Answers
Answer:
√3/3
Step-by-step explanation:
To obtain Tan θ ;
From trigonometry, tan θ = sin θ / cosθ
Given the paired value : (√3/2, 1/2)
The (cosine, sine ) pair ;
Tan θ = sin (1/2) / cos (√3/2)
Tan θ = (1/2 ÷ √3 / 2) = 1 / 2 * 2 / √3 = 2 / 2√3 = 1 / √3
Tan θ = 1 / √3
Rationlaizing the denominator :
1/√3 * √3/ √3 = √3/√9 = √3/3
Related Questions
To mix weed killer with water correctly, it is necessary to mix 18 teaspoons of weed killer with 3 gallons of water. How many gallons of water are needed to mix with the entire box if it contains 24 teaspoons of weed killer
Answers
20,30,13,10,14,10,10,?,?,?
Answers
Answer:
10,13,14,20,30.............
Leanne is planning a bridal shower for her best friend. At the party, she wants to serve 33 beverages, 33 appetizers, and 22 desserts, but she does not have time to cook. She can choose from 1313 bottled drinks, 77 frozen appetizers, and 1313 prepared desserts at the supermarket. How many different ways can Leanne pick the food and drinks to serve at the bridal shower
Answers
Answer:
She can pick the food and drinks in 780,780 different ways.
Step-by-step explanation:
The drinks, appetizers and desserts are independent of each other, so the fundamental counting principle is used.
Also, the order in which the beverages, the appetizers and the desserts are chosen is not important, which means that the combinations formula is used to solve this question.
Fundamental counting principle:
States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.
Combinations formula:
[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]
Beverages:
3 from a set of 13. So
[tex]C_{13,3} = \frac{13!}{3!10!} = 286[/tex]
Appetizers:
3 from a set of 7, so:
[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]
Desserts:
2 from a set of 13, so:
[tex]C_{13,2} = \frac{13!}{2!11!} = 78[/tex]
How many different ways can Leanne pick the food and drinks to serve at the bridal shower?
286*35*78 = 780,780
She can pick the food and drinks in 780,780 different ways.
A rocket is fired upward with an initial velocity v of 100 meters per second. The quadratic function S(t)=-5t^2+100t can be used to find the height s of the rocket, in meters, at any time t in seconds. Find the height of the rocket 7 seconds after it takes off. During the course of its flight, after how many seconds will the rocket be at a height of 450 meters?
Answers
The rocket will be at the height of 450metres at 13.16secs and 6.84secs
Given the expression modeled by the height S(t)=-5t^2+100t where
t is the time taken by the rocket to take off
s is the height traveled by rocket
In order to find the height of the rocket 7 seconds after it takes off, we will substitute t = 7 into the equation
S(7) = -5(7)²+100(7)
S(7) = -5(49)+700
S(7) = -245+700
S(7) = 455metres
Hence the height of the rocket 7 seconds after it takes off is 455metres
Given that S = 450m, we can also get the time taken by the rocket at this height.
Recall that S(t)= -5t²+100t
450 = -5t²+100t
Rearrange
-5t²+100t - 450 = 0
5t²-100t + 450 = 0
Divide through by 5
t²-20t + 90 = 0
On factorizing above equation;
t= 10+√10 or t=10−√10
t = 10+3.1623 or 10 - 3.1623
t = 13.16 and 6.84secs
Hence the rocket will be at the height of 450metres at 13.16secs and 6.84secs
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substitute for A,P and T in the fomula A=P (1+r)^t,give that A=1 000 000,P=10 000 and T=2,and express as a quadratic equation
Answers
A = 10,00,000
P = 10,000
T = 2
1000000 = 10000(1+r/100)^2
1000000 = 10000((100 + r)/100)^2
1000000 = 10000× 100 + r/100 × 100 + r/100
1000000 = 10000 + r^2
1000000 - 10000 = r^2
990000 = r^2
√99000 = r
Quadratic Equation
10000(1+r/100)^2
Two ice cream stands are deciding where to set up along a 1-mile-long beach. The people are uniformly located along the beach, and each person sitting on the beach buys exactly 1 ice cream cone per day from the nearest stand. Each ice cream seller wants the maximum number of customers. True or False: The two stands will most likely be 1/3 mile away from each other. True
Answers
Answer:
Each ice cream seller wants the maximum number of customers:
True
The two ice cream stands will most likely be 1/3 mile away from each other.
True
Step-by-step explanation:
This distance enables the two ice cream stands to give access to the maximum number of customers at the beach, which will be almost equal at their right-hand and left-hand sides. Therefore, the two ice cream stands will most likely be 1/3 mile away from each other. Such positioning exposes the ice cream stands to almost equal number of customers since the people standing along the beach are uniformly located. Taking the extreme locations along the 1-mile-long beach will shrink location opportunities for both stands.
A publisher reports that 54% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 200 found that 44% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim
Answers
The null and alternate hypotheses are
H0 : u = 0.44 vs Ha: u > 0.44
Null hypothesis: 44% of readers own a personal computer.
Alternate Hypothesis : greater than 44% of readers own a personal computer.
This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is Z > ±1.28
The given values are
p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56
Using z test
Z = p1-p2/√p2(1-p2)/n
Z= 0.54-0.44/ √0.44*0.56/200
z= =0.1/ 0.03509
z= 2.849
Since the calculated value of Z= 2.849 is greater than Z= 1.28 reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.
Null hypothesis is rejected
There is sufficient evidence to support the executive's claim at 0.10 significance level.
https://brainly.com/question/2642983
What is the slope of the line that passes through the points (-7, -4) and
(-11, -2)? Write your answer in simplest form.
Answers
Answer:
-1/2
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -4)/( -11 - -7)
=( -2+4)/( -11+7)
= 2 / -4
= -1/2
Please help! Thank you.
Answers
Answer:
B at -1 minus we go to - ∞
at -1 plus we to + ∞
Step-by-step explanation:
x^2 -x
g(x) = ---------
x+1
Factor out x
x(x-1)
g(x) = ---------
x+1
As x is to the left of -1
x is negative (x-1) is negative
x+1 will be slightly negative
g(-1 minus) = -*-/ - = - and we know that the denominator is very close to zero we are close to infinity so we go to - ∞
As x is to the right of -1
x is negative (x-1) is negative
x+1 will be slightly positive
g(-1 plus) = -*-/ + = + and we know that the denominator is very close to zero we are close to infinity so we go to ∞
I Will Mark Brainliest
The figure shows a rectangue with its length and breadth as indicated,
Give that the perimeter of a rectangle is 120cm, find the area of rectangle .
Answers
Answer:
Length = 2x+y cm and since it's a rectangle,
2x+y=3x-y ---------------- (i)
width = 2x-3 cm
It's perimeter,
2(2x+y+2x-3)=120 ---------------- (ii)
Solving both equations,
x = 14 cm
y = 7 cm
so length is, 2×14+7 = 35 cm
and width is, 2×14-3 = 25 cm
so area will be, 35×25 = 875 cm²
Answered by GAUTHMATH
Answer:
len = 35
width = 25
Step-by-step explanation:
3x-y = 2x+y
1) x-2y = 0
9x -6= 120
x = 14
y = 7
Simplify the algebraic expression by combining like (or similar) terms.
2x−y2+3−3y2+2x+1
Answers
Answer:
-4y^2 + 4x +4
Step-by-step explanation:
add -y^2 and -3y^2 = -4y^2
add 2x + 2x = 4x
add 3+1 = 4
and then rearrange
The gcf of two numbers is 3 and their lcm is 180, if one of the numbers is 45 then found the second number
Answers
Answer:
answer is 12
Step-by-step explanation:
gcf = 3
lcm = 180
let 45 be y
let unknown be X
to get x
X=( lcm * gcf) / y
X=(180*3)/45
X=(540)/45
X=12
the other number is 12
please give me correct answer
Answers
Answer:
answer of question number 1 is 2400, 2880, 3600 respectively.
answer of question number 2 is 1384 and 1680.
Step-by-step explanation:
100×24=2400
120×24=2880
150×24=3600
692×2=1384
420×4=1680
find the missing length indicated
Answers
Answer:
c = 175
Step-by-step explanation:
When the height of a right triangle is shown this way (at right angles with the hypotenuse, It can be found by using the way the hypotenuse is broken up. The following proportion works.
576/x = x / 49 Cross multiply
x^2 = 576 * 49
sqrt(x^2) = sqrt(576*49)
x = 24 * 7
x = 168
But that's not what you want (although it is close).
What you want is the hypotenuse to the small lower triangle
c = ?
a = 49
b = 168
c^2 = 49^2 + 168^2
c^2 = 2401 + 28224
c^2 = 30625
c = sqrt(30625)
c = 175
find an odd natural number x such that LCM (x,40)= 1400
Answers
The odd natural number x such that the LCM of x and 40 is 1400 is 35
Lowest Common MultipleThe least common multiple the lowest multiple of two or more numbers.
From the question, we need to determine the value of x of the LCM of the numbers is 1400
LCM (x,40) = 1400
Find a possible value of x
x = 1400/40
x = 35
Hence the odd natural number x such that the LCM of x and 40 is 1400 is 35
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The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts
Answers
Answer:
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 102, standard deviation of 12:
This means that [tex]\mu = 102, \sigma = 12[/tex]
Sample of 63:
This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?
Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.
Probability the mean is below 98.6.
p-value of Z when X = 98.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
2*0.0122 = 0.0244
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
If Logx (1 / 8) = - 3 / 2, then x is equal to what?
Answers
Answer:
Logx(1/8) = -3/2
x = 4
Answered by GAUTHMATH
help with math it would help with summer school
Answers
Answer:
[tex]A). \ \ \frac{(72\pi + 9\pi )}{4} \ in^2[/tex]
Step-by-step explanation:
Given;
radius of the circle, r = 9 inches
the part of the circle cut out = one-forth of the complete circle
the angle of the sector cut out θ= ¹/₄ x 360 = 90⁰
Area of the complete circle = πr² = π x 9² = 81π in²
Area of the sector cut out = [tex]= \frac{\theta }{360} \pi r^2 = \frac{90}{360} \pi (9^2) = \frac{1}{4} \times 81\pi = \frac{81 \pi}{4} = \frac{(72\pi + 9\pi)}{4} \ in^2[/tex]
Therefore, the only correct option is A. [tex]\frac{(72\pi + 9\pi )}{4} \ in^2[/tex]
What is the equation of the line that passes through the point (6, -6) and has a slope
of – 5/3?
Answers
Answer:
y = -5/3x + 4Step-by-step explanation:
Use the point-slope equation:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given pointThe line is:
y - (-6) = -5/3(x - 6) y + 6 = -5/3x + 10y = -5/3x + 4help please! I need the answer quickly! thank you!
Answers
Answer:
B) 1 unit to the left
Step-by-step explanation:
Please help 20 points. I will give Brainly to who ever get it right.
Answers
Answer:
Step-by-step explanation:
(-∞,2)
If a runner jogs 3 miles west and then jogs 8 miles
north, how far is the runner from her starting point
if she plans to run straight back? Remember to
simplify your answer.
Answers
If they run 3 miles west then 8 miles north, it forms a right triangle. So just use the Pythagorean Theorum.
A^2+B^=C^2
3^2+8^3=C^2
9+64=C^2
Square root 73=C or 8.54=C (Miles)
The runner is 8.54 miles from her starting point if she plans to run straight back.
From the question, a runner jogs 3 miles west and then jogs 8 miles north.
An illustrative diagram for the journey is shown in the attachment below.
In the diagram, S is the starting point. That is, the runner jogs 3 miles west to a place R and then 8 miles north to a place E.
The cardinal points (North, East, West and South) are indicated beside the diagram.
Now, to calculate how far she is from her starting point if she plans to run straight back, we will determine the length of /ES/ in the diagram.
The diagram is a right-angled triangle and /ES/ can be determined using the Pythagorean theorem.
The Pythagorean theorem states that, in a right-angled triangle, the square of the longest side ( that is hypotenuse) equals sum of the squares of the other two sides.
In the diagram, hypotenuse = /ES/
∴ /ES/² = /SR/² + /RE/²
/SR/ = 3 miles
/RE/ =8 miles
/ES/² = 3² + 8²
/ES/² = 9 + 64
/ES/² = 73
/ES/ = [tex]\sqrt{73}[/tex]
/ES/ = 8.54 miles
Hence, the runner is 8.54 miles from her starting point if she plans to run straight back.
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PLEASE HELP!!
Indicate the method you would use to prove the two ▵‘s ≅. If no method applies, enter “none”
A. SSS
B. SAS
C. ASA
D. AAS
E. None
(I attached the triangle thing that goes with the question)
Answers
A tourist from Britain wants to exchange her British pounds for US dollar. She has 25 British pounds. How many US dollars would she get in exchange for her British pound if 1 British pound can be exchanged for 1.53 US dollars?
Answers
Answer:
$38.25 US dollars.
Step-by-step explanation:
25 / 1 = 25
To find the number of US dollars that can be exchanged for 25 British pounds, multiply 1.53 by 25 to get $38.25 US dollars.
Hope this helps!
if there is something wrong, just let me know.
The graph below displays a fire department’s response time, which measures the time from when the alarm is sounded at the firehouse to the time the first fire engine leaves the station.
A histogram titled Fire Department Response Times has response time (seconds) on the x-axis and relative frequency on the y-axis. 20 to 30, 0.07; 30 to 40, 0.08; 40 to 50, 0.2; 50 to 60, 0.32; 60 to 70, 0.18; 70 to 80, 0.13; 80 to 90, 0.04.
Which interval accounts for the lowest percentage of response times?
20–30 seconds
30–40 seconds
70–80 seconds
80–90 seconds
I think its (D), 80-90 seconds. Someone check me.
Answers
Answer:
I also think this is D.
Step-by-step explanation:
This question isn't asking for a lot of math so.
According to the graph, the 80-90 seconds response times are the shortest, meaning it is the least frequent or common.
Plus, it would be a bad thing if it was average anyways, and is outlined by the histogram.
Pls if anyone knows the answer with work included/steps that will be greatly appreciated :)
Answers
Answer:
3. 3x^2 + 15x
4. x=36
Step-by-step explanation:
The area of a rectangle is
A = l*w
A = (3x)*(x+5)
Distribute
3x^2 + 15x
2/3x - 4 = 20
Add 4 to each side
2/3x -4+4 = 20+4
2/3x = 24
Multiply each side by 3/2
2/3*3/2 =24*3/2
x = 12*3
x=36
Please help asap! Easy question :)
Two fair dice are rolled. Determine the following probability:
P(one number is a multiple of 4 and the other is a multiple of 6)
Answers
Answer:
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
One multiple of 4 and one multiple of 6.
2 possible outcomes: (4,6) or (6,4)
Probability:
2 outcomes out of 36, so:
[tex]p = \frac{2}{36} = \frac{1}{18}[/tex]
Then
P(one number is a multiple of 4 and the other is a multiple of 6) = 1/18
The time it takes me to wash the dishes is uniformly distributed between 8 minutes and 17 minutes.
What is the probability that washing dishes tonight will take me between 14 and 16 minutes?
Give your answer accurate to two decimal places.
Answers
The time it takes to wash has the probability density function,
[tex]P(X=x) = \begin{cases}\frac1{17-8}=\frac19&\text{for }8\le x\le 17\\0&\text{otherewise}\end{cases}[/tex]
The probability that it takes between 14 and 16 minutes to wash the dishes is given by the integral,
[tex]\displaystyle\int_{14}^{16}P(X=x)\,\mathrm dx = \frac19\int_{14}^{16}\mathrm dx = \frac{16-14}9 = \frac29 \approx \boxed{0.22}[/tex]
If you're not familiar with calculus, the probability is equal to the area under the graph of P(X = x), which is a rectangle with height 1/9 and length 16 - 14 = 2, so the area and hence probability is 2/9 ≈ 0.22.
find the perimeter of the polygon
Answers
Answer:
50
Step-by-step explanation:
19-7=12
6+6+7+19+12
Jenny has borrowed K2500from a bank at 9.25% p.a. invested for 185 days. How much will she pay back to the bank?
Answers
Answer:
115.625
PRT/100
