Answer:
see explanation
Step-by-step explanation:
Given
[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π
let
[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so
x = tanA, y = tanB , z = tanC
Substituting values
A + B + C = π ( subtract C from both sides )
A + B = π - C ( take tan of both sides )
tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )
[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )
tanA + tanB = - tanC( 1 - tanAtanB) ← distribute
tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )
tanA + tanB + tanC = tanAtanBtanC , that is
x + y + z = xyz
P,W,R & S form the vertices of a quadrilateral. PQR = 74 degrees
RSP = 121 degrees
Find the value of SPQ
Answer:
∠ SPQ = 75°
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Subtract the sum of the 3 angles from 360 for ∠ SPQ
∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°
Help. The graph shows the system of equations below.
2x -3y = -6
y = - 1/3x -4
9514 1404 393
Answer:
(a) The blue line ... solution ... (-6, -2)..
Step-by-step explanation:
The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.
The blue line represents the equation 2x -3y = -6.
The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
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6( n - 2) in word form please c:
Answer:
six in parenthesis n minus two
Step-by-step explanation:
2 ways could be:
A. N minus two then multiply by six
B. Six times parentheses n minus two end parentheses
In a class of students, the following data table summarizes how many students have a cat or a dog. What is the probability that a student who has a cat also has a dog?
Has a cat Does not have a cat
Has a dog 7 6
Does not have a dog 8 2
Which is the equation of the line with slope o passing through the point (-3,-1)?
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Answer:
y = -1
Step-by-step explanation:
We assume you want the line with a slope of zero. That is a horizontal line, so y is a constant. In order to make the line go through the point with y=-1, the equation of the line is ...
y = -1
What should be subtracted from 13/(-56) to get 11/28
Answer:
-5/8
Step-by-step explanation:
13/ -56 -x = 11/28
Add 13/56 to each side
13/ -56 + 13/56 -x = 11/28+ 13/56
-x = 11/28 + 13/56
Get a common denominator
-x = 11/28 *2/2 +13/56
-x = 22/56 + 13/56
-x = 35/56
Divide top and bottom by 7
-x = 5/8
Multiply both side by -1
x = -5/8
PLEASE HELP! 50 POINTS
Identify the intervals on which the function is increasing, decreasing or constant. Write your answers in interval notation. Write the end behavior for each function in limit notation.
f(x)=-4x^4+3x^3-2x^2+x-9
(Type a 0 before the decimal to hold the ones place for answers that don't have a value in the ones place. Ex. 0.24)
Use inf for infinity
(PLEASE ITS ACTUALLY MY LAST ONE HELP)
Which two figures represent circles of the same size?
A) D and G
B) C and G
C) none of them.
D) C and D
Answer:
B) C and G
Step-by-step explanation:
The radius is equal to 1/2 the diameter
r = 1/2 d
G has a diameter of 45
1/2 (45) = 22.5
C and G are the same
Answer:
c and g!
Step-by-step explanation:
The rate of change for yyy as a function of xxx is
, therefore the function is
.
For all values of xxx, the function value y\:yy
\:000.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
When x=1x=1x, equals, 1, the function value y=\:y=y, equals
.
everything seems to be correctly filled.
if you wanted confidence by confirmation: here, take some
It is an exponentially decaying function.
What is an exponential function ?An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.
Exponential functions are of two types one is exponentially growing function and exponentially decaying function.
when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.
In the given question f(x) = 8e⁻ˣ
when, x = 0 f(x) = 8
f(x) = 8e⁻ˣ
f(0) = 8e⁰
f(0) = 8
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The decimal for an irrational number never terminates or repeats. The
rational and irrational numbers together form the set of real numbers.
If false, explair:
Answer:
Step-by-step explanation:
No that is true. I can't make anything more out of it.
Identify the domain of the graph given below.
Answer:
(-∞,∞) is the domain.
2 is the range
Step-by-step explanation:
I need help please thank you
Answer:
A
Step-by-step explanation:
in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.
recall this formula :
(a-b)(a+b) = a^2 - b^2
in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of 3 -
after multiplying the denominator by its conjugate, we get:
(3 - [tex]\sqrt{6x}[/tex]) (3 +
at this point there is no need to solve the numerator as there is only one answer with this denominator.
hope this helps :)
Answer:
Step-by-step explanation:
The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.
Answer:
Step-by-step explanation:
x+y = 67
2x-y = 38
Add the equations together
3x = 108
x = 36
y = 67-x = 31
A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed
Answer:
It will be 31.4 cm rounded off for circumference
It will be 78.53 cm2 rounded off for area
Step-by-step explanation:
Diameter = 10 cm
Radius = 10/2 cm = 5 cm
Circumference = 2×pi×radius
= 2pi×5
= 31.4 cm
Area = pi × r square
= 25 pi
= 78.53cm2
Need help!
given rectangle ABCD find m<CAB
Answer:
∠ CAB = 60°
Step-by-step explanation:
∠ CAD and ∠ BCA are alternate angles and congruent , so
∠ CAD = 30°
∠ BAD = 90° ( angle in a rectangle ) , then
∠ CAB = 90° - ∠ CAD = 90° - 30° = 60°
The measure of the angle m∠CAB is 60.
What is a rectangle?A rectangle is a 2-D shape with length and width.
The length and width are different.
If the length and width are not different then it is a square.
The area of a rectangle is given as:
Area = Length x width
We have,
The rectangle has 90 degrees on all the vertices.
So,
In ΔABC,
The sum of the angles = 180
So,
30 + 90 + m∠CAB = 180
m∠CAB = 180 - 120
m∠CAB = 60
Thus,
The measure of the angle m∠CAB is 60.
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Product A sells 1.5 times more than Product B. Product B sells 70% less than Product C. Product C sold 34,000 units this month.
How many units of Product A were sold?
10,200
15,300 23,800 35,700 51,000
Answer:
15,300 units
Step-by-step explanation:
First, find how many units of Product B were sold:
34,000(0.3)
= 10,200
Find how many units of Product A were sold:
10,200(1.5)
= 15,300
So, 15,300 units of Product A were sold.
Product A sold 15,300 units that is 1.5 times more than product B
Given :
Product A sells 1.5 times more than Product B. Product B sells 70% less than Product C.
Product C sold 34,000 units this month
Product C sold = 34000
Product B is 70% less than product C
So, product B is 100-70% =30% of product C
[tex]Product B=\frac{30}{100} \cdot 34000\\Product B \; sold = 10200[/tex]
Lets find out product A sold
Product A sold = 1.5 times more than product B
[tex]Product A= 1.5 \cdot product B\\Product A=1.5 \cdot 10200=15300[/tex]
15,300 units of product A were sold.
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GIVING 15 POINTS PLS FAST
Drag the tiles to the boxes to form correct pairs.
Match each addition operation to the correct sum.
-24 8 + 30
131.87
28.98+(-52.22)
65
45%+39
-23.24
56.75 +75.12
Reset
Next
Next
Answer:
Hope this helps! All you needed to do was add and subtract. Go through the slides, I added the step by step explanation, as well as the final table which contains the answers.
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
We have,
Expressions:
-24(5/9) +30(7/9)
Simplifying the fractions.
This can be written as,
= (-24 + 30) +(-5/9 + 7/9)
= 6 + 2/9
= 6(2/9)
45(2/9) +39(3/9)
= (45 + 39) + (2/9 + 3/9)
= 84 + 5/9
= 84(5/9)
28.98 + (-52.22)
= 28.98 - 52.22
= -23.24
56.75 + 75.12
= 131.87
Thus,
The value of the expressions are:
24(5/9) +30(7/9) = 6(2/9)
45(2/9) +39(3/9) = 84(5/9)
28.98 + (-52.22) =-23.24
56.75 + 75.12 = 131.87
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3. (02.01)
Solve for x:
wim
(x – 4) = 2x. (1 point)
2
-2
-8
-4
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?
Answer:
a.
[tex] \frac{36}{40} [/tex]
Solve 2x2 – 3x = 12 using the quadratic formula.
Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a
2x^2 - 3x = 12
2x^2 - 3x - 12 = 0
a = 2
b = -3
c = -12
(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)
3 +/- sqrt( 9 + 96 ) / 4
3 +/- sqrt(105) / 4
Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]
Hope this helps!
What effect will replacing x with (x - 4) have on the graph of the equation y = (x - 3) ^ 2
A. Slides the graph 4 units up
B. Slides the graph 7 units down
C. Slides the graph 4 units right
D. Slides the graph 1 units
Answer:
C)slides graph 4 units to the right
Jamie kept track of the total hours and minutes she worked this week at the local health food store.
Monday - 3 hours
Thursday - 5 hours 30 minutes
Saturday - 3 hours 30 minutes
Sunday - 6 hours 45 minutes
How many decimal hours did Jamie work this week? (2 points)
17.11
18.05
18.75
Answer:
18.05
Step-by-step explanation:
-p/3-8=3 what is the variable
Answer:
-33
Step-by-step explanation:
-p/3-8=3
or,(-p-24)/3=3
or,(-p-24)=9
or,-p=33
Therefore, p=-33
What is the purpose for post tests?
Answer:
The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.
What is the inverse of the function ? f(x)=x+1 over x?
plato
Answer:
[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]
Step-by-step explanation:
bxhrrrhi5u44ftj7gttjoy
Answer:
x = (y+1)/y
xy = (y+1)
xy -y = 1
y(x-1)=1
y = 1/(x-1)
Step-by-step explanation:
SOMEONE PLS HELP!!!!
Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 3x + 1
A) This is a polynomial.
B) The base is x + 1.
C) The base is 3.
D) This is not an exponential function because the variable is in the exponent position.
Answer:
Step-by-step explanation:
Is the function f(x) = 3x+1, f(x) = 3ˣ⁺¹, or f(x) = 3ˣ+1 ?
f(x) = 3x+1 is not an exponential function. It is a straight line.
f(x) = 3ˣ⁺¹ Is an exponential function. The base is 3.
f(x) = 3ˣ+1 is an exponential function. The base is 3.
An investment of $8,120 is earning interest at the rate of 5.8% compounded quarterly over 11 years. How much
interest is earned on the investment? Show your work.
Answer:
5180.56 Dollars...........
Find the exact value by using a half-angle identity.
tan seven pi divided by eight
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Answer:
1 -√2
Step-by-step explanation:
[tex]\tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}[/tex]
tan(7π/8) = 1 -√2
HaLP a beggar in need
Answer:
C) 2
Step-by-step explanation:
From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.
