The solutions to the equation `tan(x) + 2tan(z) - 3 = 0 for `x` are `x = arctan(0.18)`.
To find all solutions to the equation `tan(x) + 2tan(z) - 3 = 0. Here, x and z are in radians.
Therefore, `tan(x) = 0.18`
Given equation is `tan(x) + 2tan(z) - 3 = 0`Or, `tan(x) = 3 - 2tan(z)`
On using the identity `tan^2(z) + 1 = sec^2(z)`, we get `2tan^2(z) + 1 = 2sec^2(z)`.
Multiplying both sides of the above equation by 2, we have
`4tan^2(z) + 2 = 1 + 2tan^2(z)`Or, `tan^2(z) = 1/2`Or, `tan(z) = 1/sqrt(2)` or `-1/sqrt(2)`
Since `pi/4` is the only angle between `0` and `pi/2` for which `tan(theta) = 1`, the only angle between `0` and `pi/2` for which `tan(z) = 1/sqrt(2)` is `pi/4`.
Also, the only angle between `pi/2` and `pi` for which `tan(z) = -1/sqrt(2)` is `3pi/4`.
Hence, the solutions for `z` are `z = pi/4 or 3pi/4`. For `x`, we are given that `tan(x) = 0.18`.
Thus, `x = arctan(0.18)`.
Therefore, the solutions for `x` are `x = arctan(0.18)`We have found the solutions of `x` and `z` for the given equation.
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Anyone know if this is right?
Answer:
If you are just wanting to factor out the equation than yes, this is correct! Great job!
Step-by-step explanation:
5. in an experiment that tested how adding variable quantities of sugar to flowers in a vase made the flowers last longer, the dependent variable would be the \
For given scenario the dependent variable would be the life of flowers.
For given question,
The variable that researchers are trying to explain or predict is called the
response variable. It is also sometimes called the dependent variable
because it depends on another variable.
The variable which is used to predict the response variable is known as the explanatory variable. It is also called as an independent variable because it does not depend on another variable.
The amount of sugar would be an independent variable and the life of flowers is a dependent variable.
Therefore, for given scenario the dependent variable would be the life of flowers.
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If profits decrease by 13.8% when the degree of operating
leverage (DOL) is 3.8, then the decrease in sales is:
A) 0.28%
B) 0.52%
C) 3.63%
D) 10%
E) 52.44%
Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.
The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.
Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8
= -13.8% / x Thus, we have: x
= -13.8% / 3.8
= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage
= 13.8 / 3.8
= 3.63% The percentage decrease in sales is 3.63%.
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Tim simplified the difference 1/2p-(1/4p-4) as 3/4p. Did he find the correct answer will give brainlest for first person to answer
Answer:
I don't think so.
Step-by-step explanation:
1/2p-(1/4p-4)
1/2p-(1-16p/4p)
(2p-1+16p)/4p
(18p-1)/4p
2(9p-1)/4p
9p-1/2p
A newspaper in Germany reported that the more semesters needed to complete an academic program at the university, the greater the starting salary in the first year of a job. The report was based on a study that used a random sample of 24 people who had recently completed an academic program. Information was collected on the number of semesters each person in the sample needed to complete the program and the starting salary, in thousands of euros, for the first year of a job. The data are shown in the scatterplot below. 70 65 60 55 Starting Salary (1.000 euros) 50 45 35 30 25 5 10 15 20 Number of Semesters (a) Does the scatterplot support the newspaper report about number of semesters and starting salary? Justify your answer. b) The coefficient of determination is 0.335. Interpret this value in the context of this problem. c) Determine the value of the correlation coefficient. Interpret this value in the context of this problem.
a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.
b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.
The Correlation Coefficienta) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.
b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.
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If f(x) = 5x - 6, which of these is the inverse of f(x)?
A. f^-¹(x) = x/5 +6
B. f^-¹(x) = x/5 -6
C. f^-¹(x) = x+6/5
D. F^-¹(x) = x-6/5
To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.
So, let's start by swapping x and y in the function f(x) = 5x - 6:x = 5y - 6
Next, we'll solve this equation for y:
x + 6 = 5y
y = (x + 6)/5
Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.21) When constructing a frequency distribution, how many classes should
there be?
OA. between 8 and 12
OB. between 2 and 5
OC. between 15 and 20
OD. between 5 and 20
When constructing a frequency distribution, how many classes should
there be between 8 and 12. Option A
How ow many classes should there be when constructing a frequency distributionWhen constructing a frequency distribution, the number of classes should typically be determined based on the specific dataset and the desired level of detail. The general guideline is to have a sufficient number of classes to capture the variability in the data without having too few or too many classes.
This range allows for a reasonable level of detail while still providing a clear representation of the data distribution. It strikes a balance between having too few classes, which might oversimplify the data, and having too many classes, which might make it difficult to interpret the distribution accurately.
However, it's important to note that the optimal number of classes can vary depending on factors such as the size of the dataset, the range of values, and the specific characteristics of the data.
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Giving brainliest!!!!
Answer:
x = 21 degrees or A
Step-by-step explanation:
7x - 3 + 2x - 6 = 180
9x - 9 = 180
9x = 189
x = 21
Please help me , ASAP thank you
Answer:
(x - 4)² + (y + 3)² = 4
Remember the circle formula:
(x - h)² + (y - k)² = r²
h = X center point
k = Y center point
In this case your center point is (4,-3) and your radius is 2
If u plug everything in and simplify you should get this:
(x - 4)² + (y - (-3))² = 2²
(x - 4)² + (y + 3)² = 4
can someone solve 1/2=6x+7(-3x-1/7)
Please i need help ASAP
pls explain your answer
Answer:
\(r=5.79898987...\\A=510.31110884...\)
Step-by-step explanation:
Challenging question!
Start by constructing a square in the lower-left quadrant of the circle (that isn't shaded) that is tangent to center C, OP, and OQ:
(See picture)
With the blue line constructed, we can conclude that the blue line (the blue line is the measure from the center of the inscribed circle to the center of the quarter circle) measures \(\sqrt{2} r\) due to the Pythagorean theorem.
The orange line is the radius of the inscribed circle, so adding the blue line and the orange line gives the radius of the quarter circle, so:
\(\sqrt{2}r +r=14\)
Solve the equation with a bit of algebra to get:
\(\sqrt{2} r+r=14\\r(\sqrt{2}+1)=14\\r=\frac{14}{\sqrt{2}+1 }\\r=5.79898987...\)
Now, we will find the area of the inscribed circle:
\(A=\pi r^2\\A=\frac{22}{7} *(5.79898987...)^2\\A=105.68889115...\)
And we will now find the area of the quarter circle...:
\(A_{2} =\pi r^2\\A_{2}=\frac{22}{7}*14^2\\A_2=616\)
...and we subtract both results...:
\(A_{3}= 616-105.68889115...\\A_3=510.31110884...\)
To get the area of the shaded region.
Not sure what does the last part ("correct to 3 s. f.") meant but that's all I can do.
In a town there are 1349 families if there are an average two children attending elementary School from each family and each school can accommodate 220 student children the minimum number of elementary schools needed in the region is 6 9 or 13
Answer:
13
Step-by-step explanation:
First find the number of children attending elementary school
= 1349*2
= 2698 children
Now each school can accommodate 220 children so divide the number of children by 220
= \(\frac{2698}{220}\)
= 12.26 which is the closest to 13 in the options so the answer is 13
4<-9.9-(-10x+1) solve for x
Step-by-Step:
___________
1. We are given the following:
\(4 < -9.9-(-10x+1)\)
This being said, the first thing we need to do is switch sides, writing it as follows:
\(-9.9-(-10x+1) > 4\)
___________
2. Next, we need to add 9.9 to both sides of the equation.
\(-9.9-(-10x+1)+9.9 > 4+9.9\)
___________
3. Then, we simplify.
\(-(-10x+1) > 13.9\)
____________
4. Now, we add 1 to both sides of the equation.
\(10x-1+1 > 13.9+1\)
____________
5. We simplify again.
\(10x > 14.9\)
____________
6. Next, we divide both sides by 10.
\(\frac{10x}{10} > \frac{14.9}{10}\)
____________
7. Finally, simplify one more time.
\(x > 1.49\)
Hence, out solution is \(x > 1.49\)
Hope this helps!
2/3 of a class are girls.
w
a) What is the ratio girls to boys in the class?
Note: Give your answers
in their simplest forms.
b) What is the ratio boys to girls in the class?
Answer:
Step-by-step explanation:
https://justmaths.co.uk/2015/07/23/new-gcse-error-intervals/2/3%20of%20a%20class%20are%20girls.%20w%20a)%20What%20is%20the%20ratio%20girls%20to%20boys%20in%20the%20class?%20Note:%20Give%20your%20answers%20in%20their%20simplest%20forms.%20b)%20What%20is%20the%20ratio%20boys%20to%20girls%20in%20the%20class?
Answer:
a) 2:3
b) 1:3
Step-by-step explanation:
A train goes at a constant speed of 150 miles in 2.5 hours. How long will it take for the train to go 360 miles
Answer: 21,600 miles
Step-by-step explanation:
150/2.5 = 60
360x60 = 21,600 miles
Determine the minimum sample size required when you want to be onfident that the sample mean is within one unit of the population mean and 13.8 assume the population is normally distributed.
The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]
Solving the given question:
We know that the formula for Margin of error is:
Margin of error = z-score * (standard deviation) / root (sample size)
E = z * σ / √(n), where
E = Margin of error
z = z-score
n = Sample size
σ = standard deviation
Therefore, sample size = ( z – score * standard deviation / margin of error)²
n = ( z * σ / E )²
First, calculate the z-score for the 99% confidence level.
From the normal distribution curve, the area under 99% confidence level is given as:
Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995
From the z-score table, we find the value of z with the corresponding area of 0.995
We find the value of the z-score corresponding to 0.995 is 2.58
Also given sample mean is one unit of the population. So the margin of error is 1
E = 1
And given Standard deviation = 13.8
σ = 13.8
Putting the values in the given formula of sample size n =
n = (2.58 * 13.8 / 1 )²
n = 1267.64
n = 1268
Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )
help me plz thank you
Answer:
9 momths =270 days
Step-by-step explanation:
9 month *30=270 days
The skatebaord rita wants to buy costs $6 less than three times she has saved the skatebaord costs $69 how much did rita save
The equation that represents the given sitution is 3a-6 = 69. Rita saved $25.
What is an epression?
A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
Assume that Rita saved $a.
Given that the cost of a skateboard is $6 less than three times what she has saved.
The mathematical expression of $6 less than three times what she has saved is 3a-6
The actual cost is $69.
According to the question,
3a-6 = 69
Add 6 on both sides:
3a = 69 + 6
3a = 75
Divide both sides by 3:
a = 75/3
a = 25
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what product is greater than 2 5/6?
A. 1/8 X 2 5/6
B. 6/5 X 2 5/6
C. 5/6 X 2 5/6
D. 2 5/6 X 2/3
Answer: B
Step-by-step explanation: because 6/5 would give you a number greater than 1 so multiplying it to 2 5/6 will give you number greater than 2 5/6
How many sig figs does 602 200 000 000 000 000 000 000 molecules have ? Explain
Answer:
4
Step-by-step explanation:because 6022 is the sig figs, and 00000000000000000000 doesnt work because it is zero
6 times the sum of a number and 2
Answer:
6 times means 6 multiplied by
The sum of a number and 2 means x + 2
x = number
(2+x) × 6
If a bacteria has a doubling time of 20 min and you start with one bacterium, how many cells will you have after 1 hour (60 min)
After 1 hour (60 minutes), starting with one bacterium and with a doubling time of 20 minutes, you will have 8 cells.
To calculate the number of cells after a certain time period, we can use the formula for exponential growth:
\(N(t) = N_0 * 2^{t/d}\)
Where:
N(t) is the final number of cells after time t
N₀ is the initial number of cells
t is the time period
d is the doubling time
In this case, N0 = 1 (starting with one bacterium), t = 60 minutes, and d = 20 minutes.
Plugging the values into the formula, we have:
N(60) = 1 * \(2^{60/20}\)
N(60) = 1 * 2³
N(60) = 1 * 8
N(60) = 8
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Jim earns money doing yard work each week. During three weeks he earned a total of $168. If each week, his earnings doubled, how much did he make each week
He made $112 each week
Explanations:The total amount earned in three weeks before his weekly earning was doubled = $168
The amount earned each week before his weekly earning was doubles = $168/3
The amount earned each week before his weekly earning was doubled = $56
If his weekly earning was doubled:
The amount earned each week = 2 x $56
The amount earned each week = $112
16 students want lemonade and 32 students want iced tea. What is the ratio of the number of students who want lemonade to the total number of students?
Answer:
16:48 or 16 to 48 or 16 / 48
Step-by-step explanation:
figure out how many students want lemonade Figure out what the total number of students there are Use a colon the word to or make it a fractionAnswer:
16:48
Step-by-step explanation:
16 is the total amount of students who want lemonade.
You add 16 with 32 to get 48 students in total.
So the ratio is 16:48.
HELP PLS….Volume of cones
Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for and round your final answer to the nearest hundredth.
Answer:
20.93 units cubed
Step-by-step explanation:
\(V = \frac{3.14(2)^{2}(5) }{3} \\V = \frac{3.14(4)(5) }{3}\\V = \frac{62.8 }{3}\\V = 20.93\)
on a certain standardized test, the mean is 180 and the standard deviation is 35. which of the following is within 2 standard deviations of the mean?
Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.
Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.
To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.
The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.
The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.
Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.
It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.
Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.
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A car is traveling down a highway at a constant speed, described by the equation d=65t, where d represents the distance, in miles, that the car travels at this speed in t hours.
a. What is 65 called (vocabulary) and what does it represent?
b. How many miles does the car travel in 3 hours?
How long does it take the car to travel 26 miles a this speed?
Answer:
A)65 is the speed of the equation, because distance/time*speed
B)He will travel 195 Miles in 3 hours, 65*3
C)It will take around 25 minutes to reach 26 miles, since they are going 65 mph at the moment.
Answer:
♡ hi fairy ♡
- here are your answers.
a) 65 means distance/time multiplied by speed so that means it's speed of the equation or expression and fun fact, smallest integer that can be expressed as a sum of two distinct positive squares in two ways,
b) he will travel 195 Miles in 3 hours.
c) it will take 25 minutes to reach 26 miles.
hope this helps! have a great night/day. ♡☆
-madeline
✧・゚: *✧・゚:・゚✧*:・゚✧・゚: *✧・゚:・゚✧*:・゚✧
Step-by-step explanation:
solve the inequality x-4 > 12
Answer:
x > 16
Step-by-step explanation:
What is the domain of this quadratic function?
The graph goes on forever in both directions along the x axis. This indicates any x value can be plugged into the quadratic to get some y output. There are no restrictions. The domain is the set of all possible x inputs of a function.
HELP IM CONFUSED. NEED HELP ASAP
Answer:
Yeah good job! u got it right :)
Step-by-step explanation:
How to find perimeter?
Frist you will add up all the sides
then thats your answer :)
In this case the same logic applies
Hope this helps :3