Find the coordinates of the x- and y-intercepts for an ellipse with the equation (x+1)^2/9 + (y-2)^2/8 = 1

Answer:

  B.  A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(x). Roz must verify that f(0)=g(0)=−2, f(2)=g(2)=0, and f(−1)=g(−1)=0.

Step-by-step explanation:

In order for f(x) = g(x) to have a solution the same values of x and y must satisfy both ...

This will be the case for (x, y) = (-1, 0) or (0, -2) or (2, 0).

Ros can show this using the steps offered in answer choice B:

1. f(0)=−0^3+2(0^2)+0−2=−2; g(0)=0^2−0−2=−2. Thus, (0,−2) is a solution.

2. f(2)=−2^3+2(2^2)+2−2=0; g(2)=2^2−2−2=0. Thus, (2,0) is a solution.

3. f(−1)=−(−1)^3+2(−1)^2+(−1)−2=0; g(−1)=(−1)^2−(−1)−2=0. Thus, (−1,0) is a solution.

a. The number of 7th grade students expected to move by the end of the year is 8 students.

b. if 12 students actually moved, more 7th grade students move than expected.

how many 7th grade students are expected to move by the end of the year?

a.

Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%

Number of 7th grade students expected to move by the end of the year = Moves × number of students

= 4% × 200

= 8 students

b.

if 12 students actually moved,

This means number of of 7th grade students expected to move by the end of the year are more.

Complete question:

How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.

Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%

Answer:

a) P(8) = 0.1395

b) P(at most three) = 0.0423684

c) P(X > 8) = 0.41

Step-by-step explanation:

Data provided in the question:

Mean, μ = 8

Now,

Probability that the number of oil tankers on any given day is

a) exactly eight

using Poisson distribution

we have

P(x) = [tex]\frac{\mu^xe^{-\mu}}{x!}[/tex]

for x = 8

P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex]

or

P(8) = [tex]\frac{16777216\times e^{-8}}{40320}[/tex]

or

P(8) = 0.1395

b)  at most three

i.e P(0) + P(1) + P(2) + P(3)

thus,

P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354

P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683

P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073

P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862

⇒ P(at most three) = 0.0003354 + 0.002683 + 0.01073 + 0.02862

= 0.0423684

c) more than eight.

P(X > 8) = 1 - P(X ≤ 8)

Now,

P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354

P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683

P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073

P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862

P(4) = [tex]\frac{8^4e^{-8}}{4!}[/tex] = 0.05725

P(5) = [tex]\frac{8^5e^{-8}}{5!}[/tex] = 0.091603

P(6) = [tex]\frac{8^6e^{-8}}{6!}[/tex] = 0.1221

P(7) = [tex]\frac{8^7e^{-8}}{7!}[/tex] = 0.13958

P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex] = 0.13758

Thus,

P(X > 8) = 1 - [ 0.0003354 + 0.002683 + 0.01073 + 0.02862 + 0.05725 + 0.091603 + 0.1221 + 0.13958 + 0.13758 ]

P(X > 8) = 1 - 0.5904814

or

P(X > 8) = 0.41

Final answer:

Explains the probability of different scenarios for the number of oil tankers at a port city per day.(a) The probability of exactly eight oil tankers is 0, as it matches the mean.

(b) The probability of at most three tankers is 0.1724.

(c) The probability of more than eight tankers is 0.

Explanation:

Oil Tankers Probability:

(a) The probability of exactly eight oil tankers is 0, as it matches the mean.

(b) The probability of at most three tankers is 0.1724.

(c) The probability of more than eight tankers is 0.

Answer:Kathy is correct

Step-by-step explanation: We need to solve both equations separately in order to determine with certainty which one is correct and which one is not.

Kevin thinks the new equation should be

3(6x-1) + 2y = 43

This can now be solved as follows;

18x - 3 + 2y = 43

Add 3 to both sides of the equation

18x - 3 + 3 + 2y = 43 + 3

18x + 2y = 46

2(9x + y) = 46 (factorize the left hand side of the equation by 2)

Divide both sides of the equation by 2

9x + y = 46

The variables remain unsolved

On the other hand, Kathy thinks the new equation should be

3x + 2(6x - 1) = 43

This can now be solved as follows;

3x + 12x - 2 = 43

Collect like terms (in this equation, x)

15x - 2 = 43

Add 2 to both sides of the equation

15x - 2 + 2 = 43 + 2

15x = 45

Divide both sides of the equation by 15

x = 3

In essence, Kathy's equation has a solution (x=3) while that of Kevin remains unsolved

Final answer:

Neither Kevin nor Katy's equations are correct in the context of solving a system of linear equations, as they do not logically combine the given equations correctly.

Explanation:

The question revolves around which sibling is correct in forming a new equation to solve a system of linear equations. To determine this, we need to see which sibling correctly used the properties of equality to combine or manipulate equations. Kevin's equation, 3(6x-1)+2y=43, is an attempt to modify an existing equation by distributing a 3. Katy's equation, 3x+2(6x-1)=43, seems to combine different parts of the given equations.

Upon closer inspection, neither Kevin nor Katy is entirely correct because their proposed equations do not logically follow from the given set. To solve for a system of equations, we would typically add, subtract, multiply, or divide entire equations by constants or variables to eliminate one variable, so we can solve for the other.

Answer:

9 yards of each quilt.

Step-by-step explanation:

Let the length of each quilt be 'x'.

Given:  

Length of green felt = 15 yards

Length of blue felt = 12 yards

Total number of quilts = 3

Total length of all the quilts in terms of 'x' is given as:

[tex]Total\ length=x+x+x=3x ----(1)[/tex]

Total length is also equal to the sum of the lengths of green and blue felts. So,

[tex]Total\ length=15+12=27--- (2)[/tex]

Now, equating equations (1) and (2), we get:

[tex]3x=27\\\\x=\frac{27}{3}\\\\x=9 [/tex]

Therefore, the length of each quilt is 9 yards.

Answer:

Terry car will need 3 full tanks to complete the total distance.

Step-by-step explanation:

Given:

Total distance to be covered = 1100 miles

distance travel in full tank =400 miles.

We need to find the number of tanks Terry car needs.

Solution:

Now we can say that;

the number of tanks Terry car needs can be calculated by dividing Total distance to be covered by distance travel in full tank.

framing in equation form we get;

number of tanks Terry car needs = [tex]\frac{1100}{400}= 2.75\ tanks[/tex]

number of tanks cannot be decimal value.

Hence Terry car will need 3 full tanks to complete the total distance.

Answer:

The answer to your question is  r = 3

Step-by-step explanation:

                               2r  - 15 = - 9r + 18

Process

1.- Add 9r in both sides

                              2r + 9r - 15 = - 9r + 18 + 9r

2.- Simplify

                                    11r -15 = 18

3.- Add 15 to both sides

                                   11r - 15 + 15 = 18 + 15

4.- Simplify

                                   11r = 33

5.- Divide both sides by 11

                                   11/11 r = 33/11

6.- Simplify and result

                                   r = 3

Answer:

what ur insta?

Step-by-step explanation:

Answer:A) 1.5

Step-by-step explanation: Bob runs at the rate of 8mins per mile

In 60mins his rate would be=60/8=7.5

Let a be the distance he further runs south

2s+3.25

Total distance covered in 50mins=Time=distance/speed=

50/60

50/60=2s +3.25/7.5

Cross multiply

60(2s+3.25)=50×7.5

120s+195=375

120s=375-195

S=180/120

S=1.5

Answer:

  about $525,900

Step-by-step explanation:

Each year, the value is multiplied by (1 +4%) = 1.04. After 20 years, it will have been multiplied by that value 20 times. That multiplier is 1.04^20 ≈ 2.19112314.

The value of the house in 20 years will be about ...

  $240,000×2.19112314 ≈ $525,900 . . . . . rounded to hundreds

Answer: it would be worth $52587 in 20 years.

Step-by-step explanation:

If the value of the house increases at a rate of 4% per year, then the rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the value of the house after t years.

n represents the period of increase.

t represents the number of years.

P represents the initial value of the house.

r represents rate of increase.

From the information given,

P = $24000

r = 4% = 4/100 = 0.04

n = 1 year

t = 20 years

Therefore

A = 24000(1 + 0.04/1)^1 × 20

A = 24000(1.04)^20

A = $52587

Answer:

2 hours and 6 minutes. Second option

Step-by-step explanation:

Proportions

If two variables are proportional, it's easy to find the value of one of them knowing the value of the other and the proportion ratio. We know that each day our clock loses 6 minutes per day. It gives us the ratio between time lost vs days passed.

Three weeks (21 days) from now, from now, the clock will be behind a total time of 6 * 21 = 126 minutes.  

Two hours are 120 minutes, thus the time behind is 2 hours and 6 minutes. Second option

The clock will be behind 3 weeks later by 2 hours and 6 minutes.

To find out how much time the clock will be behind 3 weeks later, we first need to calculate the total amount of time the clock will lose in 3 weeks. Since the clock loses 6 minutes per day, we can multiply this by the number of days in 3 weeks (21 days). 6 minutes per day x 21 days = 126 minutes.

Next, we convert the minutes into hours and minutes. There are 60 minutes in an hour, so we divide the 126 minutes by 60 to get 2 hours and a remainder of 6 minutes.

Therefore, the clock will be behind 3 weeks later by 2 hours and 6 minutes.

Answer: a. 28ft/s. b. 40.08ft/s. c. 42.4ft/s. d. 43.68ft/s. e. - 20ft/s

Step-by-step explanation: Since your displacement was given that is (y) , we just have to differentiate y with respect to time t. That is the first derivative only.

I have worked it out and here is the attachment.

Final answer:

To find the average velocity during different time periods, we can calculate the changes in height and time. By substituting the given values of t into the height equation, we can determine the heights at different times. We can then calculate the average velocities by taking the change in height divided by the change in time. Additionally, to estimate the instantaneous velocity when t = 2, we can differentiate the height equation and substitute t = 2 into the derivative.

Explanation:

To find the average velocity for a given time period, we need to calculate the change in height and the change in time. Using the equation y = 44t - 16t^2, we can substitute the values of t = 2 and t = 2.5 to find the heights at these times. Then, we can find the average velocities.

(a) For the time period of 0.5 seconds starting at t = 2, we calculate the heights at t = 2 and t = 2.5: y(2) = 44(2) - 16(2^2) = 36 ft and y(2.5) = 44(2.5) - 16(2.5^2) = 35 ft. The average velocity is the change in height divided by the change in time: (35 - 36) ft / 0.5 s = -2 ft/s.

(b) For the time period of 0.1 second starting at t = 2, we calculate the heights at t = 2 and t = 2.1: y(2) = 36 ft and y(2.1) = 44(2.1) - 16(2.1^2) = 37.644 ft. The average velocity is the change in height divided by the change in time: (37.644 - 36) ft / 0.1 s = 16.44 ft/s.

(c) For the time period of 0.05 second starting at t = 2, we calculate the heights at t = 2 and t = 2.05: y(2) = 36 ft and y(2.05) = 44(2.05) - 16(2.05^2) = 37.079 ft. The average velocity is the change in height divided by the change in time: (37.079 - 36) ft / 0.05 s = 21.58 ft/s.

(d) For the time period of 0.01 second starting at t = 2, we calculate the heights at t = 2 and t = 2.01: y(2) = 36 ft and y(2.01) = 44(2.01) - 16(2.01^2) = 36.764 ft. The average velocity is the change in height divided by the change in time: (36.764 - 36) ft / 0.01 s = 76.4 ft/s.

(e) To estimate the instantaneous velocity when t = 2, we can calculate the derivative of the height function. The derivative of y(t) = 44t - 16t^2 with respect to t is dy/dt = 44 - 32t. Substituting t = 2 into this equation, we get dy/dt = 44 - 32(2) = -20 ft/s.

Answer:

Volume of cone is [tex]539.89 \ cm^3[/tex].

Step-by-step explanation:

Given:

Diameter of Cone = 8 cm

Now we know that radius is half of diameter.

radius = [tex]\frac{1}{2}\times8 =4\ cm[/tex]

Also Given:

height that is 4 times the diameter.

So we can say that;

Height = [tex]4\times8 =32\ cm[/tex]

We need to find the volume of the cone.

Solution:

Now we know that Volume of the cone is given by one third times π times square of radius times height.

framing in equation form we get;

Volume of the cone = [tex]\frac{1}{3}\pi r^2h= \frac{1}{3} \pi \times (4)^2\times 32 =539.89 \ cm^3[/tex]

Hence Volume of cone is [tex]539.89 \ cm^3[/tex].

Answer:

The least value of a = 1

Step-by-step explanation:

As it has two distinct roots . According to roll's theorem there should be a point where f'(x)=0

In a quadratic equation ax² + bx + c = 0 the point of maxima or minima is

x = - b/2a

We can find by differentiating it

2ax - b= 0

x = b/2a

So   0 < b/2a < 1

0 < b/a < 2

0 < b < 2a

a > b/2

then, the least value of b = 2 and the least value of a = 1

Answer:

203 feet.

Step-by-step explanation:

Please find the attachment.

Let h represent the height of the building.

We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.    

We know that tangent relates opposite side of a right triangle to its adjacent side.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

Upon substituting our given values in above formula, we will get:

[tex]\text{tan}(35^{\circ})=\frac{h}{290}[/tex]

[tex]290*\text{tan}(35^{\circ})=\frac{h}{290}*290[/tex]

[tex]290*0.70020753821=h[/tex]

[tex]h=290*0.70020753821[/tex]

[tex]h=203.0601860809[/tex]

[tex]h\approx 203[/tex]

Therefore, the building is approximately 203 feet high.

Final answer:

Billy and Ken both ran 1/4 of the training course before it started raining, making the distance they ran identical; neither ran further than the other.

Explanation:

Comparison of Distances Run by Billy and Ken

To determine which cross-country star, Billy or Ken, ran the furthest, we need to calculate the fractions of the total distance each one ran. Firstly, we'll look at Billy. Billy intended to run 3/4 of the course and finished 1/3 of his planned run. Therefore, the actual distance Billy ran is (3/4) × (1/3).

Now, for Ken. Ken planned to run 1/2 of the course and completed 1/2 of his intended distance. Hence, Ken's actual distance is (1/2) × (1/2). Calculating both distances:

Billy's distance: (3/4) × (1/3) = 1/4

Ken's distance: (1/2) × (1/2) = 1/4

Both Billy and Ken ran 1/4 of the total training course, hence they ran the same distance before it started raining. Therefore, neither ran further than the other.

Answer:

  4 1/5 gallons per minute

Step-by-step explanation:

Divide gallons by minutes.

  (9 4/5 gal)/(2 1/3 min) = (49/5 gal)/(7/3 min) = (49/5)(3/7) gal/min

  = 21/5 gal/min = 4 1/5 gal/min

Answer:

1. central angle

2. semicircle

3. major arc

4. minor arc

Step-by-step explanation:

1. central angle is an angle whose vertex rest on the center of a circle, with its sides containing two radii of the same circle.

2. semicircle is simply a half circle which is formed by cutting a full circle along a diameter (that is union of the endpoints of a diameter).

3. major arc is an arc that is larger than a semicircle and is bounded by a central angle whose angle is lesser than 180°.

4. minor arc is an arc that is smaller than a semicircle and is bounded by a central angle whose angle is greater than 180°.

Answer:

major arc

1

the union of two points of a circle, not the end points of a diameter; and all points of the circle that are in the exterior of the central angle whose sides contain the two points.

2. central angle

the union of two points of a circle, not endpoints of a diameter, and all points of the circle that are in the interior of the central angle whose sides contain the two points

3. semicircle

the union of the endpoints of a diameter and all points of the circle lying on one side of the diameter.

4. minor arc

an angle in the plane of a circle with the vertex at the center of the circle

Step-by-step explanation:

Answer:

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]  

By definition an outlier is a point "that diverges from an overall pattern in a sample". The residual for this outiler is usually high and when we have presence of outliers our model probably would be not significant since the tendency is not satisfied.        

By definition and influential point is a point that has "a large effect on the slope of a regression line fitting the data:. And usually represent values that are too high or low respect to the others.

Solution to the problem

For this case we assume that we have a high positive correlation between college student's age and the GPA.

So we assume that [tex] 0.7 \leq r \leq 1[/tex]

And We see that after introduce the value of 44 for the age the correlation disappears, that means decrease significantly.

Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.

Answer: an equation that represents the total costs of the gym membership based on the number of months is

y = 25x + 50

Step-by-step explanation:

Let x represent the number of months that Frank makes use of the gym at LA fitness in order to get better in shape.

Let y represent the total cost of using the gym for x months.

He has to pay a one-time enrollment fee of $50 and then membership costs $25 per month. This means that the total cist for x month would be

y = 25x + 50

Answer:

Step-by-step explanation:

Total area = Dining space + Kitchen and Storage space

Dining space = 90 multiplied by 20 = 1800 square feet

Kitchen and Storage space = 1/3 of Total area

Total area = 1800 + 1/3 of Total area

(1-1/3) Total area = 1800

2/3 Total area = 1800

Total area = 3*1800/2 = 2700

Kitchen and Storage space = 2700*1/3 = 900 square feet

Answer:

The answer to your question is  250 - 20 < 80 + 15x

Step-by-step explanation:

Data

Beth  has 250 books and sells 20 each week

Martin has 80 books and sells 15 each week

week = x

Process

1.- Write an equation for each situation

Beth         250 - 20x            

Martin       80 + 15 x

2.- Write the inequality

                   250 - 20 < 80 + 15x

Step-by-step explanation:

Size of column = 6 inch x 6 inch x 8 ft

Size of column = 0.5 ft x 0.5 ft x 8 ft

Volume of column = 0.5 x 0.5 x 8 = 2 ft³

Specific weight of concrete = 62.4 lb/ft³

Mass = Volume x Specific weight

Mass = 2 x 62.4

Mass = 124.8 lb = 124.8 x 0.454 = 56.66 kg

Weight = 56.66 x 9.81 = 555.83 N

Weight of column is 555.83 N

Answer:

Reflection over the x-axis and translation 4 units left

Step-by-step explanation:

Answer:

54 minutes

Step-by-step explanation:

From the question, we are given;

We are required to determine the time taken to exchange the air in the room;

First we are going to determine the volume of the room;

Volume of the room = length × width × height

                                  = 5.2 m × 4.3 m × 2.9 m

                                  = 64.844 m³

Then we should know, that 1 m³ = 1000 L

Therefore, we can convert the volume of the room into L

= 64.844 m³ × 1000 L

= 64,844 L

But, the rate is 1200 L/min

Thus, time = Volume ÷ rate

                  = 64,844 L ÷ 1200 L/min

                   = 54.0367 minutes

                   = 54 minutes

Therefore, it would take approximately 54 minutes

Answer:

  (x, y) = (2, 28.8)

Step-by-step explanation:

Your ability to do arithmetic should not be limited to integers. Here we see the coefficients of y are related by a factor of -5, so multiplying the first equation by 5 can make the y-terms cancel when that is added to the second equation.

  5(1.3x +0.5y) +(-0.7x -2.5y) = 5(17) +(-73.4)

  6.5x +2.5y -0.7x -2.5y = 85 -73.4 . . . . . eliminate parentheses

  5.8x = 11.6 . . . . . . collect terms

  x = 11.6/5.8 = 2 . . . . . . . divide by the coefficient of x

  1.3(2) +0.5y = 17 . . . . . . substitute for x in the first equation

  0.5y = 14.4 . . . . . . subtract 2.6

  y = 28.8 . . . . . . . . multiply by 2

The solution is (x, y) = (2, 28.8).

Answer:x = 2

y = 28.8

Step-by-step explanation:

The given system of simultaneous equations is expressed as

1.3x + 0.5y = 17 - - - - - - - - - - - - 1

-0.7 - 2.5y = -73.4 - - - - - - - - - - - - - 2

The first step multiply all the terms by 10 in order to eliminate the decimal points. The equations become

13x + 5y = 170 - - - - - - - - - - - - 1

-7 - 25y = -734 - - - - - - - - - - - - - 2

Then we would multiply both rows by numbers which would make the coefficients of x to be equal in both rows.

Multiplying equation 1 by 7 and equation 2 by 13, it becomes

91x + 35y = - 1190

91x + 325y = 9542

Subtracting, it becomes

- 290y = - 8352

y = - 8352/- 290 = 28.8

Substituting y = 28.8 into equation 1, it becomes

13x + 5 × 28.8 = 170

13x + 144 = 170

13x = 170 - 144 = 26

x = 26/13 = 2

Answer:

The answer is 4xy^2√2y

Step-by-step explanation:

Answer:

b)

Step-by-step explanation:

The correlation between amount of eroded soil and flow rate would be positive because the slope is positive. The correlation coefficient cannot be determine using the given information as the information is not enough.

If we have data value or standard deviation for y and standard deviation x then the correlation coefficient can be calculated. From the given regression equation amount of eroded sol = 0.4 + 1.3x (where x is flow rate), the intercept=0.4 and slope=1.3.

We can only tell the sign of correlation coefficient by considering the sign of slope which is positive in the given scenario.

Hence, the correlation is positive but exact value cannot be determine.

Answer:

Step-by-step explanation:

If p and w represent the speeds of the plane and wind, respectively, the speed into the wind is ...

  p - w = (3000 mi)/(6 h) = 500 mi/h

And, the speed with the wind is ...

  p + w = (3000 mi)/(5 h) = 600 mi/h

Adding these two equations gives us ...

  2p = 1100 mi/h

  p = 550 mi/h . . . . . . . divide by 2

Then the wind speed is ...

  w = 600 mi/h - p = (600 -550) mi/h

  w = 50 mi/h

The rate of the plane in still air is 550 mi/h; the rate of the wind is 50 mi/h.

Answer:

Step-by-step explanation:

let speed of plane in still air =x

speed of wind=y

(x-y)6=3000

x-y=3000/6=500   ...(1)

(x+y)5=3000

x+y=3000/5=600   ...(2)

adding (1) and (2)

2x=1100

x=1100/2=550

550 +y=600

y=600-550=50

speed of plane in still air=550 m/hr

speed of wind=50 m/hr