Start by describing the data given about the flower Heliconia's varieties. Then, conduct a significance test, possibly using ANOVA, to compare their mean lengths. However, the computation for the p-value and F-statistical is not specified in the question. You can just round your numbers according to the instructions.
Explanation:The first step in a complete analysis is the description of the data. From the question, we have three types of tropical flower Heliconia, namely H. bihai, H. caribaea red, and H. caribaea yellow. We have the respective data points for each class, n, the sample mean, x-bar, standard deviation, s, and the standard error, s_(x-bar).
The next step is to carry out a significance test. This can be done using ANOVA (Analysis of variance), which compares the means of three or more samples. The test statistic in ANOVA is the F statistic, and the null hypothesis is that the population means are equal.
Given numbers, you can compute the F-statistic, but from the question, it's unclear how the actual computation was done. The p-value can also be calculated from the F statistic; it's the probability of getting an extreme or more extreme result in your observed data, assuming the null hypothesis is true.
The instruction is explicit regarding how to round your numbers: sample mean to four decimal places, standard deviation to three decimal places, and your test statistic (F-statistic) to two decimal places. The p-value should also be rounded to three decimal places.
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A toy has various shaped objects that a child can push through matching holes. The area of the sq. Hole is 8 sq cm. The volume of a cube shaped block is 64 cubic cm. Will the block fit in the square hole?
Answer:
No
Step-by-step explanation:
The volume of a cube is the cube of the edge length, so the edge length of the cube-shaped block is ...
edge length = ∛(64 cm³) = 4 cm
Then the smallest cross-section will be a square of edge length 4 cm, so will have an area of (4 cm)² = 16 cm².
The 16 cm² shape will not fit through an 8 cm² hole.
Using given area of the square hole, we find its side length to be approx. 2.83 cm. Calculating the side length of the block using its volume, we get 4 cm. As the block is larger than the hole, it won't fit.
Explanation:The problem involves geometry, specifically the concepts of area and volume. The area of a square is given by the formula, A = s^2, where s is the side of the square. In this case, the area of the square hole is 8 sq cm, which means the side length of the square hole (s) is the square root of 8, or about 2.83 cm.
The volume of a cube is given by the formula V = s^3, where s is the side length of the cube. The volume of the cube block is 64 cubic cm, which means the side length of the block (s) is the cube root of 64, or 4 cm.
Therefore, since the side length of the block (4 cm) is greater than the side length of the square hole (2.83 cm), the block will not fit through the hole.
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Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subject's blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation? 127 150 121 120 140 128
Answer:
1. Range =30
2. Variance =137.6
3. Standard deviation=11.7303
Step-by-step explanation:
This question requires you to find the range, variance and standard deviation of sample data set.
Given the data as; 127 150 121 120 140 128
Arrange the data in ascending order;
sample set S={120, 121, 127, 128, 140, 150}
number of elements, n=6
1. Range = Maximum (S) - Minimum (S) = 150- 120 = 30
⇒Find the mean of the data set
[tex]mean= \frac{120+121+127+128+140+150}{6} = 786/6 = 131[/tex]
2. Variance is the measure of how far a set of data is spread out.Standard deviation is the square-root of variance.To find variance you need to follow the steps below;
Find the mean of the sample dataFind the deviation of each of the data from the meanSquare each value of the deviations from the meanFind the sum in the values of the squared deviations Divide the sum in the values of the squared deviations by n-1 where n is the number of elements to get the varianceFind the square-root of the variance to get the standard deviation of the sample dataFinding the deviations from the mean and their squares
Deviations Squares of deviations
120-131= -11 -11²= 121
121-131= -10 -10² =100
127-131= -4 -4² = 16
128-131= -3 -3= 9
140-131= 9 9²= 81
150-131= 19 19²= 361
Finding the sum of the squares of the deviations from the mean
[tex]=121+100+16+9+81+361=688[/tex]
Finding the variance
Variance, S²=(sum of squares of deviations from mean)/ n-1
[tex]=\frac{688}{n-1} =\frac{688}{6-1} =\frac{688}{5} =137.6[/tex]
Finding standard deviation
Standard deviation , s , is the square-root of the variance
[tex]s=\sqrt{137.6} =11.73[/tex]
Final Answer:
- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg
Explanation:
To find the range, variance, and standard deviation for the given blood pressure readings, we can follow these steps:
1. **Range:**
- The range is the difference between the highest and lowest values in the data set.
- Highest reading = 150 mmHg
- Lowest reading = 120 mmHg
- Range = Highest reading - Lowest reading = 150 - 120 = 30 mmHg
2. **Variance:**
- Variance measures the average degree to which each reading differs from the mean of the readings. Because we are dealing with a sample of the population, not the entire population, we'll use the sample variance formula.
- First, compute the mean of the readings.
- Mean (average) blood pressure reading = (127 + 150 + 121 + 120 + 140 + 128) / 6
- Mean = 786 / 6 = 131 mmHg
- Now, we'll calculate the square of the differences between each reading and the mean, sum those, and divide by (n-1), where n is the number of readings.
- Differences squared: (127-131)², (150-131)², (121-131)², (120-131)², (140-131)², (128-131)²
- = (-4)², (19)², (-10)², (-11)², (9)², (-3)²
- = 16, 361, 100, 121, 81, 9
- Sum of squared differences = 16 + 361 + 100 + 121 + 81 + 9 = 688
- Sample variance = 688 / (6 - 1) = 688 / 5 = 137.6 (mmHg)²
3. **Standard Deviation:**
- The standard deviation is the square root of the variance and provides a measure of the average distance from the mean.
- Standard deviation = √variance = √137.6 ≈ 11.73 mmHg
4. **Ideal Standard Deviation:**
- If the subject's blood pressure remains constant, and the measurement technique is applied correctly and without any error, the ideal standard deviation should be zero because all measurements would be the same, resulting in no variability.
In summary:
- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg
Which of the following describes the net of a cylinder? one square, four triangles one circle, one rectangle one rectangle, two circles one circle, two rectangles
The net of a cylinder is best described by a circle and one rectangle.
Geometrical construction of a cylinder -A cylinder is a three-dimensional solid, the most basics of curvilinear shapes which is considered as a prism with circle as its base.
A cylinder has a base radius and the height from its base to top .
Formula of surface area of cylinder is = 2πr(r + h)
Formula of Volume of cylinder is = [tex]\pi r^{2} h[/tex]
How to construct the net of a cylinder ?The net of the cylinder should have one side open such that it can be inserted within the cylinder.
As the top of the cylinder is circle, thus the net should have one circular top . Also the body of the cylinder is in the form of a rectangle which ensures the net should have also one rectangular body.
Therefore the net of a cylinder is best described by a circle and one rectangle.
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The net of a cylinder is comprised of 'one rectangle and two circles', which represent the lateral surface and the two equal-sized circular bases of the cylinder, respectively.
Explanation:The net of a cylinder consists of two equal-sized circles and one rectangle that wraps around to form the curved surface. The two circles represent the top and bottom (or base) of the cylinder, and they are identical in size because the top and the bottom of a cylinder have the same cross-sectional area. The rectangle represents the lateral surface area of the cylinder, which, if 'unrolled', resembles a rectangle whose length is equal to the circumference of the circles (the perimeter of the base) and whose height is equal to that of the cylinder. The correct option that describes the net of a cylinder is thus 'one rectangle, two circles'.
PLEASE HELP & SHOW WORK!
1. Suzette ran and bikes for a total of 110 mi in 7 h. Her average running speed was 5 mph and her average biking speed was 20 mph.
Let x = Total hours Suzette ran.
Let y = Total hours Suzette biked.
Use substitution to solve for x and y. Show your work. Check your solution.
Note: I genuinely appreciate the help. I will be sure to mark BRAINLIEST as well. Thank you in advance to all that can help!
Finding x.
Suzette ran = x
Suzette biked = 4x
7 = x + 4x --) 7 = 5x --) 1.4 = x
Suzette ran for 1.4 hours
Finding y.
Quickest way is to use Suzette biked = 4x and substitute the x for 1.4 to find how much she biked.
4 x 1.4 = 5.6
1.4 + 5.6 = 7 hours the total time exercising
And the mileage adds up to.
5(1.4) + 20(5.6) = 119
Drag the tiles to the correct boxes to complete the pairs.
Match the exponential functions to their y-intercepts.
Answer:
1. [tex]f(x)=-10^{x-1}-10[/tex] - [tex]-\frac{101}{10}[/tex]
2. [tex]f(x)=-3^{x+5}-9[/tex] - [tex]-252[/tex]
3. [tex]f(x)=-3^{x-2}-1[/tex] - [tex]-\frac{10}{9}[/tex]
4. [tex]f(x)=-17^{x-1}+2[/tex] - [tex]\frac{33}{17}
Step-by-step explanation:
We are given the exponential functions and we are to match them with their y-intercepts.
1. [tex]f(x)=-10^{x-1}-10[/tex]:
Substituting x = 0 to find the y-intercept:
[tex]f(x)=-10^{0-1}-10 = -\frac{101}{10}[/tex]
y-intercept ---> [tex]-\frac{101}{10}[/tex]
2. [tex]f(x)=-3^{x+5}-9[/tex]:
Substituting x = 0 to find the y-intercept:
[tex]f(x)=-3^{x+5}-9=-252[/tex]
y-intercept ---> [tex]-252[/tex]
3. [tex]f(x)=-3^{x-2}-1[/tex]:
Substituting x = 0 to find the y-intercept:
[tex]f(x)=-3^{x-2}-1=-\frac{10}{9}[/tex]
y-intercept ---> [tex]-\frac{10}{9}[/tex]
4. [tex]f(x)=-17^{x-1}+2[/tex]:
Substituting x = 0 to find the y-intercept:
[tex]f(x)=-17^{x-1}+2=\frac{33}{17}[/tex]
y-intercept ---> [tex]\frac{33}{17}
HELP PLEASE
must show work
Answer:
1. 4n^3
2. 4k^7
3. 3
4. -30x
5. -6
Step-by-step explanation:
1. The prime factorization of 12 is 2 x 2 x 3 and the prime factorization of 16 is 2 x 2 x 2 x 2. When you look at these two expressions you can see the common factors of these two numbers are 2 x 2, which is 4. Next, we look at the GCF of the N's which would be n^3 since n^5 has three N's in it. Therefore, we get 4n^3 when we multiply the two together.
2. The factors of 8 are 1, 2, 4, and 8. Out of these, 1, 2, and 4 are the only factors that 20 shares with it and 4 is the greatest. Then, we look at the K's and the GCF of the K's is k^7 since k^8 has seven K's. We multiply the two and we get 4k^7.
3. Since one of the numbers of the three given here does not include the variable n, there will not be any N's in the GCF of the three, so we don't have to worry about that. Now, we just find the GCF of 18, -24, and -21. The factors of 18 are 1, 2, 3, 6, 9, and 18, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, and lastly, the factors of 21 are 1, 3, 7, and 21. From these, 3 is the biggest common divisor, therefore the GCF is 3.
4. Between the two X's, X^1 is the biggest amount of X's this GCF has, so the final GCF will be some constant multiplies with X. Since we are dealing with bigger numbers on this problem, we should use prime factorization. The prime factorization of 90 is 2 x 3 x 3 x 5, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5. From these expressions, we take the biggest amount of each common factor as we can. Since these expressions both have 2, we take the smaller amount of 2's which is one two. Then we get one three from both expressions, and one five as well. 2 times 3 times 5 equals 30, therefore, we get -30x, and not 30x, because both of these numbers are negatives.
5. All of these numbers do not have an x, so there won't be an x in our GCF. Another method of quickly finding the GCF of numbers is to look at the smallest number's factors first to see what factors it shares with the other numbers. The factors of 12 are 1, 2, 3, 4, 6, and 12. 42 and 30 do not have the factor 12, so we can go down the list and see if 42 and 30 share the factor 6, which they do since 6 times 7 is 42 and 6 times 5 is 30. Since all of these numbers share the negative sign, the GCF of these three numbers is -6.
A biologist doing an experiment has a bacteria population cultured in a petri dish. After measuring, she finds that there are 11 million bacteria infected with the zeta-virus and 5.2 million infection-free bacteria. Her theory predicts that 50% of infected bacteria will remain infected over the next hour, while the remaining of the infected manage to fight off the virus in that hour. Similarly, she predicts that 80% of the healthy bacteria will remain healthy over the hour while the remaining of the healthy will succumb to the affliction Modeling this as a Markov chain, use her theory to predict the population of non-infected bacteria after 3 hour(s).
Answer:
11.4 million
Step-by-step explanation:
Let's define the variables i and i' to represent the number of infected bacteria initially and after 1 hour, and the variables n and n' to represent the number of non-infected bacteria initially and after 1 hour. The biologist's theory predicts ...
0.50i +0.20n = i'
0.50i +0.80n = n'
In matrix form, the equation looks like ...
[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right] \left[\begin{array}{c}i&n\end{array}\right]=\left[\begin{array}{c}i'&n'\end{array}\right][/tex]
If i''' and n''' indicate the numbers after 3 hours, then (in millions), the numbers are ...
[tex]\left[\begin{array}{cc}0.5&0.2\\0.5&0.8\end{array}\right]^3 \left[\begin{array}{c}11&5.2\end{array}\right]=\left[\begin{array}{c}i'''&n'''\end{array}\right][/tex]
Carrying out the math, we find i''' = 4.8006 (million) and n''' = 11.3994 (million).
The population of non-infected bacteria is expected to be about 11.4 million after 3 hours.
What percent is equivalent to 1/20 ? 5% 6% 20% 25%
For this case we must indicate the percentage that represents the following expression:
[tex]\frac {1} {20}[/tex]
By a rule of three we can solve them:
20 ----------> 100%
1 ------------> x
Where the variable x represents the percentage of 1 with a base of 20.
[tex]x = \frac {1 * 100} {20}\\x = 5[/tex]
So, we have that [tex]\frac {1} {20}[/tex] represents 5%
Answer:
Option A
The required 1/20 is equal to 5% when expressed as a percentage. Option A is correct.
To find the percent equivalent to 1/20, we need to express it as a fraction of 100.
First, we can convert 1/20 into a decimal by dividing 1 by 20, which gives us 0.05.
Next, we multiply the decimal by 100 to express it as a percentage: 0.05 * 100 = 5%.
Therefore, 1/20 is equivalent to 5%.
In conclusion, 1/20 is equal to 5% when expressed as a percentage.
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how many pieces of string that are 2/7 of an inch long can be cut from a piece of string that are 7/8 of an inch long
namely, how many times does 2/7 go into 7/8?
[tex]\bf \cfrac{7}{8}\div\cfrac{2}{7}\implies \cfrac{7}{8}\cdot \cfrac{7}{2}\implies \cfrac{49}{16}\implies 3\frac{1}{16}\impliedby \textit{3 whole times}[/tex]
A 7/8 inch long string can be cut into 3 pieces of length 2/7 inch each.
Explanation:This is an example of fraction division, which is related to Mathematics. To find out, how many pieces of string that are 2/7 of an inch long can be cut from a piece of string that is 7/8 of an inch long, you would have to divide the whole length of the string (7/8 inch) by the length of each piece (2/7 inch).
When you divide fractions, you actually multiply by the reciprocal of the second fraction. The reciprocal of a fraction is simply, flipping the numerator and denominator. So, the reciprocal of 2/7 would be 7/2.
Now simply multiply the two fractions, (7/8) times (7/2) which equals 49/16 or roughly 3.06. However, since you can't cut a string into a .06 piece, the answer would be 3 pieces.
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Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet below.
What is Kendra’s net cash flow?
a.
$295
b.
$285
c.
$275
d.
$255
need an answer within 40 min
Answer:
a. $295
Step-by-step explanation:
Add the net pay and the interest. This is the total net income.
Then add all other amounts separately. These are the expenses.
Subtract the expenses from the total net income.
The answer is a. $295
Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.
What are expenses?It is defined as the money spends on the utility, the amount of money is required to buy something, in other words, it is the outflow of money from the sole earner's income or the money incurred by any organization.
It is given that:
Kendra is working on her financial plan and lists all of her income and expenses in the spreadsheet shown in the picture.
From the spreadsheet:
Add the interest to the net pay. The overall net income is shown here.
= 2300 + 200
= $2320
Next, add each additional sum separately. The costs are as follows.
= 800+120+90+45+95+80+275+520
= $2025
From the entire net income, deduct the costs.
= 2320 - 2025
= $295
Thus, Kendra’s net cash flow is $295 because the total net income is $2320 and total expenses are $2025 option (a) is correct.
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What is the product of ( x ^ ( 2 ) )/( 6 y );( 2 x )/( y ^ ( 2 ) ) and ( 3 v ^ ( 3 ) )/( 4 x );x \neq 0;y \neq 0
Answer:
i couldnt answer please be more specific
Step-by-step explanation:
Earl writes 1/6 of a page in 1/12 of a minute. How much time does it take him to write a full page?
ASAP
Answer:
in this problem we do a comparison case t i.e if 1/12 he writes 1/6 of page what about 1 page
1/12minute = 1/6
? × 1 then we cross multiply
(1*1/12) ÷ 1/6 =1/12*6 = 1/2 minute
Larry and Paul start out running at a rate of 5 mph. Paul speeds up his pace after 5 miles to 10 mph but Larry continues the same pace. How long after they start will they be 10 miles apart?
The answer is:
They will be 10 miles apart after 3 hours.
Why?To calculate how long after they start will they be 10 miles apart, we need to assume that after 1 one hour, they were at the same distance (5 miles), then, calculate the time when they are 10 miles apart, knowing that Paul increased its speed two times, running first at 5mph and then, at 10 mph.
The time that will pass to be 10 miles apart can be calculated using the following equation:
[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]
Calculating the time to reach 5 miles for both Larry and Paul, at a speed of 5 mph, we have:
[tex]x=xo+v*t\\\\5miles=0+5mph*t\\\\t=\frac{5miles}{5mph}=1hour[/tex]
We have that to reach a distance of 5 miles, they needed 1 hour. We need to remember that at this time, they were at the same distance.
If we want to know how many time will it take for them to be 10 miles apart with Paul increasing its speed to 10mph, we need to assume that after that time, the distance reached by Paul will be the distance reached by Larry plus 10 miles.
So, for the second moment (Paul increasing his speed) we have:
For Larry:
[tex]x_{L}=5miles+5mph*t[/tex]
Therefore, the distance of Paul will be equal to the distance of Larry plus 10 miles.
For Paul:
[tex]x{L}+10miles=xo+10mph*t\\\\5miles+5mph*t+10miles=5miles+10mph*t\\\\5miles+10miles-5miles=10mph*t-5mph*t\\\\10miles=5mph*t\\\\t=\frac{10miles}{5mph}=2hours[/tex]
Then, there will take 2 hours to Paul to be 10 miles apart from Larry after both were at 5 miles and Paul increased his speed to 10 mph.
Hence, calculating the total time, we have:
[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]
[tex]TotalTime=1hour+2hours=3hours[/tex]
Have a nice day!
Which expression is equivalent to (5x + 2) + (5x + 2) + (5x + 2) for all values of x?
The expression (5x + 2) + (5x + 2) + (5x + 2) simplifies to 15x + 6 by combining like terms; three 5x's give 15x, and three 2's give 6 when added together.
The expression (5x + 2) + (5x + 2) + (5x + 2) is given by adding three identical binomials. To find an equivalent expression, you can use the distributive property of multiplication over addition, which in this case can also be seen as simply combining like terms.
Step-by-step, here's how you simplify the expression:
Combine like terms (5x from each binomial and 2 from each binomial).Since there are three 5x's, you have 3 * 5x, which is 15x.Since there are three 2's, you have 3 * 2, which is 6.Add these results together to get the final simplified expression, 15x + 6.So, (5x + 2) + (5x + 2) + (5x + 2) is equivalent to 15x + 6 for all values of x.
Which shows the domain and range of these functions?
Answer:
C. Domain: (negative infinity, infinity) Range: (0, infinity)
Step-by-step explanation:
It's correct
The domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
y = f(x)
y = g(x)
y = h(x)
y = k(x)
Then the domain of the functions will be (-∞, ∞) and the range of the functions will be (0, ∞).
Then the correct option is C.
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What is the main difference between investing and saving?
Select the best answer from the choices provided.
A.)Investing has a better annual rate of return than saving.
B.) Investing has the risk of losing principal, whereas saving does not.
C.) Invested money earns interest, whereas saved money does not.
D.)Invested money is insured by the FDIC, whereas saved money is not.
Answer:
B.) Investing has the risk of losing principal, whereas saving does not.
Step-by-step explanation:
Saving can be accomplished a number of ways, including putting the money in a cookie jar (where it will not earn interest). Most savings institutions (banks, credit unions, and the like) are governed by rules that help to ensure the availability and safety of the balance. Often, such institutions are insured so that depositors are protected against loss of principal.
Many investment opportunities are governed by no such rules. The invested amount may be unavailable for perhaps a lengthy period of time, and any return on the investment may be dependent upon factors not under the control of the party accepting the money. There is the opportunity for complete loss of the invested amount, and the possibility of incurring additional liability in some cases.
Investment in certificates that are traded on a regulated exchange will be subject to the exchange rules, generally including the requirement that the investor be fully informed of the risks. That doesn't mean there is no risk—it just means the investor is supposed to be made aware of it.
Write the equation of the parabola that has the vertex at point (5,0) and passes through the point (7,−2).
The vertex form of the equation of a parabola is
f(x) = a( x − h)^2 + k
where (h,k) is the vertex of the parabola. In this case, we are given that (h,k) = (5,0). Hence,
f(x) = a( x − 5)^2 + 0
=a( x − 5)^2
Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.
a( 7 − 5)^2 = -2
a(2)^2 = -2
4a = -2
a = -1/2
Thus, the given parabola has equation
f(x) = -1/2(x − 5)^2
You have decided both to open a savings account and to purchase a vehicle. You would like a savings account with the highest interest rate and a vehicle loan with a low interest rate. You currently have a checking account at Bank A. From the banks listed below, determine with which bank you should open a savings account and at which bank should you apply for your vehicle loan.
a.
Bank A for the car loan and Bank B for the savings account
b.
Bank C for the car loan and Bank C for the savings account
c.
Bank B for the car loan and Bank A for the savings account
d.
Bank B for the car loan and Bank B for the savings account
bank b for the loan and bank a for the savings account.
The number of acres a farmer uses for planting pumpkins will be at least 2 times the number of acres for planting corn. The difference between the acres of pumpkin and corn crops will not exceed 10. He will plant between 12 and 18 acres of pumpkins. The profit for each acre of corn is $225 and the profit for each acre of pumpkins is $360.
A) Write the constraints for the situation. Let x be the number of acres of corn and let y be the number of acres of pumpkins.
B) Write the objective function for the situation.
C) Graph the feasible region. Label the vertex points with their coordinates.
D) How many acres of each crop should the farmer plant to maximize the profit? How much is that profit?
Answer:
Step-by-step explanation:
A) Let x represent acres of pumpkins, and y represent acres of corn. Here are the constraints:
x ≥ 2y . . . . . pumpkin acres are at least twice corn acres
x - y ≤ 10 . . . . the difference in acreage will not exceed 10
12 ≤ x ≤ 18 . . . . pumpkin acres will be between 12 and 18
0 ≤ y . . . . . the number of corn acres is non-negative
__
B) If we assume the objective is to maximize profit, the profit function we want to maximize is ...
P = 360x +225y
__
C) see below for a graph
__
D) The profit for an acre of pumpkins is the highest, so the farmer should maximize that acreage. The constraint on the number of acres of pumpkins comes from the requirement that it not exceed 18 acres. Then additional profit is maximized by maximizing acres of corn, which can be at most half the number of acres of pumpkins, hence 9 acres.
So profit is maximized for 18 acres of pumpkins and 9 acres of corn.
Maximum profit is $360·18 +$225·9 = $8505.
Which of the following best describes the following set of numbers?
2, -2, 2, -2, ...
Finite arithmetic sequence
Infinite geometric sequence
Finite geometric sequence
Infinite arithmetic sequence
2, -2, 2, -2, ...
This is a geometric progression.
First term = 2
The rate of geometric progression = -1
a1 = 2
a2 = a1 × (-1) = -2
a3 = a2 × (-1) = 2
And so on
⇒ This is a infinite geometric sequence
Answer:
Infinite geometric sequence
Step-by-step explanation:
2, -2, 2, -2, ...
Lets find the difference of the terms
-2 -2=0
2-(-2)=0
LEts check with common ratio
-2/2= -1
2/-2=-1
so common ratio r=0, so its geometric
The sequence is repeating because of common ratio -1
So it goes on infinitely
Hence it is Infinite geometric sequence
You have a cone with a radius of 4 ft and a height of 8 ft. What is the height of the triangle formed by a perpendicular cross-section through the cone’s center?
Answer:
8 ft
Step-by-step explanation:
The height of the cross section through the apex will be the same as the height of the apex: 8 ft.
What is the slope of the line represented by the equation y = -2/3 -5x?
-5
Make the equation into slope-intercept form, which is y = mx + b, where m is the slope, and b is the y-intercept.
In the equation y = -5x - 2/3, the slope is -5 and the y-intercept is -2/3.
For this case we have that the equation of the line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have the following equation:
[tex]y = - \frac {2} {3} -5x[/tex]
Reordering:
[tex]y = -5x- \frac {2} {3}[/tex]
So, we have to:
[tex]m = -5\\b = - \frac {2} {3}[/tex]
Answer:
The slope is -5
HELP PLZ DUE TM!!!! 20 POINTS!!!
[tex]\displaystyle\bf\\m \overset{\frown}{HE}=360-m \overset{\frown}{HL}-m \overset{\frown}{EV}-m \overset{\frown}{VL}\\m\overset{\frown}{HE}=360^o-40^o-130^o-110^o=360^o-280^o=80^o\\\\m\widehat{EYH}=m\widehat{EYV}=\frac{m \overset{\frown}{EV}-m\overset{\frown}{HE}}{2}=\frac{130^o-80}{2}=\frac{50^o}{2}=\boxed{\bf25^o}[/tex]
The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand? Show your work.
Answer:2006
Step-by-step explanation:
[tex]A = 118e^{0.024t}[/tex]
When A = 140:
[tex]140 = 118e^{0.024t}[/tex]
[tex]\frac{140}{118} = e^{0.024t}[/tex]
[tex]ln(\frac{140}{118}) = 0.024t[/tex]
[tex]\frac{1}{0.024} ln(\frac{140}{118}) = t[/tex]
Plugging into a calculator, t is approximately 7.12. Since t represents years since 1998, we round up to the nearest whole number: t=8. So the population of the city will reach 140 thousand in the year 2006.
The population of the city reach 140 thousand will be after 7.123 years.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The equation models the number of inhabitants in a specific city, in thousands, t years after 1998 is given below.
[tex]\rm A = 118 \times e^{0.024 \times t}[/tex]
The number of years when the population becomes 140 thousands is given as,
[tex]\rm 140 = 118 \times e^{0.024 \times t}[/tex]
Take natural log on both sides, then we have
0.024 t = ln (140 / 118)
0.024 t = 0.170957
t = 7.123 years
The population of the city reach 140 thousand will be after 7.123 years.
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researchers have concluded that a dry basin began to fill with water in 1880. the water level rose an average of 1.6 millimeters (mm) per year from 1880 to 2009. the rise in water level since 1880 can be modeled by f(x) = 1.6x, where x is the number of years since 1880 and f is the total rise of the water level in mm.
1. what is the domain of f(x)?
2. by how much did the water level rise in all from 1880 to 1950?
3. in what year was the water level 100 mm higher than in 1880?
remember: 1 m = 1,000 mm
please help and thank you!!
Answer:
the domain is [0,129]112 mm1942Step-by-step explanation:
1. The function is good for years 1880 to 2009, 0 to 129 years after 1880. Values of x can be anything in the domain [0, 129].
__
2. 1950 -1880 = 70. The year 1950 corresponds to x=70, so the function tells us the water level rose ...
f(70) = 1.6·70 = 112 . . . . . mm
__
3. We want to find x when f(x) = 100. That will be the solution to ...
100 = 1.6x
100/1.6 = x = 62.5
Then 62.5 years after 1880 is year 1942.5. The water level was 100 mm higher than in 1880 in the year 1942.
1. A baseball is thrown into the air with an upward velocity of 25 ft/sec. It’s height (in feet) after t seconds can be modeled by the function h(t) = -16t^2 + 25t + 5. Algebraically determine how long will it take the ball to reach its maximum height? What is the ball’s maximum height?
2. A company that sells digital cameras has found that their revenue can be remodeled by the equation R(p) = -5p^2 + 1230p, where p is the price of the camera in dollars. Algebraically determine what price will maximize the revenue? What is the maximum revenue?
We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:
Step 1: Write the original equation:[tex]h(t)=-16t^2+25t+5[/tex]
Step 2: Common factor -16:[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16})[/tex]
Step 3: Take half of the x-term coefficient and square it. Add and subtract this value:X-term: [tex]-\frac{25}{16}[/tex]
Half of the x term: [tex]-\frac{25}{32}[/tex]
After squaring: [tex](-\frac{25}{32})^2=\frac{625}{1024}[/tex]
[tex]h(t)=-16(t^2-\frac{25}{16}t-\frac{5}{16}+\frac{625}{1024}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{5}{16}-\frac{625}{1024}) \\ \\ h(t)=-16(t^2-\frac{25}{16}t+\frac{625}{1024}-\frac{945}{1024}) \\ \\[/tex]
Step 4: Write the perfect square:[tex]h(t)=-16[(t-\frac{25}{32})^2-\frac{945}{1024}] \\ \\ \boxed{h(t)=-16(t-\frac{25}{32})^2-\frac{945}{64}}[/tex]
Finally, the vertex of this function is:
[tex](\frac{25}{32},\frac{945}{64})[/tex]
So in this vertex we can find the answer to this problem:
The ball will reach its maximum height at [tex]t=\frac{25}{32}s=0.78s[/tex]
The ball maximum height is [tex]H=\frac{945}{64}=14.76ft[/tex]
2. Algebraically determine what price will maximize the revenue? What is the maximum revenue?Also we will use completing squares. We can use the concept of derivative to find this result, but since the problem states we must use algebraic procedures, then we solve this as follows:
Step 1: Write the original equation:[tex]R(p)=-5p^2+1230p[/tex]
Step 2: Common factor -5:[tex]R(p)=-5(p^2-246p)[/tex]
Step 3: Take half of the x-term coefficient and square it. Add and subtract this value:X-term: [tex]-246[/tex]
Half of the x term: [tex]-123[/tex]
After squaring: [tex](-123)^2=15129[/tex]
[tex]R(p)=-5(p^2-246p+15129-15129)[/tex]
Step 4: Write the perfect square:[tex]R(p)=-5[(x-123p)^2-15129] \\ \\ R(p)=-5(x-123p)^2+75645[/tex]
Finally, the vertex of this function is:
[tex](123,75645)[/tex]
So in this vertex we can find the answer to this problem:
The price will maximize the revenue is [tex]p=123 \ dollars[/tex]
The maximum revenue is [tex]R=75645[/tex]
Find the area of an octagon with a radius of 11 units. Round to the nearest hundredth
Answer:
342.24 units²
Step-by-step explanation:
The area of one of the 8 triangular sections of the octagon is ...
A = (1/2)r²·sin(θ) . . . . . where θ is the central angle of the section
The area of the octagon is 8 times that, so is ...
A = 8·(1/2)·11²·sin(360°/8) = 242√2
A ≈ 342.24 units²
The area of the octagon should be 342.24 units²
Calculation of area of an octagon:Since the area of 1 of the 8 triangular sections of the octagon should be.
[tex]A = (1\div 2)r^2.sin(\theta)[/tex]
Here θ represent the central angle of the section
Since
The area of the octagon is 8 times
So,
[tex]A = 8.(1/2).11^2.sin(360\div 8) \\\\= 242\sqrt2[/tex]
A ≈ 342.24 units²
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3x+2y=8
Find the slope and y-intercept?
Please show work and how to find the slope and y-intercept in algebraic (:
The slope is 3
I am not that shure on the y intercept
The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constraints g(x,y,z)=0 and h(x,y,z)=0, where g and h are also differentiable, are gradientf=lambdagradientg+mugradienth, g(x,y,z)=0, and h(x,y,z)=0, where lambda and mu (the Lagrange multipliers) are real numbers. Use this result to find the maximum and minimum values of f(x,y,z)=xsquared+ysquared+zsquared on the intersection between the cone zsquared=4xsquared+4ysquared and the plane 2x+4z=2.
The Lagrangian is
[tex]L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)[/tex]
with partial derivatives (set equal to 0)
[tex]L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0[/tex]
[tex]L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0[/tex]
[tex]L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0[/tex]
[tex]L_\lambda=4x^2+4y^2-z^2=0[/tex]
[tex]L_\mu=2x+4z-2=0\implies x+2z=1[/tex]
Case 1: If [tex]y=0[/tex], then
[tex]4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|[/tex]
Then
[tex]x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23[/tex]
[tex]\implies x=\dfrac15\text{ or }x=-\dfrac13[/tex]
So we have two critical points, [tex]\left(\dfrac15,0,\dfrac25\right)[/tex] and [tex]\left(-\dfrac13,0,\dfrac23\right)[/tex]
Case 2: If [tex]\lambda=-\dfrac14[/tex], then in the first equation we get
[tex]x(1+4\lambda)+\mu=\mu=0[/tex]
and from the third equation,
[tex]z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0[/tex]
Then
[tex]x+2z=1\implies x=1[/tex]
[tex]4x^2+4y^2-z^2=0\implies1+y^2=0[/tex]
but there are no real solutions for [tex]y[/tex], so this case yields no additional critical points.
So at the two critical points we've found, we get extreme values of
[tex]f\left(\dfrac15,0,\dfrac25\right)=\dfrac15[/tex] (min)
and
[tex]f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59[/tex] (max)
This problem involves using Lagrangian multipliers to optimize a function with two constraints. The maximum and minimum points can be found by solving the Lagrange equations, which are derivatives of the function and constraints. These points can be confirmed by checking the positive or negative value of the second-order derivative.
Explanation:To find the maximum and minimum values of the function f(x,y,z)=x²+y²+z² subject the cone z²=4x²+4y² and the plane 2x+4z=2, we use Lagrange multipliers. We have two constraint functions here, given by the cone and the plane equations.
The first step is to set up the Lagrange equations, with and as Lagrange multipliers. From w=gradientf=gradientg+gradienth, we have three equations: 2x=*8x+2, 2y=*8y+0, 2z=*4. The second step is to solve these three equations, together with the original constraints g(x,y,z)=0 and h(x,y,z)=0.
Solving these equations will give you specific values for x, y, and z that correspond to the maximum and minimum points. To determine if a point is a maximum or minimum, one can compute the second-order partial derivatives and organize them into the Hessian matrix.
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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−5x, [0, 1] Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. Yes, f is continuous and differentiable on double-struck R, so it is continuous on [0, 1] and differentiable on (0, 1) . There is not enough information to verify if this function satisfies the Mean Value Theorem. No, f is not continuous on [0, 1]. No, f is continuous on [0, 1] but not differentiable on (0, 1). Correct: Your answer is correct. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE). c =
[tex]f(x)=e^{-5x}[/tex] is continuous on [0, 1] and differentiable on (0, 1), so yes, the MVT is satisfied.
By the MVT, there is some [tex]c\in(0,1)[/tex] such that
[tex]f'(c)=\dfrac{f(1)-f(0)}{1-0}[/tex]
The derivative is
[tex]f'(x)=-5e^{-5x}[/tex]
so we get
[tex]-5e^{-5c}=e^{-5}-1\implies e^{-5c}=\dfrac{1-e^{-5}}5\implies-5c=\ln\dfrac{1-e^{-5}}5[/tex]
[tex]\implies\boxed{c=-\dfrac15\ln\dfrac{1-e^{-5}}5}[/tex]
The function f(x) = e^-5x is both continuous and differentiable on the interval [0, 1] and performs according to the Mean Value Theorem. To find the specific numbers, c, that suit the theorem’s conclusion, we must solve the equation f'(c) = [f(b) - f(a)] / (b - a).
Explanation:The function we are considering is f(x) = e-5x. To check whether it satisfies the Mean Value Theorem (MVT) on the interval [0, 1], we have to ensure two conditions. Firstly, that the function is continuous on the closed interval [0, 1], and secondly, that it is differentiable on the open interval (0, 1).
Given that f(x) = e-5x is an exponential function, it is continuous and differentiable for all x in real numbers, R. Hence, f(x) is continuous and differentiable on [0, 1] and (0, 1), respectively. Therefore, the function satisfies the hypotheses of the Mean Value Theorem.
To find all the numbers c that satisfy the conclusion of the MVT, we have to solve the equation f'(c) = [f(b) - f(a)] / (b - a). Differentiating f(x), we get f'(x) = -5e-5x. On solving this equation for c, the value that satisfies it will be our solution.
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