Eugene has five payments left to make on his computer. If each payment is $157.90, how much does he still owe?

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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Answer:

3 hours

Step-by-step explanation:

5km = 30m

-------------------

         5

1km = 6m

*30  *30

30km = 180 m

30k = 3 hours

Answer:

4

Step-by-step explanation:

1. First you want to distribute the coefficients through the values in the parenthesis

a. 2(2x-8)=3(4-x)

b. 4x-16 = 12-3x

2. Then you want to put all of the x values on one side of the equation

a. 4x-16 = 12-3x

b. 4x+3x-16=12-3x+3x

c. 7x-16=12

3. Then do the same for the constant values

a.7x-16=12

b.7x-16+16=12+16

c.7x=28

4. Then you divide both sides by the coefficient in front of the x value

a.7x=28

b.7x/7 =28/7

c. x = 4

5. We can check this by plugging this value in to the example

a. 2(2*4-8)=3(4-4)

b. 2(8-8)=3(0)

c. 2(0)=3(0)

d. 0 = 0 :)

The area enclosed in one loop of the curve r = cos2θ will be π/8.

Any function between the dependent and independent variables can be represented in a graph diametrically.

For instance, if y = x2 forms a parabola, we may infer from the graph alone that it will always have a positive value, regardless of the range of x.

As per the given curve,

r = cos2θ

Since |cos2θ| ranges between 0 and 1.

At r = 1

cos2θ = 1 ⇒ θ = 0

At r = 0

cos2θ = 0 ⇒ θ = π/4

The area of one loop will be as,

A = 1/2∫r²dθ

A = (1/2)∫cos²2θ dθ

A = (1/2)∫(1 + cos4θ)/2  dθ

A = π/8

Hence" The area enclosed by the given function will be π/8".

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Answer:

16

Explanation:

First you convert  

80

%

into a decimal which is  

.80

then you multiply it by  

20

.

.80

×

20

=

16

We multiply it by  

20

because that's our total and by  

.80

because that's the amount that we got correct. Had it been  

100

%

then that would mean we got every question right.

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

as she usually finishes the race in 7.5 and her time for breaks are at 7.75 all you have to do is solve a simple equation of : 7.75 - 7.50 = 0.25

Answer:0.25

Step-by-step explanation:

as she usually finishes the race in 7.5 and her time for breaks are at 7.75 all you have to do is solve a simple equation of : 7.75 - 7.50 = 0.25

Info given

We have a total of people given (82). We also know that we have 54 children of under 12 years and under some children were under 3 years

We define x as the number of children under 3 years.

We want to find C for the total cost. We don't have the unitary prices but we can assume it as C1 (over 3 and lower than 12) and C2(adults) for children and adults.

Solution:

With C the total amount collected and C1 and C2 described above.

Answer:

y=1/2x+1

Step-by-step explanation:

Answer:

Step-by-step explanation:

First you want to mark 2 points. I chose (-2,0) and (2,2), it does not mater what points you chose. Once you have the two points, you need to find the slope. To calculate the slope can be seen below.

Slope (m) = ΔY/ΔX = 1/2 = 0.5

Once you have the slope, which is 0.5, you fill in this equation.

y = mx + b, where m is the slope and b is the y-intercept.

Now filling in given variables, you get this equation.

y = 0.5x + 1

Answer:

Step-by-step explanation:

1). 7x - 2y = 5 , A = 7 , B = 2 , C = 5

2). 4x - y = 1 , A = 4 , B = - 1 , C = 1

3). 5x - 2y = 3 , A = 5 , B = - 2 , C = 3

4). 4x - 3y = 3 , A = 4 , B = - 3 , C = 3

5). 2x + y = 15 , A = 2 , B = 1 , C = 15

For the given equation 2x+3y≥6 and 3x=2y≤6, the solution is (1.5, 1). Option A is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

3x=2y<=6

3x =2y

y=1.5x

3x≤6

x≤2

2y≤6

y≤3

As a result, we found that y is 1.5 times x, the value of x should be less than 2, and y should be less than 3.

We analyze each option one by one we obtained the correct values is,

(y,x) = (1.5, 1)

The values follow all the obtained condition

Thus, for the given equation 2x+3y≥6 and 3x=2y≤6 the solution is (1.5, 1). Option A is correct.

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Answer:

(0.5, 2) and (-2, 4)

Step-by-step explanation:

I did the assignment it is the correct answer.

The product of two integers is 72. One number is two less than five times the other. Which of the following equations could be used to find one of the numbers?

A. 2x2 − 5x = 72

B. 5x2 − 2x = 72

C. 2x2 − 5 = 72

D. 5x2 − 2 = 72

ab = 72

a = 5b-2

b(5b-2)= 72

5b^2 - 2b = 72

It is B :)

Step-by-step explanation:

5x2-2+72

Answer:True

Step-by-step explanation:every matrix transformation is a linear transformation

The probability of at most six individuals in the sample having used a discount broker is calculated to be approximately 0.997.

To solve this problem, we need to use the binomial distribution formula. Let X be the number of individuals in the sample who have used a discount broker. Then, X follows a binomial distribution with parameters n = 9 and p = 0.3.

The probability of at most six individuals in the sample having used a discount broker can be calculated as follows:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 6)

Using a binomial probability table or calculator, we can find the individual probabilities and sum them up. Alternatively, we can use a normal approximation to the binomial distribution if the sample size is large enough (np and n(1-p) are both greater than 5).

Using the normal approximation, we have:

mean = np = 9 x 0.3 = 2.7

variance = np(1-p) = 9 x 0.3 x 0.7 = 1.89

standard deviation = √(variance) = 1.374

To standardize the distribution, we calculate the z-score:

z = (6.5 - 2.7) / 1.374 = 2.75

Using a standard normal distribution table or calculator, we find that the probability of a z-score less than or equal to 2.75 is approximately 0.997.

Therefore, the probability of at most six individuals in the sample having used a discount broker is approximately 0.997.

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The complete question is :

What is the probability that in a random sample of nine individual investors, at most six have used a discount broker, given that the American Society of Investors survey found that 30% of individual investors have used a discount broker?

Answer:

SSS

Step-by-step explanation:

We can see that 2 sides are equal already, and because they share a side, that side is also equal. So, side side side.

Answer:

Proof:

Draw circle C with center at point A and radius AD = CD = DE.

Draw point P outside the circle C.

Draw segment AP and extend it to intersect the circle at point B.

Draw segment BD.

Draw segment CP.

Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.

Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).

Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).

Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.

Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.

Therefore, segment CP is a tangent to circle C at point B.

Hence, the proof is complete.

Answer:

I got a good grade on it yw ;)

The perimeter of the rectangle is 1 2/3 units, the perimeter of a rectangle is the total length of all four sides of the rectangle. The formula for the perimeter of a rectangle is 2(length + width).

In this case, the length is 1/3 unit and the width is 1/2 unit. Plugging these values into the formula, we get: Perimeter = 2(1/3 + 1/2) = 2(5/6) = 5/3

Dividing 5 by 3, we get 1 2/3. Therefore, the perimeter of the rectangle is 1 2/3 units.

In more detail, the perimeter of a rectangle is the distance around the outside of the rectangle. It is equal to the sum of all four sides of the rectangle. In this case, the rectangle has a length of 1/3 unit and a width of 1/2 unit. The perimeter can be calculated using the following formula:

Perimeter = 2(length + width)

Plugging in the values for length and width, we get:

Perimeter = 2(1/3 + 1/2)

= 2(5/6)

= 5/3

This means that the perimeter of the rectangle is 5/3 units, or 1 2/3 units.

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The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

Based on a random sample of books, a 95% confidence interval for the mean number of pages per book in the library is (237, 293). This means that we can be 95% confident that the true population mean of the number of pages per book falls within this interval.

A confidence interval provides a range of values within which we estimate the true population parameter to lie. In this case, the parameter of interest is the population mean number of pages per book in the library.

The given confidence interval of (237, 293) suggests that, based on the sample data, we can be 95% confident that the true population mean falls within this range. This means that if we were to repeatedly take random samples from the library and calculate confidence intervals, approximately 95% of those intervals would contain the true population mean.

The width of the confidence interval, in this case, is determined by the sample size, variability of the data, and the desired level of confidence. The larger the sample size, the smaller the variability, or the higher the confidence level, the narrower the interval would be.

Therefore, we can interpret the given confidence interval as an estimate for the population mean number of pages per book in the library, with a 95% level of confidence.

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Answer:

2.12

Step-by-step explanation:

Discussion

The answer is given in the graph I've made for you. The distance you want is a contained in a line that is perpendicular to the given line and goes through (2,-1). If I have not interpreted this correctly please leave a comment under the question and I will edit it. I have ignored the 4.

The steps needed are

Givens

line y = -x + 4

point (2,-1)

Solution

The slope of the second line is

m1 * m2 = - 1

m1=  -1                From the given equation

m2 = ?

-1 * m2 = - 1

m2 = 1

Find the equation of the new line

x = 2

y = - 1 from the given point

-1 = 2 + b             Subtract 2 from both sides

-1 - 2 = 2-2 + b    Combine

-3 = b

Equation of the new line

y = x - 3

Intersection point of the two lines

y = -x + 4

y = x - 3              Add The xs cancel

2y = 1                  Divide by 2

y = 1/2

1/2 = -x + 4          Subtract 4 from both sides

1/2 - 4 = -x + 4 -4 Combine        

-3 1/2  = -x            Multiply both sides by - 1

3 1/2 = x

So the intersection point is (3.5, 0.5)

Find the distance between (2,-1) and (3.5,0.5)

d = sqrt( (2 - 3.5)^2 + (-1 - 0.5)^2 )

d = sqrt( (-1.5)^2 + (-1.5)^2 )

d = ( 1..5 * sqrt(2) )

d = 2.12

Rounding to the nearest degree, the measure of angle 1 is 16 degrees.

We can use the formula which is C = 2πr, where C is the circumference and r is the radius, to find the radius of the circle.

C = 2πr

13.100 = 2πr

r = 13.100 ÷ (2π)

r ≈ 2.084 inches

We can use the fact that angle 1 and angle 2 are opposite angles of an inscribed quadrilateral and thus add up to 180 degrees.

angle 1 + angle 2 = 180

To find angle 2

angle 2 = angle AOB + angle ABO

We know that angle AOB is a central angle,

which is (x + x) = 5.4 inches.

angle AOB = (arc AB) ÷ r

= 5.4 ÷ 2.084

≈ 2.59 radians

We can convert this to degrees by multiplying by 180/π:

angle AOB ≈ 148.5 degrees

To find angle ABO

angle ABO = (180 - angle AOB) ÷ 2

= (180 - 148.5) ÷ 2

= 15.75 degrees

Therefore,

angle 2 ≈ 148.5 + 15.75

= 164.25 degrees

Finally, we can find angle 1 by subtracting angle 2 from 180:

angle 1 = 180 - angle 2 ≈ 180 - 164.25 = 15.75 degrees

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Answer: 16

Step-by-step explanation:

The opposite of -8 is 8. So, the equation that would get the difference would be 8 - (-8) = 16.

Answer:

0.5 assignments (or 1 grade per 2 minuites)

Step-by-step explanation:

20/40 is 0.5

( / is division)

Answer:

2 assignments per minute

Step-by-step explanation:

Divide

20 / 40 = 0.5 minutes per assignment

Divide.

1 / 0.5 = 2

Best of Luck!

Answer:

12

Step-by-step explanation:

Answer:

They are both correct.

Step-by-step explanation:

As we can see, it does not matter whether you plug in x or y in a system of equatins. One thing somebody might be skeptical about in this equation is that one of the equations does not contain a variable. BUT, if reading closer, one can see that both x and y have to be in one of the equations to make the other true.

Hope this helped!

We will see that both Jared and Nicole are correct.

So we know that Jared found an equation:

y = x + 10, then he substituted y for (x + 10) on the other equation, this would be the substitution method, and Jared is correct so far.

We also know that Nicole found the equation:

x = y - 10

And she replaced x by y - 10 on the other equation, she is also correct.

Each one just substituted a different variable, that is why they have different approaches, but in both cases the substitutions are correct.

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The upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit for standard deviation.

To find the upper control limit for an x-bar chart, we use the formula:

Upper Control Limit = X-bar + A2 * (standard deviation / \(\sqrt{(sample size)}\))

Where X-bar is the average temperature across all bottles (52 degrees Fahrenheit), A2 is a constant factor based on the sample size (for a sample size of 9, A2 is 0.729), and the standard deviation is 0.9 degrees Fahrenheit.

Plugging in these values, we get:

Upper Control Limit = 52 + 0.729 * (0.9 / \(\sqrt{9}\))
Upper Control Limit = 52 + 0.243
Upper Control Limit = 52.243 degrees Fahrenheit

Therefore, the upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit. This means that if any sample of 9 bottles has an average temperature above this limit, it may indicate a problem with the process that needs to be addressed.

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The upper control limit (UCL) for the X-bar chart is 52.9 degrees Fahrenheit.

We will use the following terms to find the upper control limit (UCL) for an X-bar chart:
Average temperature (µ) = 52 degrees Fahrenheit
Standard deviation (σ) = 0.9 degrees Fahrenheit.

Sample size (n) = 9 bottles
Number of days (m) = 105 days.

To find the UCL, we first need to find the standard error (SE) using the formula:
SE = σ / √n
Substitute the given values into the formula:
SE = 0.9 / √9 = 0.9 / 3 = 0.3 degrees Fahrenheit
Now we'll use the control chart formula to find the UCL, which is:
UCL = µ + 3 * SE
Substitute the values:
UCL = 52 + 3 * 0.3 = 52 + 0.9 = 52.9 degrees Fahrenheit.

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Answer:

1. City A
2. Exponential Growth
3. Linear

Step-by-step explanation:

The equation for exponential growth is f(x)=a(1+r/100)^x, where a is the initial growth/starting population, r is the growth rate, and x is the time intervals.

City A
f(x)=200(1+1.05/100)^x
Simplify:
f(x)=200(1.105)^x

City B
An increase in 20 people each year is NOT exponential but linear:
f(x)=20x+200

Now we plug in x for 1 to stand for 1 year and see which city has a greater number:
City A:
f(1)=200(1.105)^1
f(1)=200 x 1.105
f(1)=221

City B:
f(1)=20(1)+200

f(1)=20+200

f(1)=220

City A will have more people.

City A is an exponential function because there's a percent increase every year, and there will be more people every year because there are more people. This is kind of how compound interest also works

City B is a linear equation because a set number of people are added every year and doesn't change based on the amount of people already in it.

1. City B will have more population after 1 year.

In this case, we have been given of both the cities A and B with each year's growth factor and we have been told to find out, which city will have more population after 1 year. So to find out the comparison, first we need to find out the individual popoulation of both the cities after 1 year of interval.

So, population of City A after 1 year will be 200 * 1.05 = 210

Similarly,  population of City B after 1 year will be 200 + 20 = 220

It is clear that City B has more population as compared to City A.

Therefore, after 1 year City B has more population.

2. equation for City A is Exponential Growth Equation.

Exponential growth is the growth which takes place when a particular quantity increases at a constant rate over a fixed time period. It is given in the form of \(P = P_{0} * (1 + r)^t\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

3. equation for City B is Linear Equation.

Linear equation is a representation of a straight line when graphed on paper. It has constant coefficients and variables raised to power 1. It is given in the form of \(P = P_{0} + rt\), where P is population, \(P_{0}\) is initial population, r is the growth rate, and t is time period.

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Ok so firstly, you need to remember that when a radius is touching a tangent, the angle is always equal to 90°. So x + 57° = 90°. That means your angle is 33°. You have drawn a right angle which is correct so the left triangle's angle is 90° - 33° = 57°. Now because both sides of the triangle is radius, that means c and 57° are equal. That means c = 57°.

Answer:

c = 57 degrees.

Step-by-step explanation:

This is the Alternate Segment theorem:

The angle between a chord of a circle and a tangent to the circle = the angle subtended by the chord in the alternate segment.

So c = 57 degrees.