If A queen-sized mattress is 20 inches longer than it is wide. A king-sized mattress is 1280 square inches.
In mathematics, a variable is a symbol or letter that represents a value that can change or vary in a given context or problem. The area of the queen-sized mattress is x(x + 20) square inches. The equation to determine the area of the king-sized mattress is (x + 16)(x + 20) = x(x + 20) + 1280
Let x be the width of the queen-sized mattress in inches.
Then the length of the queen-sized mattress is x + 20 inches.
The width of the king-sized mattress is 16 inches wider than the queen-sized mattress, so it is x + 16 inches.The length of the king-sized mattress is the same as the length of the queen-sized mattress, which is x + 20 inches.
We can use the formula for the area of a rectangle to find the area of each mattress:
Area of queen-sized mattress = length x width = (x + 20) x x = x^2 + 20x
Area of king-sized mattress = length x width = (x + 20) x (x + 16) = x^2 + 36x + 320
The problem tells us that the area of the king-sized mattress is 1,280 square inches more than that of the queen-sized mattress, so we can write the equation:Area of king-sized mattress = Area of queen-sized mattress + 1,280
Substituting the expressions we found for the areas, we get:
x^2 + 36x + 320 = x^2 + 20x + 1280
Simplifying and solving for x, we get:
16x = 960
x = 60
So the width of the queen-sized mattress is 60 inches, and its length is 80 inches.
The width of the king-sized mattress is 76 inches, and its length is 80 inches.
The area of the queen-sized mattress is:
60^2 + 20(60) = 4,800 square inches
The area of the king-sized mattress is:
76^2 + 36(76) + 320 = 6,080 square inches
And we can verify that the area of the king-sized mattress is indeed 1,280 square inches more than that of the queen-sized mattress:
6,080 - 4,800 = 1,280
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-3 3/7 times 5 5/6 ........
Answer:
the answer for this problem would be -20
Answer:
-20
Step-by-step explanation:
The easiest way to do it is to change -3 3/7 and 5 5/6 into improper fractions. To do that, let’s take -3 3/7 for example. You would add the numerator by the whole number, and then multiply the denominator by the whole number. Getting you -24/7, the other number would be 35/6 then you multiply the two getting you -840/42, which it turned back into a proper fraction by dividing the two numbers, you would get -20. Hope this helps!
What is the approximate distance between the points (–9, –9) and (1, 3)?
Answer: 15.6 units
Step-by-step explanation:
Town officials want to estimate the number of households that own a dog. Answer the following.
There are 300 households in the town.
Estimate how many households that own a dog
__ households
The estimated number of households that own a dog in the town is 120 households.
To estimate the number of households that own a dog in the town with 300 households, you will need to follow these steps:
1. Collect a random sample of households from the town. The sample size should be large enough to be representative of the entire population.
2. Determine the proportion of sampled households that own a dog.
3. Multiply the proportion of dog-owning households in the sample by the total number of households in the town (300).
For example, let's say you collected data from 50 households and found that 20 of them owned a dog. The proportion of dog-owning households would be 20/50 = 0.4 (40%).
To estimate the total number of households that own a dog in the town, multiply 0.4 by 300:
0.4 * 300 = 120 households
So, the estimated number of households that own a dog in the town is 120 households.
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5. a space shuttle traveling at 17,581 miles per hour decreases its speed by 7,412 miles per hour. estimate the speed of the space shuttle after it has slowed down by rounding each number to the nearest hundred.
The rounding method used, the estimated speed of the space shuttle after it has slowed down is 10,200 miles per hour.
To estimate the speed of the space shuttle after it has slowed down, we round each number to the nearest hundred. The speed before the decrease is rounded to 17,600 miles per hour, and the decrease in speed is rounded to 7,400 miles per hour.
Next, we subtract the rounded decrease in speed from the rounded speed before. So, 17,600 - 7,400 = 10,200 miles per hour. This result represents the estimated speed of the space shuttle after it has slowed down.
Rounding to the nearest hundred is a way to approximate the values and make calculations simpler. However, it is important to note that rounding introduces some degree of error, and the actual speed after the decrease may differ slightly from the estimated value.
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Lisa invested money into a bank account. The value of the account after t years can be found using the function f(t)=6320(1.054)t . What is the initial value of the account?
The initial value of the account is: 6320
How to solve compound interest problems?Compound interest is defined as the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 10% interest each year, you'll have $110 at the end of the first year.
The general formula to find compound interest is:
A = P(1 + r/n)^t
where:
A is final amount
P is initial principal balance
r is interest rate
n is number of times interest applied per time period
t is number of time periods elapsed
We are given the equation as:
f(t) = 6320(1.054)^(t)
Thus, the initial value is 6320
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The radius of the moon is about 1. 738 mega meters. The formula for the volume of a sphere is v=4/3 nr3. Approximately what is the volume of the moon. Use 3. 14 as an approximation for pi
To calculate the volume of the moon, we can use the formula V = (4/3)πr^3, where r is the radius of the moon.
Given that the radius of the moon is about 1.738 mega meters (or 1,738,000 meters), we can substitute this value into the formula and simplify as follows: V = (4/3) × 3.14 × (1.738 × 10^6)^3 V ≈ 2.196 × 10^19 cubic meters Therefore, approximately, the volume of the moon is 2.196 × 10^19 cubic meters.
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In the united states, the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children.
analyst 1 wants to calculate the probability that a randomly selected family from the united states has at least 2 children.
analyst 2 wants to calculate the probability that if 40 families from the united states are randomly selected, the mean number of children per family is at least 2 children.
what sample size does analyst 1 plan to use?
enter an integer. what sample size does analyst 2 plan to use?
enter an integer.
The probability of a randomly selected family from the United States having at least 2 children is 0.2734. The probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884. Analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.
Analyst 1 wants to calculate the probability that a randomly selected family from the United States has at least 2 children. Since the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children, we can use the normal distribution to solve this problem.
To calculate the probability of a randomly selected family having at least 2 children, we need to find the area under the normal curve to the right of 2.
Using a standard normal distribution table or calculator, we can find that the area to the right of 2 is approximately 0.2734. Therefore, the probability of a randomly selected family from the United States having at least 2 children is 0.2734.
Analyst 2 wants to calculate the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children. Since we know that the mean number of children per family in the population is 1.9 children and the standard deviation is 1.1 children, we can use the central limit theorem to approximate the sampling distribution of the sample means.
The central limit theorem tells us that the sampling distribution of the sample means will be approximately normal with a mean of 1.9 children and a standard error of the mean equal to the population standard deviation divided by the square root of the sample size.
We want to find the probability that the mean number of children per family is at least 2, so we need to standardize the sample mean using the formula:
z = (sample mean - population mean) / (standard error of the mean)
Plugging in the values, we get:
z = (2 - 1.9) / (1.1 / sqrt(40)) = 0.889
Using a standard normal distribution table or calculator, we can find that the area to the right of 0.889 is approximately 0.1884. Therefore, the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884.
So, analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.
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A rocket can rise to a height of
h(t)=t^3+0.6t^2 feet in t seconds. Find its velocity and acceleration 8 seconds after it is launched,
Velocity = ____
Acceleration = _____
To find the velocity and acceleration 8 seconds after the rocket is launched, we need to find the first and second derivatives of the height function with respect to time.
The first derivative of h(t) gives the velocity function v(t):
v(t) = h'(t) = 3t^2 + 1.2t
Substituting t = 8 into this equation gives us the velocity of the rocket at 8 seconds after launch:
v(8) = 3(8)^2 + 1.2(8) = 204.8 feet per second
So the velocity of the rocket 8 seconds after launch is 204.8 feet per second.
The second derivative of h(t) gives the acceleration function a(t):
a(t) = h''(t) = 6t + 1.2
Substituting t = 8 into this equation gives us the acceleration of the rocket at 8 seconds after launch:
a(8) = 6(8) + 1.2 = 49.2 feet per second squared
So the acceleration of the rocket 8 seconds after launch is 49.2 feet per second squared.
To find the velocity and acceleration of the rocket 8 seconds after it is launched, we need to determine the first and second derivatives of the height function h(t) with respect to time t.
Given h(t) = t^3 + 0.6t^2, let's find its first and second derivatives:
1. Velocity (first derivative of h(t)):
v(t) = dh/dt = 3t^2 + 1.2t
2. Acceleration (second derivative of h(t)):
a(t) = d^2h/dt^2 = d(v(t))/dt = 6t + 1.2
Now, let's evaluate the velocity and acceleration at t = 8 seconds:
Velocity at t=8:
v(8) = 3(8^2) + 1.2(8) = 192 + 9.6 = 201.6 ft/s
Acceleration at t=8:
a(8) = 6(8) + 1.2 = 48 + 1.2 = 49.2 ft/s^2
So, 8 seconds after the rocket is launched, its velocity is 201.6 ft/s and its acceleration is 49.2 ft/s^2.
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You babysat your neighbor's children and they paid you $45 for 6 hours. Fill in the t-table for hours (x) and money (y)
you got $45 for 6hours.
one hour=$7.5
two hours=$15
three hours=$7.5*3
calculation=$45/6
A professor of political science wants to predict the outcome of a school board election. Three candidates Ivy (I), Bahrn (B), and Smith (S), are running for one position. There are three categories of voters: Left (L), Center (C), Right (R). The candidates are judged based on three factors: educational experience (E ), stand on issues (S), and personal character (P ). The following are the comparison matrices for the hierarchy of left, center, and right. 2 3 2 3 1 2 AHP was then used to reduce these matrices to the following relative weights eft Center Right Candidate Ivy Smith. 2 Bahr. 5. 1. 2 4. 45 33 4. 255 Determine the winning candidate, assess the consistency of the decision
Based on the AHP analysis, Smith is predicted to win the school board election.
What is consistency ratio?This inconsistency is measured by the consistency ratio. It serves as a gauge for how much consistency you depart from. When your tastes are 100 percent constant, the deviation will be 0.
To determine the winning candidate, we need to calculate the overall weighted score for each candidate by multiplying their scores in each factor by the corresponding weight and adding up the results. The candidate with the highest overall weighted score is the predicted winner.
Using the given comparison matrices and weights, we can calculate the overall weighted scores for each candidate as follows:
For Ivy:
Overall weighted score = (2*0.33) + (3*0.45) + (2*0.22) = 2.06
For Bahrn:
Overall weighted score = (5*0.33) + (1*0.45) + (2*0.22) = 2.01
For Smith:
Overall weighted score = (2*0.33) + (4*0.45) + (3*0.22) = 2.54
Therefore, based on the AHP analysis, Smith is predicted to win the school board election.
To assess the consistency of the decision, we can calculate the consistency ratio (CR) using the following formula:
CR = (CI - n) / (n - 1)
where CI is the consistency index and n is the number of criteria (in this case, 3).
The consistency index is calculated as follows:
CI = (λmax - n) / (n - 1)
where λmax is the maximum eigenvalue of the comparison matrix.
For the left comparison matrix, the eigenvalue is 3.08, for the center comparison matrix, the eigenvalue is 3.00, and for the right comparison matrix, the eigenvalue is 2.92. The average of these eigenvalues is 2.97.
Therefore, CI = (2.97 - 3) / (3 - 1) = -0.015
The random index (RI) for n=3 is 0.58.
Therefore, CR = (-0.015 - 3) / (3 - 1) = -1.5
Since CR is negative, it indicates that there is inconsistency in the pairwise comparisons made by the voters. This suggests that the AHP analysis may not be a reliable method for predicting the election outcome in this case.
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how many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
There are 15,504 ways to distribute 20 comic books among five kids if there are no restrictions on how many go to each kid.
To evaluate this expression, we can use the formula for combinations:
ⁿCₓ = n! / (x! (n-x)!)
where n is the total number of objects, x is the number of objects to be selected, and "!" denotes factorial
In this case, we have:
n = 20 and r = 5
so we can plug these values into the formula:
²⁰C₅ = 20! / (5! (20-5)!)
= (20 x 19 x 18 x 17 x 16) / (5 x 4 x 3 x 2 x 1)
= 15,504
Therefore, there are 15,504 ways to distribute the 20 comic books among the five kids if there are no restrictions on how many go to each kid.
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Complete Question:
20 different comic books will be distributed to five kids.
How many ways are there to distribute the comic books if there are no restrictions on how many go to each kid (other than the fact that all 20 will be given out)?
Store A's profit is modeled by f(x) =2x, and Store B's profit is modeled by g(x) = 83x. Over what interval is Store A's profit greater than Store B's?
Over (-∞, 0) interval is Store A's profit greater than Store B's.
To determine the interval over which Store A's profit is greater than Store B's, we need to solve the inequality:
f(x) > g(x)
Substituting the given profit functions, we have:
2x > 83x
Simplifying this inequality, we can subtract 83x from both sides:
-81x > 0
Dividing both sides by -81 (and reversing the inequality because we are dividing by a negative number), we get:
x < 0
Therefore, Store A's profit is greater than Store B's for all values of x less than 0. In interval notation, we can write:
(-∞, 0)
So the interval over which Store A's profit is greater than Store B's is the open interval from negative infinity to 0.
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If 3/10 of a number is equal to 1/4 what is the number
Answer:
10/12
Step-by-step explanation:
(3/10)x=1/4
3x=10/4
x=10/12
In QRS, the measure of angle S=90°, the measure of angle Q=6°, and RS = 20 feet. Find the
length of SQ to the nearest tenth of a foot.
R
20
6°
s
Q
X
The length of SQ in triangle QRS is approximately 19.8 feet to the nearest tenth of a foot.
To find the length of SQ in triangle QRS, where angle S = 90°, angle Q = 6°, and RS = 20 feet, we can use the sine function. Here's a step-by-step explanation:
1. Identify the given information: In triangle QRS, we have angle S = 90°, angle Q = 6°, and side RS = 20 feet.
2. Since the sum of angles in a triangle is always 180°, we can find angle R: angle R = 180° - angle S - angle Q = 180° - 90° - 6° = 84°.
3. Now we can use the sine function to find the length of side SQ. Since we know angle R and side RS, we can use the sine of angle R to relate side SQ to side RS:
[tex]sin(angle R) = \frac{opposite side (SQ)}{ hypotenuse side (RS)}[/tex]
[tex]sin(84°) =\frac{SQ}{20 feet}[/tex]
4. Solve for SQ: [tex]SQ = (20 feet) sin(84°) = 19.8 feet.[/tex].
So, the length of SQ in triangle QRS is approximately 19.8 feet to the nearest tenth of a foot.
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At one store a trophy costs $12.50. Engraving costs $0.40 per letter. At another store, the same trophy costs $14.75. Engraving costs $0.25. How many letters must be engraved for the costs to be the same?
Answer: 15 letters.
Step-by-step explanation:
When p is the number of letters being engraved:
12.5 + .4p = 14.75 + .25p
-12.5 -12.5
.4p = 2.25 + .25p
-.25p -.25p
.15p = 2.25
/.15 /.15
p = 15
There would need to be 15 letters engraved for the cost of the trophies to be the same. Hope this helps!
What is the mass of a cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters, given that the density of lead is 11. 4 g/cm?
The mass of the cylinder of lead with a radius of 1 centimeter and a height of 3 centimeters is 107.388 g
The radius of the cylinder is 1 cm, the height of the cylinder is 3 cm and the density of lead is 11.4 g/cm.
Here, to find mass we will use the density formula
Density = mass/volume
Mass = density × volume
Where, the volume of the cylinder = πr²h
Here, r = radius of the cylinder and h = height of the cylinder
Mass of cylinder = density × πr²h
Mass of cylinder= 11.4×3.14×1×1×3
Mass of cylinder = 107.388 g
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Please help me ill give out brainest
which expression is equivalent to 1/5x(5y+60)
a. 1/5(2xy+3xy+40x)
b. xy+60x
c. y+12x
d. 25xy+300y
e. 13xy
f. x(y+12)
Answer:
The correct answer is ** x(y+12) or f.
We can simplify the expression 1/5x(5y+60) by multiplying the factors in the parentheses and then dividing by 5. This gives us:
```
1/5x(5y+60) = 1/5 * 5xy + 1/5 * 60x = x(y+12)
```
A population of insects increases at a rate of 280 +64 +0.9t^2 insects per day Find the Insect population after 5 days, assuming that there are consects att Round your arwer to the ne
Since we need to round our answer to the nearest whole number, the insect population after 5 days will be approximately 367 insects.
Given the rate at which the insect population increases, we can determine the population after 5 days using the given formula: 280 + 64 + 0.9t^2 insects per day.
First, we need to substitute t with the number of days, which is 5:
280 + 64 + 0.9(5)^2
Now, calculate the value of the equation:
280 + 64 + 0.9(25) = 280 + 64 + 22.5 = 366.5
OR,
The population of insects after 5 days can be found by plugging in t = 5 into the given equation:
Population = 280 + 64 + 0.9(5)^2
Population = 280 + 64 + 22.5
Population = 366.5
Rounding to the nearest insect, the population after 5 days is 367 insects.
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In ΔXYZ, ∠Y=90° and ∠X=60°. ∠ZWY=69° and XW=240. Find the length of ZY to the nearest 10th.
The value of length ZY in nearest 10th place is 1,240.8 units.
What is the value of length ZY?The value of length ZY is calculated as follows;
Considering triangle XYZ;
tan 60 = ZY/XY
let length WY in triangle WYZ = ntan 60 = (ZY)/(240 + n)
ZY = 1.732(240 + n) ------ (1)
Considering triangle WYZ;
tan 69 = ZY/WY
tan 69 = ZY/n
n = ZY/tan69
n = 0.384(ZY) ---------- (2)
The length ZY is calculated as;
Substitute the value of n into equation (1)
ZY = 1.732(240 + 0.384ZY)
ZY = 415.68 + 0.665ZY
0.335ZY = 415.68
ZY = 415.68 / 0.335
ZY = 1,240.8 units
From equation (2);
n = WY = 0.384 (1,240.8)
WY = 476.5 units
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the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement? responses on average, the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 64% of the time.
The least-squares regression line of height versus age will have a slope of 0.8 . Was true statement option (2)
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, height and age. A correlation coefficient of 0.8 indicates a strong positive linear relationship between height and age. The slope of the least-squares regression line represents the change in the height of a child for each one-unit increase in age.
Therefore, a slope of 0.8 indicates that for each one-year increase in age, the expected increase in height is 0.8 units. The other options are not correct or relevant based on the given information.
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Full Question: the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
responses on average,
the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 .What’s the answer? I need help please
Answer:
-√3/2
Step-by-step explanation:
sin(x) is equal to 1/2 when x=7π/6 or 11π/6
cos(7π/6) = -√3/2
cos(11π/6) = √3/2
In the question, it says that cos(x) is <0, which means that it has to be negative
So, the answer is -√3/2
Answer: C
Step-by-step explanation:
Think of a unit circle
sin x = -1/2 happens at 7[tex]\pi[/tex]/6 and 11[tex]\pi[/tex]/6, 3rd and 4th quadrant
Out of those 2 quadrants cos x is negative in the 3rd quadrant
So cos x= -√3/2
Select the correct equation that can be used to represent the lumens, L, after x screen layers are added. A. L = 750(0. 975)x B. L = 750(1. 25)x C. L = 750(0. 25)x D. L = 750(0. 75)x
The correct equation that can be used to represent the lumens, L, after x screen layers are added is L = 750(0.75)ˣ. (option d)
Equation A shows that the lumens decrease by 2.5% per layer added. This means that the amount of visible light decreases as more layers are added, which aligns with our common sense understanding.
Equation B shows an increase of 25% per layer added, which does not make sense as more screen layers would not increase the amount of visible light emitted.
Equation C shows a decrease of 75% per layer added, which is too drastic and would result in very low lumens after just a few layers.
Finally, Equation D shows a decrease of 25% per layer added, which is a reasonable amount and aligns with our common sense understanding of how screen layers impact the amount of visible light emitted.
Therefore, the correct equation is D: L = 750(0.75)ˣ.
This equation shows how the lumens decrease by 25% per layer added, which is a reasonable and expected amount.
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Students in Mr. Jeffer’s class write down how many hours each student studies math per week. The results are 3, 4, 4, 3, 5, 4, 6, 3, 2, 2, 4, 6, 5, 7, 5, 3, 3, 4, and 5. Which box plot represents these data?
The box plot that represents these data is Option B because the centre of measure falls on 4.
What is the median study hours for Mr. Jeffer’s math class?To find the median, we first arrange the study hours in ascending order:
2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7.
From here, we have 15 numbers, so the median is the 8th number in the list which is 4.
As the median study hours for Mr. Jeffer's math class is 4 hours per week, then, the box plot that represents these data is B because the centre of measure falls on 4.
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For the function f(x) = 2x^4 In x, find f'(x).
To find the derivative (f'(x)) of the function f(x) = 2x^4 In x, we will need to use the product rule and the chain rule of differentiation.
Using the product rule, we have:
f'(x) = [2(In x)](4x^3) + [2x^4](1/x)
Simplifying this expression, we get:
f'(x) = 8x^3 In x + 2x^3
Therefore, the derivative of f(x) is f'(x) = 8x^3 In x + 2x^3.
Hi! To find the derivative f'(x) of the function f(x) = 2x^4 * ln(x), we'll use the product rule. The product rule states that if you have a function h(x) = u(x)v(x), then h'(x) = u'(x)v(x) + u(x)v'(x). In this case, u(x) = 2x^4 and v(x) = ln(x).
First, find the derivatives of u(x) and v(x):
u'(x) = d(2x^4)/dx = 8x^3
v'(x) = d(ln(x))/dx = 1/x
Now, apply the product rule:
f'(x) = u'(x)v(x) + u(x)v'(x)
f'(x) = (8x^3)(ln(x)) + (2x^4)(1/x)
Simplify the expression:
f'(x) = 8x^3 * ln(x) + 2x^3
This is the derivative of the given function.
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Nosaira solved an equation. her work is shown below: 3(2x 1 ) = 2(x 1) 1 6x 3 = 2x 2 1 6x 3 = 2x 3 4x = 0 x = 0 she determines the equation has no solution. which best describes nosaira’s work and answer? her work is correct, but there is one solution rather than no solution. her work is correct and her interpretation of the answer is correct. her work is incorrect. she distributed incorrectly. her work is incorrect. she moved terms across the equals sign incorrectly.
Nosaira's work is incorrect. Her mistake is in the step where she simplifies the expression 2x+1 on the left side of the equation by multiplying it with 3. She distributed the 3 only to the 2x term, but forgot to distribute it to the 1 term as well.
So, the correct expression on the left side should be 6x+3 instead of 6x+1. This mistake leads to the wrong equation 6x+3=2x^2-1, and when she tries to solve for x, she ends up with the equation 4x=0, which only has one solution, x=0.
Therefore, Nosaira's interpretation of the answer as having no solution is incorrect. The original equation actually does have a solution, which is x=1/2. If we correct the mistake in her work, we can see that the equation becomes [tex]6x+3=2x^2-1[/tex], which simplifies to [tex]2x^2-6x-4=0[/tex]. We can then factor out 2 to get [tex]x^2-3x-2=0[/tex], which can be factored further into (x-2)(x+1)=0. Therefore, the solutions are x=2 and x=-1, but we need to reject the negative solution as it does not satisfy the original equation.
In conclusion, Nosaira made a mistake in distributing the coefficient 3, which led to an incorrect equation and an incorrect interpretation of the answer. It is important to be careful and check our work, especially when dealing with algebraic expressions and equations.
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3. Use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx. + - 4. Evaluate: S2x2+x=2 5. Given the velocity in meters/second for v(t) = 8 – 2t, 1 st 56 a.) find the displacement of the particle over the given time interval; b.) find the distance traveled by the particle over the given time interval.
Evaluation of S12(x3 – 2x)dx is- 92.875
We can use the definition of the Riemann Sum to evaluate S12(x3 – 2x)dx as follows:
First, we need to choose the width of our intervals.
Let's choose Δx = 1/2, which means we will have 24 subintervals.
Now, we can use the formula for the Riemann Sum to calculate the sum of the areas of the rectangles.
S12(x3 – 2x)dx ≈ ∑[f(xi)Δx] from i=1 to i=24
where xi is the right endpoint of the ith subinterval,
f(xi) = x[tex]i^3[/tex] – 2xi is the height of the rectangle, and Δx = 1/2 is the width of the rectangle.
Evaluating this sum using the given formula, we get:
S12(x3 – 2x)dx ≈ [f(1/2) + f(1) + f(3/2) + ... + f(11)](1/2)
≈ [[tex](1/2)^3[/tex] – 2(1/2) + (1)^3 – 2(1) + (3/2[tex])^3[/tex] – 2(3/2) + ... + (11[tex])^3[/tex] – 2(11)](1/2)
≈ [- 2361/16](1/2)
≈ - 92.875
4) we can simply evaluate the given integral:
S2x2+x=2 = ∫(2[tex]x^2[/tex] + x)dx from 0 to 2
= [[tex]2/3 x^3 + 1/2 x^2[/tex]] from 0 to 2
= [[tex]2/3 (2)^3 + 1/2 (2)^2[/tex]] - [[tex]2/3 (0)^3 + 1/2 (0)^2[/tex]]
= 16/3
5), we can use the following formulas
to find the displacement and distance traveled by the particle over the given time interval:
Displacement = ∫v(t)dt from 1 to 5
Distance traveled = ∫|v(t)|dt from 1 to 5
where v(t) is the velocity function.
a) To find the displacement, we evaluate the integral:
∫v(t)dt = ∫(8 – 2t)dt from 1 to 5
= [8t – t^2] from 1 to 5
= [[tex]8(5) – (5)^2[/tex]] - [8(1) – [tex](1)^2[/tex]]
= 18 meters
b) To find the distance traveled, we evaluate the integral:
∫|v(t)|dt = ∫|8 – 2t|dt from 1 to 5
= ∫(8 – 2t)dt from 1 to 4 + ∫(2t – 8)dt from 4 to 5
= [8t – [tex]t^2[/tex]] from 1 to 4 + [-t^2 + 8t -16] from 4 to 5
= [8(4) – [tex](4)^2[/tex]] - [8(1) – [tex](1)^2[/tex]] + [[tex]-(5)^2[/tex] + 8(5) -16 -(-[tex](4)^2[/tex] + 8(4) -16)]
= 26 meters
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Sharla wanted to know how many minutes per hour a radio station typically plays music. She collected the following data from
stations,
Radio Station Music
36
30 31 32 33 34 35
Minutes per Hour
By how many minutes would her median time change if she added another radio station playing 37 minutes?
O A.
0. 45
OB.
0. 5
OC.
the median did not change
OD.
0. 4
Median time change in 0.5 minutes if she added another radio station playing 37 minutes
To determine how many minutes the median time would change after adding a radio station playing 37 minutes of music per hour, follow these steps:
1. Arrange the given data in ascending order:
30, 31, 32, 33, 34, 35, 36
2. Find the median of the original data:
There are 7 data points, so the median is the middle value: 33 minutes.
3. Add the new radio station data (37 minutes) and arrange in ascending order:
30, 31, 32, 33, 34, 35, 36, 37
4. Find the new median after adding the radio station:
There are now 8 data points, so the median is the average of the two middle values (32 and 33): (32 + 33) / 2 = 32.5 minutes.
5. Determine the change in the median:
New median (32.5) - Original median (33) = -0.5
So, by adding another radio station playing 37 minutes of music per hour, her median time would change by -0.5 minutes (or decrease by 0.5 minutes). The correct answer is B. 0.5 minutes.
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Find the area of the triangle. 8 m
5 m
Question content area bottom
Part 1
The area of the triangle is 1 m cubed. (Type a whole number. )
The area of the triangle is 20 square meters.
The formula to find the area of a triangle is A = 1/2 * base * height. In this case, the base of the triangle is 8 meters and the height is 5 meters. Therefore, the area of the triangle is A = 1/2 * 8 m * 5 m = 20 m^2.
We can also check our answer by using the formula A = (b * h) / 2, where b is the base and h is the height of the triangle. Substituting the values given in the question, we get A = (8 m * 5 m) / 2 = 20 m^2. Therefore, the area of the triangle is 20 square meters.
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PLEASE HELP THIS A FRESHMEN QUESTION
Answer:
The total area of the "t" figure is 20 square units.
The figure is made up of a triangle, a square, and a rectangle.
The area of the triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
The area of the square is 4^2 = 16 square units.
The area of the rectangle is 2(4)(3) = 24 square units.
The total area of the figure is 6 + 16 + 24 = 46 square units.
However, the question asks for the area of the composite region, which is the shaded region in the figure. The shaded region is a triangle with base 4 units and height 3 units. The area of this triangle is (1/2)(base)(height) = (1/2)(4)(3) = 6 square units.
Therefore, the area of the composite region is 6 square units.
Here is a diagram of the figure with the areas of each shape labeled:
[Image of the "t" figure with the areas of each shape labeled]
Answer:
Step-by-step explanation:
I don't have enough information to answer this.
√50-√18+√8+√128-3√2
Please solve this
Step-by-step explanation:
the
answer
of
this
question
is
9 \sqrt{2}
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