(a) y(x) = c1 e^(-4x/3) cos(2x) + c2 e^(-4x/3) sin(2x), stable node at the origin;
(b) y(x) = c1 e^(2x) + c2 e^(-4x), unstable node at the origin;
(c) y(x) = c1 e^(-x/22) cos(sqrt(119)x/22) + c2 e^(-x/22) sin(sqrt(119)x/22), stable node at the origin;
(d) y(x) = c1 e^(sqrt(3)x/2) + c2 e^(-sqrt(3)x/2), unstable saddle at the origin;
(e) y(x) = c1 e^x cos(2x) + c2 e^x sin(2x), stable spiral at the origin;
(f) y(x) = c1 cos(3x/2) + c2 sin(3x/2), stable limit cycle around the origin;
(g) y(x) = c1 e^(-x/3) + c2 e^(-x), stable node at the origin.
(a) The characteristic equation is 2r^2 + 9r + 4 = 0, with roots r1 = -4/3 and r2 = -1/2. The general solution is y(x) = c1 e^(-4x/3) cos(2x) + c2 e^(-4x/3) sin(2x). The equilibrium at the origin is a stable node since both eigenvalues have negative real parts.
(b) The characteristic equation is r^2 + 2r - 8 = 0, with roots r1 = 2 and r2 = -4. The general solution is y(x) = c1 e^(2x) + c2 e^(-4x). The equilibrium at the origin is an unstable node since both eigenvalues have positive real parts.
(c) The characteristic equation is 44r^2 - 12r + 5 = 0, with roots r1 = (3 + sqrt(119))/22 and r2 = (3 - sqrt(119))/22. The general solution is y(x) = c1 e^(-x/22) cos(sqrt(119)x/22) + c2 e^(-x/22) sin(sqrt(119)x/22). The equilibrium at the origin is a stable node since both eigenvalues have negative real parts.
(d) The characteristic equation is 2r^2 - 3 = 0, with roots r1 = sqrt(3)/2 and r2 = -sqrt(3)/2. The general solution is y(x) = c1 e^(sqrt(3)x/2) + c2 e^(-sqrt(3)x/2). The equilibrium at the origin is an unstable saddle since the eigenvalues have opposite signs.
(e) The characteristic equation is r^2 - 2r + 5 = 0, with roots r1 = 1 + 2i and r2 = 1 - 2i. The general solution is y(x) = c1 e^x cos(2x) + c2 e^x sin(2x). The equilibrium at the origin is a stable spiral since both eigenvalues have negative real parts and non-zero imaginary parts.
(f) The characteristic equation is 4r^2 + 9 = 0, with roots r1 = 3i/2 and r2 = -3i/2. The general solution y(x) = c1 cos(3x/2) + c2 sin(3x/2), stable limit cycle around the origin.
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Evaluate f(x) = 7x2 − 8 when x = 5.
Answer:
f(5) = 167
Step-by-step explanation:
To evaluate f(x) = 7x^2 - 8 when x = 5, we substitute 5 for x in the expression and simplify. Therefore, we have:
f(5) = 7(5)^2 - 8
f(5) = 7(25) - 8
f(5) = 175 - 8
f(5) = 167
So, f(5) = 167
You are going to run at a constant speed of 7.5
miles per hour for 45
minutes. You calculate the distance you will run. What mistake did you make in your calculation? [Use the formula S=dt
.]
Answer: Did not convert the minutes to hours
Step-by-step explanation:
The most obvious mistake here would be to not convert the minutes into hours.
Remember, the speed given, (7.5), is in miles per HOUR. Your time is given in MINUTES. a conversion is required. 45 minutes are 45/60 = 0.75 hrs.
NOW you can use S = DT to find your distance:
7.5 = D/0.75
.: D = 5.625 miles
I absolutely hate IQR so can someone help
The interquartile range (IQR) of the given data set is 4.
Interquartile range (IQR) is a measure of variability in a data set that measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
How to fine the interquartile range (IQR)?To find the interquartile range (IQR), we first need to find the median of the data set.
The median is the middle value of the dataset when the data is arranged in order. In this case, the data set is already in order, so the median is the middle value or the average of the two middle values:
Median = (26 + 28) / 2 = 27
Now, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.
Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.
Lower half: 22, 24, 26
Upper half: 28, 30
Q1 = median of the lower half = (24 + 26) / 2 = 25
Q3 = median of the upper half = (28 + 30) / 2 = 29
Now we can find the IQR:
IQR = Q3 - Q1 = 29 - 25 = 4
Therefore, the interquartile range (IQR) of the given data set is 4.
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We will use boosting to predict Salary in the Hitters data set. A) Remove the observations for whom the salary information is unknown, and then log-transform the salaries. B) Create a training set consisting of the first 200 observations, and a test set consisting of the remaining observations. C) Perform boosting on the training set with 1,000 trees. What is the the test set MSE
Using boosting with 1,000 trees on the Hitters data set, after removing observations with unknown salary information and log-transforming salaries, results in a test set MSE (Mean Squared Error) value.
1. Remove observations with unknown salary information from the Hitters data set.
2. Log-transform the remaining salaries.
3. Create a training set with the first 200 observations and a test set with the remaining observations.
4. Apply the boosting algorithm on the training set, using 1,000 trees as the parameter.
5. Evaluate the performance of the boosting model on the test set by calculating the Mean Squared Error (MSE). The test set MSE will give you an indication of the model's accuracy in predicting salary based on the provided data.
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Anyone who knows how to do this please help answer!! Fill in the correct numbers in both sides of the chart and answer the bottom questions.
WILL MARK BRAINLIEST!!!
a) Here is the chart showing the number of bacteria after 0 to 4 hours:
| Time (hours) | Number of bacteria |
|--------------|--------------------|
| 0 | 50 |
| 1 | 150 |
| 2 | 450 |
| 3 | 1,350 |
| 4 | 4,050 |
b) To write an expression that models the number of bacteria after a number of hours, n, we can use the formula:
Number of bacteria = Initial number of bacteria x Growth factor^nIn this case, the initial number of bacteria is 50, and the growth factor is 3 (since the number of bacteria triples every hour). Therefore, the expression that models the number of bacteria after n hours is:
Number of bacteria = 50 x 3^nc) To determine the number of bacteria that are present after 12 hours using the expression we derived in part b), we can substitute n = 12 into the expression:
Number of bacteria = 50 x 3^12= 26572050
Therefore, there are approximately 2.7 billion bacteria present after 12 hours.All of the training times of which person had the greatest spread? Explain how you know. (b) The middle 50% of the training times of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Adam’s and Miguel’s training times?
(a) Miguel had the greatest spread in training times.
(b) The middle 50% of Adam's training times had the least spread.
(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.
(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.
(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.
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Let $f(x)=3x+2$ and $g(x)=ax+b$, for some constants $a$ and $b$. If $ab=20$ and $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$, find the sum of all possible values of $a$
The sum of all possible values of $a$ is $1$.
To solve this problem, we need to use the given information to determine possible values of $a$ and $b$ in $g(x)=ax+b$ such that $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.
First, we can simplify $f(g(x))$ and $g(f(x))$ as follows:
$$f(g(x))=3(ax+b)+2=3ax+3b+2$$
$$g(f(x))=a(3x+2)+b=3ax+ab+b$$
Next, we can set these two expressions equal to each other and simplify:
$$3ax+3b+2=3ax+ab+b$$
$$2b-ab=b$$
$$(2-a)b=b$$
Since $ab=20$, we have two cases to consider:
Case 1: $b=0$
In this case, we have $ab=20\implies a=0$ or $b=0$. Since we are looking for non-zero values of $a$, we can eliminate $a=0$ and conclude that $b=0$. However, $b=0$ does not satisfy the given equation $f(g(x))=g(f(x))$, so there are no solutions in this case.
Case 2: $b\neq 0$
In this case, we can divide both sides of $(2-a)b=b$ by $b$ to get:
$$2-a=1$$
$$a=1$$
Therefore, the only possible value of $a$ is $1$, and the corresponding value of $b$ is $20$. We can verify that $a=1$ and $b=20$ satisfy the given equation $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$.
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A recent report states that 55% of U. S. Adults use Netflix to stream shows and movies. An advertising company believes the proportion of California residents who use Netflix is greater than the national proportion, because Netflix headquarters is located in Los Gatos, California. The company selects a random sample of 600 adults from California and finds that 360 of them use Netflix. Is there convincing evidence at the level that more than 55% of California residents use Netflix?
Calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix.
We can use a hypothesis testing approach to answer this question. The null hypothesis is that the true proportion of California residents who use Netflix is the same as the national proportion, or p = 0.55. The alternative hypothesis is that the true proportion of California residents who use Netflix is greater than 0.55, or p > 0.55.
We can use the sample proportion of Netflix users in California, which is 360/600 = 0.6, as an estimate of the true proportion p. The standard error of the sample proportion is:
SE = √[(p*(1-p))/n] = √[(0.55*(1-0.55))/600] = 0.024
The test statistic is:
z = (p - 0.55)/SE = (0.6 - 0.55)/0.024 = 2.08
Assuming a significance level of 0.05 and a one-tailed test (since the alternative hypothesis is one-sided), the critical z-value is 1.645.
Since our calculated test statistic of 2.08 is greater than the critical value of 1.645, we reject the null hypothesis and conclude that there is convincing evidence at the 0.05 level that more than 55% of California residents use Netflix. However, we should keep in mind that this conclusion is based on a sample of 600 adults from California, and there is always some degree of uncertainty involved in statistical inference based on samples.
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Solve system of equations by the substitution method.
Chris has $3.85 in dimes and quarters. There are 25 coins in all. How many of each type of coin does he have?
Solving a system of equations we can see that he has 9 quarters and 16 dimes.
How to solve the system of equations?Let's define the variables:
x = number of dimes
y = number of quarters.
There are 25 coins, so:
x + y = 25
The value is $3.85, so:
x*0.10 + y*0.25 = 3.85
So the system of equations is:
x + y = 25
x*0.10 + y*0.25 = 3.85
We can isolate x on the first equation to get:
x = 25 - y
Replacing that in the other one we get:
(25 -y)*0.10 + y*0.25 = 3.85
2.5 + y*0.15 = 3.85
y = (3.85 - 2.5)/0.15
y = 9
Then the other 16 coins are dimes.
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Express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4).
(Use symbolic notation and fractions where needed.)
To express u = (7, -10) as a linear combination u = rv + sw, where v = (2, 1) and w = (1,4), we need to find the values of r and s such that:
u = rv + sw
Substituting the given values, we get:
(7, -10) = r(2, 1) + s(1,4)
Using the symbolic notation, we can write this as a system of equations:
7 = 2r + s
-10 = r + 4s
We can solve this system of equations by using the elimination method:
Multiply the second equation by 2:
7 = 2r + s
-20 = 2r + 8s
Subtracting the first equation from the second, we get:
-27 = 7s
Dividing both sides by 7, we get:
s = -27/7
Substituting this value of s into the first equation, we get:
7 = 2r - 27/7
Multiplying both sides by 7, we get:
49 = 14r - 27
Adding 27 to both sides, we get:
76 = 14r
Dividing both sides by 14, we get:
r = 38/7
Therefore, u = (7, -10) can be expressed as the linear combination:
u = (38/7)(2,1) + (-27/7)(1,4)
Using fractions where needed, the answer is:
u = (76/7, 38/7) + (-27/7, -108/7)
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Y/4=3/2 what is the y and how did you get the answer
y = 6
Sorry for bad handwriting
if i was helpful Brainliests my answer ^_^
The value of Y in the equation Y/4 = 3/2 is 6.
To find the value of Y, we'll use the following steps:
1. We start with the given equation:
Y/4 = 3/2.
2. Our goal is to isolate Y. To do this, we'll multiply both sides of the equation by 4, which is the denominator on the left side.
3. Multiplying both sides by 4 gives us: (Y/4) * 4 = (3/2) * 4.
4. On the left side, the 4s cancel out, leaving just Y: Y = (3/2) * 4.
5. Now, we simplify the right side by multiplying 3/2 by 4. We can think of 4 as 4/1, so the equation becomes: Y = (3/2) * (4/1).
6. Multiply the numerators (3*4) and denominators (2*1) separately: Y = (12/2).
7. Finally, simplify the fraction: Y = 6.
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Ellen mixed 1over 4 kg of flour with 2 over 9 kg of sugar. Determine a reasonable estimate for the amount of flour and sugar combined
A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:
9/36 + 4/36 = 13/36
So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:
13 ÷ 36 ≈ 0.36
Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
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Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration.)
∫9x√(-x^2 + 9dx)
The substitution is u = -x² + 9 and the evaluated value is -4.5(2/3)(-x² + 9)³/² + C.
To evaluate the given integral ∫9x√(-x² + 9dx),
we can use the substitution u = -x² + 9. This substitution will allow us to simplify the expression under the square root.
First, we can find du/dx by taking the derivative of u with respect to x: du/dx = -2x.
Next, we can solve for dx in terms of du by dividing both sides by -2x: dx = -du/(2x).
Using the substitution and the expression for dx in terms of du, we can rewrite the integral as:
∫9x√(-x² + 9dx) = -4.5∫√udu
Now, we can integrate the simplified expression √u using the power rule of integration:
-4.5∫√udu = -4.5(2/3)u³/² + C
Substituting back for u, we get:
-4.5(2/3)(-x² + 9)³/² + C
Therefore, the solution to the integral ∫9x√(-x^2 + 9dx) using the substitution u = -x^2 + 9 is:
-4.5(2/3)(-x² + 9)³/² + C
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Si un cateto de un triángulo rectángulo y la hipotenusa miden 5 y 13cm, respectivamente, ¿cuánto mide el otro cateto?
The measure of the other side of the right triangle is given as follows:
12 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The parameters for this problem are given as follows:
Sides of 5 and x.Hypotenuse of 13.Hence the other side has the length given as follows:
5² + x² = 13²
25 + x² = 169
x² = 144
x = 12.
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Ann selects a sample of 29 students at her large high school and finds that 12 of them are planning to travel outside of the state during the coming summer. She wants to construct a confidence interval for p = the proportion of all students at her school who plan on traveling outside of the state during the coming summer, but she realizes she hasn’t met all the conditions for constructing the interval. Which condition for this procedure has she failed to meet?
Ann has failed to meet the condition called the "success-failure" condition.
In order to construct a confidence interval for the proportion (p), the sample must have at least 10 successes (planning to travel outside the state) and 10 failures (not planning to travel outside the state). In her sample of 29 students, she found 12 planning to travel (successes) and 17 not planning to travel (failures). Both numbers satisfy the success-failure condition, so she can construct the confidence interval for the proportion of students planning to travel outside the state during the coming summer.
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Answer:
C: The sample must be a random sample from the population
Step-by-step explanation:
took the test on edge
A ship headed due east is moving through the water at a constant speed of 8 miles per hour. However, the true course of the ship is 60°. If the currents are a constant 4 miles per hour, what is the ground speed of the ship? (Round your answer to the nearest whole number. )
The ground speed of the ship is approximately 10 miles per hour.
To calculate the ground speed, we need to use vector addition. The ship's velocity can be broken down into two components: its speed in the easterly direction and its speed in the northerly direction. The easterly component is 8 miles per hour (since the ship is moving due east), and the northerly component can be found using trigonometry: northerly component = 8 * sin(60°) ≈ 6.93 miles per hour
Now, we need to take into account the effect of the currents, which are moving in a southerly direction. Again using vector addition, we can find the resultant velocity (i.e., the velocity of the ship relative to the ground) by adding the ship's velocity vector to the current's velocity vector. Since the current is moving due south, its velocity vector has no easterly component, but its southerly component is 4 miles per hour. resultant velocity = (8, 6.93) + (0, -4) = (8, 2.93)
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity: |resultant velocity| = [tex]\sqrt{} (8^2 + 2.93^2)[/tex]≈ 8.6 miles per hour. Rounding to the nearest whole number, the ground speed of the ship is approximately 10 miles per hour.
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The Bullock family is looking to rent a
large truck for their upcoming move. With Heather's Moving, they would pay
$10 for the first day plus $8 per
additional day. With Newton Rent-a-
Truck, in comparison, the family would
pay $80 for the first day plus $1 per
additional day. Before deciding on which
company to use, Mrs. Bullock wants to
find out what number of additional days
would make the two choices equivalent
with regards to cost. What would the
total cost be?
To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:
Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x
To find the point at which the costs are equal, we can set the equations equal to each other:
10 + 8x = 80 + x
Now, we can solve for x (additional days):
7x = 70
x = 10
So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:
Total cost = 10 + 8(10) = 10 + 80 = $90.
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An air temperature of 30°C is equal to
1. -1°F
2. 68°F
3. 83°F
4. 86°F
Answer:
86 degrees fahrenheit
Step-by-step explanation:
(30°C × 9/5) + 32 = 86°F
You have decided to purchase a car for $25,625. The credit union requires a 10% down payment and will finance the balance with a 9% annual interest loan for 36 months. The sales tax in your city is 7. 5%, and the license and title charges are $175. 13. What is the total purchase price of the car including tax, license, and title? Round your answer to the nearest cent. A. $24,949. 80 c. $27,722. 01 b. $24,967. 32 d. $27,735. 14.
Answer is 27,529.82
To calculate the total purchase price of the car including tax, license, and title, we need to add the down payment, the financed balance, the sales tax, and the license and title charges.
First, we calculate the down payment:
10% of $25,625 = $2,562.50
Next, we calculate the financed balance:
$25,625 - $2,562.50 = $23,062.50
Then, we calculate the sales tax:
7.5% of $23,062.50 = $1,729.69
Finally, we add the license and title charges:
$1,729.69 + $175.13 = $1,904.82
So the total purchase price of the car including tax, license, and title is:
$2,562.50 + $23,062.50 + $1,904.82 = $27,529.82
Rounded to the nearest cent, the answer is option D: $27,735.14.
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In ΔEFG, g = 5. 2 cm, e = 5. 1 cm and ∠F=42°. Find the area of ΔEFG, to the nearest 10th of a square centimeter
The area of ΔEFG is approximately 6.7 square centimeters.
To find the area of ΔEFG with given sides g = 5.2 cm, e = 5.1 cm, and ∠F = 42°, you can use the formula for the area of a triangle when two sides and the included angle are known. This formula is:
Area = (1/2)ab * sin(C)
In this case, a = g, b = e, and C = ∠F. Plug in the values:
Area = (1/2)(5.2 cm)(5.1 cm) * sin(42°)
Area ≈ 6.675 square centimeters
So, the area of ΔEFG is approximately 6.7 square centimeters to the nearest 10th of a square centimeter.
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Find the missing side
17 cm
1319
a
area = 25 cm²
Answer:
a= 2.9cm
Step-by-step explanation:
area =25 so 17a=50
50/17=2.941176...
a farmer made a loss of 28% by selling a gold for1440shillings what percentage profit would have made if he had sold the goat.for.sh 2100
The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.
Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".
We can write the equation:
[tex]CP \times (1 - loss% ) = selling price (SP)[/tex]
[tex]CP \times (1 - 0.28) = 1440[/tex]
Solve for CP
[tex]CP \times 0.72 = 1440[/tex]
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.
We can write the equation:
[tex](SP_{new - CP)} / CP \times 100 = profit[/tex]
[tex](2100 - 2000) / 2000 \times 100 = profit%[/tex]
[tex]100 / 2000 \times 100 = profit%[/tex]
5% = profit%.
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How many terms are to be considered in the series with first term - 3 and common ratio r = -4 for the sum to exceed 1507
,Based on the information, we need to consider 5 terms in the series for the sum to exceed 1507.
How to explain the seriesSubstituting the given values, we get:
1507 < -3(1 - (-4)^n)/(1 - (-4))
Simplifying this inequality, we get:
-4^n < 502
Taking the logarithm of both sides, we get:
n*log(4) > log(502)
n > log(502)/log(4)
n > 4.29
n = 5
Therefore, we need to consider 5 terms in the series for the sum to exceed 1507.
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In 2012, the population of a city was 6.47 million. the exponential growth rate was 2.91% per year.
The population of the city after 5 years is approximately 7.94 million.
How to find the population of the city?Assuming that the population of the city grows exponentially, we can use the formula:
P(t) = [tex]P0 * e^(^r^t^)[/tex]
Where:
- P(t) is the population after time t
- P0 is the initial population
- r is the annual growth rate expressed as a decimal
- t is the time elapsed in years
Using the given information:
- P0 = 6.47 million
- r = 2.91% = 0.0291
Let's calculate the population after 1 year:
[tex]P(1) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^1^)[/tex]
= 6.66 million (rounded to two decimal places)
So, the population of the city after one year is approximately 6.66 million.
We can also calculate the population after 5 years:
[tex]P(5) = 6.47 million * e^(^0^.^0^2^9^1 ^* ^5^)[/tex]
= 7.94 million (rounded to two decimal places)
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Triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is drawn on the coordinate
grid below. what is the area. in square units, of triangle TUV
The area of the triangle TUV, with vertices T(2,-8), U(9,-6), and V(6,-3), is 13.58
How did we arrive at the above?First using distance calculator we derived the length of TV and the length of VU.
Since TV = Height; and
VU = Base
and the triangle is a right triangle,
Then, area is given by 1/2 base x Height
Length of TV usign distance calculator is 6.40312
Lenght of VU using distance calculator is 4.24264
So area = 1/2 * 6.40312 * 4.24264
Area = 13.58
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brandy has a rectangular wooden deck that measures 7 feet by 12 feet she builds an addition to the deck that is 4 feet longer. what is the perimeter of the deck now
Answer:
new perimeter of Brandy deck is 46 feet .
Step-by-step explanation:
The new perimeter of Brandy deck is 46 feet.
Perimeter of a rectangleThe entire length of all the sides of a rectangle is called the perimeter. As a result, we can calculate the perimeter of a rectangle by adding all four sides.
How can we find new perimeter of a deck?Using the given information,
Width = 7 Feet
Length = 12 feet
Perimeter = 2 (Width + Length)
[tex]= 2(7+12)[/tex]
[tex]=2(19)[/tex]
[tex]=38[/tex]
Perimeter when deck is 4 feet longer [tex]=38+ 4+4=46[/tex] Feet
Hence, the new perimeter of a deck is 46 feet.
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What is the money multiplier when the reserve requirement is:
(Instructions: Enter your responses rounded to three decimal places.)
(a) 0.040?
(b) 0.125?
(c) 0.400?
(d) 0.200?
The money multipliers are:
(a) 25.000
(b) 8.000
(c) 2.500
(d) 5.000
The money multiplier represents the amount of money the banking system can create through the lending process for every dollar of reserves held by the central bank. It is inversely related to the reserve requirement, which is the percentage of deposits that banks are required to hold as reserves.
When the reserve requirement is low, su
The money multiplier is given by the formula:
Money multiplier = 1 / Reserve requirement
(a) When the reserve requirement is 0.040, the money multiplier is:
Money multiplier = 1 / 0.040 = 25.000
(b) When the reserve requirement is 0.125, the money multiplier is:
Money multiplier = 1 / 0.125 = 8.000
(c) When the reserve requirement is 0.400, the money multiplier is:
Money multiplier = 1 / 0.400 = 2.500
(d) When the reserve requirement is 0.200, the money multiplier is:
Money multiplier = 1 / 0.200 = 5.000
Therefore, the money multipliers are:
(a) 25.000
(b) 8.000
(c) 2.500
(d) 5.000
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What is the volume of a container of 4 moles of gas at 200k with a pressure of 3 atm
The volume of the container is 2216 liters
How to determine the valueUsing the general gas law, we have that;
PV = nRT
Such that the parameters are given as;
P is the pressure of the gas measured in atmV is the volume of gas measured in litersn is the number of molesR is the universal gas constantT is the temperature measured in KelvinFrom the information given, we have that;
Substitute the values
3V = 4 × 8.31 × 200
Multiply the values, we have;
3V = 6648
Divide both sides by the coefficient of V, we get;
V = 2216 liters
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4 Gabriela is building a wooden box with a rectangular base that is 18 in. By 15 in.
and is 15 in. Tall.
Part A
If she wants an open box without a top, how much wood will Gabriela use?
Strow your work
Gabriela will use 1620 square inches of wood to build the open box.
The amount of wood Gabriela will use depends on the surface area of the box, which is the sum of the areas of its six faces. Since the box is open on top, it will have five faces: four sides and a bottom.
The area of the bottom is the area of a rectangle with length 18 in. and width 15 in., which is:
Area of bottom = length x width = 18 in. x 15 in. = 270 in²
The area of each side is the product of the height and the length of the corresponding base, which is:
Area of each side = height x length = 15 in. x 18 in. = 270 in²
So the total surface area of the box is:
Total surface area = 2 x (Area of bottom) + 4 x (Area of each side)
= 2 x 270 in² + 4 x 270 in²
= 1620 in²
Therefore, Gabriela will use 1620 square inches of wood to build the open box.
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point P is the image of p(-2,-2) translated by 1 unit to the left and 3 units now
To find the image of point P(-2,-2) translated 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get coordinates of P' as: (-3, -5).
How to Find the Coordinates in Translation?To translate a point to the left, we subtract from its x-coordinate, and to translate it down, we subtract from its y-coordinate.
Therefore, to translate P(-2, -2) 1 unit to the left and 3 units down, we subtract 1 from the x-coordinate and 3 from the y-coordinate to get P'(-3, -5) as the image of P after translation.
Therefore, the coordinates of P' are (-3, -5).
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Complete Question:
Point P' is the image of P(-2,-2) translated by 1 unit to the left and 3 units down. What are the coordinates of P'?
