Answer:
Proved
Step-by-step explanation:
Given
Prove that
[tex]\frac{cos x}{1 - sin x} = sec x + tan x[/tex]
[tex]\frac{cos x}{1 - sin x}[/tex]
Multiply the numerator and denominator by 1 + sinx
[tex]\frac{cos x}{1 - sin x} * \frac{1 + sin x}{1 + sin x}[/tex]
Combine both fractions to form 1
[tex]\frac{cos x (1 + sin x)}{(1 - sin x)(1 + sin x)}[/tex]
Expand the denominator using difference of two squares;
[tex]i.e.\ (a - b)(a + b) = a^2 - b^2[/tex]
The expression becomes
[tex]\frac{cos x (1 + sin x)}{(1^2 - sin^2 x)}[/tex]
[tex]\frac{cos x (1 + sin x)}{(1 - sin^2 x)}[/tex]
From trigonometry; [tex]1 - sin^2x = cos^2x[/tex]
The expression becomes
[tex]\frac{cos x (1 + sin x)}{(cos^2 x)}[/tex]
Divide the numerator and the denominator by cos x
[tex]\frac{(1 + sin x)}{(cos x)}[/tex]
Split fraction
[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex]
From trigonometry; [tex]\frac{1}{cos x} = sec x \ and\ \frac{sin\ x}{cos\ x} = tan\ x[/tex]
So;
[tex]\frac{1}{cos x} + \frac{sin x}{cos x}[/tex] = [tex]sec x + tan x[/tex]
Given the following diagram, are OC and OE opposite rays ?
Answer:
No
Step-by-step explanation:
If they were opposite, they would be equal.
But they are not, (on one of the spaces in between them is smaller and one is larger.)
Hope I have helped you, since it seems I haven't helped "other people" the last time :/
Answer:
No
Step-by-step explanation:
Two ships leave a port at the same time.
Ship A sails 12 knots on a bearing of 035°
Ship B sails 16 knots on a bearing of 270°
Calculate the distance between the ships after 2 hours
(1 knot = 1 nautical mile per hour)
Answer:
49.8 nautical miles
Step-by-step explanation:
Recall that speed = distance/time
Time = 2hours
Speed = 12knots and 16 knots respectively
D = speed×time
D1 = 12×2 = 24
D2 = 16×2 = 32
Using the 'cosine rule' we have:
a^2 = b^2+c^2-2bc cos Θ
Where a =?
b =24
c = 32
Θ = 125°
a² = 24² + 32² - 2(24)(32)cos125°
a^2 = 576+1024 - 1536cos125°
a² = 1600 - 1536(-0.57357)
a² = 1600+881.0134
a² = 2481.0134
Then, a² = 2481.013406
a =√2481.013406
Hence, a = 49.8 nautical miles
In this exercise we must use the knowledge about triangles to calculate the distance that a ship will travel, in this way we find that:
49.8 nautical miles
First, remember the formula for distance, which is:
[tex]Speed = distance/time[/tex]
And knowing that the data reported in the exercise are:
Time = 2hours Speed = 12 knots and 16 knots respectively
So putting the values informed in the distance formula, we have:
[tex]D = speed*time\\D_1 = 12*2 = 24\\D_2 = 16*2 = 32[/tex]
Using the 'cosine rule' we have:
[tex]a^2 = b^2+c^2-2bc cos \theta[/tex]
Find the a, will have:
[tex]b =24 \ \ \ c = 32 \ \ \ \theta = 125\\a^2 = 24^2 + 32^2 - 2(24)(32)cos125\\a^2 = 576+1024 - 1536cos125\\a^2 = 1600 - 1536(-0.57357)\\a^2 = 1600+881.0134\\a^2 = 2481.0134\\a=49.8[/tex]
See more about triangles at brainly.com/question/25813512
Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.
Answer:
P(odd) = 4/9P(<11) = 2/3Step-by-step explanation:
There are 9 possible outcomes for (Bill, Ben)'s cards:
(4, 4) total 8; (4, 5) total 9; (4, 6) total 10;
(5, 4) total 9; (5, 5) total 10; (5, 6) total 11;
(6, 4) total 10; (6, 5) total 11; (6, 6) total 12.
Of these 9 outcomes, 4 have an odd total; 6 are less than 11.
P(odd) = 4/9
P(sum < 11) = 2/3
How can Ari simplify the following expression? StartFraction 5 Over a minus 3 EndFraction minus 4 divided by 2 + StartFraction 1 Over a minus 3 EndFraction
Answer:
[tex]-\frac{8}{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex]
Required
Simpify
The very first step is to take LCM of the given expression
[tex]\frac{-10 -4 - 2}{6}[/tex]
Perform arithmetic operations o the numerator
[tex]-\frac{16}{6}[/tex]
Divide the numerator and denominator by 2
[tex]-\frac{16/2}{6/2}[/tex]
[tex]-\frac{8}{3}[/tex]
The expression can't be further simplified;
Hence, [tex]\frac{5}{-3} - \frac{4}{2} + \frac{1}{-3}[/tex] = [tex]-\frac{8}{3}[/tex]
Dr. Pagels is a mammalogist who studies meadow and common voles. He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices. So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Indicate which of the following is the null hypothesis, and which is the alternate hypothesis.
There food preferences among vole species are independent of one another. _____
There is a relationship between voles and food preference. ______
To test for independence, we need to calculate the Chi-square statistic.
These are the data that Dr. Pagels collected:
meadow voles common voles
apple slices 26 32
peanut butter-oatmeal 35 25
When transferring your answers, make sure you carry them out to AT LEAST SIX SIGNIFICANT FIGURES unless otherwise stated.
_____= expected meadow vole/apple slices
_____= expected common vole/apple slices
_____= expected meadow vole/peanut butter-oatmeal
_____= expected common vole/peanut butter-oatmeal
_____= chi-square value
_____= degrees of freedom (whole number only)
_____= using Statistical Table A (pg 704 of your textbook), what is the chi-square critical value with significance level of alpha=0.05?
_____= will you reject or fail to reject the null hypothesis? (answer either reject or fail to reject)
Answer:
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 28.983051
Chi-square value = χ² = 2.154239
Degree of freedom = 1
Critical value = 3.841
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
Step-by-step explanation:
He frequently traps the moles and has noticed what appears to be a preference for a peanut butter-oatmeal mixture by the meadow voles vs apple slices are usually used in traps, where the common voles seem to prefer the apple slices.
So he conducted a study where he used a peanut butter-oatmeal mixture in half the traps and the normal apple slices in his remaining traps to see if there was a food preference between the two different voles.
Null hypothesis = H₀ = There food preferences among vole species are independent of one another.
Alternate hypothesis = H₁ = There is a relationship between voles and food preference.
Data collected by Dr. Pagels:
meadow voles common voles Row Total
apple slices 26 32 58
peanut butter-oatmeal 35 25 60
Column Total 61 57 118
Where 118 is the grand total.
The expected number is given by
Expected = (row total)×(column total)/grand total
Expected meadow vole/apple slices = 58×61/118
Expected meadow vole/apple slices = 29.983051
Expected common vole/apple slices = 58×57/118
Expected common vole/apple slices = 28.016949
Expected meadow vole/peanut butter-oatmeal = 60×61/118
Expected meadow vole/peanut butter-oatmeal = 31.016949
Expected common vole/peanut butter-oatmeal = 60×57/118
Expected common vole/peanut butter-oatmeal = 28.983051
The chi-square statistic value is given by
χ² = Σ(Observed - Expected)²/Expected
χ² = (26 - 29.983051)²/29.983051 + (32 - 28.016949)²/28.016949 + (35 - 31.016949)²/31.016949 + (25 - 28.983051)²/28.983051
χ² = 2.154239
The degrees of freedom is given by
DoF = (row - 1)×(col - 1)
For the given case, we have 2 rows and 2 columns
DoF = (2 - 1)×(2 - 1)
DoF = 1
The given level of significance = 0.05
The critical value from the chi-square table at α = 0.05 and DoF = 1 is found to be
Critical value = 3.841
Conclusion:
Reject H₀ If χ² > Critical value
We reject the Null hypothesis If the calculated chi-square value is more than the critical value.
For the given case,
χ² < Critical value
We failed to reject H₀
We do not have significant evidence at the given significance level to show that there is a relationship between voles and food preference.
I need help with this exercise please. What I need to know is the measure of one side of the square. Sorry for the language of the exercise
Answer:
[tex]\boxed{\sf \ \ x=6 \ \ }[/tex]
Step-by-step explanation:
Hello,
BMN and NPC are two similar triangles so
[tex]\dfrac{BM}{MN}=\dfrac{NP}{PC}\\\\ \dfrac{10-x}{x}=\dfrac{x}{15-x}\\\\<=>(15-x)(10-x)=x^2\\\\<=>150-25x+x^2=x^2\\\\<=>25x=150\\\\<=>x=6[/tex]
espero que esto ayude
Determining Key Aspects of a Quadratic Function
Use the drop-down menus to describe the key aspects of the function f(x) = -X2 - 2x - 1.
The vertex is the
The function is increasing
The function is decreasing
The domain of the function is hs
The range of the function is
Answer:
Step-by-step explanation:
The vertex can be located most easily by completing the square of
f(x) = -X^2 - 2x - 1 (which is equivalent to -(x^2 + 2x + 1). The latter expression can be rewritten as -(x + 1)^2, which indicates that the x-coordinate of the vertex is -1. The corresponding y-value is 0. Vertex is at (-1, 0).
The function is increasing for x < -1 and decreasing for x > -1.
The domain of the function is "all real numbers."
The range is (-infinity, 0)
Using the unit circle, determine the value of cos(-150°).
Explanation:
The identity we'll use is cos(-x) = cos(x) for any value of x.
So cos(-150) = cos(150).
Then locate the angle 150 on the unit circle. The terminal point is [tex]\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)[/tex]
The x coordinate of this terminal point is the value of cos(150).
Answer:
Cos(-150°)=-√3/2
Step-by-step explanation:
-150° is found at the third quadrant so the cost value at third quadrant is negative
Cos(-150°)= -cos(30)=-cos(210)
Cos(-150°)=- (√3/2)
Cos(-150°)=-√3/2
Hope it helps
8÷2 2/9 −2 11/15 I need help and this is a whole equation I need this ASAP
Answer: (1 and 22/45)
Step-by-step explanation:
I guess that we are working with mixed numbers here, and we have the equation:
(8÷2 2/9) − (2 11/15)
first we solve: 8÷2 = 4.
Now, we can write this as:
(4 + 2/9) - (2 + 11/15)
(4 - 2) + (2/9 - 11/15)
now, 9*5 = 45
15*3 = 45
then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45
2 - 23/45
But in mixed numbers we also need to work with a positive rational, then we have:
2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45
then the solution is:
(1 and 22/45)
When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population:________
a. Does not have a normal distribution
b. Has a normal distribution
c. Has a chi-square distribution
d. Does not have a chi-square distribution
e. Has k-3 degrees of freedom
Answer:
Option B
Step-by-step explanation:
The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.
While the alternative hypothesis states that the data are not consistent with a specified distribution.
In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.
Which list orders the numbers from least to greatest
Answer:
3rd option
Step-by-step explanation:
-5 is smaller than -2.
-2 is smaller than 1
1 is smaller than 3
Answer:
the 3 one
Step-by-step explanation:
the larger the negative number,the higher up the number line it goes
so -5 is the greatest negative number,-2 the next, the 1 and 3
PLEASE I NEED HELP!!! FIRST ANSWER IS BRANLIEST!!!
Apply the distributive property to create an equivalent expression. 6(5x-3)
Answer:
30x - 18
Step-by-step explanation:
6(5x - 3)
Apply the distributive property.
6(5x) + 6(-3)
30x + - 18
Answer:
30x - 18 is your final answer
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
Find the hypotenuse of a right triangle (in cm) if one leg measures 7 cm and the other leg measures 11 cm. Round to the nearest thousandth. ____________ cm
Using the Pythagorean theorem
Hypotenuse = sqrt( 11^2 + 7^2)
= sqrt( 121 + 39)
= sqrt( 160)
= 12.694
As a young professional in the future, it is good to start saving money to have a
security for the future and have something to use when emergency cases happen
related to the need of cash. The Philippine Average Family income last 2015 was
around P276,000 per year. Lets say every year you earn the same amount and save
P76,000 yearly in your frusted bank giving 4% compounded interest annually. How much
will the account worth in the future after 40 years?
a. Solve for the future value of the account:
FV=PMT
( \frac{(1 + i) ^{n} - 1 }{i} )(i(1+i)n−1)
Answer:
Step-by-step explanation:
We would apply the future value which is expressed as
FV = C × [{(1 + r)^n - 1}/r]
Where
C represents the yearly payments of the young professional.
FV represents the amount of money
in your account at the end of 40 years.
r represents the annual rate.
n represents number of years or period.
From the information given,
r = 4% = 4/100 = 0.04
C = $76000
n = 40 years
Therefore,
FV = 76000 × [{(1 + 0.04)^40 - 1}/0.04]
FV = 76000 × [{4.8 - 1}/0.04]
FV = 76000 × 95
FV = P7220000
For f(x) = 4x +1 and g(x) = x2 - 5, find (f-8)(x).
Answer:
(f-g)(x) = -x² +4x +6
Step-by-step explanation:
We assume you want to find (f -g)(x).
[tex](f-g)(x)=f(x)-g(x)=(4x+1)-(x^2-5)\\\\\boxed{(f-g)(x)=-x^2+4x+6}[/tex]
is this right one more i think lol
Answer:
Yup P is the right one having 62.26%
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
We can set it up as
P = 33/53
Q = 20/48
R = 54/90
S = 44/83
This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.
Now we calculate =>
P = 33/53 = around 0.62
Q = 20/48 = around 0.416
R = 54/90 = 0.6
S = 44/83 = around 0.53
We find that Park P has the greatest percentage and -->
Thus, Park P is our answer and yes, you are correct.
Question
Shelly has 50 shortsin her closet. Shawnie her
Sister borrowed Some of
her shorts. Now shelly has
44 Shosts. How many
Shorts did Shawnie borrow.
A. 50-n = 44
B. 50 t n = 44
c. 50 n = 44
D.44 n =50
Answer:
A.50-n=44, 6 shorts borrowed
Step-by-step explanation:
If her sister borrowed n shorts, that means Shelly now has n less shorts. Since her amount of shorts is 50, then 50-n must equal how many shorts she has now, meaning 50-n=44. Solving the equation we get n=6. This means that her sister borrowed 6 shorts.
Answer:
A
Step-by-step explanation:
50 minus the shorts Shawnie borrowed (n) equal to 44
There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.
Answer:
620 comic books
2480 / 4 is 620.
620 x 3 is 1860.
1860 + 620 is 2480.
Done!
Use synthetic division to solve What is the quotient?
Answer:
[tex]3{x}^{3} + 2x + 5[/tex]
Step-by-step explanation:
Sorry if my notes weren't very clear.
Answer:B
Step-by-step explanation: got it right
When would you need to arrange polynomials
Kelly's first four test grades of the period were 80, 72, 96, and 88. Which inequality represents the grades she can
earn on the fifth test to have a test average of no less than 80?
V
O gs16
O 92 16
O g564
O 9264
Answer: option D on edge 2020
Step-by-step explanation:
if you reverse the formula for mean, then you just insert the numbers and you have your answer
find the value of the geometric series
1000 + 1000(1.03) + 1000(1.03)2 + . . . + 1000(1.03)9
Answer:
[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]
Step-by-step explanation:
hello
we need to compute the following
[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]
hope this helps
what is -34/15 in decimal form
Answer:
2.26 repeating
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
hope this helpes
be sure to give brainliest
Is the answer correct in this question
Answer:
Yeah, you got the answer right.
Step-by-step explanation:
What is the APPROXIMATE circumference of a circle with a radius of 9 inches? Use 3.14 for π. 28.3 in. 56.5 in. 254.34 in. 113.0 in.
Answer:
56.52 in
Step-by-step explanation:
Circumference Formula: C = 2πr
Since we are given radius r = 9, simply plug it into the formula:
C = 2π(9)
C = 18π
C = 56.5487
Answer:
56.5
Step-by-step explanation:
The circumference is the product of the diameter and PI
P = (9+9)*π = 18*3.14=56.52
what is the slope of the line given by the equation?
Answer:
the slope is 8
Step-by-step explanation:
The coefficient of x, "m" is the slope in the slope-intercept form:
y = mx + b
16. Find m<2.
a. 86°
b. 43°
C. 94°
d. 133
write 26 as repeated multiplication
Answer:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
2¹³
13 x 13
Step-by-step explanation:
We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.
Find the lowest common denominator. 1/(x+2)^2, 1/(x-2)^2, 2/(x^2-4) A. (x+2)^2 (x-2)^2 B. (x^2+2) (x^2-2)
Answer:
(x + 2) ^2 (x - 2) ^ 2 so A is the answer.
Step-by-step explanation:
Answer:
a
Step-by-step explanation: