Using a trigonometric identity, it is found that the equivalent expression is given by 1.
What are the trigonometric identities used to solve this question?Relating sine and cosine, we have that:
[tex]\sin^{2}{\beta} + \cos^{2}{\beta} = 1[/tex]
Then:
[tex]\cos^{2}{\beta} = 1 - \sin^{2}{\beta}[/tex]
For the tangent, we have that:
[tex]\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}[/tex].
For the secant, we have that:
[tex]\sec{\beta} = \frac{1}{\cos{\beta}}[/tex].
In this problem, the expression is:
[tex]\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1[/tex]
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
Evaluate the function f(r) = √r + 1 - 1 at the given values of the independent variable and simplify.
a. f(-1) b. f(24) c. f(x-1)
Step-by-step explanation:
I'm going to assume you meant to write [tex]\sqrt{r+1}[/tex] in the equation as +1 - 1 wouldn't make much sense since they would just cancel out.
a. [tex]f(-1) = \sqrt{-1 + 1} - 1\\ f(-1) = \sqrt{0} - 1\\f(-1) = 0-1\\f(-1) = -1[/tex]
b. [tex]f(24) = \sqrt{24 + 1} - 1\\ f(24) = \sqrt{25} - 1\\f(24) = 5 - 1\\f(24) = 4[/tex]
c. [tex]f(x-1) = \sqrt{(x-1)+1} -1\\f(x-1) = \sqrt{x} - 1[/tex]
Please Expand the following:
3q(r – 2q)
Answer:
3qr - 6q²
Step-by-step explanation:
3q(r - 2q) ← multiply each term inside the parenthesis by 3q
= 3qr - 6q²
Answer:
3qr – 6q²
Step-by-step explanation:
3q(r – 2q)
E X P A N D I N G :-
3qr – 6q²
Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
How to explain the information?Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
Learn more about distribution on:
https://brainly.com/question/9123296
#SPJ9
The box plots show Theo’s math scores and language arts scores.
Math
2 box plots. The number line goes from 50 to 100. For math, the whiskers range from 55 to 90, and the box ranges from 60 to 85. A line divides the box at 80. For language arts, the whiskers range from 50 to 90, and the box ranges from 60 to 80. A line divides the box at 70.
Language Arts
About 50% of Theo’s scores are in which range for each subject?
Based on the upper and lower quartiles of the box plots:
Range for Maths is 60 to 85
Range for Language arts is 60 to 80.
What is the Upper Quartile and the Lower Quartile?In a box plot, the about half of the data set lies between the upper quartile and the lower quartile which are represented at the beginning and the end of the edges of the box respectively. This makes up 50% of a data distribution.
Thus, for Maths, the Upper and lower quartiles are between 60 to 85, hike that for Language arts are between 60 to 80.
Therefore, 50% of Theos scores for Maths ranges from: 60 to 85, while for Language arts is: 60 to 80.
Learn more about the upper quartile and lower quartile on:
https://brainly.com/question/10005803
#SPJ1
(LOOK AT PHOTO) What is the quotient of the rational expression below?
x²-49 x²-14x+49
x+2
3x+6
The quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
How to determine the quotient?The expression is given as:
[tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Express x^2 - 49 as difference of two squares
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex]
Factorize other expressions
[tex]\frac{(x + 7)(x- 7)}{x + 2} \div \frac{(x -7)(x-7)}{3(x + 2)}[/tex]
Express as product
[tex]\frac{(x + 7)(x- 7)}{x + 2} \times\frac{3(x + 2)}{(x -7)(x-7)}[/tex]
Cancel the common factors
[tex]\frac{(x + 7)}{1} \times\frac{3}{(x -7)}[/tex]
Evaluate the product
[tex]\frac{3(x +7)}{(x -7)}[/tex]
Hence, the quotient [tex]\frac{x^2 - 49}{x + 2} \div \frac{x^2 - 14 +49}{3x + 6}[/tex] is [tex]\frac{3(x +7)}{(x -7)}[/tex]
Read more about quotient at:
https://brainly.com/question/8952483
#SPJ1
what is the missing pattern 7, 11, 2, 18, -7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
What is the missing element in a sequence?
A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:
[tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex] (1)
Now we prove that given expression contains the pattern:
n = 0
7
n = 1
7 + (- 1)² · 2² = 7 + 4 = 11
n = 2
7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2
n = 3
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18
n = 4
7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7
The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula [tex]n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}[/tex], equivalent to the recurrence formula [tex]a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}[/tex].
To learn more on patterns: https://brainly.com/question/23136125
#SPJ1
The midpoint of FG is point H at (–5, 2). One endpoint is G(–9, –6). What is the y-coordinate of the other endpoint? The y-coordinate of the other endpoint is
The y-coordinate of the other endpoint is 10 units.
The given coordinates are H (-5, 2) and G (–9, –6).
We need to find the y-coordinate of the other endpoint.
What is the midpoint formula?The mid-point formula is [tex](x, y)=(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2})[/tex]
Now, [tex](-5, 2)=(\frac{x_{1} +(-9)}{2} , \frac{y_{1} +(-6)}{2})[/tex]
⇒[tex]2=\frac{y_{1}-6 }{2}[/tex]
⇒[tex]4=y_{1}-6[/tex]
⇒[tex]y_{1}=10[/tex]
Therefore, the y-coordinate of the other endpoint is 10 units.
To learn more about the midpoint formula visit:
https://brainly.com/question/4728902.
#SPJ1
I will give brainliest to whoever answers!
Answer:
C 34 cm
Step-by-step explanation:
Area = L x W
72 = 8 x W then W = 9
Perimeter = 2 ( L+W) = 2 ( 8+ 9) = 34 cm
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Area of rectangle: A = wl; whereas \boxed{\textsf a} is \underline{area}, \boxed{\textsf w} is \underline{width}, \& \boxed{\textsf{l}} is}\\\large\text{\underline{length}.}[/tex]
[tex]\large\text{a = wl}\\\\\large\text{wl = a}\\\\\large\text{w(8) = 72}\\\\\large\text{8w = 72}\\\\\large\textsf{DIVIDE 8 to BOTH SIDES}\\\\\rm{\dfrac{8w}{8} = \dfrac{72}{8}}\\\\\large\text{SIMPLIFY IT!}\\\\\rm{w = \dfrac{72}{8}}\\\\\rm{w = 9}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{width = \bf 9}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
PLS answer quick
Which formula can be used to find the volume, V, of the composite solid figure represented below?
OA V = r2h + ³
r²h +
3
r²2h + 3r3
r²h + ³
OB. V
OC.
V =
V =
V =
OD. V =
The formula to find the volume of the composite solid is: C. V = πr²h + ⅔πr³.
How to Find the Volume of a Composite Solid?The volume of the composite solid in the image given = Volume of cylinder + volume of hemisphere.
Volume of cylinder = πr²h
Volume of hemisphere = ⅔πr³
Therefore, formula to find the volume is: C. V = πr²h + ⅔πr³.
Learn more about volume of composite solid on:
https://brainly.com/question/23642076
#SPJ1
Answer:
C
Step-by-step explanation:
I Just Took the Test.
Plss HELPP I neeed help on this question
Answer: 180 degrees
Step-by-step explanation:
The measure of the arc of a semicircle is 180 degrees.
If 462 subjects were studied and 99 of them expressed a preference for Brand Y, what percentage
expressed a preference for Brand Y? Round to the nearest tenth percentage. Enter the numerical value
only. For example, if your answer is 12.2%, enter 12.2 in the blank.
Answer:
20
Step-by-step explanation:
492/99x100=21.43
nearest tenth percentage is 20
Choose True or False, (T or F). Data are recorded observations used for explaining conditions of particular phenomenon
Answer:
true
Step-by-step explanation:
this is absolutely true
Solve the equation.
-x+8+3x = x-6
O x=-18
O x=-14
O x = 2
O x = 4
Answer:
x = -14
Step-by-step explanation:
- x + 8 + 3x = x - 6
- x + 8 + 3x - x + 6 = 0
x + 14 = 0
x = -14
square root of the quantity x plus 7 end quantity minus 11 equals 2
An equation is formed when two equal expressions are equated together. The value of x in the equation [√(x+7)]-11=2 is 162.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution for x in the equation [√(x+7)]-11=2 can be solved as,
[tex]\sqrt{x+7}-11=2\\[/tex]
Using the addition property of equality,
[tex]\sqrt{x+7} -11+11= 2+11\\\\\\\sqrt{x+7} = 13[/tex]
Squaring both the sides of the equation,
x + 7 = 169
Using the subtraction property of equality,
x + 7 - 7 = 169 - 7
x = 162
Hence, the value of x in the equation [√(x+7)]-11=2 is 162.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
Which number is irrational?
OA. 0.45
OB. 0.636363...
O C. √25
OD. √6
Answer:
D. Sqroot6
Step-by-step explanation:
6 is not a perfect square. So it is a non-repeating decimal that never ends
sqroot6 ~=
2.4494897428...
this is an irrational number.
The rest on the numbers can be written as a ratio:
0.45=45/100=9/20
0.63636363
= 63/99 = 7/11
sqrt25 = 5 = 5/1
that means they are rational.
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?
Answer:
[tex] \frac{?}{?} [/tex]
there are 1,500 pupils in school , 0.6 are boys how many pupils are girls
Answer:
1491 girls (99.4 percent)
Step-by-step explanation:
explanation is in the attached picture
Evaluate: √121m²n6 if m = 3, n = 2
Answer:
1188
Step-by-step explanation:
√121 (3^2)(2(6)) = 1188
Answer:
264
Step-by-step explanation:
√(121m^2 n^6) = 11 m n^3
sub in the values given for m and n
11 (3)(2^3) = 11 * 3 * 8 = 264
Unas deportivas cuestan $600 he visto que hay una rebaja del 20% cuánto dinero rebajado las reporteras
Answer:
600/100*20=6*20=120
600-120=480$
If the length of rectangle is thrice of its breadth and it's perimeter is 32 cm then finds its area.
Answer:
48 cm²
Explanation:
Let the breadth be b, then the length is 3b
P = 2(Length + Breadth)
32 = 2(3b + b)
32 = 2(4b)
8b = 32
b = 4
Breadth is 4 cm
Length: 3b = 3(4) = 12 cm
Area of rectangle:
Length × Breadth
12 × 4
48 cm²
Given :-
Length of rectangle is thrice of its breadth.Its perimeter is 32 cm.To Find :-
Area of rectangle?Solution :-
Let breadth of rectangle be x cm As it is stated in question that length of rectangle is thrice its breadth so length of rectangle will be 3x cmUsing formula;
Perimeter of rectangle = 2(L + B)Where;
L denotes length of rectangleB denotes a breadth of rectangleWe have;
Perimeter of rectangle = 32 cmLength of rectangle (L) = 3xBreadth of rectangle (B) = xBy putting all values in formula we get;
→ 2(3x + x) = 32
→ 2(4x) = 32
→ 2 × 4x = 32
→ 8x = 32
→ x = 32/8
After dividing 32 with 8, we get;
→ x = 4
Hence;
Length (L) = 3x = 3 × 4 = 12 cmBreadth (B) = x = 4 cmNow, using formula;
Area of rectangle = L × BWhere;
L denotes length of rectangleB denotes a breadth of rectangleWe have;
Length of rectangle (L) = 12 cmBreadth of rectangle (B) = 4 cmArea of rectangle = ?By putting all values in formula we get;
→ Area of rectangle = 12 × 4
By multiplying 12 with 4, we get;
→ Area of rectangle = 48 cm²
Hence, area of rectangle is 48 cm².how many units are -7 and its opposite from zero?
Answer:
-7 is -7 units away from zero. Its opposite is 7 from zero.
Step-by-step explanation: Count from 0 how many digits away it is
Given the two similar triangles below, which proportion is not true?
The proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
ProportionThe three sides of each of the rectangles should be proportional to each other
Triangle A : Triangle B
9 cm : 13.5 cm
= 9/13.5
14 cm : 21 cm
= 14 cm / 21 cm
6 cm : 9 cm
= 6 cm / 9 cm
Therefore, the proportion of sides of the triangle which is not true are 13.5/21 = 9/14, 9/13.5 = 6/21 and 14/6 = 21/9
Learn more about proportion:
https://brainly.com/question/1781657
#SPJ1
Anjali wrote a 30-item multiple choice exam and answered every question. She got 8 points for each correct item. She lost 2 points for each incorrect item. Her total score was 150 points. How many items did she answer correctly?
She did 21 question correctly.
Correct Answer :Let number of correct answers : x
Let number of wrong answer : y
Given, Total question wrote : 30
So,
x + y = 30 (i) - equation
Got 8 point on each correct answer, total point : 8*x
Got -2 point on each wrong answer, total point : (-2)*y
Total point she score was : 150 (given)
so, our next equation is
8*x - 2*y = 150 (ii) - equation
y = 30 - x [from (i) - equation]
put in (ii) - equation, we get
8*x - 2*(30 - x) = 150
8*x - 60 + 2*x = 150
10*x = 210
x = 21
Therefor, only 21 answers are correct.
To learn more about how find the total score or marks, refer :
https://brainly.com/question/462774
#SPJ2
Hello, thank all of you that helped me fix my math problems you helped me to succeed and get a good grade !!!
-5x-5<15
Solve the inequality and graph solution set. Write solution set in (a) set builder notation and (b) interval notation
-5x-5<15 [given]-5x<20 [add 5 to both sides]x>-4 [divide both sides by -5, don't forget to flip the inequality sign]
(a) [tex]\{x: x > -4 \}[/tex]
(b) [tex](-4, \infty)[/tex]
Step 1: Choose the lowest common denominator.
02 03 04 05 06 08 010 012
3/4
50/80
O
Find the sum: -and
The expression written in equivalent form with a
common denominator is
The sum is
The expression written in equivalent form with a common denominator is -1/6
Adding fractionsFractions are written as ratio of two integers. For instance a/b is a fraction.
Given the sum of the fractions shown;
-3/4 and 5/8
Sum = -3/4 + 5/8
Sum = 5/8 - 3/4
Sum = 5-6/8
Sum = -1/8
Hence the sum of the given fraction -1/3 and 5/8 is -1/6
Learn more on sum of fractions here: https://brainly.com/question/78672
#SPJ1
Nigel bought 10 pencils and 5 erasers for 8$. The price of 2
pencils was 1$. What was the price of 2 erasers?
Answer:
2 erasers cost $1.20
Step-by-step explanation:
Nigel bought 10 pencils and 5 erasers for $8.
We can write this algebraically:
10p + 5e = 8
We know that the price of 2 pencils is $1. That is $0.50/Pencil.
So, p = $0.50. Now we can plug that into out equation and find the price of one eraser:
10(0.50) + 5e = 8
5 + 5e = 8
5e = 3
e = $0.60
Now, we have the price of one eraser, $0.60, and we can multiply this by 2 to find the price of 2 erasers, which equates to $1.20.
2/5x - 1/2 = 1/3 + 5/6x
Answer:
[tex]x = \frac{25}{13} [/tex]
Step-by-step explanation:
Given:
[tex] \frac{2}{5} x - \frac{1}{2} = \frac{1}{3} + \frac{5}{6} x[/tex]
Combine like terms:
[tex] \frac{2}{5} x - \frac{5}{6} x = \frac{1}{3} + \frac{1}{2} [/tex]
Find GCF :
[tex] \frac{12}{30} x - \frac{25}{30} = \frac{2}{6} + \frac{3}{6} [/tex]
Subtraction and Addition :
[tex] \frac{13}{30} x = \frac{5}{6} [/tex]
Divide both sides by 13/30 :
[tex] \frac{ \frac{13}{30} }{ \frac{13}{30} } x = \frac{ \frac{5}{6} }{ \frac{13}{30} } [/tex]
Simplify :
Multiplication (Reciprocal) :
[tex]x = \frac{5}{6} \times \frac{30}{13} [/tex]
[tex]x = \frac{150}{78} [/tex]
[tex]x = \frac{25}{13} [/tex]
Answer :
[tex]x = \frac{25}{13} [/tex]
Hope it helps
20
Apply the 50-30-20 Rule to the context below and determine how much money is left over.
You share an apartment with two friends, and the rent and utilities are split equally by all three tenants. Find the
amount left for savings if your bi-weekly net income is $1,391.50.
Total Rent: $1,100
Public Transportation: $88
Cell Phone: $68
Total Utilities: $327
Renter's Insurance: $48.20
Gym Membership: $50
Cable & Streaming Services: $175
Dining Out / Entertainment: $300
3% of Gross into a 401k Savings Plan
Credit Cards: $102
Student Loans: $150
1. Given this monthly budget, how much net income gets applied to each of the "Need/Wants/Debt-Savings"
categories?
50%
30%
20%
2. Subtract each deduction from the monies found in 1). How much remains in each category?
50%
30%
20%
3 How much money remains? What changes would you recommend to improve this budget?
Emissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain".
The acidity of liquids is measured by pH on a scale of 0 to 14. Distilled water has pH 7.0, and lower pH values indicate acidity.
Normal rain is somewhat acidic, so "acid rain" is sometimes defined as rainfall with a pH below 5.0.
The pH of rain at one location varies among rainy days according to a Normal distribution with mean 5.43 and standard
deviations 0.54.
What proportion of rainy days have rainfall with pH below 5.0? Use software or Table A to find the answer.
(Enter your answer rounded to four decimal places.)
Using the normal distribution, it is found that 0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 5.43, \sigma = 0.54[/tex]
The proportion of rainy days have rainfall with pH below 5.0 is the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 5.43}{0.54}[/tex]
Z = -0.8
Z = -0.8 has a p-value of 0.2119.
0.2119 = 21.19% of rainy days have rainfall with pH below 5.0.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
