The equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11) is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
How to determine the ellipse equation?We have:
Vertices = (0, ± 11),
Foci = (0, ± 10)
The vertices and the foci are represented as:
Foci = (0, ± a)
Vertices = (0, ± c)
So, we have:
a = 10
c = 11
The equation of b is calculated using:
b² = c²- a²
So, we have:
b² = 11²- 10²
Evaluate
b² = 21
The equation of the ellipse is then represented as:
[tex]\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
This gives
[tex]\frac{x^2}{21} + \frac{y^2}{10^2} = 1[/tex]
[tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
Read more about ellipse equations at:
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Answer:
x^2/221+Y^2/121=1
Step-by-step explanation:
8+12/-4=5 please help
Answer:
you use the bodmas 12/-4p plus 8 =s
Step-by-step explanation:
hop it helps
Choose the correct order when finding the space between the cylinder and cone. I find the difference of the volumes Il find the volume of the cone III. find the volume of the cylinder
Answer:
D. III, II, then I
Step-by-step explanation:
To find the space between the cylinder and the cone, the first thing to do is: find the volume of the cylinder => next is to find the volume of the cone => then look for the difference in volume between the cylinder and the cone which will give us the space between the cylinder and the cone.
The correct order would be:
III, II, then I
I need the answer pls answer
Help me This is khan academy so plz help
Answer:
C
Step-by-step explanation:
:)
Bet u can’t solve this
Answer:
Step-by-step explanation:
Assuming you're solving for p:
[tex]m=2^{-1} *2^p(2^p-1)[/tex]
Let [tex]y=2^p[/tex]
Now we can re-write the equation with [tex]y[/tex] instead of [tex]2^p[/tex].
[tex]m=\frac{1}{2} y(y-1)[/tex]
[tex]2m=y^2-y[/tex]
[tex]y^2-y-2m=0[/tex]
Use the quadratic formula to get:
[tex]y = \frac{1+\sqrt{1+8m} }{2}[/tex]
or
[tex]y = \frac{1-\sqrt{1+8m} }{2}[/tex]
Therefore, using natural log and log rules:
[tex]2^p = \frac{1+\sqrt{1+8m} }{2}[/tex], [tex]ln(2^p)= ln(\frac{1+\sqrt{1+8m} }{2})[/tex],[tex]pln(2) = ln(\frac{1+\sqrt{1+8m} }{2})[/tex], [tex]p = \frac{ln(\frac{1+\sqrt{1+8m} }{2})}{ln(2)}[/tex]
or
[tex]2^p = \frac{1-\sqrt{1+8m} }{2}[/tex], [tex]ln(2^p)= ln(\frac{1-\sqrt{1+8m} }{2})[/tex], [tex]pln(2) = ln(\frac{1-\sqrt{1+8m} }{2})[/tex], [tex]p = \frac{ln(\frac{1-\sqrt{1+8m} }{2})}{ln(2)}[/tex]
If I haven't made any mistakes this should be correct!
What is the expanded form of this number?
630.052
(6×100)+(3×1)+(5×1/100)+(2×1/1,000)
(6×100)+(3×1)+(5×1/10)+(2×1/100)
(6×100)+(3×10)+(5×1/10)+(2×1/100)
(6×100)+(3×10)+(5×1/100)+(2×1/1,000)
Answer:
Expanded Notation Form:
630.052 =
600
+ 30
+ 0
+ 0.0
+ 0.05
+ 0.002
Expanded Factors Form:
630.052 =
6 × 100
+ 3 × 10
+ 0 × 1
+ 0 × 0.1
+ 5 × 0.01
+ 2 × 0.001
Expanded Exponential Form:
630.052 =
6 × 102
+ 3 × 101
+ 0 × 100
+ 0 × 10-1
+ 5 × 10-2
+ 2 × 10-3
Word Form:
630.052 =
six hundred thirty and fifty-two thousandths
Step-by-step explanation:
Answer:
Expanded Notation Form:
630.052 =
600
+ 30
+ 0
+ 0.0
+ 0.05
+ 0.002
Expanded Factors Form:
630.052 =
6 × 100
+ 3 × 10
+ 0 × 1
+ 0 × 0.1
+ 5 × 0.01
+ 2 × 0.001
Expanded Exponential Form:
630.052 =
6 × 102
+ 3 × 101
+ 0 × 100
+ 0 × 10-1
+ 5 × 10-2
+ 2 × 10-3
Step-by-step explanation:
Ling's elementary school principal wants to hire some new teachers. 6 teachers applied for one 1st grade teaching job, and 3 teachers applied for one 2nd grade teaching job. There is also a job opening for a 3rd grade teacher, and 3 teachers applied for the job. How many different ways can Ling's principal hire new teachers?
Answer:
Ling's principal can hire new teachers in 54 different ways.
Step-by-step explanation:
Since Ling's elementary school principal wants to hire some new teachers, and 6 teachers applied for one 1st grade teaching job, and 3 teachers applied for one 2nd grade teaching job, and there is also a job opening for a 3rd grade teacher, and 3 teachers applied for the job, to determine how many different ways can Ling's principal hire new teachers the following calculation has to be done:
6 x 3 x 3 = X
18 x 3 = X
54 = X
Therefore, Ling's principal can hire new teachers in 54 different ways.
Use the following number line to determine if the expressions are true or false.
A 0 B
<-------------l------------------l------------------l------------------l------------------l------------------l---------------->
true false
a > b [] []
lal > lbl [] []
a > lbl [] []
(the lines around the B and the A matter {for some reason}]
PLEASE HELP ME
Answer:
IT's a < b True /a/ =0 True /a/ < /b/ True
Step-by-step explanation:
Joan’s Nursery specializes in custom-designed landscaping for residential areas. The estimated labour cost associated with a particular landscaping proposal is based on the number of planting of trees, shrubs, and so on to be used for the project. For cost-estimating purposes, managers use two hours of labour time for the planting of a medium-sized tree. Actual times from a sample of 10 planting during the past month follow (times in hours).
1.7 1.5 2.6 2.2 2.4 2.3 2.6 3.0 1.4 2.3
Test to see whether the mean tree-planting time differs from two hours.
State the null and alternative hypothesis
Answer:
H0 : μ = 2
H1 : μ > 2
We fail to reject the null and conclude that no significant evidence exists to support that mean tree-planting time differs from two hours.
Step-by-step explanation:
Given :
X = 23.71,17.79,29.87,18.78,28.76
Sample mean, xbar = Σx / n = 22/10 = 2.2
Standard deviation, s = 0.516 (calculator)
H0 : μ = 2
H1 : μ > 2
Test statistic :
(xbar - μ) ÷ (s/sqrt(n))
n = 10
Test statistic :
(2.2 - 2) ÷ (0.516/sqrt(10))
0.2 / 0.1631735
Test statistic = 1.23
Using the Pvalue from Tscore calculator, df = n - 1 = 10 - 1 = 9
Pvalue(1.23, 9) = 0.1249
Since, Pvalue > α ; We fail to reject the null and conclude that no significant evidence exists to support that mean tree-planting time differs from two hours.
What is the exact volume of a cylinder with a radius of 4in and a height of 3 in?
The Sine Function
According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Plot the data on a scatter plot. Produce a sine regression model for the data. Round the values for a a, b, c, and d to the nearest 0.0001. Using the sine regression model predict what the temperature would be given y(30). Analyze your prediction and explain why your prediction may or may not be accurate. If it might not be accurate, explain what might make the information more accurate.
a. Accurate, nothing would help it be more accurate.
b. May not be accurate, weather is charging all the time; Information from various states would help make the information more accurate.
c. Accurate, it is easily predictable.
d. May not be accurate, information was taken over 2 year period; More information
from previous years would help the prediction be more accurate.
Please select from the best answers from choices provided
Answer:
D. May not be accurate, information was taken over 2 year period; More information from previous years would help the prediction be more accurate.
Step-by-step explanation:
I calculated it logically
100 points!!!
A triangular prism has a height of 5.5 yards and a triangular base with the following dimensions.
What is the surface area of the prism?
280 yd 2
340 yd 2
410 yd 2
100 yd 2
Answer:
340
Step-by-step explanation:
A cell phone box in the shape of a rectangular prism is shown.
The height of the box is 4 cm.
The height of the original box will be increased by 3.5 centimeters so a new instruction manual and an extra battery can be included.
Which is closest to the total surface area of the new box?
A) 707 square centimeters
B) 479 square centimeters
C) 959 square centimeters
D) 738 square centimeters
Answer: it’s 959cm squared.
Step-by-step explanation:
The total surface area of the new box will be C) 959 square centimeters.
What is the surface area of this rectangular prism?A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.
The surface area of this rectangular prism = 2( lb + bh + hl)
We are given that height of the box is 4 cm.
Also that height of the original box will be increased by 3.5 centimeters so a new instruction manual and an extra battery can be included.
The surface area of this rectangular prism = 2( lb + bh + hl)
= 2(18 x 13.5 + 13.5x 7.5 + 18 x 7.5)
= 958.5
= 959 cm sq.
Therefore, the correct option is C.
Learn more about a rectangular prism;
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
its 28
Step-by-step explanation:
C is the longest side which is 35 ye and b is 21 yd. Then you would subtract 21^2 from 35^2 and you would get 784. Then find the square root of 784 and you would get 28 as the answer! Good luck and have a great day or night!
Answer:
28 yards
Step-by-step explanation:
We can use pythagorean theorem to solve this problem; pythagorean theorem is denoted by the formula a^2 + b^2 = c^2. We already have b, as 21 yd and c, as the hypotenuse is 35 yd. We can plug these values into the formula:
a^2 + 21^2 = 35^2
a^2 + 441 = 1225
a^2 = 784
a = 28 yards
Pablo's home town temperature is about 0.55% as hot as the surface of the sun. What is 0.55% written as a decimal number?
A. 0.0055
B. 0.055
C 0.55
D. 5.5
PLEASE HURRY
Answer: A
Step-by-step explanation:
Percent means 'per 100'
So, 0.55% means 0.55 per 100 or simply 0.55/100
If you divide 0.55 by 100, you'll get 0.0055
2. How many squares are in figure 10? Explain how you know.
Answer:
We determined that the 10th figure will have 45 shaded squares. That means 100 – 45 = 55 squares will be unshaded
Step-by-step explanation:
hope this helps
Choose all the factor pairs of 12.
A. 1,12
B. 2,6
C. 3,4
D. 5,7
E. 6,6
How many fifths must be added to 3.4 to total 4?
Please Help Immediately
The ___________ of a numerical set of data is the middle number when the numbers are written in numerical order.
Answer:
median
Step-by-step explanation:
does anyone know what happened to the tutors??
Answer:
Hey! I'm honestly not sure.
Step-by-step explanation:
I dont have the app... but on the website I'm pretty sure they dont have any.
Have a nice day <3
QUESTION 2.
Trevor bought new sneakers originally listed for $64.99. They are 15% off. Which equation can be used
to find the amount Trevor will save?
A. X= 1.15(64.99)
B. x = 15(64.99)
C. x = .85(64.99)
D. x = .15(64.99)
Answer:
c
Step-by-step explanation:
19
Adam, Linda and Rytis share an amount of money,
Linda gets three times as much money as Rytis gets.
Linda gets half as much money as Adam gets.
What fraction of the amount of money does Linda gek?
Answer:
3/10
Step-by-step explanation:
From the question :
Let amount rytis get = x
Hence, amount Linda gets = 3x
Hence, amount Adam gets = 2 times what Linda gets = 2(3x) = 6x
Hence, total amount shared :
x + 3x + 6x = 10x
Amount Linda got = 3x
Therefore, fraction Linda gets = Amount gotten by Linda / total amount = 3x / 10x = 3/10
Hence, fraction gotten by Linda = 3/10
The fraction of the amount of money does Linda gets is 3/10 and this can be determined by using the arithmetic operations.
Given :
Adam, Linda, and Rytis share an amount of money, Linda gets three times as much money as Rytis gets. Linda gets half as much money as Adam gets.The following steps can be used in order to determine the fraction of the amount of money does Linda get:
Step 1 - Let the total amount of money Rytis get be 'x'.
Step 2 - So according to the given data, the total money Linda has is 3x.
Step 3 - According to the given data, the total money Adam has is 2(3x).
Step 4 - So, the total amount of money shared is:
x + 3x + 6x = 10x
Step 5 - So, the fraction of the amount of money does Linda get is:
[tex]\rm =\dfrac{3x}{10x}[/tex]
[tex]= \dfrac{3}{10}[/tex]
For more information, refer to the link given below:
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A litter of kittens consists of two gray
females, one gray male, two black
females, and two black males. You
randomly pick one kitten. The kitten is
gray or male.
the kitten would be gray
What is the difference of the whole number and the mixed number below? 8-2 7/8 A. 6 7/8 B. 6 1/8 C. 5 7/8 D. 5 1/8
Answer:
D. 5 1/8
Step-by-step explanation:
First, convert the mixed number into an improper fraction
8-2 7/8 = 8- 23/8
Calculate the difference
8-23/8 = 41/8
Simplify the fraction
41/8 = 5 1/8
3. What is area?
A. The amount of units around a figure
B. The range of colors in a painting
C. The amount of square units inside of a figure
Answer:
c is the answer
hope this helps
Help. No links. You need to find volume. Ty :3
Answer:
I can't see the image but to help the formula is volume=LENGTH x Width x Height :)
Step-by-step explanation:
based on the graphic, what can be inferred about the relationship between braking distance and tread depth of tires ?
Answer: A
Step-by-step explanation:
HELP HELP HELP HELP
What is the equation of the trend line in the scatter plot ?
Lyle wrote a 9 page report. He wrote [tex]\frac{2}{3}[/tex] of the report on Friday. He wrote the rest on Saturday. How many pages did Lyle write on Saturday
Answer:
3 pages
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
first, let's find out how much Lyle wrote on Friday.
(2/3)(9)=6
Lyle wrote 6 pages on Friday.
9-6=3
this makes sense, because since he wrote 2/3 of the report on Friday, there will be 1/3 of the report to do on Saturday. (1/3)(9)=3
LYLE WROTE 3 PAGES ON SATURDAY
hope this helped <33333333
match the letter in the picture below with the correct likelihood of an event happening.
Y’all i don’t even understand the question.. help
Answer:
A- impossible
B- unlikely
C- even chance
D- likely
E- certain
Step-by-step explanation:
A to E goes from 0 to 1 so I assume 0 means zero possibility (impossible) then to continue unlikely. now even chance at C (in the middle which makes sense) then likely and then 1 is certain
Answer:i think A is impossible, B is unlikely, C is even chance, D is likely, and E is certain
Step-by-step explanation: