$k = 3\sqrt{2}$.
We have:
\begin{align*}
\int^k_0 (2x^3 -kx^2 +2k)dx &= \left[\frac{1}{2}x^4 - \frac{k}{3}x^3 + 2kx \right]^k_0 \
&= \frac{1}{2}k^4 - \frac{k^4}{3} + 2k^2 \
&= \frac{3}{6}k^4 - \frac{2}{6}k^4 + \frac{12}{6}k^2 \
&= \frac{1}{6}k^4 + 2k^2
\end{align*}
Since we are given that this equals 12, we have:
\begin{align*}
\frac{1}{6}k^4 + 2k^2 &= 12 \
\frac{1}{6}k^4 &= 12 - 2k^2 \
k^4 &= 72 - 12k^2 \
k^4 + 12k^2 - 72 &= 0
\end{align*}
This is a quadratic in $k^2$, so we can solve for $k^2$ using the quadratic formula:
\begin{align*}
k^2 &= \frac{-12 \pm \sqrt{12^2 - 4(1)(-72)}}{2(1)} \
&= \frac{-12 \pm \sqrt{576}}{2} \
&= -6 \pm 12
\end{align*}
Since $k^2$ cannot be negative, we take the positive value:
�
2
=
6
+
12
=
18
k
2
=6+12=18
Thus, $k = \pm\sqrt{18}$. However, since $k$ represents the length of a side of the square, we must take the positive value:
�
=
18
=
3
2
k=
18
=3
2
Therefore, $k = 3\sqrt{2}$.
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The Tigers soccer team scored 38 goals last season. This is 19 fewer than the number of goals scored by the Cubs soccer team. Select a subtraction equation that could be used to find the number of goals scored by the Cubs soccer team last season.
PLEEEEEEEEEEEEASE HELP :(
Answer:
19
Step-by-step explanation:
tigers=38 goals
clubs=19 fewer than tigers
equation: 38-19=19
The quotient of x and 12
Answer:
I need to know what x is to find 12, but all i have for now is 12x
Answer:
quotient of x and 12 is 12x
Step-by-step explanation:
hope it helps
please mark me brainliest
What variables could be of interest to generate environmental data? Note: think of the variable, the sensors, and the data each Pollution levels Air quality Ozone concentration Storm intensity Vegetation density Earthquake intensity Wild life diversity You have used 1 of 4 attempts Save
The following are the variables that could be of interest to generate environmental data: Pollution levels: Pollution levels are a measure of the degree to which the air is contaminated.
Contaminants in the air, such as particulate matter and toxic gases, can be hazardous to human health and the environment, and monitoring them can provide valuable data on air quality.Air quality: Air quality refers to the level of pollution in the air. This could include measurements of various pollutants, such as nitrogen dioxide, sulfur dioxide, and particulate matter. This data can be gathered by a variety of sensors, including gas analyzers, particle counters, and spectrometers.Ozone concentration: Ozone concentration refers to the amount of ozone in the air. Ozone is a powerful oxidant that can have both beneficial and harmful effects on human health and the environment. Storm intensity: Storm intensity refers to the severity of a storm.
This could include measurements of wind speed, rainfall, and lightning activity. Data on storm intensity can be gathered using weather stations, Doppler radar, and lightning detection systems.Vegetation density: Vegetation density is a measure of how much plant life is present in a given area. This data can be used to monitor changes in ecosystems over time and to assess the impact of human activities on the environment. Vegetation density can be measured using satellite imagery, ground-based surveys, and remote sensing technologies.Earthquake intensity: Earthquake intensity refers to the strength of an earthquake. This could include measurements of ground motion, ground acceleration, and ground displacement. Data on earthquake intensity can be gathered using seismometers and other ground-based sensors. Wildlife diversity can be measured using a variety of techniques, including surveys, camera traps, and acoustic monitoring.
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Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Explain what 120 represents, and how it relates to the cows and chickens.
b. Explain what 48 represents, and how it relates to the cows and chickens.
c. Setup a system, of two equations, to help you solve this riddle.
d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
Answer:
a. 120 represents the total number of cow legs and chicken legs
b. 48 represents the total number of cow heads and chicken heads
c. System:
Let x = number of cows
Let y = number of chickens
1. 2x + 4y = 120
2. x + y = 48
d. I am going to use substitution for this problem
Step 1: Solve for y in the equation x + y = 48
1. x + y = 48 → y = -x + 48
Step 2: Substitute -x + 48 for y in 2x + 4y = 120
2. 2x + 4(-x + 48) = 120
Step 3: Solve for x
3. 2x - 4x + 184 = 120 → -2x + 184 = 120 → -2x = -64 → x = 32
Step 4: Sustitute 32 for x in x + y = 48
4. (32) + y = 48
Step 5: Solve for y
5. y = 16
Number of chickens on the farm (y) = 16
Number of cows on the farm (x) = 32
Step-by-step explanation:
All of it is above :)
square root of 2745
Answer:
52.393
the square root of 2745 is 52.393
Lamar ordered some books online for 6$ each. He paid a total of 3$ for shipping. The total cost of the purchase was 75$ . How many books did he buy?
Answer:
He bought 12 books.
Step-by-step explanation:
Here is your equation: 6 b+3=75
Step 1- Subtract 3 from both sides: 6 b+3-3=75-3
6 b=72
Step 2- Divide by 6: 6 b/6=72/6
b = 12 books in total.
what is the axis of symmetry of the function f(x)=x^2-8x+17
The axis of symmetry if the function f(x) = x² - 8x + 17 is solved to get 4
What is a quadratic function?The function f(x) = ax² + bx + c, where a, b, and c are numbers and a is not equal to zero, is a quadratic function.
A parabola is a curve that represents a quadratic function on a graph.
The line that divides the function into two is the axis of symmetry. The axis of symmetry is given by the formula
= b / 2a
Comparing with the equation in the problem
b = 8 and a = 1
= 8 / (2 * 1)
= 8 / 2
= 4
the axis of symmetry is 4
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Scientific notation
9 * 10^12 ÷ 4.5 × 10^12
Answer:
2*10 ^0 = 2
Step-by-step explanation:
9 * 10^12 ÷ 4.5 × 10^12
Divide the numbers
9/4.5
=2
Divide the exponents by subtracting
10^12 ÷ 10^12 = 10 ^(12-12) = 10^0
Put them back together
2 * 10 ^0
2
You want to install a 1 yd. Wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the walk? Use 3.14 for pi π.
Answer:
75.36 yd²
Step-by-step explanation:
To solve, you need to consider the walkway and the pool as one circle and find the are. The diameter of this circle is 25 yd. This means that the radius is 12.5 yd.
A = πr²
A = π(12.5)²
A = 156.25π
A = 490.625 yd²
Then, you need to find the area of the pool alone. Since the diameter of the pool is 23 yd., the radius is 11.5 yd.
A = πr²
A = π(11.5)²
A = 132.25π
A = 415.265 yd²
Subtract the two areas to find the are of the walk.
490.625 - 415.265 = 75.36 yd²
The area is 75.36 yd²
Find the quotient. Write the answer in the simplest form (reduce).
38) 1/2 ÷ 5 =
39) 1 3/5 ÷ 3/5 =
40) 2 1/8 ÷ 1 /4 =
41) 2/3 ÷ 2 1/3 =
42) 5/6 ÷ 1 1 /4 =
\([Hello,BrainlyUser]\)
Answer/Step-by-step explanation:
38) 1/2 ÷ 5 = 1/10
39) 1 3/5 ÷ 3/5 = 2 2/3
40) 2 1/8 ÷ 1 /4 =8 1/2
41) 2/3 ÷ 2 1/3 =2/7
42) 5/6 ÷ 1 1 /4 = 2/3
[CloudBreeze]
Answer:
[38] 1/10
[39] 2 2/3
[40] 8 1/2
[41] 2/7
[42] 2/3
Step-by-step explanation:
Dividing Fractions Formula:
\(\frac{a}{b}\) ÷ \(\frac{c}{d}=\frac{a * b}{b*c}\)
=================================================================
[38] \(\frac{1*1}{2*5}=\frac{1}{10}\)
----------------------------------------------------------------------------------------------------------
[39] \(\frac{8*5}{5*3}=\frac{40}{15}=2\frac{2}{3}\)
----------------------------------------------------------------------------------------------------------
[40] \(\frac{17*4}{8*1}=\frac{68}{8}=8\frac{1}{2}\)
----------------------------------------------------------------------------------------------------------
[41] \(\frac{2*3}{3*7}=\frac{6}{21}=\frac{2}{7}\)
----------------------------------------------------------------------------------------------------------
[42] \(\frac{5*4}{6*5}=\frac{20}{3}=\frac{2}{3}\)
----------------------------------------------------------------------------------------------------------
[RevyBreeze]
A sample is the entire set of elements in which a researcher is interested.
A. True
B. False
False.A sample is a subset of the entire set of elements in which a researcher is interested.
Is it true that a sample is the complete set of elements that a researcher is interested in studying?A sample is a subset of the entire set of elements in which a researcher is interested. The sample is typically selected to represent the characteristics of the larger population from which it is drawn.
By studying the sample, researchers can make inferences about the larger population. However, the sample is not the entire set of elements, but rather a smaller subset selected for study.
In research, the population refers to the entire set of elements that a researcher is interested in studying. This could be a group of people, animals, objects, or events that share common characteristics.
For example, if a researcher is interested in studying the effects of a new drug on patients with a certain disease, then the population would be all patients with that disease.
However, it is not always possible or practical to study the entire population. This is where sampling comes in. A sample is a smaller subset of the population that is selected to represent the characteristics.
By studying the sample, researchers can make inferences about the larger population.
For example, if a researcher wants to study the average height of people in a certain city, it would be impractical to measure the height of every single person in the city.
Instead, the researcher could select a representative sample of people and measure their height, then use statistical methods to estimate the average height of the entire population.
In summary, while the population refers to the entire set of elements in which a researcher is interested, a sample is a smaller subset of that population that is selected for study.
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Solve the system by substitution. -3x+3=y -x+3y=29
Answer: x = −2, y= 9
Step-by-step explanation:
Solving for X
-3x+3=y
-x+3y=29
Plug the top equation into the bottom one
-x+3(-3x+3)=29
Distribute
-x - 9x + 9 = 29
combine like terms
-10x + 9 = 29
-10x = 20
Divide the x
x = -2
Solving for Y:
Plug the value x into any of the equations'
-3(-2) + 3 = y
Distribute
6 + 3 = y
y = 9
To check if that is right, plug x into the other equation
-(-2) + 3y = 29
Distribute and combine like terms
2 + 3 y = 29
3y = 27
y = 9
plz help
Simplify:
- 1.2+15.45
Answer:
- 1.2+15.45=14.43
Step-by-step explanation:
.
Now perform the calculation you set up in part A. Round your answer to the nearest whole number.
Type the correct answer in the box. Use numerals instead of words.
It will take
seconds for the device to release 154 grams of the gas.
Answer:It will take 143 seconds
Step-by-step explanation:
Answer:
The device will release 154 grams of the gas in about 143.2558 seconds. The final answer can’t be more precise than the least precise value given in the problem statement. In this case, the least precise value has two significant figures. After rounding the answer to two significant figures, the final answer is 140 seconds.
Step-by-step explanation:
The dot plot below represents this set of data:
8, 7, 5, 5, 4, 2, 3, 3, 4, 6, 5, 4, 5, 5
Answer:
False
Step-by-step explanation:
There isnt two eights
What is the slope of the line that passes through the points (-9, 2)(−9,2) and (1, 27) ?(1,27)? Write your answer in simplest form. 1
Answer:
pls mark brainliest if possible:
slope is 1.5
Step-by-step explanation:
Slope = rise over run = (y2-y1)/(x2-x1)
choose y2 and corresponding x-coordinate is x2. If we choose 27 as y2, then:
x2 = 1
x1 = -9
y1 = 2
then plug everything into the equation
(27-2)/(1-(-9))
=15/10
= 1.5
slope is 1.5
hope this helps!
the twelfth term of the arithmetic sequence whose first term is 32 and whose common difference is -4.
The twelfth term of the arithmetic sequence is -12.
To find the twelfth term of an arithmetic sequence, we can use the formula:
term = first term + (n - 1) * common difference
In this case, the first term (a) is 32 and the common difference (d) is -4. We want to find the twelfth term, so n = 12.
Plugging the values into the formula, we have:
term = 32 + (12 - 1) * (-4)
= 32 + 11 * (-4)
= 32 + (-44)
= -12
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Which statement is correct about the system of linear equations graphed below? A.The system of equations has one solution because the lines will eventually intersect. B.The system of equations has one solution because the lines will never intersect. C.The system of equations does not have one solution because the lines will eventually intersect. D.The system of equations does not have one solution because the lines will never intersect.
Answer: A
Step-by-step explanation:
They have one solution because as you look at the lines they have different slopes and different y intercepts which means it has one solution.It is not parallel to each other to have no solutions. They seems to be going to one direction and eventually they will intersect.
find the difference 58.84 - 2.78
Answer:
56.06
Step-by-step explanation:
58.84
-- 2.78
______
56.06
I don't really know how else to explain this, but there ya go! Goodluck on your test or whatever you're doing! Stay safe ♥♥♥
The difference between the given decimal numbers is 56.06.
The given decimal numbers are 58.84 and 2.78.
We need to find the difference between the given decimal numbers.
How to find the difference between the decimal numbers?To subtract decimals, begin by writing the numbers in a column, with the decimal points aligned. If necessary, add zeroes as placeholders to make sure there are values in each column. Subtract from right to left. Write the decimal point in the difference directly below the decimal point in the subtrahend.
Now, 58.84 - 2.78=56.06
Therefore, the difference between the given decimal numbers is 56.06.
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f f(x) = 10-2x and g(x) = 6x - 5, then (f+g) (x) = ?
Answer:
(f+g)(x)=4x+5
Step-by-step explanation:
Just add the two functions together:
(f+g)(x)=f(x)+g(x)=(10-2x)+(6x-5)=-2x+6x+10-5=4x+5
So (f+g)(x)=4x+5
What are the 7 laws of exponents?
Answer:
1- Product of powers rule.
2- Quotient of powers rule.
3- Power of a power rule.
4- Power of a product rule.
5- Power of a quotient rule.
6- Zero power rule.
7- Negative exponent rule.
Step-by-step explanation:
Hope I helped! ^v^
what is the approximate value of the x-coordinate of the point of the intersection
Completely factor f(x)=2x^4+11x^3+2x^2-15x given that f(-3/2)=0
Due today please help
Answer:
There isn't a picture
Step-by-step explanation:
5-7*
Someone please answer this
Answer:
-2
Step-by-step explanation:
hope i helped!
Answer:
The answer is - 2
Step-by-step explanation:
5-7= - 2
Suppose that we flip a fair coin until either it comes up tails twice or we have flipped it six times. What is the expected number of times we flip the coin
The expected number of times the coin is flipped is 3.75.
What is Probability?Probability refers to the chance of occurrence of an event.
Let E be an event. Then, the probability of E = P(E)
=> P(E) = \(\frac{Number Of Favourable Outcomes Of E}{Total Number Of Outcomes}\)
Now,
When the coin is flipped two times, Total number of outcomes = 4 Total number of Favorable outcomes = 1P(Tail coming up twice) = \(\frac{1}{4}\)
When the coin is flipped three times,Total number of outcomes = 8 Total number of Favorable outcomes = 2P(Tail coming up twice) = \(\frac{2}{8}\)
When the coin is flipped four times,Total number of outcomes = 16Total number of Favorable outcomes = 3P(Tail coming up twice) = \(\frac{3}{16}\)
When the coin is flipped five times,Total number of outcomes = 32Total number of Favorable outcomes = 4P(Tail coming up twice) = \(\frac{4}{32}\)
When the coin has been flipped six times,P(Tail coming up twice) = \(1-\frac{1}{4}-\frac{2}{8}-\frac{3}{16}- \frac{4}{32} = \frac{3}{16}\)
Therefore, the expected number of times coin is flipped = \(2(\frac{1}{4}) + 3(\frac{2}{8}) + 4(\frac{3}{16} )+5(\frac{4}{32} )+6(\frac{3}{16} ) =\frac{15}{4} = 3.75\)
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the mean score on a college placement exam is 500 with a standard deviation of 100. ninety-five percent of the test takers score below what value?
The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.
As given in the question,
Given : 95% of the test takers score are below z.
z-score is given by,
z=(x-μ)/σ
Mean of the score 'μ' = 500
Standard deviation of the score ' σ' = 100
Z = 95%
= 0.95
P(z<Z) = 1-0.95
= 0.05
The value of z which corresponds to 0.05 in the table is equal to 1.96.
Substitute all the values we get,
z=(x-μ)/σ
⇒1.96 = ( x - 500 ) / 100
Multiply by 100 both the sides we get,
⇒ 196 = ( x - 500 )
⇒ x = 696
Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.
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Is triangle ABC congruent to triangle AED?.
Triangles AED and ABC are congruent to one another according to SSS congruency.
Given,
The side BC is equal to side DE.
The side AC is equal to side AD.
∠BAC = ∠DAE
We have to find that whether triangle ABC congruent to triangle AED;
Here,
The side AB = 7 units.
The side AE = 7 units.
Therefore,
The side AB is equal to side AE.
The sum of all the angle of a triangle is 180°.
Consider the triangle ABC and triangle AED.
AB = AE
AC = AD
BC = DE
So, the triangle ABC is congruent to triangle AED by SSS congruency.
That is,
The triangle AED and triangle ABC are congruent by to each other by SSS congruency.
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The image for the question is attached below.
Nell participated in a 3-day charity walk. Sheraised $0.50 for each 1/3 of mile that she walked. Thefirst day, Nell walked 12 miles. The second day, shewalked 8 miles. The third day, she walked 16 miles.How much money did Nell raise?
the Numbers of days = 3
The second statement(She raised $0.50 for each 1/3 of mile that she walked) means
1/3 miles = $0.50
For first day walk we have:
1/3 miles = $0.50
12 miles = 12 x 0.50 x 3 = $18
For Second day walk we have:
1/3 miles = $0.50
8miles = 8 x 0.50 x 3 = $12
For Third day walk we have:
1/3 miles = $0.50
16miles = 16 x 0.50 x 3 = $24
The amount she raised for the three days becomes
$18 + $12 + $24
=$54
a small computer company had a profit of $2,500 per month when it sold 450 computers. when it sold 600 computers, it had a profit of $3,100. a) write a linear function for the profit, p, in terms of the number of computers sold, x.
The linear function of the profit p in terms of the number of computers(x) sold per month is:
F(p)= 4x +1300;
Profit made on selling 450 computers a month = 2500
profit made on selling 600 computers a month= 3100
Then let F(p) be the function representing the profit in terms of the computers sold
Where the number of computer sold are a variable of x
Then,
F(p): 450x = 2500
F(p): 600x = 3100
Using two-point form as both are proportional
y - 3100 = 3100-2500/600-450(x-450)
y - 3100 = 600/150(x-450)
y-3100= 4(x-450)
y-3100= 4x - 1800
y=4x + 3100 - 1800
y = 4x + 1300
where y=F(p) i.e the profit made on the sale of x number of computers per month.
so,
F(p)= 4x +1300;
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A cell phone that was bought for 2500 was sold at 15% calculate the selling price
Answer:
The answer to your question is $375
The selling price of the cell phone is $375.
Step-by-step explanation:
15% x 2500
100 = 375
I hope this helps and have a wonderful day!