) + 180 - (3x) + x = 180

-4x + 288 = 180

4x = 288 - 188

x = [tex]\frac{100}{4}[/tex]

x = 25

Answer:

Step-by-step explanation:

Answer:

Formula for n:

[tex]n=\frac{(300-p)^{2}-1 }{0.04}[/tex]

Number sold:

62,475

Step-by-step explanation:

Solving for n:

[tex]p-300=-\sqrt{0.04n+1} \\-p+300=\sqrt{0.04n+1} \\\\(-p+300)^{2} =0.04n+1\\\\(300-p)^{2}-1=0.04n\\\frac{(300-p)^{2}-1}{0.04}=n[/tex]

Solving for number sold:

Then replace p with 250, and solve.

The equation for n is n = ((300-p)²-1) / 0.04, The number of consoles sold is 62475.

An equation is a mathematical statement formed when two expressions are equated using an equal sign.

The weekly demand for a new video game console is given by the equation,

p = 300 - √ ( 0.04n +1)

In the equation , p represents the price of the consoles sold and,

n is the number of consoles sold.

To represent the equation for n, some basic mathematical operations have to be done.

p = 300  - √ ( 0.04n +1)

√ ( 0.04n +1)  = 300 - p

Squaring both the sides of the equation.

0.04n +1 = (300-p)²

0.04n = (300-p)² -1

n = ((300-p)²-1) / 0.04

The consoles sold at a price of $250 has to be determined.

Substituting the value of p in the equation as $250

n = (( 300 - 250)² - 1) / 0.04

n = (50² -1) / 0.04

n = (2500 -1 ) / 0.04

n = 2499 / 0.04

n = 62475

Your question seems incomplete, the complete question is attached with the answer.

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Answer:

C

Step-by-step explanation:

because it's the safe bet sorry I'm really dumb

The data is visually organized, making it easier for viewers to interpret and understand the information at a glance.

The data in the table is grouped by countries, with each country having a corresponding value for the number of cell phones (in millions). To best display this data, a bar graph would be an appropriate representation.

In a bar graph, the countries can be plotted on the x-axis, and the number of cell phones (in millions) can be represented on the y-axis. Each country would have a corresponding bar whose height represents the number of cell phones.

The bar graph allows for easy visual comparison between the different countries and their respective number of cell phones. It effectively shows the relationship and disparities in the number of cell phones across the countries.

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Answer: 3.33 miles per hour.

Step-by-step explanation: To find the speed of the second runner, we can assume their speed is x miles per hour. Using the fact that the first runner's speed is 4/5 of the second runner's speed, we can set up the equation x - 0.4x = 2 to solve for x.

Solving for x, we get x = 3.33 miles per hour.

Answer:

1 11/64

Step-by-step explanation:

we will have to square root the numerator and the denominator that is 625/256 which will give us 25/16. No need to change it to mixed number then multiply 25/16 by 3/4, you can't divide through so you multiply and it will give you 75/64. Then change it to a mixed number, thats how we got 1 11/64.

The constant ratio of this converging series is -0.039 or -0.96.

The constant ratio of this converging series is calculated by applying the formula for geometric series.

S = a / (1 - r)

where;

The given parameters;

S₃ = 26

Tₙ = 27 for n ≥ 1.

S₃ = T₁ + T₂ + T₃ = 26

S₃ = a + ar + ar² = 26

Since Tₙ = 27 for n ≥ 1, then T₁ = 27, and the new equation becomes;

27 + 27r + 27r² = 26

Simply the equation further as follows;

27r² + 27r = -1

27r² + 27r + 1 = 0

Solve the quadratic equation using formula method;

a = 27, b = 27, c = 1

r = -0.039 or -0.96

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Answer:

x = -6

Step-by-step explanation:

6x + 6 = -30

Subtract 6 from each side

6x + 6-6 = -30-6

6x = -36

Divide each side by 6

6x/6 = -36/6

x = -6

From the three residual plots provided, data set A is the best fit by the Regression line. It can be observed that the residuals in data set A are randomly scattered around the zero line, and there is no visible pattern in the plot. In contrast, data set B and C's residual plots exhibit a curved pattern,

The residual plot is used to assess the validity of the assumptions about the residuals in regression analysis. Residuals are computed as the difference between the predicted and observed values of the response variable.

The residual plot displays the residuals against the explanatory variable or predictors (time, in this case), providing a visual examination of the relationship between the residuals and the response variable. From the residual plot, the validity of the following assumptions can be assessed:

The residuals should be randomly distributed and the residuals should be normally distributed, and they should have constant variance across the range of the response variable. The residuals should not have any patterns.

From the three residual plots provided, data set A is the best fit by the regression line. It can be observed that the residuals in data set A are randomly scattered around the zero line, and there is no visible pattern in the plot. In contrast, data set B and C's residual plots exhibit a curved pattern,

which is indicative of nonlinearity or a lack of fit of the regression model. Additionally, data set C's residual plot shows a pattern in the form of increasing variance as the time goes on, which indicates heteroscedasticity or non-constant variance.

The normality assumption is met in all three sets, as the residual plot follows a rough normal pattern and has a similar spread on both sides of the zero line. Hence, data set A is the best fit by the regression line because its residual plot shows no pattern or trends, and residuals are randomly distributed around zero with constant variance.

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The length of the segment IO is 6.

It is the representation of numbers in real order.

The difference between the consecutive numbers in a number line is always positive.

Example:

_____-5__-4__-3__-2__-1__0__1__2__3__4__5_____

We have,

G H  I   J  K  L  M N O

-7 -6 -5 -4 -3 -2 -1  0  1

We see that,

I  is in point -5 on the number line.

O is in point 1 on the number line.

Now,

The length of the segment IO.

This means we have to find the distance between points I and O.

So,

We simply subtract the number line point with I and O.

i.e

= 1 - (-5)

= 1 + 5

= 6

Thus,

The length of the segment IO is 6.

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Answer:   B

Step-by-step explanation:  ¼ + ⅔ = 11/12

Answer: 645 cars

Step-by-step explanation:

Divide 172 by 4 to find the multiple which is 43 so if 4 was multiplied by 43 to get 172 taxis you must multiply 15 by 43 which gives 645

The number of cars in the town is 645.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of number of cars to that of taxis = 15 : 4

Let x be the proportion of the number of cars and number of taxis in the town.

We can write,

Number of cars = 15x, and

Number of taxis = 4x

But we have number of taxis in the town is 172.

So, 4x = 172

x = 172 / 4

x = 43

So the number of cars = 15x

                                     = 15 × 43

                                     = 645

Hence the number of cars in the town is 645.

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Answer:

2(2+3)=2(2)+2(3)

Step-by-step explanation:

we can use the distributive property which is:

[tex]a*(b+c)=a*b+a*c[/tex]

Answer:

2(2+3)=2(2)+2(3)

Step-by-step explanation:

Answer: The answer to your question is B.

Explanation: Answer A equals y = 2 (positive), C equals x = -2, and D equals x = 2 (positive) so that only leaves c as the remaining answer. Hope I helped and good luck.

Answer:

13 dogs and 15 cats

Step-by-step explanation:

d= number of dogs, c= number of cats

First make you linear system of two equations like so:

100d+45c=1975 (100 dollars times an unknown amount of dogs plus 45 times an unknown amount of cats equals $1975)

d+c=28 (A certain amount of cats plus a certain amount of dogs has a total of 28 pets)

100d+45c=1975

d+c=28

We are going to solve using elimination

100d+45c=1975

-100(d+c=28)

100d+45c=1975

-100d-100c=-2800

+______________

-55c=-825

55c=825

c=15

There were 15 cats sold

Now you will plug it in to an original equation to solve for the amount of dogs

d+c=28

d+15=28

d=13

There were 13 dogs

The sum of Ray's and Ron's ages in 5 years can be calculated by adding 5 to each of their current ages. If Ray is x years old, his age in 5 years would be x + 5. Similarly, if Ron is y years old, his age in 5 years would be y + 5. Therefore, the sum of their ages in 5 years would be (x + 5) + (y + 5), which simplifies to x + y + 10.

The sum of Ray's and Ron's ages in 5 years is x + y + 10.

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Answer:

The answer is b : translate K to N and reflect across the line containing JK

Step-by-step explanation:

I just took the quiz

To map ΔHJK to ΔLMN, we (b) Translate K to N and reflect across the line containing JK.

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. The Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Transformation involves changing the position of a shape.

ΔHJK and ΔLMN are similar triangles; this means that the following sides are corresponding:

HJ and LM

HK and LN

JK and MN

The first translation would be to translate the corresponding sides K to N.

Then triangle HJK must be translated across a line that contains point K (i.e. either line JK or line HK)

By comparing the options, the true statement is:

(b) Translate K to N and reflect across the line containing JK.

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Answer:

(3/5+7i)+(0.3-7.002i)

    (5+77i)-(19/4-8i)

    (240-22i)*(247/7+2.222i)

    (33/5+99i)/(33/5-88i)

Step-by-step explanation:

Answer:

300-20x=250+20x

Step-by-step explanation:

The value of x is approximately 0.071.

To solve the equation [tex]0.929 = (1 - x)^{-8}[/tex] for x, we can follow the steps below:

Take the reciprocal of both sides of the equation to get [tex](1 - x)^8 = 1/0.929.[/tex]

Raise both sides of the equation to the power of 1/8 to eliminate the exponent on the left side, resulting in [tex](1 - x) = (1/0.929)^{1/8}[/tex]

Subtract 1 from both sides of the equation to isolate x, yielding

[tex]-x = (1/0.929)^{1/8} - 1.[/tex]

Multiply both sides of the equation by -1 to get[tex]x = 1 - (1/0.929)^{1/8}[/tex].

By plugging in the value of 0.929 into the equation, we can calculate the value of x.

Evaluating the expression yields x ≈ 0.071 (rounded to three decimal places).

Therefore, the value of x is approximately 0.071.

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