Find sin(α) and cos(β), tan(α) and cot(β), and sec(α) and csc(β). The hypotenuse is 7 and side is 4.
Answers
The triangle is missing, so i have attached it.
Answer:
1)sin(α) = 4/7
2)cos(β) = 4/7
3)tan(α) = 4/√33
4)cot(β) = 4/√33
5)sec(α) = 7/√33
6)csc(β) = 7/√33
Step-by-step explanation:
(1) sin(α)
From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.
Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7
2) cos(β)
Cosine of an angle = adjacent side/hypotenuse.
In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7
3)tan(α)
tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.
Using the pythagoras theorem,
Adjacent side = √(7² - 4²)
Adjacent side = √(49 - 16)
Adjacent side = √33.
Thus, tan(α) = 4/√33
4) cot(β)
cot of an angle is the reciprocal of tangent of same angle.
The adjacent side to β is 4 while the opposite is √33.
So, tan(β) = (√33)/4
cot(β) = 1/tan(β)
cot(β) = 1/[(√33)/4]
cot(β) = 4/√33
5)sec(α)
sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.
Thus, sec(α) = 1/cosα = 7/√33.
6) csc(β)
Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.
Thus, csc(β) = 1/sin(β) = 7/√33
Related Questions
A researcher is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 92 people are unemployed. The following is the setup for this hypothesis test:
H0:p=0.05 Ha:p<0.05
Required:
Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Answers
Answer:
[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed
[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]
Step-by-step explanation:
Information given
n=1500 represent the random sample taken
X=92 represent the number of people unemployed
[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed
[tex]p_o=0.05[/tex] is the value to value to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true proportion is lower than 0.05 or no and the system of hypothesis are::
Null hypothesis:[tex]p \geq 0.5[/tex]
Alternative hypothesis:[tex]p < 0.5[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]
Item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
Answers
Answer:
Step-by-step explanation:
item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm
You did not state the diameter or radius of the window
so, i will use 90cm as the diameter of the window
First, I'd calculate the half circumference of the window.
The formula for circumference is [tex]c = 2\pi r[/tex],
Half of it would just be [tex]c/2 = r\pi[/tex]
Since our diameter is 90 cm, our radius is 45 cm.
Circumference =
[tex]=45\pi \\= 141.37 cm[/tex]
circumference is also the same with perimeter
so, the answer is 141.37cmto nearest tenth = 141.4cmAnswer:
141.4cm
Step-by-step explanation:
=>
please give barinlist
What is the dominan of the function f(x)= -6x+7
Answers
Answer:
(-∞,∞)
Step-by-step explanation:
It's just a line
Answer:
INFINITIE, INFINITIE
Step-by-step explanation:
Area of composite shapes
Find the area of the shape shown below.
Answers
Answer:
32 units
Step-by-step explanation:
The large triangle on top has an area of 20, cause 4*10 = 40
40/2 = 20.
the square on the bottom has an area of 4, well, cause 2*2 = 4.
The smaller triangle on the left has an area of 2, cause 2*2=4
4/2=2
The triangle on the right, has an area of 6, because 6*2=12
12/2=6
20+4+2+6 = 32
Answer:
32 Units =)
Step-by-step explanation:
Find the sum of the geometric series 1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}
Answers
Answer:
S20 ≈ 4.942
Step-by-step explanation:
Sum of a geometric series is expressed as Sn = a(1-rⁿ)/1-r if r<1
a is the first term
r is the common ratio
n is the number of terms
Given the geometric series
1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}
Given a = 1,
r = 0.8/1 = 0.8²/0.8 = 0.8
n = 20 (The total number of terms in the series is 20)
Substituting this values in the formula above.
S20 = 1(1-0.8^20)/1-0.8
S20 = 1-0.01153/0.2
S20 = 0.9885/0.2
S20 ≈ 4.942
The length of human pregnancies from conception to birth is normally distributed with mean 266 days and standard deviation 16 days. What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
Please put the answer in the standard deviation percentages!
Answers
Answer:
68% of the lengths of pregnancies fall between 250 days and 282 days.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 266
Standard deviation = 16.
What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?
250 = 266 - 16
So 250 is one standard deviation below the mean.
282 = 266 + 16
So 282 is one standard deviation above the mean.
By the Empirical Rule, 68% of the lengths of pregnancies fall between 250 days and 282 days.
Answer:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days
Step-by-step explanation:
Let X the random variable that represent the The length of human pregnancies from conception to birth, and for this case we know the distribution for X is given by:
[tex]X \sim N(266,16)[/tex]
Where [tex]\mu=266[/tex] and [tex]\sigma=16[/tex]
We are interested on this probability
[tex]P(250<X<282)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]
And we can find this probability with this difference and using the normal standard table or excel:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]
So then we will have approximatetly 68.26% of the values between 250 and 282 days
what is the arc measure of minor arc DE in degrees?
help lol
Answers
Answer:
DE= 39°
Step-by-step explanation:
(4w+ 4 )+(4w+8)= 180
Solve for w
8w + 12 = 180
8w = 180-12
8w = 168
W= 21°
(4w+ 4)+(2w+11)+DE = 180
But w= 21°
((4*21 )+4)+((2*21)+11)+DE = 180
88 + 53 + DE = 180
DE = 180-88-53
DE= 39°
PLEASE HELP ME
Angles PTQ and STR are vertical angles and congruent.
Circle T is shown. Line segments T P, T Q, T R, and T S are radii. Lines are drawn to connect points P and Q and points S and R to create secants. Angles P T Q and R T S are congruent.
Which arcs are congruent?
Arc S P and Arc S R
Arc P Q and Arc S R
Arc P Q and Arc Q R
Arc S P and Arc P R
Answers
Answer:
PQ AND SR on ED
Step-by-step explanation:
Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
What is vertical angle theorem?The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.
For the given situation,
Angles PTQ and STR are vertical angles and congruent.
Line segments T P, T Q, T R, and T S are radii.
So, T P = T Q = T R = T S.
The two sides T P = T Q and T R = T S and [tex]\angle PTQ = \angle RTS[/tex],
then by SAS similarity theorem two triangles,
Δ PTQ ≅ Δ STR.
When two triangles are congruent, then the corresponding arc are also congruent.
The congruent central angles intercept congruent arcs PQ and SR.
Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.
Learn more about vertical angle theorem here
https://brainly.com/question/17702030
#SPJ2
Solve the equation: 7(8 - 5z) + 17 = 3
Answers
Answer:
z=2
Step-by-step explanation:
56-35z+17=3
73-35z=3
-35z=-70
z=2
A triangle undergoes a sequence of transformations. First the triangle is dilated by a scale factor of 1/3 about the orgin. The the triangle is reflected over the x axis. Finally, the triangle is translated left 3 units and up 2 units. How does the image triangle compare to the preimage triangle
Answers
Answer:
Since there was a dilation, the two triangles will be similar. The scale factor is less than one and is a reduction, therefore, the image will be smaller than the pre-image.
greatest common factor of (12x^3-9x^2)+(8x-6)
Answers
Answer:
[tex](4x-3)(3x^2)+2)[/tex]
Step-by-step explanation:
Answer:
The greatest common factor for the first parenthesis is 3 and the greatest common factor for the second parenthesis is 2
Step-by-step explanation:
Hope this helps plz mark brainliest!
What’s the correct answer for this question?
Answers
Answer:
C.
Step-by-step explanation:
60° in Radians = 1.047
Using Formula
s=rθ
s= 7(1.047)
s ≈ 7.36
what is the equation of the graph that represents the parent function f(x) = x4 stretched vertically by a factor of 2, and then shifted down 3 spaces
Answers
Answer:
f(x) = 2x^4 - 3
Step-by-step explanation:
First multiplying by 2 giving f(x) = 2x^4 stretches it vertically by factor 2.
Then subtract 3 to move it down 3 units:
f(x) = 2x^4 - 3.
Answer:
g(x)=2x^4-3
Step-by-step explanation:
Sue invests £9000 in an account for one year.
At the end of the year, interest is added to the account.
Sue pays tax on this interest at a rate of 20%.
She pays £30.24 tax.
Work out the percentage interest rate for the account.
Answers
Answer:
The interest rate = 1.68%
Step-by-step explanation:
Sue invests £9000 in an account for one year.
She pays £30.24 at a rate of 20%
So 20% of the interest =£ 30.24
Let the interest be x
X0.2= 30.24
X=£ 151.2
The total interest was£ 151.2
The rate R at which generated this interest
R = (100*151.2)/(1*9000)
R= 15120/9000
R= 1.68%
The interest rate = 1.68%
Thomas is in charge of selling roses for the Graduation dance. The roses sell for $3.50 each. He estimates that the expenses of the roses will be $30. Thomas wants to write an equation for the profit.
Answers
Answer:
P= $3.5x -$30
Step-by-step explanation:
Let the number of roses Thomas bought and sold be x.
Hence the total selling price would be;
$3.5 × x= $3.5x
The profit = selling price-expenses
P= $3.5x -$30
Confidence Interval Concept Check 3 1 point possible (graded) In a new experiment consisting of 150 couples, 75 couples are observed to turn their heads to the left and the remaining 75 couples turned their heads to the right when kissing. Let p denote the (unknown) parameter which specifies the probability that a couple turns their head to the right.
Which of the following statements are correct regarding this experiment? You are given that exactly one but not both of choices 3 and 4 is correct. Also, assume that the given confidence intervals are an instance of a random interval computed upon observing the given data.
10,05] is a 50% asymptotic confidence interval for p. [0.5, 1] is a 50% asymptotic confidence interval for p. 10.466, 0.533 is a 50% asymptotic confidence interval for p. 10.48, 0.52 is a 50% asymptotic confidence interval for p. O
Answers
Answer:
Step-by-step explanation:
There are four options given above.
P specifies the probability that a couple turns their head to the right when kissing. P is 0.5 because the probability of turning right when kissing is 75÷150 = 1/2 = 0.5
Assuming that the given confidence intervals are an instance of a random interval computed upon observing the given data,
The correct statements are statements 1 and 4
PLEASE ANSWER ASAP (exponential and logarithms)
Answers
Answer:
1.4650 (the first option in the list of possible answers)
Step-by-step explanation:
Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:
[tex]2+3^x=7\\3^x=7-2\\3^x=5[/tex]
Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":
[tex]3^x=5\\x=log_3(5)[/tex]
In order to find this logarithm, we use the change of base formula:
[tex]log_3(5)=\frac{log(5)}{log(3)} =1.46497...[/tex]
which rounded to four decimals gives: 1.4650
I don’t understand? Please help!
Answers
The graph of f(x) is reflected across the x-axis. Write a function g(x) to describe the new graph. g(x)=
Answers
Answer: g(x) = -f(x)
Step-by-step explanation:
When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y)
In this case we have a function reflected, and we know that we can write a function as (x, f(x))
So when we reflect it, the result will be (x, g(x)) = (x, -f(x))
So we have g(x) = -f(x)
divide a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark to the right of 0?
Answers
Answer:
1/8
Step-by-step explanation:
since it is divided to 8 equal parts then the first tick is 1/8
correct answer gets brainliest Please explain as well 3x+5y=21 4x-2y = -24
Answers
Answer:
x=-3 y=6
Step-by-step explanation:
it was a easyone ,don't forget to mark me as a brainlinest .☺️
What is the volume of the cylinder below?
O A. 70K units
O B. 2257, units
O C. 1757 units
O D. 357 units
Answers
Answer:
V = V = 175 pi units^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V =pi ( 5)^2 ( 7)
V = 175 pi units^3
Jar A contains four liters of a solution that is 45% acid. Jar B contains five liters of a solution that is 48% acid. Jar C contains one liter of a solution that is k % acid. From jar C, 2/3 liters of the solution is added to jar A, and the remainder of the solution in jar C is added to jar B. At the end both jar A and jar B contain solutions that are 50% acid. Find k.
Answers
Answer:
k= 80%
Step-by-step explanation:
Jar A contains 4*0.45 L acid, and 4 L of a solution of acid.
Jar B contains 5*0.48 L acid., and 5 L of a solution of acid.
Jar C contains 1*k/100 = k/100 acid, and 1 L of a solution.
50% = 0.5
For jar A.
(2/3)*k/100 L acid is added to jar A.
Now jar A contains 4*0.45 L + (2/3)*k/100 L acid, and it has (4+2/3)L of a solution.
L solute/L solution = 0.5
[4*0.45 L + (2/3)*k/100 L]/(4+2/3)L = 0.5
[1.8 + (2k/300)]/[(12+2)/3] = 0.5
[1.8 + (2k/300)]/[14/3] = 0.5
[1.8 + (2k/300)]= 0.5*(14/3)
(2k/300) = 0.5*(14/3) - 1.8
2k = (0.5*(14/3) - 1.8)*300
k = (0.5*(14/3) - 1.8)*300/2 =80
k= 80%
We also can find k using jar B.
(1/3)k/100 L acid is added to jar B.
Now jar B contains 5*0.48 L+ (1/3)k/100 L acid, and it has (5+1/3) L of a solution.
L solute/L solution = 0.5
[5*0.48 L+ (1/3)k/100 L ]/(5+1/3)L= 0.5
[5*0.48 + (1/3)k/100 ]/(5+1/3)= 0.5
This equation also gives k=80%
Check.
We can check at least for jar A.
Jar A has 4L solution and 4*0.45=1.8 L acid.
2/3 L of the solution from jar C was added, and now we have 4 2/3 L of solution.
(2/3)* 80%= (2/3)*0.8 acid was added from jar C.
Now we have [1.8 +(2/3)*0.8] L acid in jar A.
L solute/L solution = [1.8 +(2/3)*0.8] L /(4 2/3) L = 0.5 or 50% as it is given that jar A has 50% at the end.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answers
Answer:
4
4
Step-by-step explanation:
x litres of 15% solution + y litres of 19% solution= 8 gallons of 17% solution
disinfectant content of the final solution= 8*0.17= 1.36 gallons
0.15x+0.19y=1.36
x+y= 8 ⇒ x=8-y
0.15*(8-y)+0,19y= 1.361.2-0.15y+0.19y=1.360.04y=0.16y= 0.16/0.04y=4 gallonsx= 8-4= 4 gallonsWhat assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?
Answers
Answer:69
Step-by-step explanation:
Because i am smart.
Zara travelled in a train moving at an average speed of 120km/h and covered a distance of 40km towards East. i. Calculate the time taken by the train to cover this distance.
Answers
Answer:
20 minutes
Step-by-step explanation:
Distance= 40 km
Speed= 120 km/h
Time= distance/speed= 40/120= 1/3 hour= 20 min
Answer:
Time = 0.33 hrs
Step-by-step explanation:
Given:
Speed = 120 km/hr
Distance = 40 km
Required :
Time = ?
Formula:
Speed = Distance/Time
Solution:
Time = Distance / Speed
Time = 40/120
Time = 0.33 hrs
Is 1.06 greater than 0.6
Answers
Answer:
it is
Step-by-step explanation:
Find the future value of 575 at 5.5% compounded quarterly for 5 years. Round to the nearest cent
Answers
Answer:
Future value = $755.61 ( to the nearest cent)
Step-by-step explanation:
The formula for calculating the future value of an invested amount compounded periodically for a number of years is given as:
[tex]FV = PV (1+\frac{r}{n} )^{n*t}[/tex]
where:
FV = future value = ???
PV = present value = $575
r = interest rate in decimal = 5.5% = 0.055
n = number of compounding periods per year = quarterly = 4
t = time of investment = 5 years
∴ [tex]FV = 575 (1+\frac{0.055}{4} )^{4*5}[/tex]
[tex]FV = 575 (1+0.01375)^{20}\\FV = 575 (1.01375 )^{20}\\FV = 575 * 1.3141\\FV = 755.607[/tex]
∴ Future value = $755.61 ( to the nearest cent)
The sum of three consecutive even integers is 186. Find the Integers.
Answers
Answer:
60, 62, 64
Step-by-step explanation:
Let x, (x + 2) & (x+ 4) be three consecutive even integers.
[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]
Hence, the three consecutive even integers are 60, 62 and 64.
Which of the following source documents is used to summarize all of the costs incurred for a specific job?
Answers
Answer:
job cost sheet.
Step-by-step explanation:
When planning or working on a specific project/job all the actual costs that are incurred for that job are written down in the job cost sheet. This report is an entire compilation that should be created by the accounting department and then distributed to all the members of the management department who then analyze it and determine whether the job was correctly bided. This sheet gets updated as the job is undergoing and fully completed when the job is closed.
