The only solutions of the given equation in the interval (0, 2π) are the values of x for which sinx = 0. These are: x = 0π, 1π, 2π. So the solutions are x = 0π, π, 2π, or in terms of degrees, x = 0°, 180°, 360°.
How to Solve the Equation?The given equation is sinx(cosx−4)=0.
To solve this equation, we need to find the values of x in the interval [0, 2π) that make the product sinx(cosx−4) equal to zero.
To do that, we can set each factor equal to zero and solve for x:
sinx = 0 or cosx − 4 = 0
If sinx = 0, then x can be any multiple of π, since sinx = 0 for all even multiples of π (0, ±π, ±2π, ...), and for odd multiples of π (±π/2, ±3π/2, ...).
If cosx − 4 = 0, then cosx = 4, which has no real solutions in the interval [0, 2π).
Therefore, the only solutions of the given equation in the interval [0, 2π) are the values of x for which sinx = 0. These are:
x = 0π, 1π, 2π
So the solutions are x = 0π, π, 2π, or in terms of degrees, x = 0°, 180°, 360°.
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Please answer
The solution to an inequality is shown on the number line.
Which inequality matches the number line?
The inequality that matches the number line is given as follows:
2y + 3 ≥ -1
What are the inequality symbols?The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:
> x: the amount is greater than x -> the number is to the right of x with an open dot at the number line. -> points above the dashed horizontal line y = x on the coordinate plane.< x: the amount is less than x. -> the number is to the left of x with an open dot at the number line. -> points below the dashed horizontal line y = x on the coordinate plane.≥ x: the amount is at least x. -> the number is to the right of x with a closed dot at the number line. -> points above the solid vertical line y = x on the coordinate plane.≤ the amount is at most x. -> the number is to the left of x with a closed dot at the number line. -> points above the dashed vertical line y = x on the coordinate plane.The inequality marked on the number line is given as follows:
y ≥ 2.
The equivalent inequality is the one with the same solution, hence:
2y + 3 ≥ -1
2y ≥ -4
y ≥ -4/2
y ≥ -2.
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Carrie is told that a tree is 17 meters high. If the angle from where she is standing to the top of the tree is 53 degrees, how far from the tree is she standing?
Check the picture below.
Make sure your calculator is in Degree mode.
[tex]\tan(53^o )=\cfrac{\stackrel{opposite}{17}}{\underset{adjacent}{x}}\implies x=\cfrac{17}{\tan(53^o )}\implies x\approx 12.81~meters[/tex]
The law of
applies during online sales
of shoes that is when consumers rush to buy products at 50% discounts.
The law of
The law of demand applies during online sales of shoes; that is when consumers rush to buy products at 50% discount.
What is the law of demand?In Mathematics and Economics, the law of demand can be defined as an economic theory which states that there exist a negative relationship between the price of a product (good) and the quantity of the product (good) that is being demanded by consumers.
This ultimately implies that, holding all the other factors constant, there would be a significant decrease (fall or decline) in the demand for a product (good) and service when the price of a product (good) and service in the market increases (rises), and vice-versa in accordance with the law of demand.
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Complete Question:
The law of ___________applies during online sales of shoes; that is when consumers rush to buy products at 50% discount
3.) Which is greater: xº or 0x? Justify your answer
For the given expression - xº is greater than 0x as, xº = 1 and 0x = 0.
Explain about the exponents:The power or exponent of a number tells us how many times that number must be multiplied by itself in order to utilise it in a multiplication. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
a product's lawAccording to the law, we must add the exponents to obtain the product of exponential statements that have the same base.
quotient lawAccording to the law, we must subtract the exponents in order to divide two exponential expressions with the same base.
Given expression:
xº = 1 (any number raised to power 0 is always 1)
0x = 0 (any value multiplied with 0 becomes 0).
Thus, xº is greater than 0x as, xº = 1 and 0x = 0.
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9 x 3^15 can be written as 3^n.
What is the value of n?
Answer: n = 17
Step-by-step explanation: We can simplify 9 x 3^15 by first writing 9 as 3^2. Then we can use the rule that says when you multiply two numbers with the same base, you can add their exponents. So:
9 x 3^15 = 3^2 x 3^15 = 3^(2+15) = 3^17
Therefore, n = 17.
8 + 4 to the second power divided by 2
Consider the line shown on the graph.
Enter the equation of the line in the form v = mx + b
where m is the slope and b is the y-intercept.
An equation of this line in slope-intercept form is equal to y = 2x + 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 + 1)/(0 + 4)
Slope (m) = 8/4
Slope (m) = 2
At data point (0, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 7 = 2(x - 0)
y - 7 = 2x
y = 2x + 7
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An initial amount of $3600 is invested in an account at an interest rate of 8% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after three years.
The formula for calculating the balance of an account with continuous compounding is given by A = Pe^(rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), t is the time in years, and e is the mathematical constant approximately equal to 2.71828.
In this case, the initial principal balance P is $3600, the annual interest rate r is 8% or 0.08 as a decimal, and the time t is 3 years. Plugging these values into the formula gives us:
A = 3600 * e^(0.08 * 3)
Evaluating this expression gives us a final amount of approximately $4293.25 in the account after three years.
if i have 45 days left of school and need to do 69 lessons how many lessons a day would i need to do?
I just picked a random subject so....
500 points if answered correctly
Step-by-step explanation:
Simply divide lessons by days
69 lessons / 45 days = 1 8/15 = 1.53 lessons per day
What is the length of AC₂
Enter your answer in the box.
units
if m(x)=sin²(x), then m'(x)=?
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 9 characters long, and that each character is either a lowercase letter, (a, b, c, etc.), an uppercase letter (A, B, C, etc.) or a numerical digit (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9). Assume that the hacker makes random guesses. What is the probability that the hacker guesses the password on his first try? Enter your answer as a decimal or a fraction, not a percentage.
The probability that the hacker guesses the password on their first try is extremely low.
What is the probability that the hacker guesses the password on his first try?
There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are [tex]62^{9}[/tex] possible passwords.
The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:
Probability = 1 / ([tex]62^{9}[/tex])
Using a calculator, this can be simplified to approximately 1.2 x [tex]10^{-16}[/tex]
Therefore, the probability that the hacker guesses the password on their first try is extremely low.
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Someone tell me of number 16 is correct please.
The volume of the composite figure that comprises two cuboids is calculated as: 150 ft³.
How to Find the Volume of a Cuboid?The volume of a cuboid is given by the formula:
V = l × w × h
where V is the volume, l is the length, w is the width, and h is the height of the cuboid.
The shape in number 16 comprises two cuboids. Find each and add together.
Volume of smaller cuboid = l × w × h = 5 × 3 × 2
= 30 ft³
Volume of larger cuboid = l × w × h = 10 × 6 × 2
= 120 ft³
The total volume = 150 ft³
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An actuarial study finds that in a sample of 2000 18-year-old drivers, 124 are involved in an accident.
cost of such an accident to the insurance company is $15 000. If the company wants to make a 20% profit on policies, what should they charge 18-year-old drivers?
Answer: Let's start by calculating the probability that an 18-year-old driver is involved in an accident:
P(accident) = 124/2000 = 0.062
Let's assume that the insurance company pays the full cost of the accident, which is $15,000. Then the expected cost of covering one 18-year-old driver is:
Expected cost = P(accident) x Cost of accident = 0.062 x $15,000 = $930
If the insurance company wants to make a 20% profit on policies, they need to charge a premium that covers their expected cost plus their desired profit. The premium, denoted by P, can be calculated as follows:
P = (Expected cost + Desired profit) / (1 - Profit margin)
where Profit margin is the percentage of the premium that represents the profit. In this case, Profit margin is 20%, or 0.20.
Substituting the values we have calculated, we get:
P = ($930 + 0.20 x $930) / (1 - 0.20)
= $1,236.00
Therefore, the insurance company should charge 18-year-old drivers a premium of $1,236.00 to make a 20% profit on policies.
Step-by-step explanation:
The distribution of scores on a standardized test is approximately normal with
a standard deviation of 40. Suppose a sample of 100 students had a mean
score of 180.23.
Find the margin of error for a 90% confidence interval for the mean score of all
students on this test. Round your answer to two decimal places.
Answer: The margin of error (ME) for a 90% confidence interval using a normal distribution with a known population standard deviation is given by:
ME = z* (σ/√n)
where z* is the z-score corresponding to the desired confidence level (in this case, 90% confidence), σ is the population standard deviation, and n is the sample size.
Using a z-score table or calculator, we find that the z-score corresponding to a 90% confidence level is 1.645.
Substituting the given values, we have:
ME = 1.645 * (40 / √100) = 6.58
Therefore, the margin of error for a 90% confidence interval for the mean score of all students on this test is 6.58. We can report the 90% confidence interval as:
180.23 ± 6.58 or (173.65, 186.81)
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q =
Answer:
Step-by-step explanation:
If P = 3x² - x + 2 and Q = x² + 5x - 6, then P+ Q = 3x² - x + 2 + x² + 5x - 6 =
4x^2 +4x - 4
D = 16 + 64 = 80
x12 = [tex]\frac{-4+-\sqrt{80} }{8}[/tex]
1. a^2 – 3a + 2
2. b^2 + 4b + 3
3. c^2 +6c + 5
4. x^2 +8x + 7
5. y^2 +10y + 9
6. r^2 +12r +11
7. m^2 + 5m +4
8. a^2 -8a + 7
9. x^2 -12x +11
10. x^2 + 11x +10
11. t^2 -18t + 72
12. r^2 -16r + 60
13. z^2 -20z + 100
14. y^2 + 4y -5
15. b^2 -2b -8
16. x^2 – 3x – 40
17. 2x^2 – 5x +2
18. 3x^2 + 10x + 3
19. 2x^2 + 11x + 5
20. 2x^2 + 7x + 6
Please Write Your Answer Below:
Answer:
1. (a-1)(a-2)
2. (b+1)(b+3)
3. (c+1)(c+5)
4. (x+1)(x+7)
5. (y+1)(y+9)
6. (r+1)(r+11)
7. (m+1)(m+4)
8. (a-1)(a-7)
9. (x-1)(x-11)
10. (x+1)(x+10)
11. (t-6)(t-12)
12. (r-6)(r-10)
13. (z-10)^2
14. (y+5)(y-1)
15. (b-4)(b+2)
16. (x-8)(x+5)
17. (2x-1)(x-2)
18. (3x+1)(x+3)
19. (2x+1)(x+5)
20. (2x+3)(x+2)
Flying against the wind, an airplane travels 2370 kilometers in 3 hours. Flying with the wind, the same plane travels 10160 kilometers in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?
In still air, the jet's speed is 1030 mph, while the wind's speed 240 miles per hour.
What is velocity?It is the rate of change of an object's position with regard to time and a frame of reference. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It has a metre per second SI unit (ms-1).
What is speed?The distance travelled in relation to the time it took to travel that distance is how speed is defined. As speed simply has a direction and no magnitude, it is a scalar quantity.
Jet's velocity against wind is 2370/3=790 mile per hour and flying with wind it is 10160/8= 1270 miles per hour.
According to question,
Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.
As such its velocity against wind is x−y and with wind is x+y and therefore
x−y=790 and x+y=1270
Adding the two 2x= 2060 and x=1030
and y=240
Hence velocity of jet in still air is 1030 miles per hour and velocity of wind is 240 miles per hour.
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1/2x + 2y, when x = 7 and y=8 help me please
Answer:
39/2 or 19.5
Step-by-step explanation:
To evaluate the expression 1/2x + 2y when x = 7 and y = 8, we can substitute the values of x and y into the expression and perform the necessary calculations.
Given:
x = 7
y = 8
Plugging these values into the expression, we get:
1/2(7) + 2(8)
Now, we can follow the order of operations (PEMDAS/BODMAS) to simplify the expression:
1/2(7) + 2(8)
= 1/2 * 7 + 2 * 8 (Multiplication has higher precedence than addition)
= 7/2 + 16 (Performing the multiplications)
= 7/2 + 32/2 (Finding the common denominator for addition)
= (7 + 32)/2 (Adding the numerators)
= 39/2 (Simplifying the fraction)
So, the value of the expression 1/2x + 2y when x = 7 and y = 8 is 39/2 or 19.5.
Need help asap!!
Find the value of X
The answer is X + 5 = 10
X = 5
can anyone explain how to solve this
Mortgage (monthly)
Amount
$985.64
Cell phone (monthly)
$58.30
Groceries (twice a month
$154.00
Clothing (monthly with 25% job-related) $180.00
Water & electric (monthly)
S128.40
Weekly dinner & movie
$55.00
Property taxes (6 months)
$684.80
Car insurance (guarterly)
$330.00
Your realized income is $2.943.20/month. How much are your fixed expenses each month? How much could you save per month if you take 25% of your discretionary monies and put it in a savings account?
Answer:
To calculate the fixed expenses each month, we need to add up all the monthly expenses:
Mortgage: $985.64
Cell phone: $58.30
Groceries: $154.00 x 2 = $308.00
Clothing (with 25% job-related): $180.00
Water & electric: $128.40
Weekly dinner & movie: $55.00 x 4 = $220.00
Total monthly fixed expenses: $1,880.34
To calculate how much could be saved per month, we need to first calculate the discretionary income:
Realized income: $2,943.20
Fixed expenses: $1,880.34
Discretionary income: $2,943.20 - $1,880.34 = $1,062.86
25% of discretionary income: 0.25 x $1,062.86 = $265.72
Therefore, the amount that could be saved per month by putting 25% of the discretionary income in a savings account is $265.72.
In a 30°-60°-90° triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was 1500
grams and mass was decreasing by 10% per day. Determine the mass of the
radioactive sample at the beginning of the 10th day of the experiment. Round to the
nearest tenth (if necessary).
The radioactive isotope has a final mass of 523 grams.
How to predict the mass of a radioactive isotope in time
Herein we find the case of a radioactive isotope, whose mass is decreasing exponentially in time. Whose expression is described below:
m(x) = a · (1 - r / 100)ˣ
Where:
a - Initial mass of the radioactive isotope, in grams.r - Decrease rate, in percentage.x - Time, in daysIf we know that a = 1500, r = 10 and x = 10, then the mass of the radioactive isotope is:
m(10) = 1500 · 0.90¹⁰
m(10) = 523.018
The final mass of the radioactive isotope is equal to 523 grams.
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Solve on the interval [0,2pi):
1 - cos theta = 2-√3/2
Thus, the solution of the given cosine function is obtained for the angles- θ = 30º and θ = 330º between the intervals of [0,2pi).
Explain about the cosine function:The ratio of the triangle's side next to the angle to the hypotenuse is known as the cosine function. Thus, the cosine function does have a period of 2π, we can say.
Normally, radians rather than degrees are used when examining the cosine function in this manner. The common unit of measurement for angles in mathematics is the radian. 360° is equivalent to two radians, or one full circle.
Given data:
Function: 1 - cosθ = (2-√3)/2Interval - [0,2pi)1-cosθ = (2-√3)/2
cosθ = 1-(2-√3)/2
isolating the cosθ function:
cosθ = 1-(1-[√3/2])
cosθ = 1-1+√3/2
cosθ = √3/2
Now,
cos is √3/2 for ∏/6 = 30º and for 11∏/6 = 330º (Interval - [0,2pi))
Thus, the solution of the given cosine function is obtained for the angles-
θ = 30º and θ = 330º between the intervals of [0,2pi).
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Maya kept track of the points she scored during her first five basketball games in the table shown.Game Points Scored
1 8
2 12
3 10
4 6
5 14
QuestionAfter game 6, her mean number of points scored per game is 9.How many points did Maya score in game 6? A. 4 B. 8 C. 9 D. 10
Answer: c. 9
Step-by-step explanation:
Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.
scatter plot titled students' data, with points plotted at 1 comma 80, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 90, and 4 comma 98, and a line of fit drawn passing through the points 0 comma 70 and 1 comma 75
Find the slope of the line of fit and explain its meaning in the context of the data.
80; a student who studies for 0 hours is predicted to earn 80% on the test
70; a student who studies for 0 hours is predicted to earn 70% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
The y-intercept of the line, which is represented by the point (0,70) on the line of fit, indicates that a student who performs no studying is expected to receive a grade of 70%.
what is slope ?The angle of inclination of a linear or a segment of a line that connects two points is measured in mathematics as slope. Its definition is the ratio of the rise, which is the vertical difference between two points, to the run, which is the horizontally change between those same two sites. The letter "m" is frequently used to represent slope. Although a negative slope denotes a downhill incline, a positive slope denotes an upward incline.
given
The line of fit has a slope of 10. This means that a student's projected test grade rises by 10% for every additional hour they spend studying.
In other words, there is a positive linear relationship between a student's test score and the amount of time they spend studying.
The slope of the line measures the expectation that students who study more would perform higher on the test.
The y-intercept of the line, which is represented by the point (0,70) on the line of fit, indicates that a student who performs no studying is expected to receive a grade of 70%.
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Help me Please and thank you
The name of the fifth student selected is Wahib, and the answer is (A) Wahib.
What is meant by selection?
Selection refers to the process of choosing or picking out something from a group or set of options based on specific criteria or requirements. It can involve evaluating and comparing different options and making a decision based on factors such as quality, suitability, relevance, or preference. Selection is a common process in various contexts, including recruitment, product design, and research.
According to the given information
To use the line of random numbers to select students, we can take the last two digits of each number and use them to select a student from the list. For example, if the random number is 02, we select Chandler because he is the second student on the list.
Using this method, the first 6 students selected are:
Chandler (02)
Cindy (03)
Heather (08)
Hsin-Chi (09)
Wahib (26)
Xavier (27)
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Use long division to rewrite the following expression.
Write your answer in the format of q (x) +
r(z)
36x²8x+11
4x²7x-5
Putting the expression together in the format q(x) + r(x)/b(x): 9 + (55x + 56) / (4x² - 7x - 5)
How to rewrite the expression using long division?First, we need to divide the first term of the numerator (36x²) by the first term of the denominator (4x²):
36x² / 4x² = 9
Now, multiply the entire denominator by 9 and subtract the result from the numerator:
(9 (4x² - 7x - 5)) = (36x² - 63x - 45)
4x² - 7x - 5 | 36x² - 8x + 11
- (36x² - 63x - 45)
_________________
55x + 56
Now, we cannot divide any further because the degree of the remaining expression (55x + 56) is less than the degree of the denominator (4x² - 7x - 5). So, the result of the long division is:
q(x) = 9
r(x) = 55x + 56
b(x) = 4x² - 7x - 5
Putting it all together in the format q(x) + r(x)/b(x):
9 + (55x + 56) / (4x² - 7x - 5)
The above answer is in reference to the question below;
Use long division to rewrite the following expression.
Write your answer in the format of q (x) + r(x)/b(x)
36x² - 8x + 11
4x²- 7x - 5
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There are three different sections to sit in at at a baseball park. The number of people who can sit in each section is described below rest section seats.
red section seats 200 people.
blue section seats 20 fewer people than the red section.
green section seats 2 times as many people as the blue section.
what is the total number of people who can sit in the baseball park?
Answer:
560 is the answer hope the helps.
Step-by-step explanation:
The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 155 grams of a radioactive isotope, how much will be left after 5 half-lives?
Use the calculator provided and round your answer to the nearest gram.
Answer:
After 5 half-lives, the remaining mass of the radioactive isotope will be 155 * (1/2)^5 = 4.84375 grams. Rounded to the nearest gram, the answer is 5 grams.
Step-by-step explanation: