Answer:
z = (2xy-x)
Step-by-step explanation:
Let the first number be x and the other number is z.
According to question,
The average of two number is xy i.e.
[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]
So, the value of z is (2xy-x) i.e. the other number is (2xy-x).
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?
1. Find the exact value of sin( a−B), given that sin a=−4/5 and cos B=12/13, with a in quadrant III and B in quadrant IV.
2. Find all real numbers in the interval [0,2pi) that satisfy the equation.
3sec^2 x tan x =4tan x
3. Simplify the following trigonometric expressions, using identities as needed:
sin(x)/1−cos(x) + 1−cos(x)/sin(x)
(1) Recall that
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
sin²(x) + cos²(x) = 1
Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have
• sin(α) < 0 and cos(α) < 0
• sin(β) < 0 and cos(β) > 0
Solve for cos(α) and sin(β) :
cos(α) = -√(1 - sin²(α)) = -3/5
sin(β) = -√(1 - cos²(β)) = -5/13
Then
sin(α - β) = sin(α) cos(β) - cos(α) sin(β) = (-4/5) (12/13) - (-3/5) (-5/13)
==> sin(α - β) = -63/65
(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,
sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)
==> tan²(x) + 1 = sec²(x)
Rewrite the equation as
3 sec²(x) tan(x) = 4 tan(x)
3 (tan²(x) + 1) tan(x) = 4 tan(x)
3 tan³(x) + 3 tan(x) = 4 tan(x)
3 tan³(x) - tan(x) = 0
tan(x) (3 tan²(x) - 1) = 0
Solve for x :
tan(x) = 0 or 3 tan²(x) - 1 = 0
tan(x) = 0 or tan²(x) = 1/3
tan(x) = 0 or tan(x) = ±√(1/3)
x = arctan(0) + nπ or x = arctan(1/√3) + nπ or x = arctan(-1/√3) + nπ
x = nπ or x = π/6 + nπ or x = -π/6 + nπ
where n is any integer. In the interval [0, 2π), we get the solutions
x = 0, π/6, 5π/6, π, 7π/6, 11π/6
(3) You only need to rewrite the first term:
[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]
Then
[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]
In a test of a heat-seeking rocket, a first rocket is launched at 2000 fts and the heat-seeking rocket is launched along the same flight path 20 s later at a speed of 3000 fts. Find
the timest, and t, of flight of the rockets until the heat-seeking rocket destroys the first rocket
What are the times of the flight?
Answer:
Time of flight of first rocket = 60 seconds
Time of flight of second rocket = 40 seconds
Step-by-step explanation:
Let the time of flight of first rocket be t1.
Since the second rocket is launched 20 seconds later, then it means that;
t1 = t2 + 20
Where t2 is the time of flight of the second rocket.
When destruction has occurred, it means that both of the rockets would have covered the same distance.
We know that;
Distance = speed × time
Thus;
2000t1 = 3000t2
We know that t1 = t2 + 20
Thus;
2000(t2 + 20) = 3000t2
2000t2 + 40000 = 3000t2
3000t2 - 2000t2 = 40000
1000t2 = 40000
t2 = 40000/1000
t2 = 40 seconds
Thus;
t1 = 40 + 20
t1 = 60 seconds
Need help with this really fast
Answer:
6
Step-by-step explanation:
You can apply the proportion of 9/6 to 4 to get 6:
6*(9/6)= 9
So
4*(9/6) = Length LA
6= Length LA
Answer:
Option C, or [tex]2\frac{2}{3}[/tex]
Explanation:
We can see that the Line FM in the smaller triangle dialates to Line LK in the bigger triangle by the scale factor of:
FM/LK
6/9 or 2/3
So we would know that to find out the value of LA in the bigger triangle we would have to dialate it’s corresponding side FI in the smaller triangle by the same scale factor:
4 * 2/3
=> [tex]2\frac{2}{3}[/tex] = LA
Hope this helps!
is y=3x^2-x-1 a function
Answer: Yes it is a function.
This is because any x input leads to exactly one y output.
The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
F(x) =-2x-4 find x if f(x)=14
Answer:
14=-2x-4
18=-2x
x=-9
Hope This Helps!!!
i need help solving this .
Answer:b
Step-by-step explanation:
Answer:
just be smart trust me u dont need us to give u the answer ur super smart
Step-by-step explanation:
make me brainliest to help people be encourage
The club will use the majority criterion method to determine the final winner. However, while finalizing the votes, a member of the club discovers that Mason did not meet the original criteria to be considered for the vacation package, because he is a county deputy, not a city police person, so Mason is eliminated from the votes. Who actually will win the tickets? Is the irrelevant alternative criterion supported in this case?
Answer and Explanation:
The irrelevant alternative criterion states that if two candidates A and B contest for an election and candidate B is preferred to candidate A then any other candidate X should not cause candidate A to win the election.
In this case if Mason was candidate A, then candidate B should still win by the majority criterion method and the irrelevant alternative criterion would still be supported. However if he is candidate B then the irrelevant alternative criterion is not supported.
A driver must decide whether to buy a new car for $24,000 or lease the same car over a four-year period. Under the terms of the lease, she can make a down payment
of $3000 and have monthly payments of $150. At the end of the four years, the leased car has a residual value (the amount she pays if she chooses to buy the car at
the end of the lease period) of $11,000. Assume she can sell the new car at the end of the four years at the same residual value. Is it less expensive to buy or
to lease?
Answer:
3000 is the answer this question.
Given: triangle ABC with side lengths a, b, and c, and height h
Prove: Area = 1/2absin C
Answer:
Step-by-step explanation:
Statements Reasons
1). ΔABC with side lengths a, b, c, and h 1). Given
2). Area = [tex]\frac{1}{2}bh[/tex] 2). Triangle area formula
3). [tex]\text{sin}C=\frac{h}{a}[/tex] 3). Definition of sine
4). asin(C) = h 4). Multiplication property of
equality.
5). Area = [tex]\frac{1}{2}ba\text{sin}C[/tex] 5). Substitution property
6). Area = [tex]\frac{1}{2}ab\text{sin}C[/tex] 6). Commutative property of
multiplication.
Hence, proved.
Identify an equation in point-slope from for the line perpendicular to y=-4x-1 that passes through (-2, 4)
Answer:
y - 4 = ¼(x + 2)
Step-by-step explanation:
Point-slope form equation is given as y - b = m(x - a). Where,
(a, b) = a point on the line = (-2, 4)
m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)
✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).
y - 4 = ¼(x - (-2))
y - 4 = ¼(x + 2)
None of the options are correct
when a number is added to 1/5 of itself, the result is 24. the equation that models this problem is n+1/5n=24. what is the value of n?
if side of square is 4.05 find its area
Answer:
A
≈
16.4
please give brain listProbabilityyyyyyyyyyyyyyy
Answer:
Reduce if needed, asked or necessary
Step-by-step explanation:
1. 4/10
2. 2/6
3. 4/10
4. more likely
Answer:
Since Probability Is Usually Written In Fraction Form OR Ratios
(Although It Really Doesn't Matter):
1. 4/10 (2/5)
2. 2/6 (1/3)
3. 6/10 (3/5)
(All Fraction Form)
Last Question:
I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.
Step-by-step explanation:
This is the basic fraction form : ____ / ____
Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!
How would I draw the reflection over the line y=2x+5?
Answer:
Step-by-step explanation:
What is the coefficient of x2 in the expansion of (x + 2)??
O A.
2
OB.
3
O C.
4
OD.
6
x+2 in expansion of (x+2) ?
A
By converting to an exponential expression, solve log2 (x + 5) = 4
Step-by-step explanation:
just insert a base of two at on both sides and solve.
The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The logarithmic equation is given below.
㏒₂(x + 5) = 4
Simplify the equation, then we have
㏒ (x + 5) / ㏒ 2 = 4
㏒ (x + 5) = 4 × ㏒ 2
㏒ (x + 5) = ㏒ 2⁴
Take antilog on both sides, then we have
(x + 5) = 2⁴
(x + 5) = 16
x = 11
The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
Please answer & number. Thank you! <33
Answer:
2）=2
4）=3
5）=5
8）=-1
Step-by-step explanation:
just divide the number by the number with variable
On Monday, 27 adults visited an amusement park. On Tuesday, 23 adults visited the amusement park. The enterance fee for the adults is Rs. 100. How much amount is collected from the adults in these two days?
PLEASE TELL FULL SOLUTION.
Answer:
5000
Step-by-step explanation:
Add the number of adults first: 27+23=50
Then multiply the number of adults by 100 for the fee.
50*100 = 5000
Answer:
within the two days a total of 5000$ where collected in the two days
Solution:
R= 100 per adult
1 adult = 100
27(R)+ 23(R) = 27(100)+ 23(100)
27(100)+23(100) =5000
or add both 27 and 23 and multiple by 100
50•100 = 5000
pls answer fast I need to submit in 5 mins !!
What is the volume of the prism?
Enter your answer, as a mixed number in simplest form, in the box.
Solve the equation 2sin^2(x) = 1 for x ∈ [-π,π], expressing all solutions as exact values. please help its urgent !!
Answer:
2sin.2(x) sd s
Step-by-step explanation:
In a family of 3 children, what is the probability that there will be exactly 2 boys assuming that the sexes are equally likely to occur in each birth
Answer:
There is a 60.00 percent probability of a particular outcome and 40.00 percent probability of another outcome.
sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB
Answer:
6
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.
n(AnB) maximum = 3
so n(AUB) = 3+6-3 = 6
Create a circle such that its center is point A and B is a point on the circle.
Answer:
The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.
I need help with this.
Answer:
A and b Are in quadrant 2. F and D are in quadrant 1. F is in quadrant 3 and C is in quadrant 4
Step-by-step explanation:
each quadrant is in the boxes and the question is asking what is each coordinate is in what quadrant
Simplify. v80
A. 16v5
B. 5v4
C. 4v5
D. 20v4
Hi!
√80 = √(16 • 5) = √(4² • 5) = 4√5
You are dealt one card from a 52-card deck.
a) Find the odds in favor of getting a red king.
b) Find the odds against getting a red king.
Answer:
(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.
(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.
The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
You are dealt one card from a 52-card deck.
Total events = 52
The odds in favor of getting a red king will be
Favorable events = 2
Then the probability will be
P = 2/52
P = 1/26
The odds against getting a red king will be
q = 1 – P
q = 1 – 1/26
q = 25/26
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ2
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
Answer:
22608 mm³/s
Step-by-step explanation:
Applying chain rule,
dV/dt = (dV/dr)(dr/dt)............... Equation 1
Where dV/dr = rate at which the volume is increasing
But,
V = 4πr³/3
Therefore,
dV/dr = 4πr²............... Equation 2
Substitute equation 2 into equation 1
dV/dt = 4πr²(dr/dt).............. Equation 3
From the question,
Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm
Consatant: π = 3.14
Substitute these values into equation 3
dV/dt = 4×3.14×30²×2
dV/dt = 22608 mm³/s
