Main Answer: To achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
Supporting Question and Answer:
How does the total yield of apples per acre change as more trees are planted?
The total yield of apples per acre changes as more trees are planted. Initially, as more trees are added, the total yield increases because there are more trees producing apples. However, each additional tree planted per acre results in a decrease in the average number of apples yielded by each tree. Therefore, there is a trade-off between the total number of trees and the average yield per tree. At some point, adding more trees will start to decrease the total yield due to the diminishing average yield per tree. To determine the optimal number of trees per acre for maximum yield, we need to find the balance between adding more trees and maintaining a satisfactory average yield per tree.
Body of the Solution:To solve this optimization problem, let's follow the steps you provided:
1.Define the variables: Let's define the variable "x" as the number of additional trees planted per acre.
2.Write the objective function: The objective is to maximize the total yield of apples per acre. Since each tree yields fewer apples as more trees are planted, we need to consider the trade-off. The total yield can be calculated as follows:
Total yield = (46 + x) × (392 - x)
3.Determine the domain for the objective function: In this case, we should consider realistic constraints. The number of trees cannot be negative, and we assume a reasonable upper limit. Let's say we want to consider up to 100 additional trees. Thus, the domain for the objective function is: 0 ≤ x ≤ 100.
4.List any constraint equations/inequalities: The only constraint in this problem is the domain constraint mentioned above: 0 ≤ x ≤ 100.
5.Find the optimal solution and interpret it in the context of this situation: To find the optimal solution, we need to maximize the objective function within the given domain. We can either graph the objective function and find its maximum value or use calculus to find the critical points.
Taking the derivative of the objective function with respect to x and setting it equal to zero, we can find the critical point:
d/dx [(46 + x) × (392 - x)] = 0
(392 - x) - (46 + x) = 0
392 - x - 46 - x = 0
346 - 2x = 0
2x = 346
x = 346/2
x = 173
The critical point is x = 173, which means planting an additional 173 trees per acre would result in maximum yield.
However, we need to ensure this critical point falls within the domain constraints. Since 0 ≤ x ≤ 100, the optimal solution is x = 100, which represents planting an additional 100 trees per acre for maximum yield.
Therefore, to achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
Final Answer: Hence, to achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
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To achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
The total yield of apples per acre changes as more trees are planted. Initially, as more trees are added, the total yield increases because there are more trees producing apples. However, each additional tree planted per acre results in a decrease in the average number of apples yielded by each tree. Therefore, there is a trade-off between the total number of trees and the average yield per tree. At some point, adding more trees will start to decrease the total yield due to the diminishing average yield per tree. To determine the optimal number of trees per acre for maximum yield, we need to find the balance between adding more trees and maintaining a satisfactory average yield per tree.
To solve this optimization problem, let's follow the steps you provided:
1. Define the variables: Let's define the variable "x" as the number of additional trees planted per acre.
2.Write the objective function: The objective is to maximize the total yield of apples per acre. Since each tree yields fewer apples as more trees are planted, we need to consider the trade-off. The total yield can be calculated as follows:
Total yield = (46 + x) × (392 - x)
3. Determine the domain for the objective function: In this case, we should consider realistic constraints. The number of trees cannot be negative, and we assume a reasonable upper limit. Let's say we want to consider up to 100 additional trees. Thus, the domain for the objective function is: 0 ≤ x ≤ 100.
4.List any constraint equations/inequalities: The only constraint in this problem is the domain constraint mentioned above: 0 ≤ x ≤ 100.
5.Find the optimal solution and interpret it in the context of this situation: To find the optimal solution, we need to maximize the objective function within the given domain. We can either graph the objective function and find its maximum value or use calculus to find the critical points.
Taking the derivative of the objective function with respect to x and setting it equal to zero, we can find the critical point:
d/dx [(46 + x) × (392 - x)] = 0
(392 - x) - (46 + x) = 0
392 - x - 46 - x = 0
346 - 2x = 0
2x = 346
x = 346/2
x = 173
The critical point is x = 173, which means planting an additional 173 trees per acre would result in maximum yield.
However, we need to ensure this critical point falls within the domain constraints. Since 0 ≤ x ≤ 100, the optimal solution is x = 100, which represents planting an additional 100 trees per acre for maximum yield.
Therefore, to achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
Hence, to achieve the maximum yield, the apple orchard should plant 100 additional trees per acre, resulting in a total of 146 trees per acre.
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Andy has 11 builders he can use to build a wall.
He knows that 8 builders would take 15 days to build this wall.
Andy believes that he has enough builders to finish this wall in less than 11 days.
Is he correct? Yes/No
Show your working.
Yes; using proportions, Andy is correct to believe that he has enough builders to finish this wall in less than 11 days.
What is proportion?Proportion refers to the ratio of one quantity or value compared to another.
Proportions are fractional values that are depicted in decimals, fractions, or percentages.
The number of builders that build Andy's wall in 15 days = 8
The number of days it would take 8 builders to finish the wall = 15 days
Proportionately, if 8 builders would take 15 days to build the wall, 11 builders would take 10.9 days (15 × 8) ÷11], which is approximately 11 days.
Thus, we can conclude that Andy is correct as 11 builders would take less than 11 days to finish the wall.
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write each combination of vectors as a single vector. (a) ab l 1 bc l (b) cd l 1 db l (c) db l 2 ab l (d) dc l 1 ca l 1 ab
(a) ab l 1 bc l = ab + bc
(b) cd l 1 db l = cd - db
(c) db l 2 ab l = 2ab + db
(d) dc l 1 ca l 1 ab = -ab + ca + dc
In each of the given combinations of vectors, we need to add or subtract the given vectors.
In case (a), the vectors are parallel and have the same direction, so we can simply add them to get the resultant vector: ab + bc = ac.
In case (b), the vectors are also parallel and have opposite directions, so we can subtract them to get the resultant vector: cd - db = cb.
In case (c), we need to double the vector db and subtract it from vector ab to get the resultant vector: ab - 2db = ab - db - db = ac - db.
In case (d), we need to add vector dc and subtract vectors ca and ab to get the resultant vector: dc - ca - ab = db. Therefore, the resultant vectors are: (a) ac, (b) cb, (c) ac - db, (d) db.
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Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 9 and b = 4?
The standard equation of a hyperbola with a vertical transverse axis, centered at the origin, and values of a = 9 and b = 4 is y^2/81 - x^2/16 = 1.
The standard equation of a hyperbola centered at the origin with a vertical transverse axis is given by (y^2/a^2) - (x^2/b^2) = 1. In this case, we are given that a = 9 and b = 4, so substituting these values into the equation, we get:
(y^2/81) - (x^2/16) = 1
This is the standard equation of the hyperbola in question. It tells us that the center of the hyperbola is at the origin (0,0), the transverse axis is vertical (parallel to the y-axis), and the distance from the center to the vertices is 9 units (which is the value of a).
The distance from the center to the foci is given by c = sqrt (a^2 + b^2), which in this case is sqrt (81 + 16) = sqrt (97). The asymptotes of the hyperbola are the lines y = (a/b) x and y = -(a/b) x, which in this case are y = (3/4) x and y = -(3/4) x.
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Assume that the helium porosity of coal samples taken from any particular seam is Normally distributedwith true standard deviation 0.75.a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20specimens from the seam was 4.85.b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with asample average of 4.56.c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99%confidence?
a. We are 95% confident that the true average porosity of the seam is between 4.25 and 5.45.
b. We are 98% confident that the true average porosity of the seam is between 3.68 and 5.44.
c. A sample size of at least 14 is necessary.
d. A sample size of at least 138 is necessary.
a. To compute a 95% confidence interval for the true average porosity of a certain seam, we use the formula:
CI = x ± tα/2 (s/√n)
where x is the sample average porosity, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with n-1 degrees of freedom and α/2 probability (0.025 for a 95% confidence interval).
Substituting the given values, we get:
CI = 4.85 ± 2.093 (0.75/√20)
= (4.25, 5.45)
Therefore, we are 95% confident that the true average porosity of the seam is between 4.25 and 5.45.
b. To compute a 98% confidence interval for the true average porosity of another seam, we use the same formula as in part (a), but with a different t-value (2.602 for a 98% confidence interval).
Substituting the given values, we get:
CI = 4.56 ± 2.602 (0.75/√16)
= (3.68, 5.44)
Therefore, we are 98% confident that the true average porosity of the seam is between 3.68 and 5.44.
c. To find the necessary sample size for a 95% confidence interval with a width of 0.40, we use the formula:
n = (tα/2 (s/width))^2
Substituting the given values and solving for n, we get:
n = (1.96 (0.75/0.40))^2
= 13.55
Therefore, a sample size of at least 14 is necessary.
d. To find the necessary sample size for a 99% confidence interval with a width of 0.2, we use the same formula as in part (c), but with a different t-value (2.576 for a 99% confidence interval).
Substituting the given values and solving for n, we get:
n = (2.576 (0.75/0.2))^2
= 137.68
Therefore, a sample size of at least 138 is necessary.
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Find the probability that a randomly
selected point within the circle falls in the
red-shaded square
The probability that a randomly selected point within the circle falls in the red-shaded square is: 0.50
What is the probability of selection?The formula for the area of a circle is:
A = πr²
where:
A is area
r is radius
Thus:
A = π * 4²
A = 50.265 unit²
Area of square = side * side
Area = 5 * 5
Area = 25 unit²
Thus:
P(selected area falls in the read square) = 25/50.265
P(selected area falls in the read square) = 0.497 ≈ 0.50
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if factor a has levels and factor b has levels in a two-way anova, we have a __ factorial design.
If factor a has r levels and factor b has c levels in a two-way ANOVA, we have a r x c factorial design.
In statistics, a factorial design is a study design where all possible combinations of levels of two or more independent variables (factors) are studied. In a two-way ANOVA, two factors are considered, and each factor has multiple levels.
For example, a two-way ANOVA can be used to study the effect of fertilizer type and watering frequency on plant growth, where fertilizer type has three levels and watering frequency has two levels. The resulting design is a 3x2 factorial design.
The number of treatments (unique combinations of levels of factors) in a factorial design is equal to the product of the number of levels of each factor. The advantage of a factorial design is that it allows for the investigation of interactions between factors, which cannot be detected in a one-way ANOVA.
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14. Find the reciprocal of 20.95 to4 decimal places using the tables of reciprocals (1mk)
The reciprocal of 20.95 to 4 decimal places using the table of reciprocals is 0.0478.
Reciprocal of a numberTo find the reciprocal of 20.95, we can look up the reciprocal of 20.9 or 21 in the table and then interpolate to get a more accurate value for 20.95.
reciprocal of 20.9 = 0.04784reciprocal of 21 = 0.04762To interpolate, we can calculate the difference between 20.95 and 20.9, which is 0.05, and the difference between the reciprocals of 20.95 and 20.9, which is 0.00009.
Then we can use the formula:
reciprocal of 20.95 = reciprocal of 20.9 + (difference / interval) x (reciprocal of 21 - reciprocal of 20.9)
where interval is the difference between the numbers in the table (which is 0.1 in this case).
Thus:
reciprocal of 20.95 = 0.04784 + (0.05 / 0.1) x (0.04762 - 0.04784)
= 0.04784 + 0.025 x (-0.00022)
= 0.04784 - 0.0000055
= 0.0478345
In other words, the reciprocal of 20.95 to 4 decimal places using the tables of reciprocals is 0.0478.
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A company wants to estimate the time its trucks take to drive from city A to city B. Assume that the standard deviation is known to be 12 minutes. What is the sample size required in order that error will not exceed � 2 minutes, with 95 percent confidence?
A sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.
To calculate the sample size required for this scenario, we need to use the formula for the sample size for a mean:
n = (z² * s²) / E²
where:
n = sample size
z = z-score for desired confidence level (95% = 1.96)
s = standard deviation (12 minutes)
E = desired margin of error (2 minutes)
Substituting in the values given, we get:
n = (1.96^2 * 12^2) / 2^2
n = 138.2976
We round up to the nearest whole number to get:
n = 139
Therefore, a sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.
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Which measure of center and measure of variability best describe the data set? Explain
When two data sets are both symmetric, then the appropriate measure of center to describe them would be the mean.
How to explain the informationThe mean, also known as the average, is calculated by adding up all the values in the data set and dividing by the total number of values. It represents the "center" of the data because it balances out the values on both sides of the distribution.
The mean is a good measure of center for symmetric data sets because it captures the balance of the distribution and provides a single value that summarizes the data.
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Which measure of center should you use to describe two data sets that are both symmetric?
what was the approximate number of mobile cellular subscriptions per 100 people in zimbabwe in 2003? the display gives the result of performing an exponential regression on a data set where the inputs are years since 2000 and the outputs are the corresponding mobile cellular subscriptions per 100 people in zimbabwe.
The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.
Exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,
Exponential model is a mathematical function which express in the form of a = [tex]e^{x}[/tex] where, x is power and the function is increasing exponentially.
[tex]y = ab^{x}[/tex]
Where,
a=1.067905095,
b=1.501755837,
y = [tex]1.067905095(1.501755837 )^{x}[/tex]
Thus, for finding the number of subscriptions in 2003,
x = 3,
Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is
y = [tex]1.067905095(1.501755837 )^{3}[/tex] = 4
The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.
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The given question is incomplete the complete question is :
Answer:4
Step-by-step explanation:
Find the slope of a line that is perpendicular to the line containing the points (–2, –1) and (2, –3).
A. m = –2
B. m = 2
C. m = -1/2
D. m = –1
HELLPP!! ASAPPPPP!! WILL HIVE BRAINLYIST!!
Answer: C 3
Step-by-step explanation:
Each of the sides from D have been multiplied by 3 to get D'
3 is the factor
C 3
Identify the area of the figure.
20 cm
12 cm
6 cm
10 cm
10 cm
7 cm
26 cm
24 cm
Answer:
476 cm²
Step-by-step explanation:
area of top rectangle = 20 X 7 = 140.
area of bottom rectangle = 12 X (10 + 6) = 12 X 16 = 192.
area of small triangle = 1/2 X 6 X (20 - 12) = 1/2 X 6 X 8 = 24.
area of large triangle = 1/2 X 10 X 24 = 120.
area of the figure = 140 + 192 + 24 + 120 = 476 cm²
What is the percentage equivalent to 21 over 70?
30%
35%
49%
92%
Answer:
The percentage equivalent of 21/70 can be found by dividing 21 by 70 and then multiplying by 100 to convert to a percentage.
In order to find a percentage just divide two numbers which the numerator divided by the denominator x 100 = to answer%
(21/70) x 100 = 30%
Therefore, the answer is 30%.
solve using linear same systems 4x-5y=-2
-8x+10y=4
Answer:
The lines are the same. (Infinite Solutions)
Step-by-step explanation:
To solve this, we need to get either x or y to cancel out and equal 0 first.
Let's look at our two equations.
4x-5y=(-2)
-8x+10y=4
I'm going to divide the -8x by 2. Remember when dividing to divide both sides of the equation, otherwise you will end up with something completely different than what you started out with.
-8x+10y=4 (divided by 2)
Our new equation is -4x+5y=2.
Now let's take our other equation. Please see the screenshot to see how this is solved.
Forgive the horrible handwriting, I'm on a computer :(
What figure is created from the coordinate points (3, 2), (3, 6), and (5, 2)? square rectangle triangle parallelogram
Answer:
it's a triangle
Step-by-step explanation:
For a one-tailed dependent samples t-Test, what specific critical value do we need to overcome at the p < .05 level for a study with 30 participants?1.7011.6991.6981.69None of the above
For a one-tailed dependent samples t-Test with 30 participants at the p < .05 level, we need to overcome a specific critical value of 1.697.
This value can be obtained from a t-table or calculated using statistical software. It is important to note that the critical value may vary depending on the specific alpha level chosen and the study's degrees of freedom (df). However, for a one-tailed dependent samples t-Test with 30 participants at the p < .05 level, the critical value of 1.697 is appropriate. This critical value represents the minimum t-value that must be obtained to reject the null hypothesis and conclude that there is a significant difference between the two dependent groups being compared.
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for the following scenarios, state the null hypothesis and the alternative hypothesis to be used when a hypothesis test is performed
i) Null hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is equal to 2/3.
Alternative hypothesis: Proportion of Americans who believe that nuclear capabilities of other countries seriously threaten world peace is different from 2/3.
ii) Null hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is less than or equal to 9%. Alternative hypothesis: Proportion of gaming headsets with manufacturing flaws that make game-play impossible is greater than 9%.
iii) Null hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is less than or equal to 106°F. Alternative hypothesis: Mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe is greater than 106°F.
In hypothesis testing, the null hypothesis is the default assumption, while the alternative hypothesis is what the researcher wants to prove.
The next step is to conduct a hypothesis test, where a test statistic is calculated, and its probability of occurrence is determined assuming that the null hypothesis is true.
If this probability is very small (usually less than 5%), then the null hypothesis is rejected in favor of the alternative hypothesis.
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Complete Question
1. For the following scenarios, state the null hypothesis and the alternative hypothesis to be used when a hypothesis test is performed.
Scenario i) After the Cold War, it was claimed that two of three Americans say that the chances of world peace are seriously threatened by the nuclear capabilities of other countries. Is there evidence that this proportion is actually different? To investigate this, a random sample of 400 Americans was taken, and it was found that only 248 hold this view.
Scenario ii) JP wants to test whether at least 9% of gaming headsets have manufacturing flaws that make game-play impossible. A sample of 150 headsets revealed that 12 contained a defect.
Scenario iii) The mean water temperature downstream from JP's Power Plant's cooling tower discharge pipe should be no more than 106°F. Past experience has indicated that the standard deviation of temperature is 2°F. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 99°F
is the relationship linear, exponential, or neither? x 5 191 33 47 y −1,−6,−36,−216
The relationship between x and y is neither linear nor exponential. To determine if the relationship between x and y is linear, exponential, or neither, we can create a table of values and see if there is a constant rate of change or a constant ratio between the values of x and y.
x | y
---|---
5 | -1
19 | -6
33 | -36
47 | -216
Looking at the table, we can see that there is no constant rate of change between the values of x and y. Therefore, the relationship is not linear. To determine if the relationship is exponential, we can check if there is a constant ratio between the values of y and x.
y/x = (-1)/5 = -0.2
(-6)/19 = -0.3158
(-36)/33 = -1.0909
(-216)/47 = -4.5957
Since the ratio between y and x is not constant, the relationship is not exponential either.
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shawndra made the two statements to marcella: it is not possible to draw a trapezoid that is a rectangle it is possible to draw a square that is a rectangle. marcella said that both statements are possible: it is possible to draw a trapezoid that is a rectangle it is possible to draw a square that is a rectangle. who is correct? explain your answer using the properties of quadrilaterals.
Shawndra is correct
(A) It is not possible to draw a trapezoid that is a rectangle true.
(B) it is possible to draw a square that is a rectangle true.
A. A trapezoid cannot be drawn as a rectangle.
The statement is true because we cannot draw a trapezoid that is a rectangle as a rectangle is a parallelogram with two pairs of parallel sides having opposite sides equal in length whereas a trapezoid is a quadrilateral with exactly one pair of parallel sides.
B. A square can be drawn as a rectangle.
The statement is true because we can draw a square that is a rectangle as any parallelogram with right angles is referred to be a rectangle whereas a parallelogram with right angles that has two pairs of opposite sides is a square. Despite being a unique type of rectangle with equal-length sides, squares are all rectangles.
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A study of commuting times reports the travel times to work of a random sample of 1000 employed adults in Chicago.The mean is x = 40.0 minutes and the standard deviation is s = 56.9 minutes.What is the standard error of the mean?1.8021.886.991.09
After considering all the given options we conclude that the standard error of the mean is 1.80, which is Option A under the condition that the mean is x = 40.0 minutes and the standard deviation is s = 56.9 minutes.
The formula derived for standard error of the mean (SEM) is expressed as:
SEM = σ/√n
Here,
SEM = standard error of the sample,
σ = sample standard deviation
n = sample size.
For the given case, we have x = 40.0 minutes and s = 56.9 minutes for a sample size of 1000 employed adults in Chicago. Therefore,
SEM = s/√n
= 56.9/√1000
≈ 1.80
Therefore, the answer is A) 1.80.
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The complete question
A study of commuting times reports the travel times to work of a random sample of 1000 employed adults in Chicago. The mean is x = 40.0 minutes and the standard deviation is s = 56.9 minutes.
What is the standard error of the mean?
A) 1.80
B) 21.88
C) 6.99
D) 1.09
pls help asap with homework!!!!
The exact value of cos 30 degrees is √3/2.
The exact value of sin 45 degrees is 1/√2 or √2/2.
The exact value of tan 30 degrees is 1/√3 or √3/3.
We have,
The exact value of cos 30 can be found using the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane.
On the unit circle, the angle of 30 degrees is measured counterclockwise from the positive x-axis and intersects the circle at a point where the x-coordinate is √3/2 and the y-coordinate is 1/2.
Therefore, Cos 30 is equal to √3/2.
The exact value of sin 45 can also be found using the unit circle. In this case, the angle of 45 degrees intersects the unit circle at a point where both the x-coordinate and y-coordinate are 1/√2.
Therefore, Sin 45 is equal to 1/√2, which can be simplified to (√2)/2.
The exact value of tan 30 can be found using the relationship between tangent and sine/cosine: tan x = sin x / cos x.
Therefore, tan 30 = sin 30 / cos 30.
From the unit circle, we know that sin 30 is equal to 1/2 and cos 30 is equal to √3/2. Substituting these values into the formula, we get,
tan 30 = (1/2) / (√3/2) = 1/√3 = √3/3.
Thus,
The exact value of cos 30 degrees is √3/2.
The exact value of sin 45 degrees is 1/√2 or √2/2.
The exact value of tan 30 degrees is 1/√3 or √3/3.
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find the particular solution to the differential equation. 4y2 dx = 9x2 dy when x = 4, y = −3
Thus, the equation of the curve that satisfies the differential equation and passes through the point (4,-3) is y = -3x^2/5 + 57/5.
To find the particular solution to the given differential equation, we first need to separate the variables. We can do this by rearranging the equation as follows:
4y^2 dx = 9x^2 dy
dy/dx = 4y^2/9x^2
Now, we can integrate both sides with respect to their respective variables. Integrating the left-hand side gives us y as a function of x:
∫dy = ∫4y^2/9x^2 dx
y = -3x^2/5 + C
To find the value of the constant C, we can use the initial condition provided in the problem. When x = 4 and y = -3, we have:
-3 = -3(4)^2/5 + C
C = 57/5
Therefore, the particular solution to the differential equation is:
y = -3x^2/5 + 57/5
This is the equation of the curve that satisfies the differential equation and passes through the point (4,-3).
In summary, the process of finding a particular solution to a differential equation involves separating the variables, integrating both sides, and using the initial conditions to determine the value of the constant of integration. The resulting function is the particular solution to the differential equation.
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PLEASE HELP OR I AM DEAD.
I only need Q9 answers
By algebra properties, the simplified form of the expressions are listed below in the following four cases:
Case 1: 6
Case 2: 1 / 5
Case 3: √3
Case 4: - 3
How to simplify expressions involving powers and roots by algebra properties
In this problem we must simplify expressions involving powers and roots by algebra properties, mainly power and root properties. Now we proceed to show how each expression is simplified:
Case 1
[tex](1^{3}+2^{3}+ 3^{3})^{\frac {1}{2}}[/tex]
[tex](1 + 8 + 27)^{\frac{1}{2}}[/tex]
[tex]36^{\frac{1}{2}}[/tex]
√36
6
Case 2
[tex]\left[\left(625^{-\frac{1}{2}}\right)^{-\frac{1}{4}}\right]^{2}[/tex]
[tex]\left[\left[\left(625^{\frac{1}{2}}\right)^{-1}\right]^{-\frac {1}{4}}\right]^{2}[/tex]
[tex]\left[\left(\frac{1}{25}\right)^{\frac{1}{4}}\right]^{2}[/tex]
[tex]\left(\frac{1}{25} \right)^{\frac{1}{2}}[/tex]
√(1 / 25)
1 / 5
Case 3
[tex]\frac{9^{\frac{1}{2}}\times 27^{- \frac {1}{3}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}[/tex]
[tex]\frac{(3^{2})^{\frac{1}{2}}\times (3^{3})^{-\frac{1}{3}}}{3^{\frac{1}{6}}\times 3^{-\frac{2}{3}}}[/tex]
[tex]\frac{3\times 3^{- 1}}{3^{\frac{1}{6}}\times 3^{- \frac{2}{3}}}\\[/tex]
[tex]\frac{1}{3^{-\frac{1}{2}}}[/tex]
[tex]3^{\frac{1}{2}}[/tex]
√3
Case 4
[tex]64^{-\frac{1}{3}}\cdot \left[64^{\frac{1}{3}}-64^{\frac{2}{3}}\right][/tex]
[tex]64^{-\frac{1}{3}}\cdot 64^{\frac{1}{3}}-64^{-\frac{1}{3}}\cdot 64^{\frac{2}{3}}[/tex]
[tex]1 - 64^{ \frac{1}{3}}[/tex]
1 - ∛64
1 - 4
- 3
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PLEASE HLPP
Verify that the segments are parallel. CD || ĀB
The slopes are not equal (7/6 ≠ 7/2), we can conclude that the segments CD and AB are not parallel in triangle ABCDE.
To verify that the segments CD and AB are parallel in triangle ABCDE, we need to show that the corresponding sides have the same slope.
Let's first find the slope of segment CD. Given that point C is the origin (0,0) and point D has coordinates (EC, ED) = (12, 14), the slope of CD can be calculated as follows:
slope_CD = (ED - 0) / (EC - 0)
= 14 / 12
= 7 / 6
Now, let's find the slope of segment AB. Given that point A is the origin (0,0) and point B has coordinates (CA, DB) = (4, 42/3), the slope of AB can be calculated as follows:
slope_AB = (DB - 0) / (CA - 0)
= (42/3) / 4
= (14/1) / (4/1)
= 14 / 4
= 7 / 2
If the slopes of CD and AB are equal, then the segments are parallel. Let's compare the slopes:
slope_CD = 7 / 6
slope_AB = 7 / 2
Since the slopes are not equal (7/6 ≠ 7/2), we can conclude that the segments CD and AB are not parallel in triangle ABCDE.
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find the nth term of the geometric sequence whose initial term is a 1 = 5.5 a1=5.5 and common ratio is 3 3 .
The nth term of this geometric sequence is simply 5.5, regardless of the value of n.
The nth term of a geometric sequence with first term a1 and common ratio r is given by the formula:
an = a1 * r^(n-1)
In this case, the first term a1 is given as 5.5 and the common ratio r is 3/3 = 1. Therefore, the formula becomes:
an = 5.5 * 1^(n-1) = 5.5 * 1 = 5.5
So, the nth term of this geometric sequence is simply 5.5, regardless of the value of n.
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Marked price 39 selling price 31 what is the discount offered
Marked price: 39 dollars
Selling price: 31 dollars
Discount: ???
First stepSubtract the post-discount price from the pre-discount price.
31-39=-8
Second stepDivide this new number by the pre-discount price.
-8/39=-0.20512820512
Third step:Multiply the resultant number by 100.
-0.20512820512×100= -20.512820512
Fourth stepRound the number
-20.512820512 → -20.5
Answer:The discount was %20.5 off
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a quality control expert at life batteries wants to test their new batteries. the design engineer claims they have a standard deviation of 62 minutes with a mean life of 606 minutes. if the claim is true, in a sample of 99 batteries, what is the probability that the mean battery life would differ from the population mean by greater than 18.4 minutes? round your answer to four decimal places.
The probability that the mean battery life would differ from the population mean by greater than 18.4 minutes is 0.0148. The formula for the standard error of the mean is SE = σ/√n
To solve this problem, we need to use the Central Limit Theorem (CLT) which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
The formula for the standard error of the mean is:
SE = σ/√n
Where SE is the standard error, σ is the population standard deviation, and n is the sample size.
In this case, we are given that the population standard deviation (σ) is 62 minutes, the population mean is 606 minutes, and the sample size (n) is 99 batteries. Therefore, the standard error of the mean is:
SE = 62/√99 = 6.231
Next, we need to find the z-score associated with the difference between the sample mean and the population mean of 18.4 minutes. The formula for the z-score is:
z = (x - μ) / SE
Where x is the sample mean, μ is the population mean, and SE is the standard error.
Substituting the values we have:
z = (606 + 18.4 - 606) / 6.231 = 2.96
Using a standard normal distribution table, we find that the probability of getting a z-score greater than 2.96 is 0.0148. Therefore, the probability that the mean battery life would differ from the population mean by greater than 18.4 minutes in a sample of 99 batteries is 0.0148, or about 1.48%.
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Assume that a wheel on a car has a radius of 36cm. Find the angle (in radians) that the wheel turns while the car travels the given distance. (Two Answers)
2 meters (200 cm) 5 meters
The central angle is solved and wheel turns while the car travels 2 meters is 5.5556 radians, and while the car travels 5 meters, it is 13.8889 radians
Given data ,
To find the angle (in radians) that the wheel turns while the car travels a given distance, we can use the formula:
Angle (in radians) = Distance / Radius
a)
For a distance of 2 meters (200 cm):
Angle (in radians) = 200 cm / 36 cm
Angle (in radians) = 5.5556 radians
b)
For a distance of 5 meters:
Angle (in radians) = 500 cm / 36 cm
Angle (in radians) = 13.8889 radians
Hence , the angle (in radians) that the wheel turns while the car travels 2 meters is approximately 5.5556 radians, and while the car travels 5 meters, it is approximately 13.8889 radians
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Which of the following functions has the greatest y-intercept? (1 point) f(x) x y −3 9 −2 4 −1 1 0 0 1 1 2 4 g(x) = 5 cos(3x) − 5 f(x) g(x) Not enough information f(x) and g(x) have the same y-intercept
Answer : they have the same y-intercept
Both function have same y - intercept.
The two given functions are;
x: -3 -2 -1 0 1 2
f(x): 9 4 -1 0 1 4
And, g(x) = 5 cos (3x) - 5
Since, We know that;
The y-intercept occurs when x=0.
Therefore,
⇒ f(x) has a y-intercept of 0
(from given tabular data).
And, g(x) has a y-intercept of at x = 0
g(0) = 5 cos (0) - 5
= 5 - 5
= 0
Hence, Both function have same y - intercept.
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