Which of the following form a fundamental set of solution for the differential equation 32y" +32y' + 8y = 0? A. yi -x/2 = e -x/2 and y = xe B. -13x/2 P = xe and 2.-13x/2 V2 = xe O C. None of these. D.

Answer:

8. G 9. C 10. G 11. A 12.?

Step-by-step explanation:

The truth set of each predicate with the domain being the set of integers is

The truth set of a predicate is the set of all elements in the domain that make the predicate true.

For the given predicates, with the domain being the set of integers,

P(x): x^3 ≥ 1

The inequality x^3 ≥ 1 is satisfied for all x such that x ≥ 1 or x ≤ -1. This is because any integer raised to an odd power will always have the same sign as the integer itself, and the only integers whose cubes are less than 1 in absolute value are 0 and 1. Therefore, the truth set of P(x) is {x | x ≤ -1 or x ≥ 1}.

Q(x): x^2 = 2

There are no integers x such that x^2 = 2. Therefore, the truth set of Q(x) is the empty set, ∅.

R(x): x < x^2

The inequality x < x^2 is satisfied for all x such that x < 0 or x > 1. If 0 ≤ x ≤ 1, then x^2 ≤ x, and the inequality does not hold. Therefore, the truth set of R(x) is {x | x < 0 or x > 1}.

Learn more about truth set here

brainly.com/question/27990632

#SPJ4

On solving the provided question, we can say that since an equilateral triangle so, each angle will be 60

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since an equilateral triangle has a side measure of 10 in.

and it is a equilateral triangle

so, all sides will be 10

so, each angle will be 60

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer: HEY THERE!

Step-by-step explanation: HERE IS YOUR ANSWER

5.6 cm * 0.01 m = 0.056 m

1 cm

A real number is in between 14 square root and 15 square root is 3.8.

It should be noted that real numbers include rational and irrational numbers.

✓14 = 3.74

✓15 = 3.87

Therefore, a real number is in between 14 square root and 15 square root is 3.8.

It should be noted that this implies a number that can be sent between the square roots.

Learn more about real numbers on:

brainly.com/question/563320

#SPJ1

The answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).

This is not a polynomial because it contains a fraction (1/x). A polynomial is an expression consisting of variables, constants, and exponents. It can be of any degree, but it must not contain any fractions. The other three options (a, b, and d) are all polynomials because they only contain variables, constants, and exponents.

For example, option a: √3x^2-2√3x+3, can be written as 3x2-2x+3, which is the standard form of a polynomial. Similarly, option b: 3x3/2-5x2-1/√2x-1, can be written as 3x2-5x+1, and option d: 5x2-3x+√2, can be written as 5x2-3x+2, which are both in the standard form of a polynomial.

Therefore, the answer is c: x+1/x, which is not a polynomial because it contains a fraction (1/x).

Learn more about polynomial here:

https://brainly.com/question/11536910

#SPJ4

Answer:

he actual densities of pure, dry, geologic materials vary from 880 kg/m3 for ice (and almost 0 kg/m3 for air) to over 8000 kg/m3 for some rare minerals. Rocks are generally between 1600 kg/m3 (sediments) and 3500 kg/m3 (gabbro).

Step-by-step explanation:

Answer:

B is the answer....I did this math problem

The zeroes of the quadratic function given are 5/2 + √31 / 2 and  5/2 - √31 / 2.

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given quadratic function is

f(x) = 2x² - 10x - 3

We can find the roots of the quadratic function using the quadratic formula.

Quadratic formula for the quadratic function f(x) = ax² + b x + c is,

x = [-b ± \(\sqrt{b^2-4ac}\)] / 2a

Here, a = 2, b = -10 and c = -3

Substituting the values,

x = [-(-10) ± \(\sqrt{(-10)^2-(4*2*-3)}\)] / (2 × 2)

  = (10 ± √(100 + 24) ) / 4

  = (10 ± √124) / 4

  = (10 ± √(31 × 4)) / 4

  = (10 ± √31 √4) / 4

  = (10 ± 2√31) / 4

  = 10/4 ± 2√31 / 4

  = 5/2 ± √31 / 2

Hence the roots are 5/2 + √31 / 2 and  5/2 - √31 / 2.

Learn more about Roots of Quadratic Functions here :

https://brainly.com/question/9155953

#SPJ7

To set up a definite integral that yields the area of the region for the function g(y) = y^3, we first need to determine the interval of integration. Since you did not provide the specific bounds for the region, I will use general variables a and b as the lower and upper limits, respectively.

The given function is: g(y) = y³. We are to set up a definite integral that yields the area of the region. The region is a 2D figure whose area is bounded by the given curve g(y) = y³ and the x-axis. We know that the area of the region can be found using the following formula: ∫a b f(x)dx, where a and b are the bounds of integration. To find the bounds of integration, we need to find the intersection of the curve g(y) = y³ and the x-axis. For y³ = 0, we have y = 0. Thus, the lower bound of integration is 0. To find the upper bound of integration, we need to solve the equation y³ = 1 for y. We have:y³ = 1⇒ y = 1The upper bound of integration is 1. Thus, the definite integral that yields the area of the region is: ∫₀¹ g(y) dy = ∫₀¹ y³ dy. Note: We are not asked to evaluate the integral.
The definite integral representing the area of the region can be written as:
∫[a, b] y^3 dy

Learn more about definite integral here:

https://brainly.com/question/27256027

#SPJ11

Answer:

-4

Step-by-step explanation:

Answer:

-4

Multiply (-7) and (4) to get -28

Then combine 24-28=-4

The cost of producing x bottles is given by the equation c = 0.35x + 2100.  The cost of producing 600 bottles is $2310.

The cost of producing x bottles is given by the equation c = 0.35x + 2100. To find the cost of producing 600 bottles, we substitute x = 600 into the equation.

Plugging in x = 600, we have c = 0.35(600) + 2100.

Simplifying, c = 210 + 2100 = 2310.

Therefore, the cost of producing 600 bottles is $2310.

Learn more about cost here:

https://brainly.com/question/29172437

#SPJ11

Answer:

(a) 0

(b) -3/26

Step-by-step explanation:

(a)

We essentially plug 1 in for x and 2 in for y.

Our expression is \(\frac{2x-y}{y^2+1}\), so making the correct substitutions yields:

\(\frac{2x-y}{y^2+1}=\frac{2*1-2}{2^2+1}=\frac{2-2}{4+1} =\frac{0}{5} =0\)

So, the answer for part (a) is 0.

(b)

Again, we're now plugging in 1 for x and 5 for y:

\(\frac{2x-y}{y^2+1}=\frac{2*1-5}{5^2+1}=\frac{2-5}{25+1} =\frac{-3}{26} =-\frac{3}{26}\)

So, the answer for part (b) is -3/26.

Step-by-step explanation:

So we have the rational expression \(\frac{2x -y}{y^{2} +1}\\\). All we have to do is to just plug the given values for what x and y are.

\(\frac{2x -y}{y^{2} +1}\\ \frac{2(1) -(2)}{(2)^{2} +1} \\ \frac{2 -(2)}{4+1} \\ \frac{0}{5} \\ 0\)

\(0\)

\(\frac{2x -y}{y^{2} +1}\\ \frac{2(1) -(5)}{(5)^{2} +1} \\ \frac{2 -(5)}{25+1} \\ \frac{-3}{26} \\ -\frac{3}{26}\)

\(-\frac{3}{26}\\\)

Answer:

The value of y is 18 at x = 70

Step-by-step explanation:

The equation of the directly proportional is y = k x, where k is the constant of proportionality.

∵ The value of y is directly proportional to the value of x

→ By using the equation above

∴ y = k x

∵ x = 140 and y = 36

→ Substitute them in the equation above

∴ 36 = k(140)

∴ 36 = 140k

→ Divide both sides by 140

∵ \(\frac{36}{140}\) = k

∴ \(\frac{9}{35}\) = k

→ Substitute the value ok in the equation

∴ y = \(\frac{9}{35}\) x ⇒ equation of proportionality

∵ x = 70

→ Substitute in the equation to find y

∴ y =  \(\frac{9}{35}\) × 70

∴ y = 18

∴ The value of y is 18 at x = 70

The surface area and volume of cement block is  1336 in² and 880 in³

To find the total surface area of a cuboid, add the areas of all six faces. Suppose l, b and h be the length, breadth and height of a cuboid, then the total surface area will be 2(lb + bh + hl). The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

Surface area of given cement block is = 10×8×2+20×10×2+(20×8 - 6×4×3)×2 + 4×10×2×3 +6×10×2×3

= 160 + 400 + 176 + 240 + 360

= 1336 in²

Volume of cement block is 20 × 8× 10 - 3×6×4×10

= 1600 - 720

= 880 in³

Hence, the surface area and volume of cement block is  1336 in² and 880 in³

Learn more about Surface area of cuboid here

https://brainly.com/question/26403859

#SPJ1

60 minute tapes: $4.00 each

90 minute tapes: $4.80 each

An algebraic equation is an equation that can be written using only algebraic operations.

This question is an example of an algebraic equation.

Step 1: Calculate the cost of 1 sixty minute tape.

We know that the cost of 5 sixty minute tapes and 9 ninety minute tapes is $71.40.

Total cost = 71.40

Number of sixty minute tapes = 5

Cost of 1 sixty minute tape = 71.40/5 = 14.28

Step 2: Calculate the cost of 1 ninety minute tape.

We know that the cost of 8 sixty minute tapes and 7 ninety minute tapes is $74.65.

Total cost = 74.65

Number of ninety minute tapes = 7

Cost of 1 ninety minute tape = 74.65/7 = 10.66

Therefore, the cost of 1 sixty minute tape is $14.28 and the cost of 1 ninety minute tape is $10.66.

To learn more about Algebraic equation refer to:

brainly.com/question/30294173

#SPJ1

1.521 is the probability when the die is rolled at least two times which is greater than 3.

Probability: It is an event that depends upon the number of favorable outcomes and the total outcomes, and also defines the ratio of the number of favorable outcomes to the total outcomes in that sample space.

The general formula for probability is:

P(A)=n/N=outcomes in A/outcomes in sample space.

Here, a number greater than 3 we can take as 4 or 5 so the total number of dies rolled is 4, and the total number of the die is 6 which is rolled 2 times greater than 3.

\(P(A)=2-(\frac{5}{6} )^4\\\\P(A)=2-(\frac{625}{1296} )\\\\P(A)=\frac{2592-625}{1296} \\\\P(A)=\frac{1971}{1296} \\\\P(A)=1.5208333\)

Thus, the total probability is 1.521

To know more about Probability:

https://brainly.com/question/1580794

#SPJ4

Answer:

\(\pink{\boxed{{\colorbox{white}{Answer}}}}\)

\(\purple {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \)

In the figure, the slope of mid-segment DE is -0.4. The slope of segment AC is?

A.) 0.4

B.) -0.4

C.) 2

D.) -2

\(\purple {\overline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \)

Step-by-step explanation:

\( \pink{\boxed{{\colorbox{white}{- MsTiyana}}}}\)

# i hope it helps you

# mark me brainliest thank you

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

Answer:

The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

From the given figure

∵ The line passes through points (0, 2) and (2, 3)

∴ x1 = 0 and y1 = 2

∴ x2 = 2 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = \(\frac{3-2}{2-0}\) = \(\frac{1}{2}\)

∴ m =  \(\frac{1}{2}\)

→ b is the value of y at x = 0

∵ At x = 0, y =2

∴ b = 2

→ Substitute the value of m and b in the form of the equation above

∵ y =  \(\frac{1}{2}\) x + 2

∴ The equation of the line is y =  \(\frac{1}{2}\) x + 2

∵ The line is dashed

∵ The shaded area is over the line

∴ The sign of inequality is >

→ Replace = in the equation by >

∴ y >  \(\frac{1}{2}\) x + 2

∴ The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Answer:

3

Step-by-step explanation:

Substitute x with 24

(24)/4 - 9

Divide

6 - 9

Subtract

3

a. The cumulative relative frequency plot can be constructed by plotting the cumulative relative frequency on the y-axis and the years survived on the x-axis.

The plot will consist of step functions connecting the data points. The plot for the given data is as follows:

Years Survived: | Cumulative Relative Frequency:

0 to <2 | 0.10

2 to <4 | 0.52

4 to <6 | 0.54

6 to <8 | 0.64

8 to <10 | 0.68

10 to <12 | 0.70

12 to <14 | 0.72

14 to <16 | 1.00

b. Using the cumulative relative frequency plot:

i. The approximate proportion of patients who lived fewer than 5 years after treatment can be determined by looking at the cumulative relative frequency at the interval 0 to <4. The cumulative relative frequency at the end of this interval is 0.54. Therefore, approximately 54% of patients lived fewer than 5 years after treatment.

ii. The approximate proportion of patients who lived fewer than 7.5 years after treatment can be determined by looking at the cumulative relative frequency at the interval 0 to <8. The cumulative relative frequency at the end of this interval is 0.68. Therefore, approximately 68% of patients lived fewer than 7.5 years after treatment.

iii. The approximate proportion of patients who lived more than 10 years after treatment can be determined by subtracting the cumulative relative frequency at the interval 10 to <12 (0.70) from 1. Since the cumulative relative frequency at 10 to <12 represents the proportion of patients who lived up to 10 years, subtracting it from 1 gives us the proportion of patients who lived more than 10 years. Therefore, approximately 30% of patients lived more than 10 years after treatment.

To know more about  cumulative relative frequency click here: brainly.com/question/13646998

#SPJ11

The solution to the equation 1/5x - 2 = 4 is given by x = 30.

Given data:

To solve the equation (1/5)x - 2 = 4, we will isolate the variable x as:

Step 1: Add 2 to both sides of the equation to eliminate the -2 term on the left side:

(1/5)x - 2 + 2 = 4 + 2

On simplifying:

(1/5)x = 6

Step 2: Multiply both sides of the equation by 5 to get rid of the fraction (1/5):

5 * (1/5)x = 5 * 6

On simplifying:

x = 30

Hence, the solution x = 30.

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ6

Pilar climb 6.5 feet and Jake climbed 9.5 feet.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

slope of pilar = 3-2/3-1 = 1/2

After 10 steps let the height covered by x.

then, slope= x-2/10-1

1/2 = x-2/ 9

9 = 2x -4

13 = 2x

x= 6.5 feet

now, slope of Jake= 8-5/7-1 = 3/6 = 1/2

After 10 steps let the height covered by y.

then, slope= x-5/10-1

1/2 = y-5/9

2y- 10 = 9

2y= 19

y= 19/2

y= 9.5 feet

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ5

Answer:

3 is the answer because it's value only add by the 3

Answer:

25 percent of 20 is 5 percent

Answer:

Step-by-step explanation:

percentage:

80%

messed up saying it was 125% so say thanks to the person who commented below mine-

Answer:

Yes

Step-by-step explanation:

y=6x+11

0=6x+11

-6x=11

x=-11/6

So its a solution

Cosine distance is used in the k-means clustering algorithm to remove outliers. It is a metric used to determine the similarity between two documents. In k-means clustering, cosine distance is used to calculate the distance between data points.

Cosine distance is used to normalize the data so that it is not affected by the length of the data vectors or the scale of the data. The cosine distance is calculated as follows:

Cosine distance = 1 - Cosine similarity,

where Cosine similarity = dot product of two vectors/ product of the magnitude of two vectors.

To remove the outliers from the k-means clustering algorithm, we can set a threshold value for the cosine distance. If the cosine distance between two data points is greater than the threshold value, then those data points are considered outliers and they are not included in the cluster. This helps to ensure that the clustering algorithm only groups together data points that are similar and ignores the outliers.

You can learn more about outliers at: brainly.com/question/26958242

#SPJ11

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

For more questions on population mean

https://brainly.com/question/26941429

#SPJ11