By completing squares, we will see that the solutions of the given quadratic equation are:
x = -3 ± √(21/2)
How to solve the quadratic equation?
Here we know that Inga is solving the quadratic equation below:
2x² + 12x - 3 = 0
The steps that she can do is try to complete squares, first we can take the 2 as a common factor to get:
2(x² + 6x) - 3 = 0
Now we can add 18 in both sides, then we will get:
2(x² + 6x) - 3 + 18 = 18
We can put that 18 inside the first term:
2(x² + 6x + 9) - 3 = 18
And now we can complete squares, because:
x² + 6x + 9 = x² + 2*3*x + 3² = (x + 3)²
Replacing that we will get:
2(x + 3)² - 3 = 18
2(x + 3)²= 18 + 3 = 21
2(x + 3)² = 21
(x + 3)² = 21/2
x = -3 ± √(21/2)
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Determine the mean, median, standard deviation, and interquartile range for each data set. Then, use the graphing tool to determine the value of the standard deviation.
Number of Days Member Used Facility Last Month
Manuel’s Data Gretchen’s Data
3 22
6 4
8 7
11 8
12 12
8 15
6 10
3 7
10 9
5 6
14 13
9 3
7 8
10 10
8 10
Question
Complete the table for Manuel’s and Gretchen’s data sets.
Type the correct answer in each box. Use numerals instead of words.
The mean, median, standard deviation, and interquartile range for each data set is given below.
How to calculate the valuesThe IQR is a measure of the middle 50% of values when they are organized from lowest to highest. To get the interquartile range, find the median (middle value) of the lower and upper half of the data (IQR).
These are the values for the quartiles 1 (Q1) and 3 (Q3). The IQR is the distinction between Q3 and Q1.
Using the statistical tool, the following were arrived at for Manuel:
Standard Deviation = 3.13961
Mean = 8
Median = 8
IQR = Q3-Q1 = 10 - 6 = 4
Using the statistical tool, the following were arrived at for Gretchen:
Standard Deviation = 4.68737.
Mean = 9.6
Median = 9
IQR = IQR = Q3-Q1 = 12 - 7 = 5.
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A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave. The first six bats will be the control group, the second six will be treatment group 1, and the last six will be treatment group 2.
Which component is missing from the biologist’s process?
A) The biologist should have chosen a random night to catch the bats.
B) The biologist did not randomly assign the bats to the treatment groups.
C) The biologist did not allow each bat the same chance to be in each treatment group.
D) The biologist should have used random sampling when deciding which bats to catch.
The component that is missing from the biologist's process is:
c) The biologist did not randomly assign each of the bats to the treatment groups.
What is the Importance of the Random Assignment of Subjects into Groups?When carrying out a research study where you have groups created that you want to study, differences between and within groups can be satisfactory ensuring that they are not systematic when subjects are randomly assigned to groups.
Given, A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area.
a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2).
Thus, it gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently ascribed to experimental treatments.
Therefore, the component that is missing from the biologist's process is: c. The biologist did not randomly assign each of the bats to the treatment groups.
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Solve , x2-50=0where x is a real number. Round your answer to the nearest hundredth.
The value of 'x' in x² - 50 = 0 is either - 7.07 or + 7.07.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A quadratic equation x² - 50 = 0, where x belongs to R.
x² = 50.
x = ± √50.
x = ± 7.07.
So, The value of x can be - 7.07 or it can be + 7.07 squaring both numbers will result to approximately 50.
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The requried solution of the given expression is given as x = 7.07, -7.07.
What are the zeros of equations?Zeros of an equation are defined as the value of the independent variable where the equation or function gives zero.
Here,
Given expression,
x² - 50 = 0
x² = 50
x = √50
x = ±7.07
Thus, the requried solution of the given expression is given as x = 7.07, -7.07.
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Let a be a 32 matrix. explain why the equation ax b cannot be consistent for all b in . generalize your argument to the case of an arbitrary a with more rows than columns.A. When written in reduced echelon form, any 3x2 matrix will have at least one column of all zeros. Since there is not a pivot in every column, the matrix cannot be consistent B. When written in reduced echelon form, any 3x2 matrix will have at least one row of all zeros. When solving Ax = b. that row will represent an equation with infinitely many solutions C. When written in reduced echelon form, any 3x2 matrix will have at least one row of all zeros. When solving Ax=b, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side. D. When written in reduced echelon form any 3x2 matrix will have a pivot in every row.
When written in reduced row echelon form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side.
This means that there is no solution for the equation Ax=b for that specific b, making the system inconsistent.
Generalizing this argument to the case of an arbitrary A with more rows than columns, if the number of rows in A is greater than the number of columns, the reduced row echelon form of A will have at least one row of all zeros, and the corresponding equation in Ax=b will have no solution, making the system inconsistent for that specific b.
Hence, the correct answer is B.
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--The given question is incomplete; the complete question is
"Let A be a 3 times ×2 matrix. Explain why the equation Ax=b cannot be consistent for all b in a set of real numbers R3.
Generalize your argument to the case of an arbitrary A with more rows than columns.
Why is the equation Ax=b not consistent for all b in a set of real numbers R3?
A. When written in reduced row echelon form, any 3 ×2 matrix will have at least one column of all zeros. Since there is not a pivot in every column, the matrix cannot be consistent.
B. When written in reduced row echelon form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b, that row will represent an equation with a zero on the left side and a possibly nonzero entry of b on the right side.
C. When written in reduced row echelon form, any 3 ×2 matrix will have at least one row of all zeros. When solving Ax=b, that row will represent an equation with infinitely many solutions.
D. When written in reduced row echelon form, any 3 ×2 matrix will have a pivot in every row. Because there are more rows than columns, this is too many pivots, and the system will be inconsistent."--
show thatf′(x) = 0 at least once for the functionf(x) = 1−ex (e−1) sinπ2xon the interval [0,1]
the function is defined on the interval [0,1], we must have 0 ≤ x ≤ 1. Therefore, the value of x for which[tex]f'(x)=0 is x = 0.[/tex]
To find the value of x for which[tex]f'(x)=0[/tex], we need to differentiate the given function.
[tex]f'(x) = (e-1)(π/2)(ex)(cos(π/2x)) - (sin(π/2x))[/tex]
Now, set [tex]f'(x) = 0[/tex]and solve for x.
[tex](e-1)(π/2)(ex)(cos(π/2x)) - (sin(π/2x)) = 0(e-1)(π/2)(ex) = (sin(π/2x))ex = (sin(π/2x))/(e-1)(π/2)[/tex]
Taking natural log on both sides
[tex]xln(e) = ln(sin(π/2x)) - ln((e-1)(π/2))xln(e) = ln(sin(π/2x)) - ln(e-1) - ln(π/2)x = (ln(sin(π/2x)) - ln(e-1) - ln(π/2))/ln(e)[/tex]
Since the function is defined on the interval [0,1], we must have 0 ≤ x ≤ 1.
Therefore, the value of x for which [tex]f'(x)=0 is x = 0.[/tex]
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Suppose X has an exponential distribution with rate parameter λ1. Suppose Y has an exponential distribution with rate parameter λ2. Suppose X and Y are independent. Calculate P(X > Y).
The probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y multiplied by the probability of Y being less than or equal to X, which can be expressed as 1 minus (1 - e^(-(λ1 + λ2)t))/2, or e^(-(λ1 + λ2)t)/2.
P(X > Y) = 1 - P(X ≤ Y) = 1 - (1 - e^(-(λ1 + λ2)t))/2 = e^(-(λ1 + λ2)t)/2
1. P(X > Y) = 1 - P(X ≤ Y)
2. P(X ≤ Y) = P(X ≤ Y ∩ Y ≤ X)
3. P(X ≤ Y ∩ Y ≤ X) = P(X ≤ Y)P(Y ≤ X) (Since X and Y are independent)
4. P(X ≤ Y) = 1 - P(X > Y)
5. P(Y ≤ X) = 1 - P(Y > X)
6. P(X > Y) = 1 - P(X ≤ Y)P(Y ≤ X)
7. P(X > Y) = 1 - (1 - e^(-(λ1 + λ2)t))/2
8. P(X > Y) = e^(-(λ1 + λ2)t)/2
The probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y. Since X and Y are independent, the probability of X being less than or equal to Y and Y being less than or equal to X is equal to the product of the probabilities of X being less than or equal to Y and Y being less than or equal to X. The probability of X being less than or equal to Y is equal to 1 minus the probability of X being greater than Y, and the probability of Y being less than or equal to X is equal to 1 minus the probability of Y being greater than X. Therefore, the probability of X being greater than Y is equal to 1 minus the probability of X being less than or equal to Y multiplied by the probability of Y being less than or equal to X, which can be expressed as 1 minus [tex](1 - e^(-(λ1 + λ2)t))/2, or e^(-(λ1 + λ2)t)/2.[/tex]
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How many M is 5 foot 4 inches?
1.6256 Meters in 5 foot 4 inches
How to convert feet to inches?So, to convert a measurement in feet to inches, all you need to do is multiply the number by 12. This is an exact number, so if you're working with significant figures, it won't limit themConversion of feet into inches where in both are imperial units of measuring length. The standard unit to measure the length in centimeters. One feet is equal to 12 inchesThis is my height also, I am 5'7"tall. The conversion factor I remember is that there are 2.54 centimeters in 1 inch, so first I would change the feet to inches. 5 12 = 60 so 5'7" = 67"To learn more about convert feet to inches refers to:
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There are 1.6256 Meters in 5 foot 4 inches
How do you convert an inch to a foot?As a result, multiplying a measurement by 12 will convert it from feet to inches. Since it is an exact number, there will be no restrictions on utilising significant figures.
Conversion of feet to inches where both length measurement units are in the imperial system. the standard unit for centimetre length measurements. Twelve inches are equivalent to one foot.
This is also how tall I am because I'm 5'7". I would first convert the feet to inches using the closest I can remember conversion factor of 2.54 centimetres to 1 inch.
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(HELP ME I BEG YOU) rewrite each expression as a product of 2 fractions one of which is equal to 1 then write it as an equivalent just simpler expression.
[tex] \frac{10}{10} {}^{5}{2}[/tex]
the large 2 is supposed to be at the bottom 10
The equivalent exponential expression to 10^5/10² is given as follows:
10³.
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
10^5/10².
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.
The subtraction of the exponents in this problem is given as follows:
5 - 2 = 3.
Hence the equivalent exponential expression to 10^5/10² is given as follows:
10³.
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(6) I'm stuck with my math pls show all ur steps
Answer:
Alice: y = 11 +1xBenito: y = 1 +3x16 cards after 5 daysStep-by-step explanation:
Alice starts with 11 cards and buys 1 per day. Benito starts with 1 card and buys 3 per day. You want equations for Alice and Benito that describe the number of cards they have (y) in terms of the number of days (x) that have passed. you also want graphs of these equations and when and where the numbers of cards are the same.
EquationsIt really should be no mystery that the number of cards will be the sum of the initial number and the product of the number of days and the number of cards acquired each day:
Alice: y = 11 +1x
Benito: y = 1 +3x
GraphSee the attachment for a graph and the point where the graphs intersect:
x = 5, y = 16 . . . . . both have 16 cards after 5 days.
__
Additional comment
The equations are defined for negative x- and y-values, but in the context of this problem the only values that make sense are ones where x ≥ 0 and y > 0.
Question 3 of 10
What are the more appropriate measures of center and spread for this data
set?
0 2
4
5 8 10
H
14
24
6 8 10 12 14 16 18 20 22 24 26 28 30
Select two choices: one for the center and one for the spread.
A. Better measure of spread: the standard deviation
B. Better measure of center: the median
C. Better measure of spread: the interquartile range (IQR)
D. Better measure of center: the mean
The two choices that reflect one for the center and one for the spread are:
A. Better measure of spread: the interquartile range (IQR)
B. Better measure of center: the median
Why are they the selected choices?For the first data set, the values appear to be unordered, so it would be difficult to determine the mean. The median is a more appropriate measure of center for this data set, as it would provide a value that separates the data into two halves.
The interquartile range (IQR) is a better measure of spread for this data set, as it provides a robust measure of spread that is less sensitive to outliers. The IQR is the difference between the 75th percentile and the 25th percentile of the data, and it provides a measure of the spread of the middle 50% of the data.
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Is Into the Radius VR worth it?
It's definitely one of the more rewarding survival experiences that has hit the platform.
Is Into the Radius VR worth it?
Now the studio says it's bringing the open world game to Quest 2 starting next month. Update (August 31st, 2022): CM Games has announced that Into the Radius is arriving on Quest 2 on September 8th. You can wishlist it over on the Meta Store here.Now the studio says it's bringing the open world game to Quest 2 starting next month. Update (August 31st, 2022): CM Games has announced that Into the Radius is arriving on Quest 2 on September 8th. You can wishlist it over on the Meta Store here.Just like with any other technology, overexposure to VR can lead to increased alterations in the brain, resulting in headaches and nausea.To learn more about radius refers to:
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hurry pls this is urgent
A rectangular swimming pool has a perimeter of 150 m the length of the pool is twice the width of the pool what is the length of the pool
The length of the rectangular swimming pool is, 50 m.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
A rectangular swimming pool has a perimeter of 150 m.
And, The length of the pool is twice the width of the pool.
Now, Let the width of the pool = x
Then, The length of the pool = 2x
We know that;
Perimeter of rectangle = 2 (Length + Width)
Substitute all the given values, we get;
⇒ 150 = 2 (2x + x)
⇒ 150 = 2 × 3x
⇒ 150 = 6x
⇒ x = 150 / 6
⇒ x = 25
Thus, The length of the rectangular swimming pool = 2x
= 2 × 25
= 50 m
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at aeropostale, david bought 4 t shirts and 3 pairs of jeans for $181. at the same store, jennifer bought 1 t shirt and 2 pairs of jeans for $94. the t shirts and jeans were the same price in both instances. what is the price of the t shirts?
The price of a t-shirt is $43.50.
Let's call the price of a t-shirt "t" and the price of a pair of jeans "j".
For David:
4t + 3j = 181
For Jennifer:
t + 2j = 94
We can use these two equations to solve for t and j. Subtracting the second equation from the first, we have:
3t + j = 87
Next, we can substitute the second equation into the third equation to eliminate t:
3(t + 2j) = 3 * 94 = 282
Expanding the left side, we have:
3t + 6j = 282
Subtracting j from both sides:
3t + 5j = 282 - j
Combining like terms:
3t + 6j = 282
Subtracting the first equation from the third equation:
2t = 181 - 94
Combining like terms:
2t = 87
Finally, solving for t:
t = 87 / 2 = 43.5
The price of a t-shirt is $43.50.
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The price of a t-shirt is $43.50.
Let's call the price of a t-shirt "t" and the price of a pair of jeans "j".
For David:
4t + 3j = 181
For Jennifer:
t + 2j = 94
We can use these two equations to solve for t and j. Subtracting the second equation from the first, we have:
3t + j = 87
Next, we can substitute the second equation into the third equation to eliminate t:
3(t + 2j) = 3 * 94 = 282
Expanding the left side, we have:
3t + 6j = 282
Subtracting j from both sides:
3t + 5j = 282 - j
Combining like terms:
3t + 6j = 282
Subtracting the first equation from the third equation:
2t = 181 - 94
Combining like terms:
2t = 87
Finally, solving for t:
t = 87 / 2 = 43.5
The price of a t-shirt is $43.50.
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Rectangle A measures 9 in. by 3 in. Rectangle B is a scaled copy of Rectangle A.
Select all of the measurement pairs that could be the dimensions of Rectangle B.
4.5 in. by 1.5 in.
8 in. by 2 in.
10 in. by 4 in.
13.5 in. by 4.5 in.
90 in. by 30 in.
14 in. by 8 in.
According to the information, the options that correspond to the possible scale copies of the original rectangle would be 4.5 in. by 1.5 in. yes, 13.5 in. by 4.5in. Yes, and 90 in. by 30in. Yeah.
How to calculate the possible scales?To calculate the possible scales we must carry out the following procedure: First we must make a division between the two lengths of the sides of the rectangle:
9 / 3 = 3
So, the relationship between these two lengths would be 3. Now we just have to check which options follow this proportional relationship. According to this procedure they would be the following:
4.5in. by 1.5in
13.5in. by 4.5in
90 in. by 30in
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if kvk = 4 and kwk = 7, what are the smallest and the largest possible values of kv − wk? what are the smallest and the largest possible values of v · w?
if |v| = 4 and |w| = 7, what are the smallest and the largest possible values of |v − w|
smallest and the largest possible values of v · w
v and w are vectors, not numbers. v*w indicates the dot product of these vectors and l v l and l w l their magnitudes.
Assuming v and w are vectors with any direction but with definite magnitudes
||v − w|| ≤ ||v|| + ||w|| = 11
and ||v − w|| ≥ ||v|| − ||w||| = 3,
while
|v · w| = ||v||||w|| cos θ ≤ ||v|| · ||w|| = 28,
so −28 ≤ v · w ≤ 28.
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using u = 1 x , we can write h(x) = 1⁄x arctan(t) dt 1 as h(u) = u arctan(t) dt. 1
H(u) = u arctan(x) - (1) arctan(t) dt is obtained by integrating u arctan(t) with respect to t from 1 to x.
The original function h(x) = 1/x arctan(t) dt can be rewritten as h(u) = u arctan(t) dt by substituting u = 1/x. This is accomplished by substituting 1/u for each instance of x in the original equation.
The result of integrating this equation from 1 to x with regard to t is h(u) = u arctan(x) - (1) arctan(t) dt. The integral of u arctan(t) from 1 to x less the integral of arctan(t) from 1 to x can be used to represent this. The integration variable for the first integral is u, while the variable for the second integral is t.
By adding u = 1/x to the equation, the value of h(u) can then be utilised to determine the value of h(x). To accomplish this, all occurrences of u are replaced.
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Yep here we go again:
The price of a cell phone is usually $250. Elena’s mom buys one of these cell phones for $150. What percentage of the usual price did she pay?
Elena’s dad buys another type of cell phone that also usually sells for $250. He pays 75% of the usual price. How much did he pay?
If you don't or not sure of an answer please don't answer it.
I will mark brainliest to the best answer!!
For the first question, the percentage of the usual price that Elena's mom paid is 60%, and for the second question, the price that Elena's dad paid is $187.50.
For the first question, to find the percentage of the usual price Elena's mom paid, you can divide the actual price by the usual price and multiply by 100:
$150 ÷ $250 × 100 = 60%
So, Elena's mom paid 60% of the usual price for the cell phone.
For the second question, you can use the percentage of the usual price to find the actual price:
$250 × 75/100 = $187.50
So, Elena's dad paid $187.50 for the other type of cell phone, which is 75% of the usual price.
To summarize, Elena's mom paid 60% of the usual price of $250 and paid $150, while Elena's dad paid $187.50, which is 75% of the usual price.
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Each of the following events result in a tax payment. Which is an example of a direct tax?
A. Charles sells a 25-acre lot, which includes a barn.
B. Sammy stops to pump gas on a cross-country road trip.
C. Ingrid's cable bill contains extra fees that weren't listed in the plan.
D. Javier owes money to the federal government based on job earnings.
Each of the following events result in a tax payment, an example of a direct tax is D. Javier owes money to the federal government based on job earnings.
How Do Direct Taxes Work?A direct tax is one that is paid by an individual or group of individuals directly to the body that levied it. Taxes on assets, real estate, personal property, and income are a few examples that are all paid by an individual taxpayer directly to the government.
Direct taxes are those that you pay to the government directly. You have paid a direct tax, for instance, if you pay income tax, property tax, or capital gains tax. On the other side, an indirect tax is when you make a purchase and someone else subsequently pays the tax on your behalf through a sales tax.
Therefore, option D is correct.
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What are Sum and Difference Formulas?
When it is simpler to describe an angle as the sum or difference of distinct angles (0°, 30°, 45°, 60°, 90°, and 180°), the sum and difference formulae in trigonometry are used to determine the value of the trigonometric functions at those particular angles.
What is trigonometric function?Angles are the basis of trigonometric functions. They are employed to connect the side lengths of a triangle to its angles. Sine, cosine, and tangent are the three fundamental operations of trigonometry. The remaining three functions, cotangent, secant, and cosecant, are derived from these three basic ones. The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of the lengths of the two sides. All geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more, utilise them extensively. This is due to the fact that, in comparison to other branches of mathematics, trigonometry is still seen as being extremely challenging and abstract.To learn more about trigonometric function, refer to:
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Find the value of x and measure of angle V if ABCD~TUVW
How do you know if a graph is positive or negative correlation?
As the y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.
What is a graph?A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.
The points on a graph are typically used to depict the relationships between two or more things.
Making a diagram that shows the link between two or more objects is known as developing a graph.
Scatterplots frequently reveal relationships or trends.
We say there is a positive correlation between the variables when the y variable tends to rise when the x variable rises.
We say there is a negative correlation between the variables when the y variable tends to decline as the x variable rises.
Therefore, a y variable tends to increase when the x variable increases, we say the variables have a positive correlation. When the y variable tends to decrease as the x variable rises, we say there is a negative correlation between the variables.
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find the general solution to enter your answer as . use to denote the arbitrary constant in your answer. tln(t)dr/dt r =5te^4
The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.
The general solution to the differential equation d(r)/dt = 5tln(t) can be found using the method of integrating factors.
First, we find the integrating factor:
I = e^∫5ln(t)dt = e^(5t - 5)
Next, we multiply both sides of the equation by the integrating factor:
I * d(r)/dt = I * 5tln(t)
Now, we can integrate both sides of the equation:
∫I * d(r)/dt = ∫I * 5tln(t)dt
Using the substitution u = r and du/dt = d(r)/dt, we can simplify the left side of the equation:
du/dt = I * d(r)/dt
And on the right side, we use integration by parts:
∫I * 5tln(t)dt = (5/2)t^2ln(t) - 5te^5 + C
Finally, we can solve for r:
r = (5/2)t^2ln(t) - 5te^5 + C
The general solution to the differential equation d(r)/dt = 5tln(t) is:
r = (5/2)t^2ln(t) - 5te^5 + C.
Note that C is an arbitrary constant and represents the freedom in choosing the initial conditions for the solution.
Therefore, The general solution to the differential equation d(r)/dt = 5tln(t) is: r = (5/2)t^2ln(t) - 5te^5 + C.
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The art club is designing a rectangular mural for the school hallway. Three corners are located at (21, 21), (21, 1), and (4, 1) on a coordinate plane. Find the fourth vertex using the coordinate plane below.
ASAP - 20 pts
The fourth vertex of the rectangle using the coordinate plane is; (4, 21)
How to find the coordinate of a rectangle?The three coordinates of the rectangle are expressed as;
(21, 21)
(21, 1)
(4, 1)
Now, when we tal about a rectangle, it is pertinent to note that two points must have the same y coordinates while two points must also have the same x -coordinates because the two parallel sides of a rectangle are equal.
Thus, we already have two sides with 21 as x-coordinate but only one with 4 as x-coordinate and as such the fourth point will have 4 as x-coordinate.
Similarly, only one point has 21 as y-coordinate and as such the fourth point will have its' y-coordinate as 21.
(4, 21)
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what is the 10 year to 3 month term premium
The 10-year to 3-month term premium will be 0.079%.
Now, According to the question:
The premiums that are the regularly scheduled installments that are finished to pay the inclusion of the insurance contract are less expensive in term life coverage than in real money life coverage as the term just covers the recipients for the period the contract is purchased for instance: a half year. On the off chance that the individual who claims the arrangement passes on in a half year, the insurance agency needs to pay the recipients the capital set in the strategy.
Anyway assuming the individual passes on after the a half year or doesn't bite the dust the insurance agency pay nothing to the buyer of the strategy.
In the money life coverage the individual gets one last installment though the individual lives or passes on as the strategy goes about as a saving arrangement.
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The complete question is:
What is the 10-year to 3-month term premium of the following yield curve?
Pls i need answers quickly
Answer:
[tex] \red{ \boxed{\sf{c = 0.81s}}}[/tex]
Step-by-step explanation:
(total cos t) = k (songs)
total cost / songs = k
8.1/10 = k
0.81 = k
now substitute 0.81 in for k in your equation
c = 0.81s
follow..
a piece of paper is to display 128 128 space, 128, space square inches of text. if there are to be one-inch margins on both sides and two-inch margins at the bottom and top, what are the dimensions of the smallest piece of paper (by area) that can be used?
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
The area of a square with sides of one inch is equal to one square inch (plural: square inches).
We have that:
Let the dimension of the paper be x and y.
Such that:
Length = [tex]x[/tex]
Width = [tex]y[/tex]
So:
Area = [tex]x*y[/tex]
Substitute 128 for Area
[tex]128=x*y[/tex]
Make x the subject.
[tex]x=\frac{128}{y}[/tex]
When 1 inch margin is at top and bottom
The Length becomes:
[tex]Length =x+1+1[/tex]
[tex]Length = x+2[/tex]
When 2-inch margin is at both sides
The width becomes:
[tex]Width = y+2+2[/tex]
[tex]Width = y+4[/tex]
The New Area (A) is then calculated as:
[tex]A = (x+2)*(y+4)[/tex]
Substitute [tex]\frac{128}{y}[/tex] for x
[tex]A = (\frac{128}{y}+2 )*(y+4)[/tex]
Open Brackets
[tex]A = 128 + \frac{512}{y} + 2y + 8[/tex]
Collect Like Terms
[tex]A = \frac{512}{y} + 2y + 8+128[/tex]
[tex]A = \frac{512}{y} +2y+136[/tex]
[tex]A = 512y^{-1} +2y + 136[/tex]
To calculate the smallest possible value of y, we have to apply calculus.
Differentiate A with respect to y
[tex]A' = -512y^{-2}+2[/tex]
Set
[tex]A' = 0[/tex]
This gives:
[tex]0=-512y^{-2}+2[/tex]
Collect Like Terms
[tex]512y^{-2} = 2[/tex]
Multiply through by [tex]y^{2}[/tex]
[tex]y^{2} *512y^{-2} = 2*y^{2}[/tex]
[tex]512 = 2y^{2}[/tex]
Divide through by 2.
[tex]256 = y^{2}[/tex]
Take square roots of both sides.
[tex]\sqrt{256= y^{2} }[/tex]
[tex]16 =y\\\\y=16[/tex]
Recall that:
[tex]x = \frac{128}{y}[/tex]
[tex]x = \frac{128}{16}[/tex]
[tex]x=8[/tex]
Recall that the new dimensions are:
[tex]Length = x+2[/tex]
[tex]Width = y+4[/tex]
So:
[tex]Length = 8+2[/tex]
[tex]Length = 10[/tex]
To double-check.
Differentiate A'
[tex]A' = -512y^{-2}+2[/tex]
[tex]A'' = -2 * -512y^{-3}[/tex]
[tex]A'' = 1024y^{-3}[/tex]
[tex]A'' = \frac{1024}{y^{3} }[/tex]
The above value is:
[tex]A'' = \frac{1024}{y^{3} } > 0[/tex]
In other words, the estimated numbers are at their lowest.
Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
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The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
The area of a square with sides of one inch is equal to one square inch (plural: square inches).
We have that:
Let the dimension of the paper be x and y.
Such that:
Length = x
Width = y
So:
Area = xy
Substitute 128 for Area
128 = xy
Make x the subject.
x=128/y
When 1 inch margin is at top and bottom
The Length becomes:
length = x+2
When 2-inch margin is at both sides
The width becomes:
width = y+4
The New Area (A) is then calculated as:
A = (x+2)(y+4)
Substitute for x
A = (128/y +2)(y+4)
Open Brackets
A = 128 +512/y + 2y +8
Collect Like Terms
A = 512/y + 2y +136
To calculate the smallest possible value of y, we have to apply calculus.
Differentiate A with respect to y
A' = -512/y*y +2
Set
A' = 0
This gives:
y = 16
Recall that:
x = 128/y
x = 8
Recall that the new dimensions are:
Length = x +2
Width = y+4
So:
Length = 10
To double-check.
Differentiate A'
A'' = 1024/y*y*y
The above value is greater than 0
In other words, the estimated numbers are at their lowest.
Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches.
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the admission fee at an amusement park is $1.50 for children and $4 for adults. on a certain day, 238 people entered the park, and the admission fees collected totaled $632.00. how many children and how many adults were admitted?
There were 128 children and 155 adults.
Let us first set up our system by assigning x and y to mean something. Let x = the number of children and y = the number of adults.
First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5.
This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $632. To get this amount, we must add 1.5x and 4y.
1.5x+4y=632 --------(1)
Second equation: Total amount of people on the given day is 238. To get this number, we must add together x and y, or the number of children and adults.
x + y = 238-----(2)
System of equations:
1.5x+4y=632
x+y = 238
Let's use the substitution of the x variable to solve the system.
x+y=238.
y=238-x
Substitute y = 238 - x into the first equation.
1.5x + 4 (238 - x) =632
1.5x + 952 - 4x = 632
952- 2.5x = 632
-2.5x = -320
x = 128
Substitute x =128 back into y = 238 - x
y = 283-128
y=155
There were 128 children and 155 adults.
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yummy bakery and oh so good bakery had a contest with these results: yummy sold 9 fewer rolls than twice what oh so good sold. together they sold a total of 639 rolls. find the number of rolls sold by each bakery. provide the work that shows how u arrived at your answer.
The yummy bakery sold 216 roles and oh so good bakery sold 523 roles.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that yummy bakery and oh so good bakery had a contest with these results: yummy sold 9 fewer rolls than twice what oh so good sold. together they sold a total of 639 rolls.
We can write the relation as -
2x - 9 + x = 639
3x - 9 = 639
3x = 648
x = 216
So, we can write -
2x - 9 = 2 x 216 - 9 = 532 - 9 = 523
Therefore, the yummy bakery sold 216 roles and oh so good bakery sold 523 roles.
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Calculate the area of a rhombus having diagonals equal to 6 cm and 8 cm?
A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.
In the case of provided diagonals, what is the formula to get the area of a rhombus?The product of the lengths of the diagonals divided by two equals the area of a rhombus. The formula Area = (d1 d2)/2 sq. is used to determine the area of a rhombus using diagonals.
The product of the lengths of the diagonals divided by two equals the area of a rhombus.
Knowing that, First diagonal, d1=6 cm. Diagonal 2, d2 = 8 cm Rhombus surface area is given by A=d1d22 =682 =482 =24 cm2. So, the rhombus has a 24 cm2 surface area.
A rhombus has 6 and 8 centimeter diagonals, 24 cm2 is the size of the rhombus.
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