Answers
The question is somewhat poorly posed because the equation doesn't involve θ at all. I assume the author meant to use x.
sec(x) = csc(x)
By definition of secant and cosecant,
1/cos(x) = 1/sin(x)
Multiply both sides by sin(x) :
sin(x)/cos(x) = sin(x)/sin(x)
As long as sin(x) ≠ 0, this reduces to
sin(x)/cos(x) = 1
By definition of tangent,
tan(x) = 1
Solve for x :
x = arctan(1) + nπ
x = π/4 + nπ
(where n is any integer)
In the interval 0 ≤ x ≤ 2π, you get 2 solutions when n = 0 and n = 1 of
x = π/4 or x = 5π/4
Related Questions
Name the three digit number. My ones digit is an even number which is three times as much as my tens digit. My tens digit is the same as my hundreds digit. The sum of all my digits is 10. What number am i?
A. 424
B. 028
C. 226
D. 622
Answers
Find equation of linear function represented by the table below in slope intercept form
Answers
Answer:
y=4x+3
Step-by-step explanation:
The slope of the line is (13-7)/(2-1)=4. The line equation is hence y=4x+3
Find the volume of the figure. If necessary, round the answer to the nearest whole number.
Answers
Answer:
V = 108 ft³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Rectangular Prism Formula: V = lwh
l is lengthw is widthh is heightStep-by-step explanation:
Step 1: Define
Identify variables
l = 4 ft
w = 3 ft
h = 9 ft
Step 2: Find Volume
Substitute in variables [Volume of a Rectangular Prism Formula]: V = (4 ft)(3 ft)(9 ft)Evaluate [Order of Operations]: V = 108 ft³Flying against the wind, an airplane travels 3360 kilometers in hours. Flying with the wind, the same plane travels 7560 kilometers in 9 hours. What is the rate of the plane in still air and what is the rate of the wind?
Answers
Answer:
606.6 and 233.3 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*9=7560 and (x-y)*9=3360. Solving it, we get x=606.6 and y=233.3
Select the correct answer.
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answers
Answer: Choice B) 0.27
=========================================================
Explanation:
There are a lot of data values here, and it's possible to easily get lost in them. However, we're asked only about students with blond hair. So we only focus on the first row. Ignore everything else.
We see that there are 78 of these students total. Of this total, 21 have green eyes.
Therefore, the relative frequency of blonds with green eyes is 21/78 = 0.2692 which rounds to 0.27; so that's why the answer is choice B.
Pauline mixed 0.32 liter of syrup with 12 times as much water to make orange squash.She split 1.28 liter of orange squash.Then she poured the remaining orange squash equally into 4 bottles.How much orange squash were there in each bottle.Give your answer in Liters.
Answers
Answer:
0.72 litres
Step-by-step explanation:
Litres of syrup = 0.32 litres
Litres of water = 12 times the amount of syrup = 12 * 0.32 = 3.84 litres
Litres of orange squash = litres of syrup + litres of water
Litres of orange squash = (0.32 + 3.84) = 4.16 litres
Amount of orange squash litres split = 1.28 litres
Amount of orange squash left = (4.16 - 1.28) = 2.88 litres
Splitting the amount of squash left equally into 4 :
2.88 litres / 4 = 0.72 litres
у
х
9
3
Find the value of y.
Answers
9514 1404 393
Answer:
(d) 6√3
Step-by-step explanation:
There are several ways to work multiple-choice problems. One of the simplest is to choose the only answer that makes any sense. Here, that is 6√3.
y is the hypotenuse of the medium-sized right triangle, so will be longer than that triangle's longest leg. y > 9
The only answer choice that meets this requirement is ...
y = 6√3
__
In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio. For y, we're interested in the ratio of long leg to hypotenuse.
long leg/hypotenuse = y/(9+3) = 9/y
y² = 9(9+3) = 9·4·3
y = 3·2·√3 . . . . . . take the square root
y = 6√3
__
Additional comments
You may notice that y is the root of the product of the longer hypotenuse segment (9) and the whole hypotenuse (9+3 = 12). We can say that y is the "geometric mean" of these segment lengths. Similarly (pun only partially intended), x will be the root of the product of the short segment (3) and the whole hypotenuse (12)
x = √(3·12) = 6
This is another "geometric mean" relation.
Further, the altitude will be the geometric mean of the two segments of the hypotenuse:
h = √(9·3) = 3√3
A way to summarize all of these relations is to say that the legs of the right triangle that are not the hypotenuse are equal to the geometric mean of the segments of the hypotenuse that the leg intercepts.
x = √(3·12)
y = √(9·12)
h = √(3·9)
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x – 9y = -72
Answers
the slope-intercept form of the given equation is y = x/3 + 8.
What is the slope?The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.
The slope-intercept form of a line is Y = m*X +C.
Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.
3x-9y = -72
9y = 3x + 72
y = 1/3 * x + 8
Therefore y = x/3 + 8 is the slope-intercept form of the given equation. where its slope is 1/3.
Learn more about slope here:
https://brainly.com/question/3605446
#SPJ2
3/4 pound of Colby cheese costs $1.69. Find the unit price per pound. (3/4 pound=12)
Answers
Answer:
2.25
Step-by-step explanation:
We can write a ratio to solve
1.69 x
------ = ---------------
3/4 lb 1 lb
Using cross products
1.69 * 1 = 3/4 *x
1.69 = 3/4 x
Multiply by 4/3
1.69 * 4/3 = x
x=2.25333
Rounding to the nearest cent
Graph: y – 3 = 1/2 (x + 2)
Answers
Answer:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Step-by-step explanation:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Answer: See below
Concept:
There are different forms of linear equations:
Slope-intercept form: y = mx + bPoint-slope form: y - y₁ = m (x - x₁)Standard form: Ax + By = CIntercept form: x / x₁ + y / y₁ = 1Solve:
Given: y - 3 = 1/2 (x + 2)
Here, we can see the linear equation is in the form of point-slope form.
x₁ = -2
y₁ = 3
m = 1/2
Point included in the graph = (-2, 3)
Slope of the graph = 1/2
Hope this helps!! :)
Please let me know if you have any questions
What is the solution to the system of equations? 5x-2y=-16 4x-5y=-23
Answers
Answer:
The solution set is {-2, 3}.
Step-by-step explanation:
We can do this by elimination after manipulating the 2 equations so that the coefficients of y will disappear after addition:
5x - 2y = -16 Multiply this by -5:
-25x + 10y = 80 ...........(A)
4x - 5y = -23 Multiply this by 2:
8x - 10y = -46..............(B)
Now add A and B:
-17x = 34
x = 34/-17
x = -2.
Now substitute x = -2 into the first original equation:
5(-2) - 2y = -16
-2y = -16 +10 = -6
y = -6/-2
y = 3.
Confirm these results by substitution in the second original equation:
4(-2) - 5(3)
= - 8 - 15 = -23.
Checks OK.
What is the distance between the following points?
WILL GIVE BRAINLIEST
Answers
Answer:
D.√85
Step-by-step explanation:
We can find the distance between two points using the distance between two points formula
Distance between two points formula:
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the given points
We are given the two points (-2,7) and (7,9)
Using these points let's define the variables ( variables are x1, x2, y1, and y2)
Remember points are written as follows (x,y)
The x value of the first point is -2 so x1 = -2
The x value of the second point is 7 so x2 = 7
The y value of the first point is 7 so y1 = 7
The y value of the second point is 9 so y2 = 9
Now that we have defined each variable let's find the distance between the two points
We can do this by substituting the values into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9
Substitute values in formula
d = √(7 - (-2))² + (9 - 7)²
Evaluation:
The two negative signs cancel out on 7-(-2) and it changes to +7
d = √ (7+2)² + (9-7)²
Add 7+2 and subtract 9 and 7
d = √ (9)² + (2)²
Simplify exponents 9² = 81 and 2² = 4
We then have d = √ 81 + 4
Finally we add 81 and 4
We get that the distance between the two points is √85
Can you please me me
Answers
Step-by-step explanation:
1 since a tank holds 121/2 gallons of gas 121/2 multiplied by two it gives 25 -30 it gives 5 450 divided by two it gives 225-25 i guess.
I thought of a number. I added 15, tripled it and then subtracted 3 from the result. I got 42. What was my number?
Answers
Answer:
45
Step-by-step explanation:
15 x 3 = 45 - 3 = 42
An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an (alpha level of 0.05.)
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
Required:
What is the appropirate test?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
The appropriate test is a paired t test :
d = difference between May and August
d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
The test statistic :
T = dbar / (Sdbar/√n)
Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.
Using calculator :
dbar = - 7.777 ; Sdbar = 9.052
Test statistic = - 7.777 / (9.052 /√9)
Test statistic = - 2.577
The Pvalue, df = n - 1 = 9 - 1 = 8
Pvalue(-2.577, 8) = 0.0327
At α = 0.05
Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score
If 15% of the customer's total is $22.05, then the customer's total is
Answers
Answer:
$147
Step-by-step explanation:
0.15x = $22.05
Divide both sides by 15
22.05/0.15 = $147
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling an 8.
The probability of rolling an 8 is:
Answers
This is because there's one side we want (that's labeled "8") out of 12 sides total. This is of course if each side is equally likely.
Side note: this 12-sided die is known as a dodecahedron.
I need some help please!!!
Answers
9514 1404 393
Answer:
13 < √181 < 14
Step-by-step explanation:
Apparently, you're supposed to know that ...
13² = 169
14² = 196
so √181 will lie between 13 and 14.
13 < √181 < 14
Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of complaints are contained in the file BBB. Click on the datafile logo to reference the data. a. Construct a frequency distribution for the number of complaints by industry. Category Observed Frequency Bank Cable Car Cell Collection Total b. Using , conduct a hypothesis test to determine whether the probability of a complaint is the same for the five industries. The test-statistic is (to 3 decimals). -value (to 4 decimals) What is your conclusion
Answers
Answer:
χ² = 19
Pvalue = 0.0008 ( 4 decimal places)
WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries
Step-by-step explanation:
H0 : probability of complaint is the same for the 5 industries.
H1: probability of complaint is not the same for the 5 industries.
Category ____ observed frequency
Bank _______ 26
Cable _______44
Car _________42
Cell _________60
Collection ____ 28
Total ________200
The test statistic ;
χ² = (O - E)² / E
O = Observed Frequency ; E = Expected Frequency
Expected Frequency, E = (1 / n) * total
n = number of industries = 5
Expected frequency, E = (1/5)*200 = 40
Expected frequency is the same for all, thus E for all 5 industries = 40
χ² = Σ(O - E)² / E;
χ² = (26-40)² / 40 + (44-40)² / 40 + (42-40)² / 40 + (60-40)² / 40 + (28-40)² / 40
χ² = 19
At α = 0.05 ; df = n-1 = 4 ; χ²critical = 0.000786
Since Pvalue < α ; WE reject the H0 and conclude that probability of complaint is not the same for the 5 industries.
To host an event at a popular convention center, it costs $300 plus $45 per person attending. Step 1 of 3 : Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.
Answers
Answer: (300 + 45x) / x
Step-by-step explanation:
Based on the information given in the question, the total cost will be the addition of the fixed cost and the variable cost which will be:
= 300 + (45 × x)
= 300 + 45x
The amount that needs to be charge for each attendee in order to cover the cost of hosting the event will be:
= (300 + 45x) / x
Lily wants to put a ribbon border around two round clocks. Each clock has a diameter of 24 centimeters. Using 3.14 for π, approximately how many meters of ribbon does Lily need?
Answers
Answer:
1.5 meters
Step-by-step explanation:
You need to use circumference for this problem and the formula is dπ.
Plug in:
24π
Solve with pi:
24×3.14 = 75.36
Since there is two clocks, multiply:
75.36 × 2 = 150.72
In 1 meter there is 100 centimeters so divide
150.75 ÷ 100 = 1.5
So you will need 1.5 meters of ribbon.
Pls solve this for me ryt now wai abeg
...The first three terms of an arithmetic progression (A.P) are (x+1),(4x-2) and(6x-3) respectively .If the last term is 18,find the
a.Value of x b.Sum of the terms of the progression
Answers
Answer:
[tex]x = 2[/tex]
[tex]S_n = 63[/tex]
Step-by-step explanation:
Given
[tex]a_1 = x + 1[/tex]
[tex]a_2 = 4x -2[/tex]
[tex]a_3 = 6x -3[/tex]
[tex]a_n = 18[/tex]
Solving (a): x
To do this, we make use of common difference (d)
[tex]d = a_2 - a_1[/tex]
[tex]d = a_3 - a_2[/tex]
So, we have:
[tex]a_3 - a_2 = a_2 - a_1[/tex]
Substitute known values
[tex](6x - 3) - (4x - 2) = (4x - 2) - (x + 1)[/tex]
Remove brackets
[tex]6x - 3 - 4x + 2 = 4x - 2 - x - 1[/tex]
Collect like terms
[tex]6x - 4x- 3 + 2 = 4x - x- 2 - 1[/tex]
[tex]2x- 1 = 3x- 3[/tex]
Collect like terms
[tex]2x - 3x = 1 - 3[/tex]
[tex]-x = -2[/tex]
[tex]x = 2[/tex]
Solving (b): Sum of progression
First, we calculate the first term
[tex]a_1 = x + 1[/tex]
[tex]a_1 = 2 + 1 = 3[/tex]
Next, calculate d
[tex]d = a_2 - a_1[/tex]
[tex]d = (4x - 2) - (x +1)[/tex]
[tex]d = (4*2 - 2) - (2 +1)[/tex]
[tex]d = 6 - 3 = 3[/tex]
Next, we calculate n using:
[tex]a_n = a + (n - 1)d[/tex]
Where:
[tex]a_n = 18[/tex]
[tex]d = 3; a = 3[/tex]
So:
[tex]18 = 3 +(n - 1) * 3[/tex]
Subtract 3 from both sides
[tex]15 = (n - 1) * 3[/tex]
Divide both sides by 3
[tex]5 = n - 1[/tex]
Add 1 to both sides
[tex]6 = n[/tex]
[tex]n = 6[/tex]
The sum of the progression is:
[tex]S_n = \frac{n}{2} * [a + a_n][/tex]
So,, we have:
[tex]S_n = \frac{6}{2} * [3 + 18][/tex]
[tex]S_n = 3 * 21[/tex]
[tex]S_n = 63[/tex]
Which expression is equivalent to the given expression?
Answers
Answer:
a³b
Step-by-step explanation:
(ab²)³/b⁵
= a³b⁶/b⁵
= a³b
From September 1991 to September 1994 the enrollment at a particular school declined by 20 percent. If the number of students enrolled at that school in September 1994 was 720, what was the enrollment in September 1991
Answers
Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
Can I get help with this? Ez points
Answers
9514 1404 393
Answer:
(-1, -1), (-1, 5), (2, -1)
Step-by-step explanation:
All of the blanks are filled with -1. (see attached)
_____
The attachment also shows the solutions that maximize or minimize the value of z.
In my town, it's rainy one third of the days. Given that it is rainy, there will be heavy traffic with probability 1/2, and given that it is not rainy, there will be heavy traffic with probability 1/4. If it's rainy and there is heavy traffic, I arrive late for work with probability 1/2. On the other hand, the probability of being late is reduced to 1/8 if it is not rainy and there is no heavy traffic. In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is 0.25. You pick a random day.
a. What is the probability that it’s not raining and there is heavy traffic and I am not late?
b. What is the probability that I am late?
c. Given that I arrived late at work, what is the probability that it rained that day?
Answers
Answer:
a) 0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b) 0.2292 = 22.92% probability that I am late.
c) 0.5454 = 54.54% probability that it rained that day.
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.
Question a:
2/3 probability of not raining.
If not raining, 1/4 probability of heavy traffic.
1 - 0.25 = 0.75 = 3/4 probability of not late.
So
[tex]p = \frac{2}{3} \times \frac{1}{4} \times \frac{3}{4} = \frac{2}{16} = 0.125[/tex]
0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b. What is the probability that I am late?
0.5 of (1/3)*(1/2) = 1/6(rainy and heavy traffic).
0.25 of (1/3)*(1/2) = 1/6(rainy and no traffic).
1/8 = 0.125 of (2/3)*(3/4) = 1/2(not rainy and no traffic).
0.25 of (2/3)*(1/4) = 1/6(not rainy and traffic). So
[tex]P(A) = 0.5\frac{1}{6} + 0.25\frac{1}{6} + 0.125\frac{3}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25 + 3*0.125 + 0.25}{6} = 0.2292[/tex]
0.2292 = 22.92% probability that I am late.
c. Given that I arrived late at work, what is the probability that it rained that day?
Event A: Late
Event B: Rained
0.2292 = 22.92% probability that I am late.
This means that [tex]P(A) = 0.2292[/tex]
Probability of late and rain:
0.5 of 1/6(rain and heavy traffic).
0.25 of 1/6(rain and no traffic). So
[tex]P(A \cap B) = 0.5\frac{1}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25}{6} = \frac{0.75}{6} = 0.125[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.2292} = 0.5454[/tex]
0.5454 = 54.54% probability that it rained that day.
the polygons in each pair are similar find the scale factor smaller figure to the larger
Answers
Answer:
smaller figure/larger figure = ½
Step-by-step explanation:
The scale factor = any of the side length of the smaller figure / the corresponding side length of the larger figure
Side length of smaller figure = 3
Corresponding sides length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = smaller figure/larger figure = ½
i need help asap !!!
Answers
rose says the quantity of four dollars is a terminating decimal. Sharon says it is an integer.Do you agree witheither of them
Answers
Answer:
Agree with Sharon
Step-by-step explanation:
A terminating decimal includes numbers beyond the decimal point.
An integer is a whole number.
4 is a whole number so it's an integer which is what Sharon said.
Diện tích xung quanh của hình chóp tứ giác đều có cạnh bằng 6cm và độ dài trung đoạn bằng 10cm là:
A. 120 cm2 B. 240 cm2 C. 180 cm2 D. 60 cm2
Answers
Answer:
B. 240 cm2
Step-by-step explanation:
Chu vi đáy: 10x=40
Diện tích xung quanh: Sxq=1/2 x40x12=240
