If θ lies in the fourth quadrant, then sin(θ) < 0 and cos(θ) > 0. So we have from the Pythagorean identity,
sin²(θ) + cos²(θ) = 1 ==> cos(θ) = +√(1 - sin²(θ)) = √21/5
Then
sec(θ) = 1/cos(θ) = 5/√21
and
tan(θ) = sin(θ)/cos(θ) = (-2/5)/(√21/5) = -2/√21
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
For octagon =1080.......
Explanation:
180(8-2)
180×6
1080°
The time I spend waiting for the bus on any given day has a distribution with mean 4 min- utes and variance off 0.5 minutes. What is the probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month (30 days)? You may assume that waiting times on different days are independent of each other. HINT: Is there a sum of random variables somewhere in here?
Answer:
0.0049 = 0.49% probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month.
Step-by-step explanation:
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.
n instances of a normal variable:
For n instances of a normal variable, the mean is:
[tex]M = n\mu[/tex]
[tex]s = \sigma\sqrt{n}[/tex]
Mean of 4 minutes, standard deviation of 0.5 minutes:
This means that [tex]\mu = 4, \sigma = \sqrt{0.5}[/tex]
30 days:
[tex]M = 30(4) = 120[/tex]
[tex]s = \sqrt{0.5}\sqrt{30} = \sqrt{0.5*30} = \sqrt{15}[/tex]
What is the probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month (30 days)?
2 hours and 10 minutes is 2*60 + 10 = 130 minutes, so this probability is 1 subtracted by the p-value of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this context, due to the 30 instances of the normal variable:
[tex]Z = \frac{X - M}{s}[/tex]
[tex]Z = \frac{130 - 120}{\sqrt{15}}[/tex]
[tex]Z = 2.58[/tex]
[tex]Z = 2.58[/tex] has a p-value of 0.9951.
1 - 0.9951 = 0.0049
0.0049 = 0.49% probability that I spend more than 2 hours and 10 minutes waiting for the bus in one month.
Can someone check my answers if they are correct or incorrect? If it is incorrect, please let me know why it is incorrect please.
The survey included a random sample of 640 western residents and 540 northeastern residents. 39% of the western residents and 51% of the northeastern residents reported that they were completely satisfied with their local telephone service. Find the 99% confidence interval for the difference in two proportions
Answer:
The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Western residents:
39% out of 640, so:
[tex]p_1 = 0.39[/tex]
[tex]s_1 = \sqrt{\frac{0.39*0.61}{640}} = 0.0193[/tex]
Eastern residents:
51% out of 540, so:
[tex]p_2 = 0.51[/tex]
[tex]s_2 = \sqrt{\frac{0.51*0.49}{540}} = 0.0215[/tex]
Distribution of the difference:
[tex]p = p_2 - p_1 = 0.51 - 0.39 = 0.12[/tex]
[tex]s = \sqrt{s_2^2+s_1^2} = \sqrt{0.0215^2+0.0193^2} = 0.0289[/tex]
Confidence interval:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.12 - 2.575*0.0289 = 0.0456[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.12 + 2.575*0.0289 = 0.1944[/tex]
The 99% confidence interval for the difference in two proportions is (0.0456, 0.1944).
Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
in the box of Stones ,the ratio of red marbles is 2:5. the ratio of green stones to the total stones is 3:10 .if the stones that are neither red nor green are blue ,how many blue are in the box.if there are 40 marbles in the box?.
Given: Measure of arc AB = measure of arc BC,
Measure of angle x = 60°, measure of angle y = 15°
Find: Measure of arc AC
9514 1404 393
Answer:
100°
Step-by-step explanation:
The relevant relation for angle x is ...
x = (AB +DE)/2
and for angle y, it is ...
y =(AC -DE)/2
Using the second relation to write an expression for DE, we have ...
DE = AC -2y
In the first equation, this lets us write ...
x = (AB +(AC -2y))/2 = (AB +(2AB -2y))/2
2x = 3AB-2y . . . . . . . . . . . . . . multiply by 2
(2x +2y)/3 = AB = AC/2 . . . . . add 2y; divide by 3
AC = (4/3)(x +y) = (4/3)(60° +15°) . . . . multiply by 2, substitute known values
AC = 100°
Can someone help please
( x - 2 )( x - 8 )( x + 5 ) =
( x^2 - 10x + 16 )( x + 5 ) =
x^3 - 10x^2 + 16x + 5x^2 - 50x + 80 =
x^3 + ( - 10 + 5 )x^2 + ( 16 - 50)x + 80 =
x^3 - 5x^2 - 34x + 80
The number of cubic feet of water in a curved container can be approximated by V=0.95h^2.9 find the amount of water in the container when h=8 feet round to the nearest tenth
Answer choices:
A. 0.9
B. 358.4
C. 395.1
D. 314.9
Answer:
C. 395.1
Step-by-step explanation:
Substitute the value for x:
[tex]V=0.95(8)^{2.9}\\V=395.1[/tex]
Define business.Write the type of business
Answer:
A company or an entrepreneurial entity engaged in commercial, industrial, or professional activity is referred to as a business. A limited liability company (LLC), a sole proprietorship, a corporation, and a partnership are examples of different types of businesses.
Form a union for the following sets.
M = {1, 2, 4, 8)
N = (2,5,8)
Answer:
Step-by-step explanation:
When you are asked to find the union of sets you find numbers that are present in both sets.
So a number that appears in both the sets of M and N are 2 and 8.
So M U N = { 2,8} where U is the symbol for union.
find the perimeter of 6 CM 6 CM 6 CM 6 CM
Answer:
P = 24
Step-by-step explanation:
Since all the sides are the same length, the shape is a square.
Multiply all sides by 6.
6 cm x 4 sides = 24
Not sure how to do this
PLSSS HELP IM STRUGGLING SO HARD !!! ———————
Answer:
C)
Step-by-step explanation:
Just see the length of the R line, A and B are almost the same large when you add them.
I need help ASAP pleasee
Answer:
The answer is 4 1/2
Step-by-step explanation:
Because A to C is 2 1/4 so all you have to do add 2 1/4 + 2 1/4 which will equal 4 1/2
If 15% of the customer's total is $22.05, then the customer's total is
Answer:
$147
Step-by-step explanation:
0.15x = $22.05
Divide both sides by 15
22.05/0.15 = $147
Can someone help me out
Answer:
236m^2
Step-by-step explanation:
8x5=40x2=80
6x5=30x2=60
6x8=48x2=96
80+60+96=236
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to thegiven statistics and confidence level. Round the margin of error to four decimal places.1)99% confidence; n
Answer:
[tex]E = 0.0158[/tex]
Step-by-step explanation:
Given
[tex]n = 5900[/tex]
[tex]x = 1770[/tex]
[tex]CI = 99\%[/tex]
Required
The margin of error (E)
First, calculate proportion p
[tex]p = x/n[/tex]
[tex]p = 1770/5900[/tex]
[tex]p = 0.3[/tex]
Given that:
[tex]CI = 99\%[/tex]
Calculate the alpha leve;
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1- 0.99[/tex]
[tex]\alpha= 0.01[/tex]
Divide by 2
[tex]\alpha/2= 0.01/2[/tex]
Subtract from 1
[tex]1 - \alpha/2= 1 - 0.01/2[/tex]
[tex]1 - \alpha/2= 0.995[/tex]
The corresponding z value is:
[tex]z =2.576[/tex]
So, the margin of error is:
[tex]E = z * \sqrt{p * (1 - p)/n}[/tex]
So, we have:
[tex]E = 2.576 * \sqrt{0.3 * (1 - 0.3)/5600}[/tex]
Using a calculator, we have:
[tex]E = 0.01577471394[/tex]
Approximate
[tex]E = 0.0158[/tex]
I NEED THE ANSWER SOON PLEASE!!?!?! hopefully someone sees this
Answer:
1 and 1/25
Step-by-step explanation:
If x+7 is an even number, is x+11 an even number or odd number?
Answer:
x + 11 is an even number.
Step-by-step explanation:
Even numbers can only be obtained from the sum of two odd numbers or two even numbers. Since we know that x + 7 is even, x + 11 must be even as well.
in how many ways can be arranged 2 different words in necklace?
Answer:
3
Step-by-step explanation:
chain by chain
parllel
series
Solve.
x^2 - 9x + 3 = 0
x= or x=
Answer:
Step-by-step explanation:
x^2 - 9x + 3 = 0 is a quadratic whose coefficients are a = 1, b = -9 and c = 3.
Use the quadratic formula to solve it.
The discriminant, b^2 - 4ac, is 81 - 4(1)(3), or 81 - 12, or 69.
The roots are:
-b ± √(discriminant)
x = -------------------------------
2a
And these roots in this particular problem are:
-(-9) ± √69 9 ± √69
= ------------------------------- = ----------------
2(1) 2
si 40/a = 35/7 entonces cual es el valor de a
Respuesta:
a = 8
Explicación paso a paso:
Para obtener el valor de a en la ecuación:
40 / a = 35/7
Cruzamos multiplicamos:
40 / a = 35/7
40 * 7 = 35 * a
280 = 35a
Dividir ambos lados por 35
280/35 = 35a / 35
8 = a
a = 8
Find the length of the missing side. If necessary, round to the nearest tenth. 40 and 35
Answer: 53.2
Step-by-step explanation:
Using pythagorean theorem, a^2 + b^2 = c^2
40^2 + 35^2 = sqrt of 2825
which is 53.15
rounded up to nearest tenth is 53.2
Drag the tiles to the boxes to form correct pairs.
Match the pairs of equivalent expressions.
metal is made using copper, zinc and lead in thr ratio 13:6:1 . if the mass of the zinc is 90kg, calculate the mass of the lead
============================================
Explanation:
Let x be the mass of the lead, and this mass is in kg.
The ratio 13:6:1 can be scaled up to 13x:6x:1x after multiplying all parts by x.
The portion in the middle (6x) represents how much zinc we have, while the last part (1x or simply x) is the amount of lead.
----------------
We're told that we have 90 kg of zinc. Set this equal to 6x and solve for x
6x = 90
6x/6 = 90/6 ..... dividing both sides by 6
x = 15
So we have 15 kg of lead
Side note: we also have 13x = 13*15 = 195 kg of copper.
what is the length of GN, given that figure LMNO is a square PLZ HELP!!!!!
Answer:
A. 4
Step-by-step explanation:
The diagonals are also congruent to each other. Diagonals of a square bisect each other. This implies that:
MO bisects LN, thereby dividing LN into two equal segments, LG and GN.
Thus, LG = GN.
Since the length of LG = 4, therefore:
GN = 4
Need to know Anwser yes or no
Answer:
Reflective symmetry over the line y = 4 is No
Reflective symmetry over the line y = 1/7x + 3 is Yes
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the sample mean?
Choose the correct answer below.
A. 15.0 mm
B. 52.5 mm
C. 7.5 mm
D. Somewhere between 45mm and 60mm, but the exact value cannot be determined without more information.
Answer:
I cannot understand this question
Step-by-step explanation:
I don't know what is in the question
210
To rationalize the denominator of
3.11,You should multiply the expression by which fraction?
11
2- V10
2- 10
3- V11
3- V11
We should multiply the expression by √11/ √11 fraction.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
To rationalize this, we multiply both the denominator and denominator by the conjugate of the denominator.
The denominator is 2-√10 and its conjugate is; (2+√10).
(2√10)/(3√11) = (2√10)/(3√11)
= ((2√10)√11/(3√11) √11
= (2√110)/33
This is the rationalized expression.
Learn more about multiplications;
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