We first found sin θ using the Pythagorean identity, then found tan θ, and finally used the double-angle formula for tan to find tan 2θ.
Explanation:To find the value of tan 2θ when cos θ = 8/17 and θ is in Quadrant I, you need first to find the value of sin θ. Since we are in Quadrant I, both cos and sin are positive. You can use the Pythagorean Identity for sin, cos, and tan, which states sin² θ + cos² θ = 1, to find sin θ. Substituting the given value of cos θ in this identity, we can find that sin θ = sqrt(1 - (8/17)²) = 15/17.
With sin and cos known, we can now find tan θ using the formula tan θ = sin θ/cos θ which gives tan θ = (15/17)/(8/17) = 15/8.
Finally, to find tan 2θ, use the Double-Angle formula for the tangent, which states tan 2θ = 2 tan θ / (1 - tan² θ). Substituting tan θ = 15/8 into this formula, we get tan 2θ = 2 * (15/8) / (1 - (15/8)²).
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To find tan 2θ, given cos θ is 8/17 and θ is in the first quadrant, first find sin θ using the Pythagorean identity, then use the double-angle formula where tan 2θ equals 2 tan θ divided by 1 minus tan squared θ, yielding -2.
To find tan 2θ given that cos θ is 8/17 and θ is in the first quadrant, we first need to find the value of sin θ. Since θ is in the first quadrant, all trigonometric functions are positive. Using the Pythagorean identity, we have:
sin θ = √(1 - cos² θ)
Substituting cos θ = 8/17:
sin θ = √(1 - (8/17)²) = √(1 - 64/289) = √(225/289) = 15/17.
Next, we use the double-angle formula for tangent:
tan 2θ = (2 tan θ) / (1 - tan² θ)
To find tan θ, we use:
tan θ = sin θ / cos θ = (15/17) / (8/17) = 15/8
Now, substitute tan θ into the double-angle formula:
tan 2θ = (2 × 15/8) / (1 - (15/8)²)
= (30/8) / (1 - 225/64)
= (30/8) / (-161/64) = -1920/1288 = -15/7.5 = -2
The complete question is :
Given that [tex]\(\cos \theta = \frac{8}{17}\)[/tex] with [tex]\(\theta\)[/tex] in the first quadrant, determine [tex]\(\tan 2\theta\).[/tex]
A single person earns a gross biweekly salary of $780 and claims 6 exemptions. What is the person's net pay?
a.
It is the same as the gross pay.
b.
It is $11 more than the gross pay.
c.
It is $11 less than the gross pay.
d.
It is $13 less than the gross pay
Answer:
A. It is the same as the gross pay.
Explanation:
To get the amount of income tax withheld, we use the table attached.
We are given that:
1- This biweekly gross salary is $780, therefore, we will go to the row having a minimum payment of $780 (red border)
2- The number of claimed allowances is 6, therefore, we will go to the column with 6 claimed allowances (blue border)
We now find the intersection between the row and the column. As we can see in the table, it is zero.
This means that the deducted taxes based on the givens is zero which means that the net pay is the same as the gross pay.
Hope this helps :)
Final answer:
To calculate the net pay, deduct the taxes and other deductions from the gross salary. Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay.
Explanation:
To calculate the net pay, we need to deduct the taxes and other deductions from the gross salary. The main deductions to consider are Social Security, Medicare, and federal and state taxes. Let's break it down.
Calculate Social Security deduction: Gross biweekly salary x 6.2%.Calculate Medicare deduction: Gross biweekly salary x 1.45%.Calculate federal and state taxes: Gross biweekly salary x 15%.Add up all the deductions.Subtract the total deductions from the gross salary to find the net pay.
Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay. Therefore, the correct answer is option c. $11 less than the gross pay.
A pilot can fly an airplane 2240 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 40 mph, find the speed of the plane in still air.
In a recent local taste contest testing Coke against Pepsi it was found that 3/5 of all people surveyed preferred to taste the Coke. if 7,500 people were in the survey how many chose Pepsi ?
Answer: 3,000
Step-by-step explanation:
Given : In a recent local taste contest testing Coke against Pepsi it was found that [tex]\dfrac{3}{5}[/tex] of all people surveyed preferred to taste the Coke.
If 7,500 people were in the survey , then the number of people chose coke will be :-
[tex]\dfrac{3}{5}\times7500=3\times1500=4500[/tex]
Now, the number of people chose Pepsi = 7,500-4,500=3,000
Hence, there are 3,000 people who chose Pepsi.
If the slope of a straight line Is 0 and the y-intercept is -2, what is the equation of the line
it is simply y=-2
hoped I helped :)
Grape juice comes in a 64 oz bottle. Apple juice comes in a 80 ounce bottle. Both juices will be poured into cups of equal size so that no juice remains in either bottle. How many ounces is the largest possible cup that can be used for both juices?
Quadrilateral STWR is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary. Circle Q is shown with an inscribed quadrilateral labeled RSTW.
Answer:
Step-by-step explanation:
Arc STR measures twice the measure of angle R, and arc WRS measures twice the measure of angle T.
STR = 2 x ∠R and WRS = 2 x ∠T --- This is because of the Inscribed Angle Theorem
If the measure of arcs STR and WRS are added together, the total would be 360° since a full circle is made up of 360°.
So mSTR + mWRS = 360°
Substituting the angle measures of R and T in for the arcs, the equation becomes:
2 • ∠R + 2 • ∠T = 360°
Simplifying further:
2 • [∠R + ∠T] = 360°
∠R + ∠T = 360° / 2
∠R + ∠T = 180° - This proves that opposite angles of a quadrilateral inscribed in a circle are supplementary.
Exactly 1/20 of the students in mr.perez's class has a bird. what percentage of his students has a bird.
1) Which number rounds up when rounded to the nearest tenth?
55. 24
170.93
0.12
8.15
___________
2)
Estimate the value of 2968 + 9912 by rounding each number to the thousands.
14,000
13,000
12,000
7000
___________
3)
Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4
25 times 4 = 100
30 times 5 = 150
27 times 4 = 108
20 times 4 = 80
_____________
4)
Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.
30
33
123
130
___________
5)
Determine which answer is reasonable for 4. 8 times 9.2.
14
45.36
432
870.4
Answer:
1)8.15
2)13,000
3)25 x 4 =100
4) 130
5)45.3
Step-by-step explanation:
the point(-2,4) is on the line given by the equation below
A.y=x -4
B.y=x+4
C.y=2x
D.y=-2x
A tape that records one hour and 30 minutes on each side moves at cm a second through the tape player. How long, in metres, is the tape?
The points L(10,9) M(10,-5) N(-1,-5) and O(-1,9) form rectangle L M N O Which point is halfway between O and N.
A.) (-1,0)
B.) (-1,7)
C.) (-1,2)
D.) (2,-1)
Answer:
C.) (-1, 2)
Step-by-step explanation:
You can plot the points on a graph, or you can just find the midpoint:
midpoint = (O + N)/2 = ((-1, 9) +(-1, -5))/2 = (-1-1, 9-5)/2 = (-2, 4)/2
midpoint = (-1, 2)
is okay you lease a car at $415 per month for 4 years estimate the total cost of the least
The total cost of the least is $19,920.
Here,
lease a car at $415 per month for 4 years.
We have to find the total cost of the least.
What is Multiplication?
Multiplication is the process of calculating the total of one number multiplied by another.
Now,
lease a car at $415 per month for 4 years.
1 years = 12 month
4 years = 4 x 12 = 48 months.
Hence, total cost of the least = $415 x 48
= $19,920
So, The total cost of the least is $19,920.
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An investigator wants to estimate caffeine consumption in high school students. how many students would be required to estimate the proportion of students who consume coffee? suppose we want the estimate to be within 5% of the true proportion with 95% confidence.
We can solve this problem by referring to the standard probability distribution tables for z.
We are required to find for the number of samples given the proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value of z equivalent to:
z = 1.96
Since the problem states that it should be within the true proportion then p = 0.5
Now we can find for the sample size using the formula:
n = (z^2) p q /E^2
where,
p = 0.5
q = 1 – p = 0.5
E = estimate of 5% = 0.05
Substituting:
n = (1.96^2) 0.5 * 0.5 / 0.05^2
n = 384.16
Around 385students are required.
Given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
(A ) - {}
(B) - {a,e}
(C ) - {a, b, e, g, i, l, o, r, u}
What is the distance between the two points?
16. Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Valerie predicts she will be able to hold her breath for 31 second while underwater. If she actually held her breath for 34 seconds, what was Valerie's percent error? Round your answer to the nearest tenth of a percent.
If she actually held her breath for 34 seconds. Then the percentage error will be 8.82%.
What is the percentage error?The amount of error is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Valerie predicts she will be able to hold her breath for 31 seconds while underwater.
If she actually held her breath for 34 seconds.
Then the percentage error will be
[tex]\rm error \ \% = \dfrac{34-31}{34} \times 100\\\\\\error \ \% = \dfrac{3}{34} \times 100\\\\\\error \ \% = 8.82 \%[/tex]
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Find AB if BC = 4 , BD = 5, and AD =4
a study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 chevrolet cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 64 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.6 hours
Since we know the population standard deviation and the sample size is above 30, then we use the z statistic. The formula for z score is:
z = (x – u) / s
where,
x = the sample mean or sample value = 8.6 hours
u = the population mean = 8.4 hours
s = the standard deviation = 1.8 hours
Substituting into the given equation:
z = (8.6 – 8.4) / 1.8
z = 1.11
Using the standard probability distribution tables for z, a value of z = 1.11 has a probability of:
p = 0.8665
However this is still not the correct answer since this refers to the left of z. What we are trying to find is to the right of z since problem ask for exceeds 8.6 hours, therefore the correct answer is:
P (x>8.6 hours) = 1 – 0.8665
P (x>8.6 hours) = 0.1335
Therefore there is a 13.35% chance that the mean rebuild time is greater than 8.6 hours.
This only has one solution and I needz some halp with this. f - 6 = f + 8
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism? a base area of 4y square units and height of 4y2 + 4y + 12 units a base area of 8y2 square units and height of y2 + 2y + 4 units a base area of 12y square units and height of 4y2 + 4y + 36 units a base area of 16y2 square units and height of y2 + y + 3 units
Answer:
D!
a base area of 16y2 square units and height of y2 + y + 3 units
The area of a rectangle is 27 m^2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
Length: ___m
Width: ____m
Which graph represents the solutions to the inequality |2x − 4| less than or equal to 14?
A)number line with an open circle on negative 5, shading to the right and an open circle on 9, shading to the left
B) number line with a closed circle on negative 5, shading to the right and a closed circle on 9, shading to the left
C) number line with an open circle on negative 5, shading to the left and an open circle on 9, shading to the right
D) number line with a closed circle on negative 5, shading to the left and a closed circle on 9, shading to the right
Most teachers enjoy teaching students. Most teachers are college graduates. Assuming these two statements are true, do some college graduates enjoy teaching students?
Answer:
yes some some college graduates enjoy teaching students.
Step-by-step explanation:
This question is based on reasoning.
Most teachers enjoy teaching students.
Most teachers are college graduates.
A syllogism is a form of logical reasoning formed by the joining of two or more premises to arrive at a conclusion.
So, here we can say that yes some some college graduates enjoy teaching students.
Scotty is planning to order 1 cubic yard of topsoil for his 15' by 24' garden expecting that if evenly spread, he would end up with 2 inches of topsoil. Is he correct? Explain.
2 inches = 0.1666 feet
15 x 24 x 0.1666 = 59.98 cubic feet
1 cubic yard = 27 cubic feet
59.98 is greater than 27 so 1 cubic yard of topsoil will not be enough
A square is inscribed in a circle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
The probability of the point will be in the shaded region is 0.64 or 64%.
A square is inscribed in circle. Probability of point to be pick from the square to be find out.
Venn diagram are the Figures of probabilities to understand better.
Here, diameter of circle = d and radius r =d/2, edge of the square = a
By Pythagorean theorem,
a²+a²=d²
2a²= (2r)²
a²=2r²
Area of the square =2r²
Area of the circle = πr²
Now probability = Area of the square/Area of the circle
= 2r²/πr²
= 2/π
= 0.64
Thus, The probability of the point will be in the shaded region is 0.64 or 64%.
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Explain why you would want to keep some, but not all, receipts as part of your financial records.
You or we keep only those receipts
1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.
2. We keep those receipts of goods,which are under warranty period or for which you are paying EMI.
3. Receipt of those goods which has very high amount printed on it, and it mismatch with our income ,i.e not correlated with our income Someone can make false claim to entangle you.
Answer:
1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.
Step-by-step explanation:
Jason deposits $5,000 in a bank account that will pay him 4% simple interest annually. If Jason deposits no more than the initial 5,000 , how much money will be in the account at the end of 5 years ?
A ship traveled at an average rate of 22 miles per hour going west. It then traveled at an average rate of 12 miles per hour heading north. If the ship traveled a total of 158 miles in 9 hours, how many miles were traveled heading north?
If the revenue for the week is $2000, and labor cost consist of two workers earning $8 per hour who works 40 hours each, whay is labor cost aa percentage of revenue?