Answers
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
Related Questions
Michael was 1.0 metres tall, and could
only reach up to the 1st floor lift button. .
From the 1st floor, he had to walk up 100
steps to reach the 6th floor.
Vinh was 1.4 metres tall, and could reach
the 5th floor button. He had to walk up
20 steps to reach the 6th floor.
Lucy was 1.1 metres tall. To reach the
6th floor, how many steps did she have to
walk up?
Answers
Answer:
Lucy must walk up 80 steps to reach the 6th floor.
Step-by-step explanation:
Since Michael was 1.0 meters tall, and could only reach up to the 1st floor lift button, and from the 1st floor, he had to walk up 100 steps to reach the 6th floor; while Vinh was 1.4 meters tall, and could reach the 5th floor button, and he had to walk up 20 steps to reach the 6th floor; If Lucy was 1.1 meters tall, to determine how many steps did she have to walk up to reach the 6th floor, the following calculation must be performed:
1 = 100
1.4 = 20
1.4 - 1 = 100 - 20
0.4 = 80
0.1 = X
0.1 x 80 / 0.4 = X
20 = X
100 - 20 = 80
Therefore, Lucy must walk up 80 steps to reach the 6th floor.
Which parabola opens upward?
y = 2x – 4x^2 – 5
y = 4 – 2x^2 –5x
y = 2 + 4x – 5x^2
y = –5x + 4x^2 + 2
Answers
Answer:
D) y = –5x + 4x^2 + 2
Step-by-step explanation:
You can tell by the first number being positive or negative. To check use Desmo graphing calculator and enter your equation for next time.
9.
Find the area of the shaded region.
6
6
The exact area is A =
square units.
Answers
Answer:
8. 36
Step-by-step explanation:
8.
The diameter of the square is x=[tex]\sqrt{6^{2} +6^{2} }\\[/tex] = [tex]\sqrt{72}[/tex] = 6 [tex]\sqrt{2}[/tex]
The diameter of the square is the diameter of the circle, therefore the radius of the circle is r = 6 [tex]\sqrt{2}[/tex]/2 = 3[tex]\sqrt{2}[/tex]
The area of the shaded region, which is a circle is A= π[tex]r^{2}[/tex] = π[tex](3\sqrt{2} )^{2}[/tex] = 36π
Find the standard deviation of the following data. Round your answer to one decimal place. x 0 1 2 3 4 5 P(X
Answers
Answer:
[tex]\sigma = 1.8[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} \ \\ P(x) & {0.2} & {0.1} & {0.1} & {0.2} & {0.2}& {0.2} \ \end{array}[/tex]
Required
The standard deviation
First, calculate the expected value E(x)
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 0 * 0.2 + 1 * 0.1 + 2 * 0.1 + 3 * 0.2 + 4 * 0.2 + 5 * 0.2[/tex]
[tex]E(x) = 2.7[/tex]
Next, calculate E(x^2)
[tex]E(x^2) = \sum x^2 * P(x)[/tex]
So, we have:
[tex]E(x^2) = 0^2 * 0.2 + 1^2 * 0.1 + 2^2 * 0.1 + 3^2 * 0.2 + 4^2 * 0.2 + 5^2 * 0.2[/tex]
[tex]E(x^2) = 10.5[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{E(x^2) - (E(x))^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 2.7^2}[/tex]
[tex]\sigma = \sqrt{10.5 - 7.29}[/tex]
[tex]\sigma = \sqrt{3.21}[/tex]
[tex]\sigma = 1.8[/tex] --- approximated
(x-5)(X+12)=-70
[tex](x - 5)(x + 12) = - 70[/tex]
Answers
Answer:
[tex]x = - 2[/tex]
[tex]x = - 5[/tex]
Step-by-step explanation:
Give
[tex](x - 5)(x + 12)[/tex]
Apply FOIL Method
[tex]x {}^{2} + 7x - 60 = - 70[/tex]
Add 70 on both sides
[tex] {x}^{2} + 7x + 10[/tex]
Factor
[tex](x + 2)(x + 5)[/tex]
So our roots are
x=-2
x=-5
Answer:
dtet
Step-by-step explanation:
dgbyn
is the equation x^3 - 2x^2 + 1 = 0 a quadratic equation?
Answers
Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP
1
:
Equation at the end of step 1
(((x3) - 2x2) + 2x) - 1 = 0
STEP
2
:
Checking for a perfect cube
2.1 x3-2x2+2x-1 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-2x2+2x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 2x-1
Group 2: -2x2+x3
Pull out from each group separately :
Group 1: (2x-1) • (1)
Group 2: (x-2) • (x2)
A cyclist rides at an average speed of 25 miles per hour. If she wants to bike 195 km, how long (in hours) must she ride
Answers
1km = 0.621371miles
195 km= ?
cross multiplication
= 121.167 miles
25 miles= 1hour
121.167miles = ?hours
121.167=25x
divide by 25x both sides
=4.84 hours
approx 5hours
She must ride for 5 hours if she wants to bike 195 km.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
Given that cyclist rides at an average speed of 25 miles per hour.
Since 1 km = 0.621371 miles
So 195 km = 121.167 miles
The speed of the cyclist (s) = 24 miles per hour.
Distance covered by the rider = 195 km
Distance covered by the rider (d) = 121.167 miles
By using the formula, time taken by a body, we calculate the time,
⇒ t = d/s
Substitute the value of d and s in above the equation
⇒ t = 121.167/ 24
Apply the division operation,
⇒ t = 5
Hence, she must ride for 5 hours if she wants to bike 195 km.
Learn more about the average speed here :
brainly.com/question/12322912
#SPJ2
Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 13 years. What is the probability of failure in the first 5 years
Answers
Answer:
The right answer is "0.3193".
Step-by-step explanation:
According to the question,
Mean,
[tex]\frac{1}{\lambda} = 13[/tex]
[tex]\lambda = \frac{1}{13}[/tex]
As we know,
The cumulative distributive function will be:
⇒ [tex]1-e^{-\lambda x}[/tex]
hence,
In the first 5 years, the probability of failure will be:
⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]
[tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]
[tex]=1-e^(-\frac{5}{13})[/tex]
[tex]=1-0.6807[/tex]
[tex]=0.3193[/tex]
Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.
Answers
Answer:
The sum is 2275
Step-by-step explanation:
Given
[tex]75,76,77....99,100[/tex]
Required
The sum
Using arithmetic progression, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where:
[tex]T_1 = 75[/tex] --- first term
[tex]T_n = 100[/tex] --- last term
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 100 - 75 + 1 = 26[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]
[tex]S_n = 13*175[/tex]
[tex]S_n = 2275[/tex]
In 2006, there were 160 teachers in College A, and three fourth of them had their own vehicles. In 2007, 20 new teachers came to the school and 6 of them had own vehicles. Calculate the percentage increase in the numbers of teacher who had own vehicles.
Answers
Answer: 5%
Step-by-step explanation:
In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:
= 3/4 × 160
= 120
In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:
= 120 + 6
= 126
The percentage increase will be:
= Increase / Old vehicle owners × 100
= 6/120 × 100
= 1/20 × 100
= 5%
The Percentage increase is 5%.
a bag contain 3 black balls and 2 white balls.
1. A ball is taken from the black and then replaced, a second is taken. what is the probabilities that.
(a) there are both black,
(b)one is black one is white,
(c) at lease one is black,
(d) at most one is one is black.
2. find out if all the balls are chosen without replacement.
please kindly solve with explanation. thank you.
Answers
Answer:
Step-by-step explanation:
Total number of balls = 3 + 2 = 5
1)
a)
[tex]Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\[/tex]
b)
[tex]Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}[/tex]
c)
Probability of at least one black( means BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}[/tex]
d)
Probability of at most one black ( means WW or WB or BW)
[tex]=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}[/tex]
2)
a) Probability both black without replacement
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
b) Probability of one black and one white
[tex]=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}[/tex]
c) Probability of at least one black ( BB or BW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}[/tex]
d) Probability of at most one black ( BW or WW or WB)
[tex]=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}[/tex]
There are twelve shirts in my closet. Five are red, four are blue, and three are green. What is
the probability that I choose a red or blue shirt to wear tomorrow?
O 65%
0 75%
0 80%
60%
58%
Answers
Answer:
the probability that I chose red or blue is 75%
75%
The diagram below shows rectangle ABC is a midtsin of
BC, such that D,E and F are on the same line API AD
i = 53, 13" BE-sm
and DE 2 EF
84
2176
F
with reasons
3.1 Prove
AB - BF
3.2. Calculate AD
3.3 Complece. In are rigter angled A BEF, son 53, 13" - BE
Answers
Answer:
4x2+3=
Step-by-step explanation:
Help me please I need help 6
Answers
Answer:
69.6
Step-by-step explanation:
sin 55 = x / 85
0.8191520443 = x / 85
x = 69.6
need help now!!! Please and thanks
Answers
Answer:
the answer of r is 8 i hope it will help
Factor 2x2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors.
Answers
9514 1404 393
Answer:
rewrite: 2x^2 +5x +20x +50factored: (x +10)(2x +5)Step-by-step explanation:
I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.
You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.
100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10
The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.
The trinomial can be rewritten using these factors as ...
2x^2 +5x +20x +50
Then it can be factored by grouping consecutive pairs:
(2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)
_____
Additional comment
It doesn't matter which of the factors of the pair you write first. If our rewrite were ...
2x^2 +20x +5x +50
Then the grouping and factoring would be (2x^2 +20x) +(5x +50)
= 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring
Donald and Sara are surveying their neighbors about the community playground. Their questions, written on the survey, are below:
Donald: How many times do you visit the playground in a month?
Sara: Did you visit the playground this month?
Who wrote a statistical question and why?
Sara, because there will be variability in the responses collected
Donald, because every neighbor can give a different answer
Sara, because there can be only one answer to the question
Donald, because every neighbor will give the same answer
Answers
Answer:
B
Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too
write an equation rectangular room 3 meters longer than it is wide and its perimeter is 18 meters
Answers
width = x
length = 3 + x
perimeter = x + x + ( 3 + x ) + (3+x)
18 = x + x + ( 3 + x ) + (3+x)
x + x + ( 3 + x ) + (3+x) = 18
6 + 4x = 18
4x = 12
x = 3
Deon bought a desk on sale for $105.60. This price is 67% less than the original price. What was the original price?
Answers
Answer:
.33x = 105.60
$371
Step-by-step explanation:
Answer:
63.44
Step-by-step explanation:
its 63.44697 but you round so its 63.44
a circle has a radius that is 4 centimeters long. if a central angle has a measure of 3 radiants, what is the length of the arc that corresponds to the angle ?
A. 12 centimeters
B. 4 centimeters
C. 3 centimeters
D. 7 centimeters
Answers
Answer:
A number is right 12 centimetres
Cross out three digits in the number 51489704 so that the resulting number is divisible by 45. What number is left?
Answers
The factors of 45 are 9 and 5.
A number divisible by 45 needs to be divisible by both 9 and 5.
For a number to be divisible by 9 the sum of the digits must also be divisible by 9 and the number needs to end with either a 0 or a 5 to be divisible by 5.
This means the number needs to end with the 0 so cross out the last number (4)
Now find a sum of 5 remaining numbers divisible by 9.
5 + 1 + 4 + 8 + 0 = 18 which is divisible by 9
Cross out 9,7 and the last number 4 to get the number: 51480
Convert the following to a simplified fraction. Show all your work.
Answers
Answer:
11/6
Step-by-step explanation:
When 4 times a positive number is subtracted from the square of the number, the result is 5. Find the number.
Answers
Answer:
5
Step-by-step explanation:
x² - 4x = 5
x² - 4x - 5 = 0
the solution of a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = -4
c = -5
x = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2
x1 = (4 + 6)/2 = 5
x2 = (4 - 6)/2 = -1
since we are looking only for a positive number, x=5 is the answer.
A box contains 5 orange pencils, 8 yellow pencils, and 4 green pencils.
Two pencils are selected, one at a time, with replacement.
Find the probability that the first pencil is green and the second pencil is yellow.
Express your answer as a decimal, rounded to the nearest hundredth.
Answers
Answer:
total pencil = 5 orange pencils + 8 yellow pencils + 4 green pencils
= 17 pencils
P (g n y) = 4/17 + 8/17
= 0.706
Step-by-step explanation:
1. first find the total number of pencils
2. since there is a replacement the demoinator remains the same
3. find the probability of each green and yellow
4. add the two probability
in a board game you must roll two 6-sided number cubes. you can only start the game if you roll a 3on at least one of the number cubes.
Answers
Answer:
[tex]1-(5/6)^2[/tex]
31% chance
1 in 3.272727273 rolls
Step-by-step explanation:
Given the points (-7, -1) and (8, 5) find the slope.
Answers
Answer:
(-7, -1) =(x1,y1)
(8, 5)=(x2,y2)
now
[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]
[tex]or = \frac{5 + 1} {8 + 7} [/tex]
[tex]or = \frac{6}{15} [/tex]
[tex]or = \frac{2}{5} [/tex]
Step-by-step explanation:
Explanation is in the attachmenthope it is helpful to you ☺️
find the least common multiple of two two-digit numbers. SHOW WORK
Answers
Answer:
The LCM of 20 and 30 is 60.
Step-by-step explanation:
LCM means the least common multiple.
The LCM of two numbers means the least multiple both numbers share.
Use the listing method:
Multiples of 20:
20, 40, 60, 80, 100, ......
Multiples of 30:
30, 60, 90, 120, 150, ...
The LCM is 60 because that is the least common multiple 20 and 30 have.
Hope this helps
Someone please help me ASAP!
Answers
Answer:
The 3rd
Step-by-step explanation:
If x goes to infinity, f(x) goes to infinity too:
[tex]lim \: \frac{2 {x}^{2} }{3x - 1} = lim \frac{2x}{3 - \frac{1}{x} } = \frac{ 2 \times \infty }{3 - 0} = \infty [/tex]
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answers
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Find the third term of a geometric progression if the sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
Answers
Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
