Answers
If we want to solve this problem we first need to list a few properties of trigonometric functions:
[tex]\begin{gathered} \text{cot }\theta=\frac{\cos\theta}{\sin\theta} \\ \sin^2\theta+\cos^2\theta=1 \end{gathered}[/tex]We are told that cot(θ)=1/2. Using the first equation and this data we obtain the following:
[tex]\frac{1}{2}=\frac{\cos\theta}{\sin\theta}[/tex]We multiply both sides and we get an expression for the cosine of θ:
[tex]\begin{gathered} \frac{1}{2}\sin\theta=\frac{\cos\theta}{\sin\theta}\cdot\sin\theta \\ \cos\theta=\frac{1}{2}\sin\theta \end{gathered}[/tex]Now we are going to take the second property I wrote in the begining and replace the cosine of θ with this new expression that we found:
[tex]\begin{gathered} \sin^2\theta+\cos^2\theta=\sin^2\theta+(\frac{1}{2}\sin\theta)^2=1 \\ \sin^2\theta+\frac{1}{4}\sin^2\theta=1 \\ \frac{5}{4}\sin^2\theta=1 \end{gathered}[/tex]We must solve this equation for the sine of θ. We can multiply both sides by 4/5:
[tex]\begin{gathered} \frac{4}{5}\cdot\frac{5}{4}\sin^2\theta=1\cdot\frac{4}{5} \\ \sin^2\theta=\frac{4}{5} \end{gathered}[/tex]And we apply a square root to both sides:
[tex]\begin{gathered} \sqrt{\sin^2\theta}=\sqrt{\frac{4}{5}} \\ |\sin\theta|=\frac{2}{\sqrt{5}} \end{gathered}[/tex]We are told that θ is located in quadrant I which means that its sine is positive. Therefore we get:
[tex]\sin\theta=\frac{2}{\sqrt{5}}[/tex]AnswerThen the answer is 2/√5
Related Questions
15 m 9 m 9 m 9 m Find the area of this figure. I m2
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we divide the figure to calculate each area and add them at the end
Parallelogram Area
[tex]\begin{gathered} A_P=b\times h \\ A_P=15\times9 \\ A_P=135 \end{gathered}[/tex]
Triangle Area
[tex]\begin{gathered} A_T=\frac{b\times h}{2} \\ \\ A_T=\frac{6\times9}{2} \\ \\ A_T=27 \end{gathered}[/tex]Total Area
[tex]\begin{gathered} A=A_T+A_P \\ A=27+135 \\ A=162 \end{gathered}[/tex]the are of this figure is 162 square meters
help with more than 1 question pls and ty if nkt i will report u its not fair
Answers
SOLUTION
9.
[tex]\begin{gathered} (x+10)^2\text{ = ( x + 10 ) ( x + 10 )} \\ =x^2\text{ + 10 x + 10x + 100} \\ =x^2\text{ + 20 x + 100} \end{gathered}[/tex]10.
[tex]\begin{gathered} (x-10)^2\text{ = ( x - 10 ) ( x - 10 )} \\ =x^2\text{ -10 x - 10 x + 100} \\ =x^2\text{ - 20 x + 100} \end{gathered}[/tex]11. ( x + 10 ) ( x - 10 ) ( Difference of two squares)
[tex]\begin{gathered} x^2\text{ - 10 x + 10 x - 100} \\ =x^2\text{ - 100} \end{gathered}[/tex]Given the diagram below, whereAB||CD, find the measure of xand y.
Answers
Notice that there are two triangles between the parallel lines.
Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.
[tex]160+y=180[/tex]We solve for y.
[tex]\begin{gathered} y=180-160 \\ y=20 \end{gathered}[/tex]On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.
[tex]x=30[/tex]Therefore, x = 30° and y = 20°.Jenna can spend at most $200 on school clothes which inequality represents the amount that Jenna can spend on clothes
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x is the quantity Jenna spend on clothes
[tex]x\le200[/tex]if x varies directly as y, and x = 10 when y = 5, find x when y = 9. x = ______
Answers
Solution:
Since x varies directly as y, consider the following diagram:
by cross-multiplication, we get:
[tex]5x\text{ = (9)(10)}[/tex]this is equivalent to:
[tex]5x\text{ = 90}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{90}{5}=18[/tex]so that, we can conclude that the correct answer is:
x = 18.
It turns out that as ice cream consumption increases, drowning deaths increase. In other words, there is a positive association between ice cream consumption and drowning deaths. However, ice cream consumption does not cause drowning deaths. So why is there a positive association? Explain.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ice cream consumption ====> increases
drowning deaths ====> increase
Step 02:
We must analyze the question to find the solution.
positive association:
There is an association because both values increase, that is, a positive association suggests that when one variable increases, the value of the other variable also increases.
That is the solution.
Multiply and simplify. 3/9 x 5/9
Answers
Answer:
5/27
Step-by-step explanation:
3/9 x 5/9
= ( 3 x 5 )/( 9 x 9 )
9 can be splitted as 3 x 3
= ( 3 x 5 )/( 3 x 3 x 9 )
= 5/( 3 x 9 )
= 5/27
Answer:
[tex]\frac{5x}{27}[/tex]
Step-by-step explanation:
Cancel the number 3/9 = 1/3
= 1/3 x 5/9
Apply the function rule
1 · x · 5
3 · 9
Multiply the numbers 1 · 5 = 5
[tex]\frac{5x}{3 }[/tex]· [tex]9[/tex]
Now just Multiply the numbers: 3 · 9 = 27
= [tex]\frac{5x}{27}[/tex]
Hi, could you please help me understand why I got some of the answers wrong?
Answers
For the figure in the right up
The two triangles have 2 equal angles and one equal side
Then it should be AAS
Triangle AOC is congruent to triangle BOC
You must write the name of the triangles with equal angles
Since < AOC = < BOC ------- Given
Since Since OC = OC ------- common side
By using the AAS theorem of congruency
Then triangle AOC is congruent to triangle BOC
For the figure in the right down
Since OX // YC, then
Since
Since OC = CB ------- Given
Then by using the AAS theorem of congruency
Triangle XCO is congruent to triangle YBC
To make 6 cups of ramen, 2/3 cups of noodles is needed. How many cups of ramen can you make with 1 3/4 cups of noodles?
Answers
Explanation
The question calls for using the direct proportion concept. This can be seen below.
Let the number of cups of ramen you can make with 1 3/4 cups of noodles be x. Therefore;
[tex]\frac{6}{x}=\frac{\frac{2}{3}}{1\frac{3}{4}}[/tex]We can them crossmultiply
[tex]\begin{gathered} \frac{2}{3}x=\frac{7}{4}\times6 \\ \frac{2}{3}x=21 \\ 2x=63 \\ x=\frac{63}{2} \\ x=31\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]31\frac{1}{2}\text{cups}[/tex]Answer:
31.5
Step-by-step explanation:
Dirk is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. Knee pain Ankle pain 3 3 0-12 years old 13-19 years old 2 3 What is the probability that a randomly selected patient is 13-19 years old or suffers from ankle pain? Simplify any fractions.
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The probability of a patient being 13-19 years old is
[tex]P=\frac{5}{11}[/tex]The probability of a patient who suffers from ankle pain is
[tex]P=\frac{6}{11}[/tex]Then, we use the following formula
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]Where,
[tex]P(A\cap B)=\frac{5}{11}\cdot\frac{6}{11}=\frac{30}{121}[/tex]Then,
[tex]P(A\cup B)=\frac{5}{11}+\frac{6}{11}-\frac{30}{121}=\frac{91}{121}\approx0.75[/tex]Hence, the probability is 91/121, or 75%.I really need help with number 6find the value of x that makes abcd a parallelogram.
Answers
Given:
The adjacent angles of the parallelogram are,
[tex]28,\text{ and }3x[/tex]To find:
The value of x.
Explanation:
We know that,
The sum of the two adjacent angles between the parallel lines is supplementary.
So, we write,
[tex]\begin{gathered} 28+3x=180 \\ 3x=180-28 \\ 3x=152 \\ x=50.66 \\ x\approx50.7 \end{gathered}[/tex]Thus, the value of x is 50.7.
Final answer:
The value of x is 50.7.
A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t - 6t^2 meters in t seconds. How high does the rock go? How long does it take the rock to reach its highest point?1190 m, 10 sec600 m, 10 sec1200 m, 20 sec2280 m, 20 sec
Answers
Substitute t = 10, and t = 20, to the given equation and we get
[tex]\begin{gathered} \text{If }t=10 \\ s=120t-6t^2 \\ s=120(10)-6(10)^2 \\ s=1200-6(100) \\ s=1200-600 \\ s=600 \\ \\ \text{If }t=20 \\ s=120t-6t^{2} \\ s=120(20)-6(20)^2 \\ s=2400-6(400)^2 \\ s=2400-2400 \\ s=0 \end{gathered}[/tex]We therefore have t = 10 as the time it takes to reach the highest point, with the rock reaching 600m.
Therefore, we choose second option.
A small toy rocket is launched from a 12-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formulah=−2tcubed2−2+12How long will it take the rocket to hit the ground?t= (Separate answers by a comma if applicable. Write answers as integers or reduced fractions.)
Answers
Solution
Gievn:
[tex]h=-2t^2-2t+12[/tex]When the rocket hits the ground. The distance is zero
Set h = 0 and solve for t
[tex]\begin{gathered} -2t^2-2t+12=0 \\ 2t^2+2t-12=0 \\ 2t^2+6t-4t-12=0 \\ 2t(t+3)-4(t+3)=0 \\ (t+3)(2t-4)=0 \end{gathered}[/tex][tex]\begin{gathered} t+3=0\text{ or 2t-4=0} \\ t=-3\text{ or 2t=4} \\ t=-3\text{ or t=}\frac{4}{2}=2 \end{gathered}[/tex]But, time can not be in negative, hence the answer t = 2
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 42 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 7000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.) The company will accept % of the shipments and will reject % of the shipments, so (Round to two decimal places as needed.)
Answers
Solution
Here, we would calculate the probability that one is defective, two are defective, three are defective and the probability that none are defective and sum them together.
The probability that any individual battery is not defective = 1 - 2% = 0.98
We need 42 of them,
Therefore, P(that none are defective) = (0.98)^42 = 0.4281
The probability that a specific battery will be the only defective battery is (0.02)*(0.98)^41
Since we have 42 of them, ((0.02)*(0.98)^41)*42 = 0.367
Note that
[tex]42C2=\frac{42!}{(42-2)!2!}=861[/tex]=> ((0.02)^2*(0.98)^40)*861 = 0.1535
Therefore, 0.4281 + 0.367 + 0.1535 = 0.9486
The probability shows that about 94.86% of all shipments will be accepted
Misty the cat loved to eat tuna. He wanted to make sure he had enough for the whole week. If misty ate 1\2can of tuna every day,how many cans would he need for a whole week
Answers
Answer:
3.5
Step-by-step explanation:
0.5 * 7 = 3.5
Hope this helps!
Please mark as Brainliest.
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
Answers
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
Where C(x) is in hundreds Of dollars. How many bicycles should the shop build to minimize the average cost per bicycle
Answers
The average cost is given by the next equation:
[tex]C(x)=0.1x^2-0.5x+5.582[/tex]The graph of the function is
As we can see the parabola opens upwards therefore the minim will be located in the vertex
[tex]x=\frac{-b}{2a}[/tex]in our case
b=-0.5
a=0.1
[tex]x=\frac{0.5}{2(0.1)}=2.5[/tex]2.5 hundred
Then
[tex]2.5\times100=250[/tex]Therefore, the shop should build 250 bicycles
Since f is parallel to line g, use the diagram to the right right to answer the following question
Answers
Step 1
[tex]\begin{gathered} m\angle2=m\angle6=117^o(\text{ corresponding angles are equal)} \\ m\angle6=m\angle7=117^o(vertically\text{ opposite angles are equal)} \\ \end{gathered}[/tex]Step 2
[tex]undefined[/tex]Please help I don’t know which to multiply or decide
Answers
a)
Answer:
Explanation:
From the information given, it costs $23 to rent a bike for 4 hours. Let x represent the number of hours that a customer gets per dollar. We have the following equations
4 = 23
x = 1
By cross multiplying,
x * 23 = 4 * 1
23x = 4
x = 4/23 = 0.17
A customer gets 0.17 hour per dollar
Which of the following functions best describes this graph?O A. y=x2- 8x+15O B. y=x+8x+15O c. y = x + x - 12O D. y=x2-5x+6
Answers
We will investigate how to best represent a parabolic graph using a function description.
All parabolas are denoted as either a " U " or inverted " U ". There are two principal parameters of a parabola. The vertex i.e the maximum or minimum point attained by the parabola. The line of symmetry or focus point: The line of symmetry can either be vertical or horizontal but it always passes through the focus point.
We are given a graph of a parabola that has two zeros which can be read off from the plot.
We will locate these zeros and write them down:
[tex]\begin{gathered} x\text{ = 3} \\ x\text{ = 5} \end{gathered}[/tex]All parabolas are expressed by a quadratic polynomial function. The quadratic polynomial can be expressed in factorized form as follows:
[tex](\text{ x - }\alpha\text{ )}\cdot(x\text{ - }\beta\text{ )}[/tex]Where,
[tex]\begin{gathered} \alpha\text{ = 3 ( First Zero )} \\ \beta\text{ = 5 , ( Second Zero )} \end{gathered}[/tex]We will express our located zeros in the factorized quadratic expressed above:
[tex](\text{ x - 3 )}\cdot(x\text{ - 5 )}[/tex]Then we will try to solve the parenthesis and expand the factorized form as follows:
[tex]\begin{gathered} -5\cdot(x\text{ - 3 ) + x}\cdot(x\text{ - 3 )} \\ -5x+15+x^2\text{ - 3x} \end{gathered}[/tex]Group the similar terms and simplify:
[tex]x^2\text{ - 8x + 15 }[/tex]Therefore the function that best describes the given plot is:
[tex]y=x^2\text{ -8x + 15 }\ldots\text{ Option A}[/tex]Which angle forms a linear pair with
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A linear pair angle must add up to 180 degrees. The angle that form a linear pair with angle MON is expressed below
[tex]\begin{gathered} \angle MON+\angle QOM=180\text{ degre}es \\ \text{therefore} \\ \angle MON\text{ and }\angle QOM\text{ are linear pair} \end{gathered}[/tex]Create a box and whisker plot (Label everything!!)
Answers
Solution
We have the following data:
11,16,11,15,9,10,11,13,15,17,10,14,17,10,13,15,11,12,12,11,12,14,15,15,13,10,15,12,11
We can calculate the median and the respective quartiles so we need to sort the data and we have:
9 10 10 10 10 11 11 11 11 11 11 12 12 12 12 13 13 13 14 14 15 15 15 15 15 15 16 17 17
Then we have:
Min = 9
Q1 = 11
Median = 12
Q3= 15
Max = 17
And then we can create the boxplot and we got:
Use your number sense to find the values for x and y that satisfy the equations.4y = 8
Answers
y = 2
Explanation:The given equation is 4y
Divide both sides of the equation by 4
[tex]\begin{gathered} \frac{4y}{4}=\frac{8}{4} \\ \end{gathered}[/tex]y = 2
Also, since we are asked to use our number sense, we can find what we will multiply by 4 to give 8
Since 4 x 2 = 8, then y = 2
Anjali's Bikes rents bikes for $15 plus $7per hour. Aliyah paid $57 to rent a bike.For how many hours did she rent the bike?
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From the question;
Anjali's Bikes rents bikes for $15 plus $7 per hour.
Let h represent the number of hours she rent the bike;
the total amount she will pay for h hours is;
[tex]T=15+7h[/tex]Given that; Aliyah paid $57 to rent a bike.
T = $57
The equation becomes;
[tex]T=15+7h[/tex]the sophomores are planning a homecoming dance they want to hire a band band a charges $600 to play for the night Band B charges $375 plus $10 for each ticket sold at the sophomore sold 30 tickets which band Chargers higher
Answers
• Charges $600 to play for the night.
Notice that this cost is to play the whole night, it's a fixed cost.
[tex]A=600[/tex]Band B.• Charges $375 plus $10 for each ticket sold.
,• The sophomore sold 30 tickets.
This band has a fixed cost plus a fee of $10, which is $300 more because they sold 30 tickets.
So, the cost of this band would be
[tex]B=350+10(30)=350+300=650[/tex]Therefore, Band B will charge more than Band A.Find the slope from real world application. At pizza galore a two topping pizza costs $9. A pizza with four toppings costs $12. How much does each topping cost?
Answers
The slope is:
[tex]m=\frac{12-9}{4-2}[/tex][tex]m=\frac{3}{2}=1.5[/tex]Hence, each topping of the pizza cost $1.5
Identify the underlined place and 27.3856. Then round the number to that place.
Answers
Based on the positiion of the underlined decimal places, the underlined number is in the hundredths place.
Rounding it off, next to 8 in the hundredths place is 5 in the thousandths place.
If the number is 5 or greater, we add 1 to the previous decimal place therefore it is rounded to 27.39
According to a pencil company's advertising campaign, 2 out of 3 students prefer the company's pencils to their competitor's pencils. A representative of the company went to a high school with 1479 students for alq & A session, and one of the students asked, "If this is true, in this high school, how many more students are there who prefer your pencils than students who prefer your competitor's pencils?" Help the company's representative come up with an answer. Assume that the company's claim is true.Part 1: How many of the students in the high school prefer the company's pencils? Part II: Out of 3 students, how many prefer the pencils of the company's competitor?Part III: How many of the students in the high school prefer the pencils of the company's competitor? Part IV: In the high school, how many more students are there who prefer the company's pencils than students who prefer their competitor's pencils?
Answers
Data:
2 of 3 students prefer the company's pencils to their competitor's pencils
high school with 1479 students
Part 1:You have 1479 students in total and know that 2 of 3 students prefer the company's pencils, then you multiply the toatl number of students by the factor 2/3
[tex]1479\cdot\frac{2}{3}=\frac{2958}{3}=986[/tex]Then, 986 students in the high school prefer the company's pencilsPart 2:Of 3 students 1 prefer the pencils of the company's competitorPart 3:Substract the number of students that prefer the company's pencils from the total of students:
[tex]1479-986=493[/tex]Then, 493 students in the high school prefer the pencils of the company's competitorPart 4:Substract the number of students who prefer the competitor's pencils fom the students that prefer the company's pencils:
[tex]986-493=493[/tex]Then, in the high school there are 493 students more that prefer the company's pencils than students who prefer their competitor's pencilsThe US consumes an average of 5.25 million metric tons of bananas per year. There are 317 million people in the US and there are 1000 kg in 1 metric ton. How many kilogram of bananas are consumed per person in a year? Round answer (except last one) to three significant digits. 365 days in a year.
Answers
The US consume 5.25 million metric tons of banana per year.
This is equivalent to 5.25 million x 1000kg = 5250 000 000 kg
US population = 317 million = 317 000 000
The number of kilogram of bananas consumed per person per year
= 5250 000 000 kg / 317 000 000
=16.6 kg
Therefore, the number of kilogram of bananas that are consumed per person per year is 16.6kg
Drag each shape to the correct location on the table. Each shape can be used more than once, but not all shapes will be used.
Consider the given square pyramid.
Answers
Vertical cross-section ⇒
Isosceles triangle, figure 5Horizontal cross-section ⇒
Square, figure 4Vertical cross-section through base and two lateral faces ⇒
Isosceles trapezoid, figure 1
Answer:
In the image
Hope this helps!
Step-by-step explanation:
