Answer:
[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Step-by-step explanation:
Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).
Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0
To find b we use the equation of the focus which is:
[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]
Substituting the values of a, b, h and k:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Select the correct answer from each drop-down menu. The gasoline prices in seven states are $1.96, $2.09, $1.79, $1.61, $1.75, $2.11, and $1.84. The median gasoline price is _____. The difference of the first and third quartiles in this set of gas prices is ______ .
Answer:
The median is 1.84 and the difference between the first and third quartile is 0.34
Step-by-step explanation:
When you write them out 1.84 is the median (middle number). To find the difference I just subtracted the third quartile (2.09) by the first quartile (1.75)
========================================================
Explanation:
Original data set = {1.96, 2.09, 1.79, 1.61, 1.75, 2.11, 1.84}
Sorted data set = {1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11}
Notice that 1.84 is in the middle of the sorted set. Three values are smaller than it, and three values are larger than it.
Therefore, 1.84 is the median.
The values {1.61, 1.75, 1.79} are smaller than the median. We'll call this set L for lower set.
The values {1.96, 2.09, 2.11} are larger than the median. We'll call this set U for upper set.
From set L = {1.61, 1.75, 1.79}, the median here is 1.75. This is the value of the first quartile Q1
The value of Q3 is 2.09 as it is in the direct middle of set U = {1.96, 2.09, 2.11}
The interquartile range (IQR) is the difference of Q3 and Q1
IQR = Q3 - Q1
IQR = 2.09 - 1.75
IQR = 0.34
Write 36 143/1000 as a decimal number.
Answer:
36.143
Step-by-step explanation:
143/1000=0.143
36+0.143=36.143
The amount of rainfall in January in a certain city is normally distributed with a mean of 3.1 inches and a standard deviation of 0.4 inches. Find the value of the quartile Q 1.
Answer:
2.83
Step-by-step explanation:
For a normally distributed data :
Mean = 3.1 inches
Standard deviation = 0.4 inches
Find the value of the quartile Q1:
The quartile Q1 represents the first quartile which is the Lower 25% of the distribution
25% = 0.25
Using the z-table :
0.25 = - 0.68
The z- score formula
Z-score = ( x - mean / standard deviation)
-0.68 = ((x - 3.1) / 0.4)
x - 3.1 = (-0.68 * 0.4)
x - 3.1 = - 0.272
x = - 0.272 + 3.1
x = 2.828
x = 2.83
which function's graph has asymphotes located at the values x=+=n pi ? 1. y=csc x 2. y= cos x 3. y=tan x 4. y=cot x answer choices: A. 2 only B. 1 and 4 only C. 1 only D. 1 and 3 only please help!! ):
Abel and Cedric will share a total of $180. Abel will receive half as much as Cedric. What amount. in dollars, will Cedric receive (Disregard the $ sign when gridding your answer.)
Answer:
Abel receives $60, and Cedric receives $120
Step-by-step explanation:
Let Abel's share = A
Let Cedric's share = C
we are given the following
A + C = 180 - - - - - (1) (Abel and Cedric will share a total of $180)
[tex]A = \frac{C}{2}\ - - - - - - - (2)[/tex] (Abel will receive half as much as Cedric. )
from equation 2:
[tex]A = \frac{C}{2}\\ C = 2A\ - - - - - - (3)[/tex]
putting this value of C in eqn (3) into eqn (1)
A + (2A) = 180
3A = 180
∴ A = 180 ÷ 3 = 60
to find C, let us replace the value of A in eqn (3) with 60
C = 2A - - - - (3)
C = 2 × 60
C = 120
Therefore, Abel receives $60, and Cedric receives $120
In a recent survey of 100 students, 34 said that they took a Math class as a freshman, 59 said that they took an English class as a freshman and 12 said they took both classes.
Required:
How many students took neither class as a freshman?
Answer:
19 studentsStep-by-step explanation:
We will use the set notation to solve this question.
let n(U) be the total number of students surveyed = 100
n(M) be the number of student that took math = 34
n(E) be the number of student that took English = 59
n(M∩E) be the number of student that took both classes= 12
n(M∪E)' be the number of student that took neither class = ?
Using the formula n(U) = n(M∪E) + n(M∪E)'
n(M∪E)' = n(U)-n(M∪E)
Before we can get the number of student that took neither class i.e n(M∪E)' we need to get n(M∪E).
n(M∪E) = n(M)+n(E)- n(M∩E)
n(M∪E) = 34+59-12
n(M∪E) = 81
Since n(M∪E)' = n(U)-n(M∪E);
n(M∪E)' = 100-81
n(M∪E)' = 19
Hence 19 students took neither class as a freshmen.
SHALL GIVE BRAINLIEST ANSWER!! A 40% solution of fertilizer is to be mixed with an 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
20 gallons of the 40% solution, 60 gallons of the 80% solution
Step-by-step explanation:
Let x = the gallons of the 40% solution, and y = the gallons of a 80% solution. The first thing we want to do here is to convert each percentage into decimal form - including the 70% solution mixture.
40% = 0.40,
80% = 0.80, respectively 70% = 0.70
As you can tell, 0.40 is associated with x gallons, 0.80 is associated with y gallons, and the mixture contains 0.70 [tex]*[/tex] 80 solution, as 0.70 is associated with 80. Therefore we can formulate the following expression,
0.40x + 0.80y = 0.70 [tex]*[/tex] 80
At the same time x + y = 80, as the solution ( mixture ) is present with 80 gallons. Isolating x, x = 80 - y. Let us plug that into our expression, solving for y, following by x gallons.
[tex]0.40\left(\:80\:-\:y\:\right)\:+\:0.80y\:=\:0.70\:\cdot \:80[/tex]
[tex]0.4\left(80-y\right)+0.8y=56[/tex] ( Multiply either side by 10 )
[tex]4\left(80-y\right)+8y=560[/tex] ( Expand )
[tex]320-4y+8y=560[/tex]
[tex]320+4y=560[/tex]
[tex]4y=240[/tex]
[tex]y = \frac{240}{4} = 60[/tex] ( Substitute to solve for x )
[tex]x = 80 - y = 80 - 60 = 20[/tex]
As you can see there are 20 gallons of the 40% solution, and 60 gallons of the 80% solution.
Annie tried to solve an equation step by step. Find Annie's mistake. *
Answer:
Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .
maybe you should type in the steps before it is answered. thanks
Answer:
answer= C
Step-by-step explanation:
5 x 5 = 10 x 5= 20 x 5 = Answer these 3 problems and then tell how they are
related.
Step-by-step explanation:
First we need to find out what they all 3 equal, with multiplication.
5×5=25
10×5=50
20×5=100
In each of these problems, the answer is multiplying itself by 2 in order to get to the next answer. So this is how they are related
Which choice shows the product of 22 and 49 ?
Answer:
1078
Step-by-step explanation:
The product of 22 and 49 is 1078.
Answer:
1078 is the product
Step-by-step explanation:
A train is running at the speed of 90 mph. The length of the train is 300 ft. How long would it take to cross a railway platform 492 ft long?
Answer:
Time = 1.45152 seconds
Step-by-step explanation:
1 foot = 0.000189 mile
300 ft = 300*0.000189
300 ft = 0.0567 miles
492 ft = 492*0.000189
492 ft = 0.092988 miles
Distance left to be covered by the train
= 0.092988-0.0567
= 0.036288 miles
Speed= 90mph
Time taken = distance/speed
Time taken= 0.036288/90
Time = 4.032*10^-4 hour
Time = 4.032*10^-4*60*60
Time = 1.45152 seconds
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below where x denotes seed density, and y denotes lawn quality.x 1 1 2 3 3 3 4 5y 30 40 40 40 50 65 50 50The sample linear correlation coefficient is r=0.600. At the 1% significance level, do the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated?
Answer:
I think it -1.50 to 10.58
Step-by-step explanation:
PLEASE ANSWER ASAP!!!
Fill in the box for the missing numerator in the set of equivalent expressions in the picture
Answer options are also shown in picture
any unrelated answer will be reported
Answer:
A. 14z - 28
Step-by-step explanation:
simplify z² - 3z
a. z(z - 3)
the denominator on the right has z(z - 3). but it is also multiplied by (z - 2)
this means the numerator must also be multiplied by (z - 2)
14 x (z - 2) = 14z - 28
hope this helps :)
Put the following numbers in order from least to greatest: π/2,-4,0.09,17,√3,-1/7,√225
Answer:
-4, -1/7,0.09,π/2,√3 ,√225,17
Step-by-step explanation:
π/2, is approx 1.5
-4,
0.09,
17,
√3 is approx 1.7
,-1/7, is approx -.143
√225 = 15
From most negative to greatest
-4, -1/7,0.09,π/2,√3 ,√225,17
Answer:
[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]
Step-by-step explanation:
So we have the numbers:
[tex]\pi/2, -4, 0.09, 17, \sqrt3, -1/7, \sqrt{225}[/tex]
(And without using a calculator) approximate each of the values.
π is around 3.14, so π/2 is around 1.57.
17 squared is 289, so 1.7 squared is 2.89. Thus, the square root of 13 is somewhere between 1.7 and 1.8.
-1/7 can be divided to be about -0.1429...
And the square root of 225 is 15.
Now, use the approximations to place the numbers:
[tex]\pi/2\approx1.57; -4; 0.09;17;\sqrt3 \approx1.7; -1/7\approx-0.14;\sqrt{225}=15[/tex]
The smallest is -4.
Next is -1/7 or about -0.14
Followed by the first positive, 0.09.
And then with π/2 or 1.57
And then a bit bigger with the square root of 3 or 1.7.
And then with the square root of 225 or 15.
And finally the largest number 17.
Thus, the correct order is:
[tex]-4, -1/7, 0.09, \pi/2, \sqrt3, \sqrt{225}, 17[/tex]
Janet has 8 points after the first round of the same game. how far does she travel to get to 2 points?
Answer:
Step-by-step explanation:
8-2=6
answer is 6
Answer:
2 x 4
Step-by-step explanation:
She need to travel 4 times before she reach the same points again
In the figure below. MN is the arc of a circle with center L. If the length of arc MN is 6π, what is the area of sector LMN?
On a number line, the coordinates of X, Y, Z, and W are −7, −2, 2, and 7, respectively. Find the lengths of the two segments below. Then tell whether they are congruent. XY and
use the diagram to answer the question. AB corresponds to which line segment?
Answer:
DE
Step-by-step explanation:
I hope this helps!
if 80% of 2 is 200.what is 70% of 27
Answer:
18.90
Hope i got it right
Draw two normal curves that have the same mean but different standard deviations. Describe the similarities and differences. Compare the two curves. The two curves will have ▼ the same line different lines of symmetry. The curve with the larger standard deviation will be ▼ more less spread out than the curve with the smaller standard deviation.
Answer:
The same mean ⇒ the same symmetry axis
Bigger standard deviation major spread
Step-by-step explanation: See Annex
The annex shows two different normal curves:
1.- N (μ₀ ; σ₁ )
2.- N (μ₀ ; σ₂ )
Where σ₁ > σ₂
They both have the same symmetry axis ( they have the same mean and both curves have to be symmetrically related to the mean )
Normal distribution curves spread symmetrically at both sides of the mean, but the wider curve is the one that has the bigger standard deviation. Standard deviation is a measure of the spread of the curve.
Whenever deviation is high, the data is more dispersed than when deviation is low.
Let the mean be 2.
Let the standard deviation be 0.3 for first graph. The data is more clustered around mean.
Let the standard deviation be 0.6 for second graph. The data is less clustered more dispersed from mean.
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The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing company, claims that the sales representatives make an average of 43 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 29 sales representatives reveals that the mean number of calls made last week was 44. The standard deviation of the sample is 4.1 calls. Using the 0.050 significance level, can we conclude that the mean number of calls per salesperson per week is more than 43? H0: μ ≤ 43 H1: μ > 43 Compute the value of the test statistic. (Round your answer to 3 decimal places.)
Answer:
The critical region for α= 0.05 is Z > ± 1.645
The calculated value of Z= 1.100
Step-by-step explanation:
The null and alternate hypotheses are given
H0: μ ≤ 43
H1: μ > 43 one tail test
∝= 0.05
n= 29
Standard Deviation= s= 4.1
Mean = μ0 = 44
For one tail test the z value of α= ± 1.645
The critical region for α= 0.05 is Z > ± 1.645
The test statistic is given by
z=μ0-μ/ s/√n
Z= 44-43/4.1/√29
Z= 1/4.1/√29
Z= 1.100
Since the calculated value Z= 1.100 does not fall in the critical region , We reject H0 and may conclude that the mean number of calls per salesperson per week is not more than 43
[09.01]
Identify the domain of the equation y=x2 - 6x + 1. (1 point)
Answer:
All real numbers.
Step-by-step explanation:
As there are no restrictions on the values of x, the domain is all real numbers.
Answer:
All real numbers.
Step-by-step explanation:
1. The mean performance score on a physical fitness test for Division I student athletes is 947 with a population standard deviation of 205. Select a random sample of 64 of these students. Hint: we have a sample so use the standard error. What is the probability the mean of the sample is below 900
Answer:
0.033316
Step-by-step explanation:
We use the z score formula to solve for this question.
Since we are given the number of samples in the question, our z score formula is given as:
z = (x-μ)/ S.E
where x is the raw score
μ is the sample mean
S.E is the Standard error.
x is the raw score = 900
μ is the sample mean = Population mean = 947
Standard error =
This is calculated as Population standard deviation/ √No of samples
= 205/√64.
= 205/8
= 25.625
We proceed to calculate the z score
z = (x-μ)/ S.E
z = 900 - 947/25.625
= -1.83415
Using the z score table for normal distribution,
P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)
P(x<900) = 0.033316
Therefore, the probability the mean of the sample is below 900 is 0.033316
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
An artifact was found and tested for its carbon-14 content. If 72% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years).
Answer:
2700 years
Step-by-step explanation:
The exponential function for the fraction remaining is ...
r(t) = (1/2)^(t/5730)
where r is the remaining fraction and t is the time in years. We can solve for t to get ...
log(r) = (t/5730)log(1/2)
t = 5730·log(r)/log(1/2)
For the given r=0.72, the age of the artifact is estimated to be ...
t = 5730·log(0.72)/log(0.5) ≈ 2700 . . . years
How would you simplify and rationalize this expression? [tex]\frac{5\sqrt[4]{2}}{4\sqrt[4]{162} }[/tex]
Answer:
5/12
Step-by-step explanation:
(5 * 2^1/4)/4 * 162^1/4) = (5 * 2^1/4)/4 * 3 *2^1/4)
multiply top and bottom by 2^3/4
(5 * 2)/4 * 3 * 2) = 10/24 = 5/12
You are rolling a 6-sided number cube with the numbers 1 through 6. Which of the following represents the probability of rolling an even number?
0
1/6
1/2
1
Answer:
1/2
Step-by-step explanation:
The probailty of an event A is:
● P(A) = ( outcomes that give A) / (total number of possible outcomes)
Let A be the event in wich we get an even number.
● The sample space is {2,4,6}
So there are 3 possible outcomes that give A .
The six-sided dice has 6 outcomes
● { 1,2,3,4,5,6}
■■■■■■■■■■■■■■■■■■■■■■■■■■
● P(A) = 3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
i took the test
Lauren has 108 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 9 kids on her block. Write an equation to show how many pieces of candy each kid will receive. 9 + x = 108 x = 108 − 9 x = one hundred eight divided by nine x = nine divided by one hundred eight
Answer:
9 x =108
Step-by-step explanation:
Let the number of candies be x.
According to the question,
x=108/9
We can also write it as,
9 x=108
By the way ,each child will get 12 candies.
Thank you!
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
Gail bought 5 pounds of oranges and 2 pounds of bananas for $14. Her husband later bought 3 pounds of oranges and 6 pounds of bananas for $18. What was the cost per pound of the oranges and the bananas?
Answer:
1 pound of Oranges = $2
1 pound of Bananas = $2
Step-by-step explanation:
O = Oranges
B = Bananas
=> 5o + 2b = 14
=> 2b = 14 - 5o
=> b = 14/2 - 5/2o
=> b = 7 - 2.5o
3o + 6b = 18
=> 3o + 6( 7 - 2.5o ) = 18
=> 3o + 42 - 15o = 18
=> -12o + 42 = 18
=> -12o = -24
=> -o = -2
=> o = 2
One pound of oranges costs $2.
So,
5 (2) + 2b = 14
=> 10 + 2b = 14
=> 2b =4
=> b = 2
One pound of bananas also costs $2.
Match the base to the corresponding height.
Base (b)
Height (h)
b
h
h
b
The base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
What is a triangle?Triangle is the closed shaped polygon which has 3 sides and 3 interior angles. The height of the triangle is the dimension of the elevation from the opposite peak to the length of the base.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
In the given figure, three triangles is shown with base and height. Here,
The base 1 is matched with height 2, as the height shown in figure 2 is the dimension of the elevation from the opposite peak to the length of the base 1.Similarly, base 2 is matched with height 3.Base 3 is matched with height 1.
Thus, the base 1 is matched with height 2, base 2 is matched with height 3 and base 3 is matched with height 1. The base to the corresponding height is matched in the attached figure.
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