(15-x) x 4 =10 PLS HELP!!!
IT IS DUE TODAY
Answers
Answer:
x = 12.5
Step-by-step explanation:
Related Questions
there were x quarts of liquid in a con-tainer. first, 3 4 of the liquid in the container was removed. then another 1 2 quart was poured into the container. write an expression in terms of x for the number of quarts of liquid in the container at the end. then write another equivalent expres-sion.explain
Answers
The another equivalent expression of total liquid is (x+2)/4.
Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.
x quarts liquid in the container 3/4 part of liquid is removed
Then remaining liquid in container = X - \(\frac{3}{4}X\)
Then remaining liquid in container = x/4quarts
Another 1/2 quart is poured into container
Then total liquid = \(X-\frac{3}{4}X+\frac{1}{2}\) quarts
total liquid = \(\frac{X+2}{4}\) quarts
So, then the another equivalent expression of total liquid is (x+2)/4.
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A supermarket gives a special
offer to cus-
tomers who purchase at least a pack of
vests and a pack of T-shirts. The offer is
restricted to a total of 7 of these items.
a) Write down three inequalities which
must be satisfied.
(b) Draw the graphs of the above condi-
tions and shade the region that satis-
fies them.
(c) If the supermarket makes a gain of N5
on each vest and N8 on each T-shirt,
find the maximum gain made by the
supermarket.
Answers
A) the three inequalities that must be satisfied are:
The number of vests, represented by x, must be a non-negative integer: x ≥ 0.The number of T-shirts, represented by y, must also be a non-negative integer: y ≥ 0.The total number of vests and T-shirts must not exceed 7: x + y ≤ 7.B) Graph shaded and satisfying all conditions is attached.
What is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.
It is most commonly used to compare the sizes of two numbers on a number line.
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Write the polnt-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
y- 6 = 1(x + 5)
y+6= -1(x - 5)
y- 6 = -1(x + 5)
y+ 6 = 1(x - 5)
Answers
Answer:
y - 6 = -1 (x+5)
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula \(m = \frac{y_2-y_1}{x_2-x_1} \\\). Substitute the x and y values of (-5,6) and (0,1) into the formula and simplify like so:
\(m = \frac{(1)-(6)}{(0)-(-5)} \\m = \frac{1-6}{0+5} \\m = \frac{-5}{5} \\m = -1\)
So, the slope of the line is -1.
2) Now we have enough information to write the equation of the line in point-slope form. Use the point-slope formula \(y-y_1 = m (x-x_1)\) and substitute real values for the \(m\), \(x_1\), and \(y_1\).
Since \(m\) represents the slope of the line, substitute -1 in its place. Since \(x_1\) and \(y_1\) represent the x and y values of a point the line intersects, substitute the x and y values of (-5, 6) in those places as well. This gives the following equation and answer:
\(y-6 = -1(x+5)\)
Solve for x. −4≤16−4x
Answers
Answer:
the answer for x<5
Step-by-step explanation:
Step 1: Simplify both sides of the inequality.
−4<−4x+16
Step 2: Flip the equation.
−4x+16>−4
Step 3: Subtract 16 from both sides.
−4x+16−16>−4−16
−4x>−20
Step 4: Divide both sides by -4.
−4x
−4
>
−20
−4
x<5
The position of a particle moving along the x-axis varies with time according to x(t)=7.4t
2
−4.8t
3
m.
v(t)=14.8t−14.4t
2
a(t)=
(b) Find the velocity (in m/s ) and acceleration (in m/s
2
) at t=2.0 s. (Indicate the direction with the sign of your answer.)
v(2.0 s)=m/s
a(2.0 s)=
(c) Find the time t>0 (in s) at which the position is a maximum. I s (d) Find the time t>0 (in s) at which the velocity is zero. \& s (e) For time t>0, find the maximum position (in m ). (Indicate the direction with the sign of your answer.
Answers
Given,x(t) = 7.4t² − 4.8t³m
We need to find the following.(b) Velocity (in m/s) and acceleration (in m/s²) at t = 2 s and indicate the direction with the sign of your answer.
(c) Find the time t > 0 (in s) when the position is at a maximum.
(d) Find the time t > 0 (in s) when the velocity is zero.
(e) Find the maximum position (in m) for time t > 0 and indicate the direction with the sign of your answer.
To calculate velocity, we need to differentiate position with respect to time.
That is,
v(t) = x′(t)
= 14.8t - 14.4t²m/s
We can calculate acceleration by differentiating velocity with respect to time.
That is,
a(t) = v′(t) = 14.8 - 28.8t m/s²
Now, we can substitute t = 2 s to find velocity and acceleration.
v(2.0 s) = 14.8(2.0) - 14.4(2.0)² = 4.4 m/s (The direction is positive because velocity is positive at t = 2 s) a(2.0 s) = 14.8 - 28.8(2.0) = -42.8 m/s²
(The direction is negative because acceleration is negative at t = 2 s)
Now, we can find the time when the position is at a maximum.
To find the maximum, we need to differentiate position with respect to time and equate it to zero.
dx/dt = 14.8t - 14.4t²
= 0.
Simplifying, we get 14.8t(1 - t) = 0.
Hence,t = 0, 1 s.To determine the time when velocity is zero, we set the expression for velocity to zero and solve for t.
v(t) = 0 = 14.8t - 14.4t² => 14.8t = 14.4t² => t(14.4t - 14.8) = 0.
Hence,t = 0, 1.028 s (rounded to three decimal places).
To find the maximum position, we substitute t = 1 s into the expression for position.
x(1.0 s) = 7.4(1.0)² − 4.8(1.0)³
= 2.6 m.
(The direction is positive because the particle is moving in the positive direction).
Therefore, the answers are,v(2.0 s) = 4.4 m/s (positive direction)a(2.0 s) = -42.8 m/s² (negative direction)t = 1 st = 0, 1.028 sx = 2.6 m (positive direction).
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Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come from a random sample and use a 5% significance level.
Test H0 : p=0.25 vs Ha : p<0.25 using the sample results p^=0.16 with n=100
test statistic =
p-value =
Answers
The p-value is 0.0023, which is less than the significance level of 0.05. This further supports our rejection of the null hypothesis.
To test the hypothesis, we can use the one-sample z-test for the proportion. The test statistic is given by:
z = (p^ - p) / sqrt(p*(1-p)/n)
where p is the hypothesized proportion under the null hypothesis, p^ is the sample proportion, and n is the sample size.
Plugging in the values, we get:
z = (0.16 - 0.25) / sqrt(0.25*(1-0.25)/100) = -2.83
Using a significance level of 5%, the critical z-value for a one-tailed test is -1.645. Since the calculated test statistic is less than the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the true proportion is less than 0.25.
The p-value for this test is the probability of observing a sample proportion of 0.16 or less if the true proportion is 0.25. Using a standard normal table or calculator, we find the area to the left of z = -2.83 is 0.0023. Therefore, the p-value is 0.0023, which is less than the significance level of 0.05. This further supports our rejection of the null hypothesis.
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Which gases are needed for animal and plant respiration? Select two options. FAST ITS TIMED
oxygen
nitrogen
carbon dioxide
neon
carbon
Answers
Answer:
It oxygen. hope this'll help. All the best.
What is the polar form of -9-9i√3?
Answers
Answer:
18(cos(4pi/3) + i sin(4pi/3))
Step-by-step explanation:
step 1: find the modulus (|z|=√(a^2 + b^2)
|z|=√((-9)^2+(-9√3)^2)= 81+243= 324 => √324=18
step 2: find the argument using theta =tan^-1 (y/x)
theta=tan^-1((-9√3)/-9) = √3
the tangent value of √3 in the third quadrant has the degree measure of 240 and the radian measure of 4pi/3.
Now put them together!
Answer:
D
Step-by-step explanation:
Ed2021
A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book. With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book. For how many books produced will the costs from the two methods be the same?
Answers
The number of books published by a small publishing company is 3240.
Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of books be x.
With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.
That is, 44,714+11.50x
With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.
That is, 17,174+20x
Now, the number of books produced will the costs from the two methods be the same.
So, 44,714+11.50x=17,174+20x
⇒ 44,714-17,174=20x-11.50x
⇒ 8.5x = 27540
⇒ x=3,240
Therefore, the number of books published by a small publishing company is 3240.
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The major shortcoming of the general linear probability model y = β0 + β1x1 + β2x2 + … + βkxk + ε, is that the predicted values of y can be sometimes ________.
Multiple Choice
at least 0 and no more than 1
greater than 0 and less than 1
less than 0 or greater than 1
less than 1 but more than 0
Answers
The major shortcoming of the general linear probability model y = β0 + β1x1 + β2x2 + … + βkxk + ε, is that the predicted values of y can be sometimes greater than 1 or less than 0.
The linear probability model does not take into account the fact that probabilities are bounded between 0 and 1. As a result, the predicted values of y can sometimes fall outside of this range, which is not meaningful or interpretable in terms of probability. To address this issue, alternative models such as logistic regression or probit regression can be used, which are specifically designed to model probabilities and ensure that predicted values fall within the appropriate range. These models use non-linear functions to map the values of the independent variables to probabilities, thereby avoiding the problem of predicted values falling outside the valid range.
Therefore,the major shortcoming of the general linear probability model y = β0 + β1x1 + β2x2 + … + βkxk + ε, is that the predicted values of y can be sometimes greater than 1 or less than 0.
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The owner of Britten's Egg Farm wants to estimate the mean number of eggs laid per chicken. A sample of 18 chickens shows they laid an average of 20 eggs per month with a standard deviation of 5 eggs per month.
(a-1) What is the value of the population mean?
20
It is unknown.
5
(a-2) What is the best estimate of this value?
Best estimate
(c)
For a 95% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
Value of t
(d)
Determine the 95% confidence interval for the population mean. is (Round your answers to 2 decimal places.)
Confidence interval to
(e-1) Would it be reasonable to conclude that the population mean is 17 eggs?
No
Yes
(e-2) What about 18 eggs?
Yes
No
Answers
(a-1) The value of the population mean is unknown.
(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.
(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).
(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.
(e-2) It would be reasonable to conclude that the population mean is 18 eggs.
(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.
(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.
(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.
Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.
(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.
In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.
(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.
(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.
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2x + y = -8
3x - 5y = -25
It’s substitution
Answers
Answer:
x = -5 , y = 2
Step-by-step explanation:
Solve the following system:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{y + 2 x = -8
-5 y + 3 x = -25
Hint: | Solve for y.
Subtract 2 x from both sides:
{y = -2 x - 8
-5 y + 3 x = -25
Hint: | Perform a substitution.
Substitute y = -2 x - 8 into the second equation:
{y = -2 x - 8
3 x - 5 (-2 x - 8) = -25
Hint: | Expand the left hand side of the equation 3 x - 5 (-2 x - 8) = -25.
3 x - 5 (-2 x - 8) = (10 x + 40) + 3 x = 13 x + 40:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{y = -2 x - 8
13 x + 40 = -25
Hint: | Isolate terms with x to the left hand side.
Subtract 40 from both sides:
{y = -2 x - 8
13 x = -65
Hint: | Solve for x.
Divide both sides by 13:
{y = -2 x - 8
x = -5
Hint: | Perform a back substitution.
Substitute x = -5 into the first equation:
{y = 2
x = -5
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = -5 , y = 2
Chelsea made monthly payments for four years before her $13,440 loan was paid off. The loan had an interest rate of 5. 86%, compounded monthly. Chelsea paid $156. 60 in service charges. To the nearest tenth, what percentage of the total cost of the loan did her finance charges comprise? Round all dollar values to the nearest cent. A. 13. 6% b. 10. 9% c. 9. 4% d. 11. 9%.
Answers
There are 11.9% of the total cost of the loan did her finance charges comprise, the correct option is D.
How to find the total finance charge?The total finance charge is the amount of money a consumer pays for borrowing money on a credit card.
Given
Chelsea made monthly payments for four years before her $13,440 loan was paid off.
The loan had an interest rate of 5. 86%, compounded monthly.
Chelsea paid $156. 60 in service charges.
The percentage of the total cost of the loan did her finance charges comprise is;
\(\rm\dfrac{ 13,440(\dfrac{0.0586}{12})}{(1-(1+\dfrac{0.0586}{12})^{-48}})= 15,109.44 \\\\15,109.44 + 156.60 = 15,266.04\\\\ 15,266.04 - 13,440.00 = 1,826.04 \\\\=\dfrac{1,826.04}{15,266.04}\\\\ =11.96\ Percentage\)
Hence, there are 11.9% of the total cost of the loan did her finance charges comprise.
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Answer:
Step-by-step explanation:
am trying to find the answer
consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s in the $n^{\rm{th}}$ block. what is the sum of the first $1234$ terms of this sequence?
Answers
Therefore, the sum of the first 1234 terms of this sequence is 1234.
To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.
Let's examine the pattern of the sequence:
Block 1: 2's
= 1's
= 1 (1 2)
Block 2: 2's
= 2's
= 22 (1 22 1)
Block 3: 2's
= 3's
= 222 (1 222 1)
Block 4: 2's
= 4's
= 2222 (1 2222 1)
...
We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.
Now, let's calculate the number of blocks required to reach the 1234th term:
To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.
The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).
Let's solve this equation:
(n/2)(n+1) = 1234
\(n^2 + n - 2468 = 0\)
Using the quadratic formula:
n = (-1 + √(1 + 4*2468)) / 2
n ≈ 61.76
Since n must be a whole number, we take the ceiling of n, which gives us 62.
Therefore, there are 62 blocks in the sequence.
Next, let's calculate the number of 1's in each block:
In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.
So, the number of 1's in each block is (n + 1) - n = 1.
Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.
Finally, let's calculate the sum of the first 1234 terms:
Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).
Sum of (n + 1) repeated 62 times = 62(n + 1)
= 62 * 2
= 124.
In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.
So, the sum of the first 1234 terms is 62 + 1172 = 1234.
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write 1.452 x 10^3 as an ordinary number
Answers
Step-by-step explanation:
1.452 * 10³ in ordinary number.
= 1.452 * 1000
= 1452
Hope it will help :)
An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
Answers
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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What is the volume of the figure below
Answers
Of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
Is that true or false? please explane
Answers
The statement "the interquartile range is least influenced by an outlying value in the data set" is true.
The range is simply the difference between the maximum and minimum values in a data set.
The variance is a measure of the spread of a data set, and is calculated by finding the average of the squared differences between each data point and the mean of the data set.
The interquartile range, on the other hand, is a measure of the spread of the middle 50% of the data set. It is calculated by finding the difference between the upper quartile and the lower quartile.
Because the interquartile range only takes into account the middle 50% of the data, it is less influenced by outliers than the range and variance. This is because outliers can greatly impact the range and variance, but have little effect on the interquartile range.
In conclusion, the interquartile range is a more robust measure of spread for a data set, as it is less influenced by outliers.
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The range of a data set is 32. if the largest number in the set a 30 what is the
Answers
The smallest number of the data set is -2
How to find the smallest number?
The range of a data set is the difference between the largest number and smallest number in the data set. It is a simple measure of variability that gives an idea of how spread out the data is.
Range = largest number - smallest number
32 = 30 - smallest number
smallest number = 30 - 32 = -2
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Complete Question
The range of a data set is 32. If the largest number in the set is 30. what is the smallest number?
2. A certain drug is eliminated from the human body according to an exponential model. After 2 hours, there are 32 mg left. Five hours after taking a dose of this drug, there are 10 mg remaining in the body. a) State the two points you will use to solve this problem or make a table. “Five hours after taking a dose of this drug, there are 10 mg remaining in the body. hours, there are 32 mg left. b) Find the equation that models this behavior. c) How much of the drug was present in the body one hour after taking the dose? I d) When will there be 1 mg of the drug remaining in the body?
Answers
The exponential function is given by \(y = 69.5(0.6786)^x \\\)
Exponential functionAn exponential function is in the form:
\(y=ab^x\)
Where a is the initial value of y and b is the multiplier factor
Let y represent the amount of drug after x hours.
After 2 hours, there are 32 mg left. Hence:
32 = ab² (1)After 5 hours, there are 10 mg left. Hence:
10 = ab⁵ (2)From equation 1 and 2, b = 0.6786, a = 69.5
The exponential function is given by \(y = 69.5(0.6786)^x \\\)
At 1 hour:
y = 69.5(0.6786) = 47 mg
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Compare the budgets of Hong Kong, United States of America, and
Korea based on your definition of a budget, in terms of contents,
formats, advantages, and disadvantages, etc.
Answers
The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.
A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:
Hong Kong Budget:Contents: The Hong Kong budget comprises revenue and expenditure. It provides a detailed analysis of expected sources of income and the allocation of funds.Format: The Hong Kong budget is presented in a clear and concise format, including charts and graphs to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability.Disadvantages: It does not provide detailed information on tax expenditures and lacks public participation in the budget process.
United States Budget:
Contents: The US budget comprises revenue, expenditures, and deficit or surplus. It includes an analysis of taxes, social security, and Medicare.Format: The US budget is presented in a complex and lengthy format, including tables, graphs, and other financial documents.Advantages: The budget provides detailed information on tax expenditures and encourages public participation in the budget process.Disadvantages: The budget can be challenging to understand due to its complexity, and it may not provide an accurate depiction of federal spending.Korean Budget:
Contents: The Korean budget comprises revenue, expenditures, and surplus or deficit. It includes detailed information on taxes, social security, and public welfare.Format: The Korean budget is presented in a clear and concise format, including tables and charts to aid understanding.Advantages: The budget is easy to understand, and it promotes transparency and accountability. It also provides detailed information on social welfare expenditures.Disadvantages: The budget may not provide an accurate depiction of government spending, and it may not include information on hidden expenditures.Learn more about Budget:
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A newspaper randomly chooses 100 names from it's subscriber database and then survey's those subscribers to find if they read the restaurant review is this biased or non biased
Answers
Answer:
Non biased (kind of)
Step-by-step explanation:
It depends on how they randomly chose but if it was truly random it would be non biased as many people will read newspapers for things such as sports or catalogs
the profit earned by a hot dog stand is a linear funsion of the number of hot dogs sold.It cost the owner $48 dollars each morning for the day's supply of hot dogs,but he earnes $2 profit for each hot dog sold which equation represent y, the profit earned bye the hot dogs sold
Answers
Answer:
Step-by-step explanation:
If he earns $2 per hot dog sold, then the algebraic expression for this is 2x, where x is the number of hot dogs sold. If he has to put out $48 to buy the supplies, that is represented as -48. The function, then, that represents the profit earned by selling the hot dogs is
y = 2x - 48
Answer:
c
Step-by-step explanation:
I need help!!!!!!!!!!!
Answers
Answer:
its B :)
Step-by-step explanation:
I hope this helps ^^
The likelihood of the frequency of an event in repeated trials under similar conditions is?
Answers
The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.
What is Statistical analysis?The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.
What accomplishes statistical analysis?Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.
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Find the first six terms of the Maclaurin series for the function f(x) = cos(3x) – sin(x²) E
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The first six terms of the Maclaurin series for the function f(x) = cos(3x) - sin(x²) are 1 - 8x² - x³/3 + 83/3x⁴ + 0(x⁵).
To find the Maclaurin series for the given function f(x) = cos(3x) - sin(x²), we can use the Taylor series expansion formula.
The Taylor series expansion of a function centered at x = 0 is called the Maclaurin series.
We begin by finding the derivatives of the function with respect to x.
f'(x) = -6sin(3x) - 2xcos(x²)
f''(x) = -18cos(3x) + 2cos(x²) - 4x²sin(x²)
f'''(x) = 54sin(3x) - 4sin(x²) - 8xcos(x²) - 8x³cos(x²)
f''''(x) = 162cos(3x) + 4cos(x²) - 24xsin(x²) - 24x³sin(x²) - 24x⁵cos(x²)
Next, we evaluate these derivatives at x = 0 to find the coefficients of the Maclaurin series.
f(0) = cos(0) - sin(0) = 1
f'(0) = -6sin(0) - 2(0)cos(0) = 0
f''(0) = -18cos(0) + 2cos(0) - 4(0)²sin(0) = -16
f'''(0) = 54sin(0) - 4sin(0) - 8(0)cos(0) - 8(0)³cos(0) = -4
f''''(0) = 162cos(0) + 4cos(0) - 24(0)sin(0) - 24(0)³sin(0) - 24(0)⁵cos(0) = 166
Using these coefficients, we can write the first few terms of the Maclaurin series:
f(x) ≈ 1 - 16x²/2! - 4x³/3! + 166x⁴/4! + 0(x⁵)
Simplifying the terms, we get:
f(x) ≈ 1 - 8x² - x³/3 + 83/3x⁴ + 0(x⁵)
Therefore, the first six terms of the Maclaurin series for f(x) = cos(3x) - sin(x²) are 1 - 8x² - x³/3 + 83/3x⁴ + 0(x⁵).
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Find sin 0, where is the angle shown.
Give an exact value, not a decimal approximation.
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Answer:
\(\displaystyle \sin\theta=\frac{12}{13}\)
Step-by-step explanation:
Recall that in a right triangle, sine is the ratio of the opposite side to the hypotenuse:
\(\displaystyle \sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)
We are actually not given the opposite side in this case. However, since we know the hypotenuse and the adjacent side, we can use the Pythagorean Theorem to find the opposite side. So:
\(a^2+b^2=c^2\)
Let a be the adjacent side and b be the opposite side. c will be the hypotenuse.
Substitute:
\((5)^2+b^2=(13)^2\)
Solve for b:
\(b=\sqrt{169-25}=\sqrt{144}=12\)
So, the opposite side measures 12.
Then sine will be:
\(\displaystyle \sin\theta=\frac{12}{13}\)
Plz help me, im stuck on this question, It says
Find the perimeter of the following rectangle,
Write your answer as a mixed number in simplist form,
Be sure to include the correct unit in your answer.
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\(perimeter = 2(3 \frac{1}{10}) + 2 (\frac{3}{4}) \)
\(perimeter = \frac{31}{5} + \frac{3}{2} \)
\(perimeter = \frac{62}{10} + \frac{15}{10} \)
\(perimeter = \frac{77}{10} \)
\(perimeter = 7 \frac{7}{10} \)
The unit is just cm.
//
I might not be right. Double check to make sure. Hope that gives you a general idea of how to do it.
Answer:
Perimeter of rectangle =2(l+b)
=2(3*1/10+3/4)
=2(3/10+3/4) (lcm=40)
=2(12/40+30/40)
=2(42/40)
=42/20
= 21/10
=21/10 cm
8. Evan spent a total of $18 on gourmet jellybeans and chocolate-covered almonds. The jellybeans cost $12/kg. The almonds cost $21/kg.
a) Write an equation to represent Evan’s purchases.
b) Isolate the variable for the quantity of jellybeans in your equation.
c) If Evan bought 250 g of almonds, how many grams of jellybeans did he buy?
d) If Evan bought 100 g of almonds, how many grams of jellybeans did he buy?
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Answer:
no idea lol
Step-by-step explanation:
i just need points
7x9=(7 × 10) - (7 × ▲) what is the value of the triangle
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Answer: 1
Step-by-step explanation:
Very simple both of them have the same base is 7. And we know that the number is 7x9, so the triangle is 1 because when both numbers have the same base, we will subtract the other number to get the answer!