The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.
Explanation:The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.
First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.
By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.
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In the diagram which angles are alternate interior angles with angle 14?
Consider the equation 5/3v +4 +1/3v =8 What is the result of the equation after the first step in the solution
In the formula that gives the circumference of a circle, which quantity is multiplied by 2Ï€ ?
A. Diameter
B. Radius
C. Area
D. Circumference
The circumference of an object is the total length of the line that forms the object. For a circle, the formula is:
C = 2 π r
We can see that in the formula, what is multiplied by 2 π is the radius (r).
Therefore the answer to this is
B. Radius
An urn holds 5 white and 3 black marbles. if 2 marbles are to be drawn at random without replacement and x denotes the number of white marbles, find the probability distribution for x
i = [tex]p(0) = \frac {3} {8} x \frac {2} {7} = \frac {3} {28} ; p (1) = \frac {3} {8} x \frac {5} {7} + \frac {5} {8} x \frac {3} {7} = \frac {15} {28}; p (2) = \frac {5} {8} x \frac {4} {7} = \frac {5} {14} [/tex]
(a) i. The probability mass function of X is 5 / 14
Hypergeometric Distribution is the probability distribution of a hypergeometric random variable.
The hypergeometric distribution is used to calculate the statistical importance of having drawn a specific k successes (out of n total draws) from the aforementioned population in the hypergeometric test uses.
ii. Please see attached image for the answer.
To find the probability distribution for x, consider the possible values of x and calculate the probability of each value. When 2 marbles are drawn without replacement, there are two possible outcomes. The probability distribution for x is P(x = 0) = 3/28, P(x = 1) = 15/56, and P(x = 2) = 5/14.
Explanation:To find the probability distribution for x, we need to consider the possible values of x and calculate the probability of each value.
Since there are 5 white marbles and 3 black marbles in the urn, the total number of marbles is 8.
When 2 marbles are drawn without replacement, there are two possible outcomes: (1) both marbles are white and (2) one marble is white and one marble is black.
Let's calculate the probabilities:
P(x = 0) = P(both marbles are black) = (3/8) * (2/7) = 6/56 = 3/28
P(x = 1) = P(one marble is white and one marble is black) = (5/8) * (3/7) = 15/56
P(x = 2) = P(both marbles are white) = (5/8) * (4/7) = 20/56 = 5/14
Therefore, the probability distribution for x is:
P(x = 0) = 3/28
P(x = 1) = 15/56
P(x = 2) = 5/14
$1,100 at 8%, for 15 years, compounded annually. Total Amount = $ Interest Amount = $
Final answer:
Compound interest plays a crucial role in determining the final amount of an investment over time, showcasing the power of compounding. In this scenario, with an initial amount of $1,000, an interest rate of 10.1%, and 47 years of compounding annually, the total interest earned would be $91,045.80.
Explanation:
Compound interest is calculated on the principal amount plus the interest earned over time. In this case, with an initial amount of $1,000, an interest rate of 10.1% compounded annually, and an end amount of $92,045.80 after 47 years, compound interest plays a significant role in determining the final amount.
To calculate the total interest earned over the 47 years, you subtract the initial principal amount of $1,000 from the end amount of $92,045.80. This gives you the total interest earned. In this scenario, the total interest earned would be $92,045.80 - $1,000 = $91,045.80.
Compound interest is crucial in understanding how investments grow over time, and it showcases the power of compounding when money is invested wisely and for a long period.
How do you subtract two negative numbers?
when you have 2 negative numbers you actually add the 2nd number to the first one
example:
-4 - -2 = becomes -4 + 2 = -2
Four times the complement increased by forty-six is the same as twice the supplement. find the measures of the angle, the complement, and the supplement
A panel containing four on-off switches in a row is to be set. assuming no restrictions on individual switches, use the fundamental counting principle to find the total number of possible panel settings.
A rope 10 feet long is cut into two pieces. One piece is used to form a circle and the other used to form a square. Find a function representing the area of both square and circle as a function of the length of one side of the square.
The functions representing the areas of the square and circle as functions of the length of one side of the square x are [tex]\[ A_s(x) = x^2 \][/tex] and [tex]\[ A_c(x) = \frac{(10 - x)^2}{4\pi} \][/tex] respectively.
Let's denote:
- [tex]\( x \)[/tex] as the length of one side of the square (in feet).
- [tex]\( 10 - x \)[/tex] as the length of the rope used to form the circle.
1. Area of the Square [tex](\( A_s \))[/tex]:
The area of a square is given by the formula: [tex]\( A_s = x^2 \)[/tex].
2. Area of the Circle [tex](\( A_c \))[/tex]:
The circumference of the circle, formed by the rope, is used to find the radius [tex]\( r \)[/tex] of the circle:
[tex]\[ \text{Circumference} = 2\pi r = 10 - x \][/tex]
Solving for [tex]\( r \)[/tex], we get: [tex]\( r = \frac{10 - x}{2\pi} \)[/tex]
The area of the circle is then given by the formula: [tex]\( A_c = \pi r^2 \)[/tex].
Substituting the value of [tex]\( r \)[/tex], we get:
[tex]\[ A_c = \pi \left(\frac{10 - x}{2\pi}\right)^2 \][/tex]
[tex]\[ A_c = \frac{(10 - x)^2}{4\pi} \][/tex]
Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price. How much does she have left to pay after making the down payment?
A.$80
B.$135.20
C. $1040.00
D. $904.80
Downpayment is the percent amount paid from a sum of money. The amount left after the downpayment is $904.80
Downpayment on a priceDownpayment is the percent amount paid from a sum of money. If Zoey put a $1040 item on layaway by making a down payment of 13% of the purchase price, the amount he have left is;
Amount left = (100 - 13)% * 1040
Amount left .= 87% of 1040
Amount left = 0.87 * 1040
Amount left = $904.80
Hence the amount left after the downpayment is $904.80
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At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours. Let x be the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
Answer: The speed of the plane with no wind is 440 miles per hour.
Step-by-step explanation:
Let the maximum speed of the plane be 'x'.
Let the maximum speed of the wind be 'y'.
Since we have given that an airplane travels 2400 miles against the wind in 6 hours.
As we know that
Downstream is given by
[tex]x+y=\dfrac{2400}{6}=400--------------(1)[/tex]
Since we have also given that flying with the wind, the plane can travel the same distance in 5 hours.
As we know tha t
Upstream is given by
[tex]x-y=\dfrac{2400}{5}=480-------------------(2)[/tex]
We just need to find the speed of the plane with no wind.
Using the elimination method,
[tex]x+y=400\\\\x-y=480\\\\-----------------------------\\\\2x=880\\\\x=\dfrac{880}{2}\\\\x=440[/tex]
Hence, the speed of the plane with no wind is 440 miles per hour.
At the beginning of the month a store had a balance of −$554. During the month the store lost another $600. What is the current balance?
Make a frequency distribution and find the relative frequencies for the following number set. Round the relative frequency to the nearest tenth of a percent. Some of the answers will be used more than once and some may not be used.
10 30 40 50 60 70
10 30 40 60 60 80
20 30 50 60 70 90
20 30 50 60 70 90
Number Frequency Relative Frequency
10 %
20 %
30 %
40 %
50 %
60 %
70 %
80 %
90 %
Solve each system:
80x+60y=85
100x-40y=20
Color of car. a. Qualitative/Ordinal b. Qualitative/Nominal c. Quantitative/Discrete d. Quantitative/Continuous
Can someone help me figure this out: Factor 12y^2-27? I keep getting the steps confused.
A bat flies at an average speed of 32 kilometres an hour. At this speed, how far will it fly in 15 minutes?
Final answer:
To find out the distance a bat will fly in 15 minutes at an average speed of 32 kilometers per hour, you multiply the speed by the time in hours (15 minutes is 0.25 hours). The bat will fly 8 kilometers.
Explanation:
To calculate how far a bat flies in 15 minutes at an average speed of 32 kilometers per hour, we need to convert the time into hours since the speed is given in kilometers per hour (km/h). 15 minutes is equal to 0.25 hours (since there are 60 minutes in 1 hour, so 15 minutes divided by 60 minutes per hour equals 0.25 hours).
We can then use the formula for distance which is:
Distance = Speed × Time
The average speed of the bat is 32 km/h, and the time is 0.25 hours.
Distance = 32 km/h × 0.25 h = 8 km
So, the bat will fly 8 kilometers in 15 minutes.
If (x,y) are the coordinates of a point p in the xy-plane, then x is called the _______ of p and y is the _______ of p.
In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
Explanation:In a Cartesian coordinate system, the x-coordinate represents the horizontal position of a point, and the y-coordinate represents the vertical position of a point.
For example, in the point (3, 5), the x-coordinate is 3 and the y-coordinate is 5.
Together, the x and y coordinates specify the precise location of a point in the xy-plane.
A student must choose to participate in two different events during field day. There are four track events, two academic events, and six team sports events. What is the approximate probability that the student will choose to participate in two team sports?
0.114
0.227
0.273
0.545
Answer:
.227
Step-by-step explanation:
Answer:
0.227
Step-by-step explanation:
Can some PLEASE help me with 8 and 9!!????
what is the distance between the points (3,7) and (15,16) on a coordinate plane?
distance = Sqrt((x2-x1)^2 +(y2-y1)^2)
15-3 =12
16-7=9
12^2 = 144
9^2 = 81
144+81 = 225
square root of 225 = 15
the distance is 15
What is the length of the hypotenuse of a right triangle if each of the two legs is 4 units? square root of 8 units 4 units square root of 32 units 8 unit?
Answer:
Well if you still need the answer around 4 years later LOL its √32
Step-by-step explanation:
Answer:
√32
Step-by-step explanation:
Because this is totally helpful 4 years later
PLEASE HELP IM RUNNING OUT OF TIME!!!!!
Which of the following radical expressions has an absolute value symbol in its simplified form?
I hope i wrote these right
MY CHOICES ARE:
a. 16x^4−−−−√4
b. 81x−−−√4
c. −125x^3−−−−−−√3
d. 64x^3−−−−√3
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2 , and a vertical shift up 3 units.
Answer:
y = sin(4x) + 3
Step-by-step explanation:
y = Asin(Bx + C) + D
A is amplitude = 1
B = 2pi/period = 2pi / (pi/2) = 4
C does not mention.
D: shift up or down = 3
=> y = sin(4x) + 3
round 0.9144 to the nearest tenth of a yard
Use the graph below to answer the question.
What is the slope of a line that is perpendicular to the line in the graph?
Answer:
Im working on it right now and its 1
Step-by-step explanation:
A parachutist's speed during a free fall reaches
207
kilometers per hour. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 5 seconds of free fall?
find the GCF 12, 18, 24
3/8 of people at a fun fair were children 3/4 of the remaining people were men there were 140 more children than women how many people went to the fun fair
The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
The four angles of the quadrilateral are °, °, °, and °, respectively.
Answer:
The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Step-by-step explanation:
Given : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
To find : The four angles of the quadrilateral are °, °, °, and °, respectively.
Solution : We have given that The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
Let the angle of the quadrilateral is x
Then all the angles are x , 2x , 5x ,4x
Complete angle formed by circle is 360 °
Sum of all the angle are 360
x + 2x + 5x + 4x = 360 .
12 x = 360 .
On dividing both sids by 12.
x = 30 .
Then
2x = 60
5x = 5 * 30 = 150 .
4x = 4 *30 = 120 .
Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.
Answer:
for plato users the answers are 45,75,135,105
Step-by-step explanation: