The solutions to the equation 15 tan^3 x=5 tan x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x =2.527, x = 5.669.
Explanation:The trigonometric equation provided in the question is 15 tan3 x=5 tan x. We can start solving this equation by dividing both sides by tan x, which gives 15 tan2 x = 5. Dividing again by 5, we get tan2 x = 1/3. The solutions to tan2 x = 1/3 are values of x in the interval [0, 2π) where the square of the tangent of x equals 1/3. However, these values cannot be easily computed, thus we use a calculator to approximate the results. We find the solutions to the equation by considering all angles whose tangent is either sqrt(1/3) or -sqrt(1/3). Therefore, the solutions for x in the interval [0, 2π) are approximately x = 0.6155, x = 3.757, x = 2.527, x = 5.669.
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how much does one pepper cost if they are priced three for 2.07
One pepper cost is 0.69.
What is Selling price?
Selling price is defined as the price that a customer pays to purchase a product.
Let one pepper cost is x,
Three peppers cost is 2.07,
x = ratio of the total cost of peppers to the number of peppers .
x= 2.07/3
x = 0.69
So, the peppers cost 69 cents each.
Hence, one pepper cost is 0.69.
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4. Meagan invests $1,200 each year in an IRA for 12 years in an account that earned 5%
compounded annually. At the end of 12 years, she stopped making payments to the
account, but continued to invest her accumulated amount at 5% compounded annually for
the next 11 years.
a. What was the value of the Ira at the end of 12 years?
b. What was the value of the investment at the end of the next 11 years?
c. How much interest did she earn?
a. The value of the Ira at the end of 12 years is $19,100.55.
b. The value of the investment at the end of the next 11 years is $32,668.43.
c. Interest earn is $18,288.43.
a. Using this formula to determine the value of the Ira at the end of 12 years
A=Pmt [(1+r)^n-1]/r
Let plug in the formula
A=1,200[(1+0.05)^12-1]/0.05
A=1,200[(1.05)^12-1]/0.05
A=$1,200(0.795856)/0.05
A=$955.02759/0.05
A=$19,100.55
b. The value of the Ira at the end of 11 years is:
$19,100.55(1+0.05)^11
=$19,100.55(1.05)^11
=$19,100.55(1.710339358)
=$32,668.43
c. Interest earn
Total investment=1200(12)
Total investment= $14,400
Now let calculate the interest earned
Interest earned = $32,668.43 - $14,400
Interest earned= $18,288.43
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Which of the following are vertical asymptotes of the function y=3cot(1/2x)-4? A. 3pi B. 2pi C. pi/2 D. 0
Answer:
B and D
Step-by-step explanation:
A moving company charges 0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 4 tons. About how much would it cost the family to move from New York to Florida?
Based on the table, which statement best describes a prediction for the end behavior of the graph of f(x)? As x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞, f(x) → ∞, and as x → –∞, f(x) → –∞ As x → ∞, f(x) → –∞, and as x → –∞, f(x) → –∞
Answer: The correct option is B, i.e., "As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞".
Explanation:
From the table it is noticed that the first row represents the value of x and the second row represents the value of f(x).
The value of f(x) is 14 at x = -5, after that the value of f(x) is decreased as the value of x increases.
The value of f(x) remains unchanged when the value of x approaches to 0 from 1.
The value of f(x) is -6 at x = 0, after that the value of f(x) is increased as the value of x increases.
From the table it is noticed that as the value of x approaches to positive infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow\infty[/tex]
From the table it is noticed that as the value of x approaches negative infinity the value of f(x) is also approaches to positive infinity.
[tex]f(x)\rightarrow\infty \text{ as }x\rightarrow-\infty[/tex]
These statement are shown in second option, therefore the second option is correct.
Answer:
The end behavior of the graph of the function f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞,
Step-by-step explanation:
Based on the table we could observe that the function f(x) is increasing to the left of -1 as well to the right of -1 and it attains the minimum value to be -6.
Hence, it can be predicted that the end behavior of the graph of the function f(x) goes to infinity in the left and also it goes to infinity in the right.
Hence, the statement that best describes the end behavior of the graph of f(x) is:
f(x) → ∞, and as x → –∞, f(x) → ∞ As x → ∞.
A store is offering a 20% discount on all sales over $50 if you purchase a T-shirt and a pair of jeans for $62.50 what is the amount of the discount you would receive
The discount on the purchase of a T-shirt and a pair of jeans costing $62.50 with a 20% discount policy is $12.50.
A store's discount policy offers 20% off for purchases over $50. The question involves calculating the discount amount when a T-shirt and a pair of jeans are purchased together for $62.50. To determine the discount, we simply multiply the total purchase amount by the discount rate.
Step-by-Step Calculation:
First, confirm the purchase amount qualifies for the discount. The combined cost of the T-shirt and jeans is $62.50, which is above $50, so the purchase qualifies for the discount.
Calculate the discount by multiplying the total purchase amount by the discount rate: $62.50 × 0.20 (which is the same as 20%).
Discount Amount = $62.50 × 0.20 = $12.50.
Therefore, the amount of the discount the customer would receive on the purchase of the T-shirt and jeans is $12.50.
Stella is renting a car for a business trip. The agency charges a flat rate of $60 plus $0.50 per mile every mile she drives over 40 miles. Stella's company will pay up to $270, excluding the cost of gasoline , for the use of the rental car. What is the number of miles Stella can drive the rental car without spending more then$270
270 =60 + 0.50(x-40)
270 =60 + 0.50x -20
210 =0.50x -20
230=0.50x
x=230/0.50 = 460 miles
check:
460-40 = 420
420*0.50=210 +60=270
she can drive 460 miles total
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x=49,6323º
Step-by-step explanation:
To solve this you just have to use the inverted sin X, remember that Sin=opposite/hyphotenuse
Sinx= 16/21
Sin x=,761904
x=-1Sin,761904
x=49,6323
So the measure of the angle X would be 49,6323.
What key features of a polynomial can be found using the fundamental theorem of algebra and the factor theorem?
Answer:
The key fundamental theorem of algebra says that degree of polynomial is equal to number of zeros in a function.The Factor Theorem states that a first degree binomial is a factor of a polynomial function if the remainder, when the polynomial is divided by the binomial, is zero.Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
n=128,
p=0.27
The mean is ______
. (Round to the nearest tenth as needed.)
The variance,
σ^2 is ______
(Round to the nearest tenth as needed.)
The standard deviation, ______
A binomial distribution is an experiment where there are two outcomes; Success and failure. In here, you are given n = 128 and p = 0.27. The formula for the variance of a binomial distribution is n*p(1 – p) or n*p*q*. They are equivalent because q = 1- p. We will use the first equation.
Variance = n*p*(1 – p)
Variance = 128*0.27*(1 – 0.27)
Variance = 25.23
To get the standard deviation, find the square root of the variance.
Standard deviation = sqrt (Variance)
Standard deviation = sqrt (25.23)
Standard deviation = 5.02
A telephone pole cast a shadow that is 34 m long find the height of the telephone pole if a statue that is 36 cm tall cast a shadow 77 cm long ?
Answer:
16 cm approximately
Step-by-step explanation:
We are given that a telephone pole cast shadow that is 34 m long .We are given that a statue that is 36 cm long and shadow of statue is 77 cm long.
We have to find the length of telephone pole
Let height of pole
Using direct proportion
[tex]\frac{x}{34}=\frac{36}{77}[/tex]
By multiply property of equality then we get
[tex]x=\frac{36}{77}\times 34[/tex]
x=[tex]\frac{1224}{77}[/tex]
x=15.896 cm
Hence, the height of telephone pole=15.896 cm=16 cm approximately
Margaret plans to deposit $500 on the first day of each of the next five years, beginning today. if she earns 4% compounded annually, how much will she have at the end of five years?
Its timed hurry lad
Evaluate the logarithm log8 (32)
Which unit rate is the lowest price per ounce? Choice A: 5 ounces of raisins for $1.49 Choice B: 12 ounces of raisins for $3.59
A = 1.49/5 =0.298 cents per ounce
B = 3.59/12 = 0.299 cents per ounce
so A has the lowest unit price
Determine the order in which an inorder traversal visits the vertices of the given ordered rooted tree.
What is a non example of a rate
write an expression for the area of the rectangle
whats the equation for
4n + 6 - 2n= 2 (n+3)
The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.
a is the .
The vertical shift, k, is the... length of a blade, height of a windmill, or numbers of rotations per minute.
a =
k =
20
5
30
Step-by-step explanation:
What is the positive root of the equation x 2 + 5x = 150?
The positive root of the given quadratic function is x = 10.
How to solve the quadratic function?We have the equation:
[tex]x^2 + 5x = 150[/tex]
First, we rewrite it as:
[tex]x^2 + 5x - 150 = 0[/tex]
Using the Bhaskara's formula, we will get:
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4*(-150)*1} }{2} \\\\x = \frac{-5 \pm 25 }{2}[/tex]
The positive solution is:
x = (-5 + 25)/2 = 10
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Savings account A and savings account B both offer APRs of 7%, but savings account A compounds interest quarterly, while savings account B compounds interest semiannually. Which savings account offers the higher APY? A. Savings account A, because it has more compounding periods per year B. Savings account B, because it has fewer compounding periods per year C. Savings account A, because it has fewer compounding periods per year D. Savings account B, because it has more compounding periods per year @countonme123 @ganeshie8
Answer:
The answer is Savings account B
Savings account A offers a higher APY because it compounds quarterly, which is more frequent than savings account B which compounds semiannually. More compounding periods per year lead to interest being earned on interest more often, resulting in a higher effective yield.
Annual Percentage Yield (APY) given that both accounts offer the same Annual Percentage Rate (APR) of 7%, but one compound quarterly and the other semiannually. The APY is a measure of how much interest an account will earn in a year, taking into account the effect of compounding.
Compounding more frequently results in a higher yield because interest is earned on interest more often. Account A compounds quarterly, meaning it does so four times a year, while Account B compounds semiannually, meaning it does so twice a year. As the frequency of compounding increases, so does the APY, because the money earns interest on the interest that has been added to the account more frequently.
Therefore, the correct answer is A. Savings account A, because it has more compounding periods per year, which means it will have a higher APY compared to savings account B which compounds less frequently.
The winner of a raffle will receive a 21-foot outboard boat. If 6000 raffle tickets were sold and you purchased 30 tickets, what are the odds against your winning the boat?
Answer: 199: 1.
Step-by-step explanation:
The odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.
Given , The winner of a raffle will receive a 21-foot outboard boat.
Total raffle tickets were sold = 6000
Number of tickets you have = 30
We assume that the lottery was fair , then, the number of possible outcome that you will win = 30
and the number of possible outcomes that one of the others wins = 6000-30= 5970
Then, the odds against your winning the boat = Number of possible outcomes that one of the others wins : Number of possible outcome that you will win
= 5970: 30 = 199:1 [∵[tex]\dfrac{5970}{30}=\dfrac{199}{1}[/tex]]
Hence, the odds against your winning the boat = 199: 1.
Evaluate x + sq root(yz) when x = 3, y = 2, and z = –8.
7i
3 + 4i
3 - 16i
3 + 16i
The value of the expression x + sqrt(yz) when x = 3, y = 2, and z = -8 is 3 + 4i.
Explanation:To evaluate the expression x + sqrt(yz), we substitute the given values for x, y, and z. Given x = 3, y = 2, and z = -8:
x + sqrt(yz) = 3 + sqrt(2*-8) = 3 + sqrt(-16) = 3 + 4i
Therefore, the value of the expression is 3 + 4i.
How many plants x should she plant in each row so that her 25 plants end up in a square (i.e., x plants in each of x rows)?
Bob drove from home to work at 50 mph. After work the traffic was heavier, and he drove home at 30 mph. His driving time to and from work was 1 hour and 4 minutes. How far does he live from his job?
At a concert there needs to be at least 1 member of staff working for every 150 members of the audience. If there are 20 members of staff, how many people are in the audience?
What is the simplified form of 5 - 4y + 2x - 3y - 2 + 5x?
A. 3 - 7y + 7x
B. 3 + 7y + 7x
C. 7 + 7y + 7x
D. 3 - y + 7x
show steps pls!
y varies inversely with x k = 1.4 What is the value of x when y is 5.6? A. x = 4 B. x = 1.4 C. x = 0.25 D. x = 7.84
To test μ for an x distribution that is mound-shaped using sample size n ≥ 30, how do you decide whether to use the normal or student's t distribution?
How many outfits are possible from 4 pairs of jeans 6 shirts and 2 pairs of shoes? Assume that outfit consists of 1 pair of jeans, 1 shirt, and 1 pair of shoes
multiply jeans by shirts by shoes
so 4 x 6 x 2 = 48 different combinations