Answers:
cos(2theta) = -119/169cos(theta) = -5/13=====================================================
The given info is:
sin(theta) = 12/13theta is in quadrant IIFrom that, we can use the pythagorean trig identity to find that cos(theta) = -5/13. Keep in mind that cosine is negative in quadrant II.
Now use the trig identity below to compute cos(2theta)
[tex]\cos(2\theta) = \cos^2(\theta)-\sin^2(\theta)\\\\\cos(2\theta) = \left(\frac{-5}{13}\right)^2-\left(\frac{12}{13}\right)^2\\\\\cos(2\theta) = \frac{25}{169}-\frac{144}{169}\\\\\cos(2\theta) = \frac{25-144}{169}\\\\\cos(2\theta) = -\frac{119}{169}\\\\[/tex]
Other options you could use are these identities
[tex]\cos(2\theta) = 2\cos^2(\theta)-1\\\\[/tex]
or
[tex]\cos(2\theta) = 1-2\sin^2(\theta)\\\\[/tex]
For # 7-10, find the number of possible 4-card hands that contain the cards specified
Answers:
Problem 7) 105,625Problem 8) 8800Problem 9) 715Problem 10) 2860Note: The answer to problem 7 is a single value. The comma is there to make the number more readable.
========================================================
Explanation for problem 7)
There are 26 red cards (13 diamonds + 13 hearts).
We have 26 ways to pick the first red card, and then 25 ways to pick the second red card. If order mattered, then we'd have 26*25 = 650 ways to do this. However, order doesn't matter. All that matters is the hand itself rather than the individual cards. By "hand" I mean the collection of cards, and not the literal physical hand holding them.
Since the count 650 is a double count, this means 650/2 = 325 is the correct count where order doesn't matter. The black cards will follow identical logic to get the same value. There are 325 ways to pick the two black cards. This is because there are an equal number of red and black cards, and we're selecting an equal number of both colors.
So we have 325*325 = 105,625 different hands possible.
To help show some context, there are 52C4 = 270,725 different ways to pick four cards without any restrictions. I'm using the nCr combination formula.
----------------------
Explanation for problem 8)
The face cards are Jack, Queen, King. There are 3 face cards per suit and 4 suits total, so 3*4 = 12 face cards in all.
We have 12*11*10 = 1320 permutations and 1320/(3!) = 1320/6 = 220 combinations. We side with combinations because like before, order doesn't matter. There are 220 different ways to pick the three face cards. Then we have 52-12 = 40 ways to pick the fourth non-face card.
Overall, we have 220*40 = 8800 different ways to pick exactly three face cards.
----------------------
Explanation for problem 9)
There are 13 diamond cards, so n = 13. We're filling r = 4 slots.
Use the nCr combination formula to find that 13C4 = 715
See the attached image below for more detailed steps.
We have 715 ways to pick all diamonds.
----------------------
Explanation for problem 10)
We'll build from problem 9. We found there are 715 ways to pick four diamonds. This is the same number of ways to pick four hearts, or four clubs, or four spades. The actual suit doesn't matter. So we have 4*715 = 2860 different ways to pick 4 cards of the same suit
In poker, having all cards of the same suit is known as a flush. Though with poker, it involves 5 cards instead of 4.
5 less than 4 times another. product is 6. find the integers
y= 4x-5
x.y = 6
x = 6/y
substitute value
y= 24/y-5
y²+5y-24=0
y²+8y-3y-24=0
y(y+8) -3(y+8) = 0
y=3 or y = -8
consider y = 3,
3 = 4x-5
x= 2!
now y = -8
-8= 4x-5
x= -3/4
The answer is 2 and 3 Or -8 and -3/4
2 is not 5 less 4 times other so the solution is -8 and -3/4
find a value of (2power-1*4power-1)
2^( - 1 ) × 4^( -1 ) =
2^( -1 ) × 2^( 2 × ( - 1) ) =
2^( - 1 ) × 2^( - 2 ) =
2^( - 1 - 2 ) =
2^( - 3 ) =
1/ 2^( 3 ) =
1/8
An urn contains 9 black and 8 pink balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are black
Answer:
0.0416
Step-by-step explanation:
Given :
Number of balls :
Pink = 8 ; black = 9
Total number of balls = 8+9 = 17
Choosing with replacement :
Probability = required outcome / Total possible outcomes
Required outcome = number of black balls
Total possible outcomes = total number of balls
P(black) = 9/17
Number of picks = 5
Hence, Probability that all 5 picks are black :
P(all black) = 9/17 * 9/17 * 9/17 * 9/17 * 9/17 = 0.0415879
= 0.0416
Mark is building a sandbox inside a play area. How much play area remains outside of the sandbox?
Answer:
What is the anwser i ned help
Step-by-step explanation:
Is 5+2y=13 a linear relationship
Answer:
Yes 5+2y=13 is a linear relationship
Jenny bought gallons of lemonade and milk for a banquet. A gallon of lemonade costs $5, and a gallon of milk costs $3. Jenny spent $120 and bought 32 total gallons. How many gallons of milk did Jenny buy?
Answer:
She Bought 40 Gallons of Milk
Step-by-step explanation:
can someone help me find the value of w please :)
Answer:
w=18.27
Step-by-step explanation:
Using Trig you have opposite and hypotenuse so use SIN
Sin(66)=w/20
20Sin(66)=w
w=18.27
Suppose that 11 inches of wire costs 44cents.
At the same rate, how many inches of wire can be bought for 24 cents?
we can bought 6 inches of wire which costs 24 cents
Help pls ………………………………
Answer:
12
Step-by-step explanation:
3 times x squared increased by 8 is 20
Answer:
3x² + 8 = 20
x = 2
Step-by-step explanation:
3 times x squared increased by 8 is 20
3x² + 8 = 20
3x² = 12
x² = 4
x = 2
For a sample size of n = 26 and a population parameter of p = 0.6, a normal
curve can be used to approximate the sampling distribution.
O A. True
O B. False
Answer:true
Step-by-step explanation:
just took the test < 3
The statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
What is normal curve?Normal curve is used to represent the class shapes in the statistical probability. Mathematically, we can describe the normal curve as -
[tex]$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}[/tex]
where -
f(x) = probability density function
σ = standard deviation
μ = mean
Given is that for a sample size of n = 26 and a population parameter of
p = 0.6, a normal curve can be used to approximate the sampling
distribution.
It is asked to identify whether the given statement regarding the normal curve is true or false. The given statement is - "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution". The given statement is true.
Therefore, the statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
To solve more questions on normal curves, visit the link below-
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Find the
vertex of this
quadratic.
([?], [ ]
2
1
X
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
Answer:
The vertex of the parabola is [tex]V(x,y) = (0, 3)[/tex].
Step-by-step explanation:
In this case, the vertex of the parabola is the absolute maximum of the graph, that is, the point [tex]V(x,y) = (0, 3)[/tex]. Mathematically speaking, the vertex of the parabola is represents the only point of the range ([tex]y[/tex]) which is related to an only value of the domain ([tex]x[/tex]).
A gymnasium floor is being covered by square shock-absorbing tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles
This question is incomplete, the complete question is;
A gymnasium floor is being covered by square shock-absorbing tiles.
The old gym floor required 864 square tiles. The new tiles are 2 inches larger in length and width than the old tiles. The new flooring will require only 600 tiles. What is the length of a side of one of the new shock-absorbing tiles
Answer:
Length of the side of one of the new shock-absorbing tiles is 12 inches
Step-by-step explanation:
Given the data in the question;
Since both the area for old tiles and new tiles are the same;
so Area of old tiles = Area of new tiles,
given that; The old gym floor required 864 square tiles and new flooring will require only 600 tiles as new tiles are 2 inches larger in length and width than the old tiles.
Now let the length of the sides of the square tiles be x
Area of a square = length × length = x × x = x²
So, Area of Old tiles = 864 × x² = 864x²
Area of New tiles = 600( x + 2 )²
= 600( x² + 4x + 4 )
= 600x² + 2400x + 2400
Now, Area of old tiles = Area of new tiles
864x² - 600x² - 2400x - 2400 = 0
264x² - 2400x - 2400 = 0
we find x
Using; x = [-b ±√( b² - 4ac )] / 2a
x = [-( -2400) ±√( (-2400)² - (4 × 264 × -2400 )] / 2( 264 )
x = [ 2400 ±√( 5760000 + 2534400) ] / 528
x = [ 2400 ±√8294400 ] / 528
x = [ 2400 ±2880 ] / 528
x = [ 2400 - 2880 ] / 528 or [ 2400 + 2880 ] / 528
x = [ -480 / 528 ] or [ 5280 / 528 ]
x = [ -0.909 ] or [ 10 ]
the length of the sides of the square tiles cannot be Negative
Hence, x = 10
Therefore, the length of a side of one of the new shock-absorbing tiles will be;
⇒ x + 2 = 10 + 2 = 12 inches
Length of the side of one of the new shock-absorbing tiles is 12 inches
can someone help 10 points
Answer:
The volume of this rectangular prism is 72 cubic units. We multiply 6*4*3 to get 72.
16. (24.6L) The time t (in minutes) that it takes Danielle
to drive to work varies inversely with the average
speed S (in miles per hour). It takes Danielle 24
minutes to get to work when he drives at an
average speed of 30 mph. What is Danielle's
average speed if he gets to work in 36 minutes.
Answer:
20 mph
Step-by-step explanation:
Varies inversely
ts = k
------------------------------
It takes Danielle 24 minutes to get to work when he drives at an average speed of 30 mph
24(30) = 720
------------------------
What is Danielle's average speed if he gets to work in 36 minutes.
36s = 720
s = 720/36
s = 20
20 mph
A square originally starts with an area of 64 cm2.
If each side of the square is increased by 2 cm, what is the area of the new square?
Answer:
100 cm2
Step-by-step explanation:
If the area is 64 cm2 that means that the side is 8 cm (square root of 64 is 8)
8 increased by 2 = 10
area 10x10 = 100 cm2
Answer:
the answer is 100cm²
since originally is 64 cm²
so square root of 64 is 8 cm.
after you get 8cm you get,
8+2 = 10cm (a side of square)
and then to find a new area you get,
10 × 10 = 100 cm²
In the 1990s the demand for personal computers in the home went up with household income. For a given community in the 1990s, the average number of computers in a home could be approximated by
q = 0.3456 ln x − 3.045 10,000 ≤ x ≤ 125,000
where x is mean household income. A certain community had a mean income of $15,000, increasing at a rate of $1,500 per year.
1. How many computers per household were there?
2. How fast was the number of computers in a home increasing?
Answer:
dvffdd
Step-by-step explanation:
How many different five digit members can be formed from the digits 5, 6, 7, 8 and 9 if digits can be repeated? If digits cannot be repeated? NO LINKS!!!
Answer:
Solution given:
5,6,7,8,9,
When repeated:
it has
5 ways for each
different five digit members can be formed from the digits:5*5*5*5*5=3125
When not repeated:
it has
5 ways for 1st
4 ways for 2nd
3 ways for 3rd
2 ways for 4th
1 ways for 5th
different five digit members can be formed from the digits:5*4*3*2*1=120
FOR 100 POINTS!!!! BRAINLIEST TOO PLEASE HELP!!!!
Estimate an equation for the line of best fit for the following scatter plot. Pic below. Open ended.
Answer:
y = 8.667x + 8Step-by-step explanation:
Use two points on the graph to get an equation:
(0, 8), (6, 60)The slope: m = (60 - 8)/6 = 8.667
The y- intercept is 8
The equation of the line of best fit:
y = 8.667x + 8The answer to your question is y = 8.667x + 8. Hope this helps; have a great day!
Relationship in Figures
Determine the unknown side length of the golden rectangle with the given side length.
s = _____ t = 9
a. 5.56
b. 4.85
c. 4.94
d. 5.26
Please select the best answer from choices provided
Answer:
A. 5.56
Step-by-step explanation:
I calculated logically
Two straight lines that intersect at a right angle are __?__ to each other.
Answer: perpendicular lines
Step-by-step explanation:
look up "Two straight lines that intersect at a right angle"
Answer:
Perpendicular! hope this helps :)
Can any one psay what is monmon meaning I think it's and alien
Answer:
Monmon is a Beast Digimon. It is a Digimon that has the appearance of an infant monkey. It has enough strength to wield a slingshot the size of its body with ease, and confidence in its abilities to prevent its prey from escaping. It often falls from treetops due to its careless personality. Its stylish traits are its tiger-printed outfit and its white-tipped tail
WILL GIVE U BRAINLIEST
ABCD is a rectangle. AB = x + 7, BC = 2x + 19. What is the CD?
A. 2x + 133
B. X + 7
C. 5x + 38
D. 2x + 14
Answer:
A rectangle has its Opposite sides Equal.
Draw one so you'd grab it better.
AB=CD
BC= AD
Since CD=AB and We're given AB=x+7...
CD = x + 7
OPTION B IS LEGIT!!
Find QR.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
QR = ___
Answer:
Step-by-step explanation:
take 64 degree as reference angle
using cos rule
cos 64=adjacent/hypotemuse
0.43=QR/10
10*0.43=QR
4.3=QR
Kyle typed 574 words in 14 minutes. How many
Answer:
Kyle typed 574 words in 14 minutes. How many...........?????????
il.l just divide 574 divided by 14= 41
Step-by-step explanation:
:)
Answer:
41 like I said in the comments.
Step-by-step explanation:
300 ml of an IV fluid contains 50 mcg of Drug A. If a patient is receiving 1000 ml of this IV fluid, how much of Drug A is this patient getting?
Answer: 166.666 mcgs
Step-by-step explanation:
If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that 300 ml of an IV fluid contains 50 mcg of Drug A. Therefore, the ratio of IV fluid to drugs A can be written as,
IV fluid / Drug A = 300ml / 50 mcg
IV fluid / Drug A = 6 ml/ mcg
Now, If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting,
IV fluid / Drug A = 6 ml/ mcg
1000 ml / Drug A = 6 ml/ mcg
Drug A = 1000 ml / 6 ml/ mcg
Drug A = 166.667 mcg
Hence, If a patient is receiving 1000 ml of this IV fluid, then the amount of Drug A the patient will be getting is 166.667 mcg.
Learn more about Ratios here:
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Divide the following complex numbers:
(4-i)/(3+4i)
A.-8/7 + 19/7i
B. 16/25 - 19/25i
C. 8/25 - 19/25i
D. -16/7 + 19/7i
Answer:
C. 8/25 - 19/25i
Step-by-step explanation:
Given that:
[tex]\dfrac{4-i}{3+4i}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)}[/tex]
[tex]= \dfrac{(4-i) (3-4i)}{(3+4i)(3-4i)} \\ \\ =\dfrac{12 -16i -3i+4i^2}{9 - 12i +12i -16i^2} \\ \\ = \dfrac{12-19i+4i^2}{9-16i^2} \\ \\ = \dfrac{8-19i}{25}[/tex]
[tex]=\dfrac{8}{25}- \dfrac{19i}{25}[/tex]
What is 2/5 in three equivalent forms
Answer:
4/10 8/20 16/40
Step-by-step explanation:
PLEASE HELP +10 BRAINLY POINT
Answer:
13 =x
Step-by-step explanation:
The width is x
The length is 2 times the width or 2x
A = length * width
A = 2x* x
338 = 2x^2
Divide by 2
338/3 = 2x^2/2
169 = x^2
Taking the square root of each side
sqrt(169) = sqrt(x^2)
13 =x