Answers
Step-by-step explanation:
To prove :
( 1 - sin x ) ( 1 + sin x ) = sec² x
LHS : -
( 1 - sin x ) ( 1 + sin x )
Formula / Identity : -
( a - b ) ( a + b ) = a² - b²
Here,
a = 1
b = sin x
( 1 - sin x ) ( 1 + sin x )
= 1 - sin² x
Identify : -
sin² θ + cos² θ = 1
cos² θ = 1 - sin² θ
Similarly,
1 - sin² x
= cos² x
= RHS
Hence verified.
Related Questions
area of circle if circumference is 132m
Answers
Answer:
1386 cm²
Step-by-step explanation:
Here's your answer!
Hope it helps :)
Answer:
1386.56m²
Step-by-step explanation:
A=C2
4π
Circumference^2/4(3.14)
Find the volume of the following figures with the given dimension
Answers
Answer:
[tex]V=192\ in^3[/tex]
Step-by-step explanation:
Given that,
The area of base, A = 24 in²
The height of the pyramid, h = 8 in
We need to find the volume of the following figure.
The volume of pyramid is given by :
[tex]V=A\times h[/tex]
Substitute all the values,
[tex]V=24\times 8\\\\=192\ in^3[/tex]
So, the volume of the pyramid is equal to [tex]192\ in^3[/tex].
determine the radius of a circle whose circumfrence is 16.52cm
Answers
Answer:
radius=2.62cm
hope it helps.
i will be sooooo thankful if u helped me
Answers
Answer:
For 35 its C
Step-by-step explanation:
Determine the scale factor for triangle ABC to Triangle A'B'C'.
Answers
Can someone help me with this question please?
Answers
Answer:
35
Each sequence has a difference of eight numbers so we add 8 numbers in each sequence
Answer:
a) (i) 36
(ii) previous+8
b) 75
Step-by-step explanation:
a) (i) 27+8=36
(ii) previous+8
b) 10 th term is 3+9×8= 75
In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25.
a. Write a mathematical expression representing the cost of operation for a month.
b. Write a mathematical expression representing sales.
c. Create an equation that will represent overall profit of the operation for a month.
d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning?
e. Describe the method of graphing the slope intercept form and also the standard form of the equation.
f. What is the domain and range of the equation? Is the relation a function, why?
g. How many snow cones do you need to sell to break even in the first month?
h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business?
Answers
Answer:
31.25 is the answer at your question
In certain parts of the world tuberculosis (a very treatable and curable illness) is present in 25% of the people. If a simple chest X-ray can be used as a diagnostic tool with an accuracy of 99% detection of TB if it is present. Only in 0.5% of the cases, normal people get a positive diagnosis. 2 If a person is selected at random and the diagnosis is positive, what is the probability that the person is actually infected.
Answers
Answer:
0.9851 = 98.51% probability that the person is actually infected.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive test
Event B: Infected
Probability of a positive test:
99% of 25%(People have the disease).
0.5% of 100 - 25 = 75%(People do not have the disease). So
[tex]P(A) = 0.99*0.25 + 0.005*0.75 = 0.25125[/tex]
Probability of a positive test and being infected:
99% of 25%, so:
[tex]P(A \cap B) = 0.99*0.25 = 0.2475[/tex]
What is the probability that the person is actually infected?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2475}{0.25125} = 0.9851[/tex]
0.9851 = 98.51% probability that the person is actually infected.
A square has a diagonal measuring 19 centimeters in length.which of the following is closest to the length of each side of the square?
Answers
Answer:
13cm
Step-by-step explanation:
Let the length of each side be x;
Using the pythagoras theorem
l² = x² + x²
l is the length of the diagonal
l² = 2x²
19² = 2x²
361 = 2x²
x² = 361/2
x² = 180.5
x =√180.5
x = 13
hence the length of each side of the square is closest to 13cm
Weather affects flights across the nation, causing delays, cancellations, and general disruption to the NAS. You have gathered a random sample of departures delayed due to weather from your airport (KXYZ) for the month of April through July. You know that across America, weather delayed an average of 59 flights per day (σ =34.83) during that time period. You want to know if weather delays on flights from your airport differ significantly from those across the nation. Your significance level is set at 0.05. Analyze the data below using the correct t-test and be sure to check assumptions of the data.
Answer the following questions:
a. What type of t test should be used to address this research question, and why?
b. What is the null hypothesis?
c. What is the alternative hypothesis?
d. What is the mean and standard deviation for amount of the population?
e. What is the mean and standard deviation for the sample?
f. What are the degrees of freedom? How do you compute it?
g. What is the effect size (Cohen’s d) if applicable?
h. What is the test value?
i. What is the t statistic?
Answers
Answer:
a.) one sample t test
b.) H0 : μ = 59.3
c.) H1 : μ > 59.3
d.) μ = 59.3 ; σ = 39.84
e.) xbar = 79.4 ; s = 61.36
Test statistic = 3.16
Step-by-step explanation:
Given the sample data:
49.00 49.00 49.00 49.00 49.00 63.00 63.00 63.00 63.00 63.00 199.00 199.00 199.00 199.00 199.00 38.00 38.00 38.00 38.00 38.00 48.00 48.00 48.00 48.00 48.00 49.00 63.00 199.00 38.00 48.00
Sample size, n = 30
Using calculator :
xbar from the data above = 79.4
Standard deviation = 61.359
H0 : μ = 59.3
H1 : μ > 59.3
Test statistic :
(Xbar - μ) ÷ (σ/sqrt(n)
σ = 34.83
(79.4 - 59.3) ÷ (34.83/sqrt(30))
20.1 ÷ 6.359
Test statistic = 3.16
4. Complete the number sentence below: *
x 102 = 2,500
Help me please !!!
Answers
[tex](4.56 \times 3.6) \div 0.12[/tex]
Answers
tttttt hheeeeeeeeeeeeeeeueh
frrref? I think'nt,
hhhhhhhhhhhhhhhhhhooh
Answers
Answer:
ooo
Step-by-step explanation:
The perimeter of a rectangle measures 26 in. Find the other
side length, if one side measures 4 in.
Answers
the rectangle is 26 in and a giving measure is 4 in. so 4+4=8 (8 is the total of two measures). then u do 26-8 and u get 18. (18 is the total of 2 sides). you are tying to find one so u divide it by 2 and you get 9
hey yall i would really appreciate your help on this plz
Answers
Answer:
the length of the opposite side (x), is 27.2
Step-by-step explanation:
For the given right triangle problem;
the opposite side of the given angle, opp. = 22
the hypothenuse side, hypo. = x
given angle of the triangle, θ = 54⁰
The length of the opposite side (x), is calculated as follows;
[tex]sin \ \theta = \frac{opp.}{hypo.} \\\\sin (54) = \frac{22}{x} \\\\x = \frac{22}{sin(54)} \\\\x = 27.2[/tex]
Therefore, the length of the opposite side (x), is 27.2
Jake bought 4.08 pounds of apples. He knows that 1.19 pounds are Gala apples and the rest are Cameo apples. How many pounds of Cameo apples did he buy? A 2.89 B 3.11 C 3.89 D5.27
Answers
Answer:
2.89
Step-by-step explanation:
4.08-1.19 = 2.89
you just do simple subtraction
Answer:
A. 2.89 pounds
Step-by-step explanation:
4.08 pounds of apples all together subtract the Gala apples 1.19 pounds and you'll get that Jake bought 2.89 pounds of Cameo apples.
4.08 - 1.19 = 2.89
PLEASE HELP !!!! ILL GIVE BRAINLIEST !!!
Answers
Answer:
Angle YXU is equal to 113 degrees. those are supplementary angles
Step-by-step explanation:
The area of a rectangle is 48ft2. The length is 3 times the width. Which of the following equations can be used to solve for the width?
Answers
Answer:
Width of rectangle = 4 ft
Step-by-step explanation:
Given:
Area of rectangle = 48 ft²
Length of rectangle = 3[Width of rectangle]
Find:
Width of rectangle
Computation:
Assume;
Width of rectangle = a
So,
Length of rectangle = 3[Width of rectangle]
Length of rectangle = 3a
Area of rectangle = l x b
48 = 3a x a
3a² = 48
a² = 16
a = 4
Width of rectangle = 4 ft
Length of rectangle = 3[Width of rectangle]
Length of rectangle = 3[4]
Length of rectangle = 12 ft
An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events. Event : The sum is greater than . Event : The sum is not divisible by .
Answers
Complete question :
Compute the probability of each of the following events.
Event : The sum is greater than 6
Event : The sum is not divisible by 2
Answer:
7/12 ; 1/2
Step-by-step explanation:
Sample space :
2, 3, 4, 5, 6, 7
3, 4, 5, 6, 7, 8
4, 5, 6, 7, 8, 9
5, 6, 7, 8, 9, 10
6, 7, 8, 9, 10, 11
7, 8, 9, 10, 11, 12
Probability that sum is greater than 6:
Number of outcomes greater Than 6 = required outcomes = (7,7,7,7,7,7,8,8,8,8,8,9,9,9,9,10,10,10,11,11,12) = 21
Total sample space = total possible outcomes = 36
Probability = required outcome / Total possible outcomes
P(sum is greater Than 6) = 21 / 36
2.)
Obtaining an even number :
Sum not divisible by 2 = required outcomes = (3, 5, 7, 3, 5, 7, 5, 7, 9, 5, 7, 9, 7, 9, 11, 7, 9, 11) = 18
Total sample space = total possible outcomes = 36
P(sum is not divisible by 2) = 18 / 36 = 1 / 2
I apologize for the messy photo but please help me with this, I’m really confused! Thank you so so so much.
Answers
1)+4
2)-4
3) 2
4) i don't know
5)
Answer: (-2)²=4
-2²=-4
square root of 4 is 2
1 over the square root of 8 is -2
1 aquare root of -8 is 2,-2
Step-by-step explanation:plug them into calculator
What is (8x + 4) added to (15x – 12)?
Answers
Answer:
23x-8
Step-by-step explanation:
8x + 15x = 23x
4 + (-12) = -8
Answer:
[tex] \boxed{23x \: – \: 8} [/tex]
Step-by-step explanation:
(8x + 4) added to (15x – 12) =
(8x + 4) + (15x – 12) =
[Group like terms]
(8x + 15x) + (4 – 12) =
[Simplify]
23x – 8
Respond to all of the questions within the topic (see that there are six questions below). 1. Explain how you can determine if the parabola opens up or down by simply examining the equation. 2. Give an example of a quadratic function with the given characteristics: its graph lies below the x-axis. 3. Explain how the number of solutions for a quadratic equation relates to the graph of the function. 4. Explain how you solve an equation by factoring. 5. In order to solve a quadratic equation by completing the square, what does the coefficient of the squared term need to be? If the coefficient is not equal to this, what does your first step need to be to complete the sqaure? 6. Explain how the discriminant can be used to determine the number of solutions a quadratic equation has.
Answers
Answer:
Step-by-step explanation:
Did you ever find the answer?/ I also am confused. please let me know
7)
Barry has several horses in a field. The
fence around the field is in the shape of
a rectangle. The width is 8 kilometers
and the length is 15 kilometers. The
length of the diagonal is
A 16 km
B 17 km
C 19 km
D 23 km
Answers
Answer:
I think the answer should be D) 23 km but if its wrong my bad
Step-by-step explanation:
The diagram shows the spot on a basketball court called the "key". what is the area of the key? Use 3.14 for pi
Answers
Please help me with this
Answers
Answer: you should study, plus give me brainliest please. lol
Step-by-step explanation:
and the other answer might be a bot sending links to websites with malware, please dont .open the link unless you want malware on your device, if its fake. and you cant make websites/ links just to post answers. this is a warning.
What is 2x10-50=x and I’m just typing this to get to 20 words or whatever
Answers
Step-by-step explanation:
sorry I don't know the answer I want some points so because I do this I really really sorry. and thanks for point
Maori created this shape out of construction paper using a ruler and scissors. She made sure that all of her angles were right angles.
What is the area of Maori's shape?
A) 36 cm2
B) 48 cm2
C) 90 cm2
D) 102 cm2
Answers
Answer:
B) 48cm²
Step-by-step explanation:
find the area of the 2 rectangles
A = bh
A = 9×4
A = 36
A = bh
A = 6×2
A = 12
add them up you get 48cm²
The diagram shows the diameter of the opening
of a waffle ice cream cone.
18 cm
Which of the following is closest to the area of
the opening in square centimeters?
A.
1,017.88 cm2
C. 254.47 cm
B.
56.55 cm2
D. 28.27 cm2
I will give brainleist
Answers
Answers
D 36
Step-by-step explanation:
77 is the area for the squared trapezoid and 36 is the closest to 77
if 12+ blank=0+12, than blank must equal
Answers
PLEASE HURRYYYYYYYYY
Answers
Answer:
12r ft
Step-by-step explanation:
you're welcome have a nice day