Choose the equation of the graph shown.
y=-2cosx
y=-2sinx
y=2cosx
y= 2sinx

Answer:

3t^2s

Step-by-step explanation:

15/3=5

t^5s/t^2s = t^3

t^2s^3/t^2s = s^2

For this case we have by definition, that a polynomial has a common factor when the same quantity, either number or letter, is found in all the terms of the polynomial.

We have the following expression:

[tex]3t ^ 5s-15t ^ 2s ^ 3[/tex]

So we have to:

[tex]3t ^ 2s[/tex] is the lowest common term in the terms of the expression:

[tex]3t ^ 2s (t ^ 3-5s ^ 2)[/tex]

Answer:

[tex]3t ^ 2s[/tex]

Answer with explanation:

Given the differential equation

y''+y=0

The two function let

[tex]y_1= sint -cost[/tex]

[tex]y_2=sint+ cost[/tex]

Differentiate [tex]y_1 and y_2[/tex]

Then we get

[tex]y'_1= cost+sint[/tex]

[tex]y'_2=cost-sint[/tex]

Because [tex]\frac{\mathrm{d} sinx}{\mathrm{d} x} = cosx[/tex]

[tex]\frac{\mathrm{d}cosx }{\mathrm{d}x}= -sinx[/tex]

We find wronskin to prove that the function  is independent/ fundamental function.

w(x)=[tex]\begin{vmatrix} y_1&y_2\\y'_1&y'_2\end{vmatrix}[/tex]

[tex]w(x)=\begin{vmatrix}sint-cost&sint+cost\\cost+sint&cost-sint\end{vmatrix}[/tex]

[tex]w(x)=(sint-cost)(cost-sint)- (sint+cost)(cost+sint)[/tex]

[tex]w(x)=sintcost-sin^2t-cos^2t+sintcost-sintcost-sin^2t-cos^2t-sintcost[/tex]

[tex]w(x)=-sin^2t-cos^2t[/tex]    

[tex]sin^2t+cos^2t=1[/tex]

[tex]w(x)=-2\neq0[/tex]

Hence, the given two function are fundamental set of function on R.

Answer:

1. x = 39.67

2. x = 15

3. x = 49.29

4. x = -12.8

5. x = 96

6. x = 42

7. x = 36

8. x = 0

9. x = 78

Step-by-step explanation:

Just remember to always isolate the unknown. Here are the solutions to your problem. I will explain each step for the first for you to give you an idea how the others were worked out.

1. [tex]\dfrac{3x}{7}-2 = 15[/tex]  

Add 2 to both sides to get rid of -2 on the left side.

[tex]\dfrac{3x}{7}-2+(2)=15+(2)///dfrac{3x}{7}=17[/tex]

Multiply both sides by 7 to get rid of 7 on the left side.

[tex]\dfrac{3x}{7}\times 7 = 17\times 7\\\\3x = 119[/tex]

Divide both sides by 3 to get rid of 3 on the left side.

[tex]\dfrac{3x}{3} = \dfrac{119}{3}\\\\x = 39.67[/tex]

You could also transpose everything by the x to the other side of the equation. Just remember that whatever OPERATION used on the original side, must be opposite on the other side. I'll use the second problem to show this.

[tex]\dfrac{2x}{5}+1=7[/tex]

Transpose  1 on the left to the right. It is addition on the left, then it would be subtraction on the other side.

[tex]\dfrac{2x}{5}+1=7\\\\\dfrac{2x}{5}=7-1\\\\\dfrac{2x}{5}=6[/tex]

Transpose 5 from the left side to the right. It is division on the left, then it would be multiplication on the right.

[tex]\dfrac{2x}{5}=6\\\\2x=6\times 5\\\\2x=30[/tex]

Transpose 2 from the left side to the right. It is multiplication on the left, then it would be division on the right.

[tex]2x=30\\\\x=\dfrac{30}{2}\\\\x=15[/tex]

Let's move on with the rest now.

3.

[tex]\dfrac{7x}{15}-1=22\\\\\dfrac{7x}{15}=22+1\\\\\dfrac{7x}{15}=23\\\\7x=23\times15\\\\7x=345\\\\x=\dfrac{345}{7}\\\\x=49.29[/tex]

4.

[tex]\dfrac{5x}{8}+10=2\\\\\dfrac{5x}{8}=2-10\\\\\dfrac{5x}{8}=-8\\\\5x=-8\times8\\\\5x=-64\\\\x=\dfrac{-64}{5}\\\\x=-12.8[/tex]

5.

[tex]\dfrac{x}{6}+4=20\\\\\dfrac{x}{6}=20-4\\\\\dfrac{x}{6}=16\\\\x=16\times6\\\\x=96[/tex]

6.

[tex]\dfrac{x}{3}-4=10\\\\\dfrac{x}{3}=10+4\\\\\dfrac{x}{3}=14\\\\x=3\times14\\\\x=42[/tex]

7.

[tex]\dfrac{x}{6}+2=8\\\\\dfrac{x}{6}=8-2\\\\\dfrac{x}{6}=6\\\\x=6\times6\\\\x=36[/tex]

8.

[tex]\dfrac{x}{9}+8=8\\\\\dfrac{x}{9}=8-8\\\\\dfrac{x}{9}=0\\\\x=0\times9\\\\x=0[/tex]

9.

[tex]\dfrac{x}{6}+7=20\\\\\dfrac{x}{6}=20-7\\\\\dfrac{x}{6}=13\\\\x=13\times6\\\\x=78[/tex]

The answers are as follows- 1. x = 17/3 or 5.67,2. x=3 . 3.x = 23/7 or about 3.29. 4.x = -8/5 or -1.6., 5.x=2, 6.x = 14/6 or about 2.33., 7. x=2, 8. x=0, 9. x = 13/9 or about 1.44.

Solving the Given Equations

Answer:

x < 33.84

Step-by-step explanation:

we have

13.48x-200 < 256.12

Solve for x

Adds 200 both sides

13.48x-200 +200 < 256.12+200

13.48x < 456.12

Divide by 13.48 both sides

13.48x/13.48 < 456.12/13.48

x < 33.84

The solution is the interval ----> (-∞, 33.84)

All real numbers less than 33.84

Answer:

Per capita income, in dollars per person, for 2005 is $42637

Step-by-step explanation:

The formula to calculate per capita income is:

per capita income = National income/total population

National income = $1,730,849,015

Total population = 40,595

per capita income in 2005 = 1,730,849,015/40,595

per capita income in 2005 = $42637

So, per capita income, in dollars per person, for 2005 is $42637

Answer:

i say option (a) is the answer its correct.

Step-by-step explanation:

Answer:

Any number of hours greater than 16

Step-by-step explanation:

First thing we have to do is write each equation for each cafe's internet access.  For Cyber Station, the rate is $1.50 per hour which is the slope of the line (slope is, after all, the rate of change of y to x...or here, cost to hours).  The flat fee is what you are charged even if you use 0 hours.  The linear equation for Cyber Station is y = 1.5x + 12

The linear equation for Web World, which only has a rate but no flat fee, is

y = 2.25x

We are asked for how many hours of access, x, is the cost, y, at Cyber Station LESS THAN the cost at Web World.  That tells me that you are working with linear inequalities in class!  We want the cost at CS to be less than that at WW so our inequality looks like this:

1.5x + 12 < 2.25x

Solving for x:

16 < x.  That means, in words, that any number of hours over 16 will make Cyber Station cheaper to use than Web World.

To solve this you must make a formula like so:

ratio of rugby over tennis = unknown over students that picked tennis

***Unknown will be x

use a proportion like so...

[tex]\frac{rugby}{tennis} = \frac{x}{tennis}[/tex]

[tex]\frac{6}{13} = \frac{x}{78}[/tex]

Now you must cross multiply

6 * 78 = 13*x

468 = 13x

To isolate x divide 13 to both sides

468/13 = 13x/13

x= 36

This means that 36 people choose rugby when there were 78 people choose tennis

To find how many people choose football you must make another proportion similar to the first proportion:

ratio of football over rugby = unknown over students that picked rugby

use a proportion like so...

[tex]\frac{3}{2} = \frac{x}{36}[/tex]

Now you must cross multiply

3* 36 = 2*x

108 = 2x

To isolate x divide 2 to both sides

108/2 = 2x/2

x= 54

This means that 54 people choose football

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: [tex]Y=-388+135X[/tex]

Step-by-step explanation:

The equation of the regression line has the general form [tex]Y=a+bX[/tex], where Y is the dependent variable , X is the independent variable , b is the slope of the line and a is the y-intercept.

Given : The slope of regression equation : [tex]b=135[/tex]

The y-intercept : [tex]a=-388[/tex]

Then , the equation of the regression line is given by :-

[tex]Y=-388+135X[/tex]

In the field of statistics, specifically regression analysis, the equation of the regression line is given by y = mx + b. Given that the slope is 135 and the y-intercept is -388, the equation of the regression line which represents the relationship between hotel ratings and their prices is y = 135x - 388.

The given problem falls under the branch of statistics, specifically under regression analysis. In a regression equation, x is the independent variable and y is the dependent variable. The equation of a regression line can be expressed in the format y = mx + b, where m represents the slope of the line, and b is the y-intercept.

In the given instance, the slope (m) is 135, and the y-intercept (b) is -388. Therefore, the equation of the regression line which represents the relationship between hotel ratings (x) and their prices (y) is y = 135x - 388.

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Answer:  y = -2x + 13

Step-by-step explanation:

Parallel lines have the same slope.  y = -2x - 2 has a slope of -2 so the line parallel to that will also have a slope of -2.

We have a point (4, 5) and a slope (-2) so we can use the point-slope formula:

y - y₁ = m(x - x₁)    ; where (x₁, y₁) is the point and m is the slope

y - 5 = -2(x - 4)

y - 5 = -2x + 8

y      = -2x + 8 + 5

y      = -2x + 13

Answer:

The equation of a line parallel to line CD is y = -2x + 13 ⇒ 1st answer

Step-by-step explanation:

* Lets revise the conditions of the parallel lines

- The slopes of the parallel lines are equal

- The form of slope-intercept equation is y = m x + c, where

 m is the slope of the line and c is the y-intercept

- The y-intercept means that the line intersect the y-axis at point (0 , c)

- To find an equation of a line parallel to another line, do these steps

# Find the slope of the given line and use it as a slope of the new line

# Substitute x and y in the equation by a point on the new line to find c

* Lets solve the problem

∵ The equation of line CD is y = -2x - 2

∵ The equation of any line is y = m x + c, where m is the slope of

  the line

∴ The slope of the line is -2

- The equation of the line parallel to CD will have the same slope

∵ The parallel line have same slopes

∴ The slope of the new line is -2

∴ The equation of the parallel line is y = -2x + c

- To find c use a point on the new line and replace x and y in the

  equation by its coordinates

∵ The parallel line contains point (4 , 5)

- Put y = 5 and x = 4 in the equation

∴ 5 = -2(4) + c ⇒ simplify

∴ 5 = -8 + c ⇒ add 8 to both sides

∴ 13 = c

- Write the equation with the value of c

∴ y = -2x + 13

* The equation of a line parallel to line CD is y = -2x + 13

Answer:

The standard deviation of 2,3,6,9,10 is √10.

Step-by-step explanation:

Standard Deviation:

It is a quantity expressing by how much the members of a group differ from the mean value for the group. Its symbol is б read as 'sigma'.

Formula:

б = √(Σ(x-mean)²/n)

Mean = Σx/n = (2+3+6+9+10)/5 = 30/5 = 6

Mean = 6

Σ(x-mean)² = (2-6)²+(3-6)²+(6-6)²+(9-6)²+(10-6)²

= 16+9+0+9+16

= 50

б = √(Σ(x-mean)²/n)

= √(50/5)

= √10

Answer:

)10

Step-by-step explanation:

A p e x

Answer:

No, the point [tex](2,3)[/tex] is not a solution to the system of equation [tex]x2+y2=13[/tex] and [tex]2x-y=4[/tex].

Step-by-step explanation:

To make sure it is, it has to work on both equation. Plugging this into the first and second equations respectivly gives us:

[tex]13=x2+y2=(2)2+(3)2=4+6=10[/tex]

[tex]4=2x-y=2(2)-(3)=4-3=1[/tex]

Since [tex]13\neq10[/tex] and [tex]4\neq 1[/tex], the point [tex](2,3)[/tex] is not a solution to the system of equation [tex]x2+y2=13[/tex] and [tex]2x-y=4[/tex].

Answer:

That is False.

Step-by-step explanation:

Answer:

No, not really.

dividing 25 into 4 equal groups, equals 6.25.

So no, you can not divide 25 into 4 equal group.

If if was 25 into 5 equal groups, then yes.

Hope this helps!!!

Please mark brainliest, if this helps. :)

Step-by-step explanation:

No, 25 cannot be divided into 4 equal groups without a remainder. Dividing 25 by 4 results in a quotient of 6 with a remainder of 1, meaning the groups would not be equal.

To determine if this is possible, we need to perform a division operation. Dividing 25 by 4 gives us a quotient of 6 with a remainder of 1. This means that 25 cannot be evenly divided into 4 equal groups, as one group would end up with one less or one more than the others.

Therefore, 25 cannot be divided into 4 equal groups .

Answer:

The words from parsley are PAR, YES, RAP, PAY,and SLAP

The words from pepper are PEEP and that is it

Step-by-step explanation:

Answer:

  102.5 g

Step-by-step explanation:

The mass is the sum of the values indicated by the sliders:

  100 g + 0 g + 2.5 g = 102.5 g

The mass, in grams, of the object being measured in the triple beam balance shown below is:

                               102.5 g

Triple Beam balance--

It is a instrument which is used to measure the mass of an object.

The advantage of using this device is that it measures the mass of an object precisely.

It has three counterweights in it.

One is of 100 gram, other is of 10 gram and the last is of 1 gram.

In order to find the mass of an object we add the weights in all the three sections.

The large slider is at 100 g, the medium slider is at 0 g, and the small slider is at 2.5 g.

                    100 g+0 g+2.5 g=102.5 g

Answer:

Step-by-step explanation:

Part A

This is a combination problem. Order does not matter.

36C6

36!/(30! 6!)

36 * 35 * 34 * 33 * 32 * 31/ 6!

1402410240/6!

1947792

Part B

1 / (36C6)

0.000000513 or

0.0000005

The values of x for which the given vectors are basis for R³ is:

                        [tex]x\neq 1[/tex]

We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.

We are given three vectors as:

(-1,0,-1), (2,1,2), (1,1, x)

The matrix formed by these vectors is:

[tex]\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right][/tex]

Now, the determinant of this matrix is:

[tex]\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-1(x-2)-2(1)+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+2-2+1\\\\\\\begin{vmatrix}-1 &2 & 1\\ 0& 1 & 1\\ -1 & 2 & x\end{vmatrix}=-x+1[/tex]

Hence,

[tex]-x+1\neq 0\\\\\\i.e.\\\\\\x\neq 1[/tex]

Answer:

a)

Kyle's z-score was 1.9 to the nearest tenth

Ethan's z-score was -0.8 to the nearest tenth

b)

The percent of the students had a final exam score lower than Ethan's score was 21.19%

Step-by-step explanation:

a) Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The exam scores are normally distributed with a mean of 105 and a

  standard deviation of 16

∴ μ = 105 and σ = 16

- Kyle and Ethan are took the final exam

- Kyle's  score was 135

- Ethan's score was 93

- Lets find the z-score for each one

∵ Kyle's  score was 135

∴ x = 135

∵ μ = 105 and σ = 16

∵ z-score = (x - μ)/σ

∴ z-score for Kyle = (135 - 105)/16 = 30/16 = 15/8 = 1.875

* Kyle's z-score is 1.9 to the nearest tenth

∵ Ethan's  score was 93

∴ x = 93

∵ μ = 105 and σ = 16

∵ z-score = (x - μ)/σ

∴ z-score for Ethan = (93 - 105)/16 = -12/16 = -3/4 = -0.75

* Ethan's z-score is -0.8 to the nearest tenth

b) To find the percent of students with a lower exam score than Ethan

   you will asking to find the proportion of area under the standard

   normal distribution curve for all z-scores < -0.8

- It can be read from a z-score table by referencing a z-score of -0.8

- Look to the attached file

∴ The value from the table is 0.2119

- To change it to percent multiply it by 100%

∴ 0.2119 × 100% = 21.19%

* The percent of the students had a final exam score lower than

  Ethan's score was 21.19%

Kyle's z-score is 1.9, and Ethan's z-score is -0.8. Approximately 21.1% of the students had a final exam score lower than Ethan's score.

For Kyle, the z-score is:

Z = (135 - 105) / 16 = 30 / 16 = 1.875, which rounds to 1.9.

For Ethan, the z-score is:

Z = (93 - 105) / 16 = -12 / 16 = -0.75, which rounds to -0.8.

Ethan's z-score correlates to a percentile that represents the percentage of students with scores lower than his. Consulting a standard normal distribution table or using a calculator that provides cumulative probabilities for the normal distribution, we find that a z-score of -0.8 corresponds to approximately 21.1%.

Therefore, about 21.1% of the students had a final exam score lower than Ethan's score.

The probability that it does not rain either today or tomorrow, based on the given independent probabilities of it raining each day, is 18%.

This problem pertains to the concept of probability in mathematics. Specifically, it revolves around calculating the probability of compound independent events.

First, we need to determine the probability of not raining each day. If there's a 70% chance of rain today, that means there's a 30% chance (100% - 70%) of no rain today. Similarly, if there's 40% chance of rain tomorrow, there's a 60% chance (100% - 40%) of no rain tomorrow.

Given that the probability it rains on each day is independent, we multiply these probabilities together to get our answer. So, the probability that it does not rain either today or tomorrow is 30% * 60% = 18%.

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The probability that there will be no rain today or tomorrow is 0.18.

The probability that there will be no rain today or tomorrow is given by the formula for the union of two independent events:

[tex]\[ P(\text{no rain today or tomorrow}) = P(\text{no rain today}) \times P(\text{no rain tomorrow}) \][/tex]

First, we need to find the probability of no rain on each day. Since the probability of rain is given, we can subtract this from 1 to find the probability of no rain:

[tex]\[ P(\text{no rain today}) = 1 - P(\text{rain today}) \][/tex]

[tex]\[ P(\text{no rain today}) = 1 - 0.70 \][/tex]

[tex]\[ P(\text{no rain today}) = 0.30 \][/tex]

Similarly, for tomorrow:

[tex]\[ P(\text{no rain tomorrow}) = 1 - P(\text{rain tomorrow}) \][/tex]

[tex]\[ P(\text{no rain tomorrow}) = 1 - 0.40 \][/tex]

[tex]\[ P(\text{no rain tomorrow}) = 0.60 \][/tex]

Now, we can calculate the probability of no rain on either day:

[tex]\[ P(\text{no rain today or tomorrow}) = P(\text{no rain today}) \times P(\text{no rain tomorrow}) \][/tex]

[tex]\[ P(\text{no rain today or tomorrow}) = 0.30 \times 0.60 \][/tex]

[tex]\[ P(\text{no rain today or tomorrow}) = 0.18 \][/tex]

Answer:

a) $42,580

b) $43,900

Step-by-step explanation:

Recall, "mode" refers to the value which occurs most frequently.

In this case, the question says that there are 2 modes,

this means $34,000 and $50,500 both share the spot for the most frequently appearing salary.

because there are only 5 employees (and hence 5 salaries), the only possible way that there are two modes is if there are two of each mode, leaving only the last salary unknown.

i.e  if we list the 5 salaries (in no particular order)

$34,000   $34,000  $50,500   $50,500   $ x

where x is the 5th unknown salary.

Given that the mean is $42,100

Then (34,000 + 34,000 + 50,500 + 50,500 + x) / 5 = 42,100

solving for x gives x = $41,500

Now we know all the values, we can rearrange them in increasing value:

$34,000   $34,000  $41,500   $50,500   $50,500  

from this, we can see that the median salary is $41,500

Given that the median salary gets a $2400 raise,

the new median salary = $41,500 + $2400 = $43,900 (Ans for part b)

new mean salary,

= ($34,000  + $34,000 + $43,900 +  $50,500  + $50,500  ) / 5

= $42,580 (answer for part a)

Maximum is the highest a graph can reach. In this case the graph continues forever therefore the maximum is:

infinity or ∞

The minimum is the lowest place the graph reaches. In this case it would be:

-6

The zeros are where the graph intersects the x axis. In this case it would have two zeros, which are:

(-3, 0) and (0.5, 0)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  -18, -26

Step-by-step explanation:

The differences are decreasing by 1 each time, so the next differences will be -7 and -8.

  -11 -7 = -18

  -18 -8 = -26

The equation of the least-squares regression line can be used to predict the beak heat loss at a specific temperature. The coefficient of determination indicates the proportion of variation explained by the relationship between beak heat loss and temperature. The correlation coefficient quantifies the strength and direction of the linear relationship.

The given data represents the relationship between the beak heat loss of the toco toucan and the outdoor temperature. To find the equation of the least-squares regression line, we need to calculate the slope, which represents the change in beak heat loss for every degree Celsius increase in temperature, and the y-intercept, which represents the predicted beak heat loss at 0 degrees Celsius. Using these values, we can then predict the beak heat loss at a temperature of 25 degrees Celsius. To determine the percent of variation explained by the straight-line relationship, we can calculate the coefficient of determination (r^2). Finally, the correlation coefficient (r) represents the strength and direction of the linear relationship between beak heat loss and temperature.

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Answer:

  (a) y = -6(x -1)

  (b) about 5.3%

Step-by-step explanation:

(a) The point used as the base for the linear approximation is (1, f(1)), where ...

  f(1) = 3 -3·1² = 0

The slope of the line at that point is ...

  f'(x) = 0 -3(2x) = -6x

  f'(1) = -6·1 = -6

So, in point-slope form, the equation of the approximating line is ...

  y = -6(x -1) +0

  y = -6(x -1)

__

(b) The approximate value of f(0.9) is then ...

  y = -6(0.9 -1) = 0.6 . . . . approximate value of f(0.9)

__

(c) The error in the approximation at x=0.9 is ...

  error% = (0.6 -f(0.9))/f(0.9) × 100%

where f(0.9) = 3(1 -0.9²) = 3·0.19 = 0.57

  error% = (0.6 -0.57)/0.57 × 100% = 0.03/0.57 × 100%

  error% ≈ 5.263% ≈ 5.3%

This solution involves finding the equation of the line that represents the linear approximation for a function at a given point. Then, the linear approximation is used to estimate a value and a percent error is calculated between the exact and approximate value.

To solve this problem, we have to use the concept of linear approximation which is also known as the tangent line approximation. Using this concept, we can write the equation of the line that represents the linear approximation to a function at a given point.

The formula is: L(x) = f(a) + f'(a)(x-a). Our function is f(x) = 3 - 3x². The derivative of f(x), f'(x) is -6x. Evaluating these at a = 1, we get f(1) = 0 and f'(1) = -6.

The equation of the tangent line at a = 1 is therefore L(x) = 0 - 6(x - 1), simplifying to L(x) = -6x + 6.

To estimate f(0.9), we plug it into our approximation equation, L(0.9) = -6*0.9 + 6 = 0.6.

Now, we calculate the percent error. First, we find the exact value by plugging 0.9 into our original function, f(0.9) = 3 - 3*(0.9)² = 1.29.

Using the given formula for percent error, we get: 100 * abs(0.6 - 1.29) / abs(1.29) which yields approximately 53.49%.

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[tex]x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x[/tex]

Divide both sides by [tex]x^2[/tex]. In doing so, we force any possible solutions to exist on either [tex](-\infty,0)[/tex] or [tex]\boxed{(0,\infty)}[/tex] (the "positive" interval in such a situation is usually taken over the "negative" one) because [tex]x[/tex] cannot be 0 in order for us to do this.

[tex]\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x[/tex]

Condense the left side as the derivative of a product, then integrate both sides and solve for [tex]y[/tex]:

[tex]\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac yx\right]=\sin x[/tex]

[tex]\dfrac yx=\displaystyle\int\sin x\,\mathrm dx[/tex]

[tex]\boxed{y=Cx-x\cos x}[/tex]

The general solution of a differential equation is to write y as a function of x.

Given

[tex]x \frac{dy}{dx} - y = x^2 \sin(x)[/tex]

Divide through by x

[tex]\frac{x}{x} \frac{dy}{dx} -\frac{y}{x} = \frac{x^2}{x} \sin(x)[/tex]

[tex]\frac{dy}{dx} -\frac{y}{x} = x \sin(x)[/tex]

Let P be function of x. Such that:

[tex]P(x) = -\frac 1x[/tex]

So, we have:

[tex]\frac{dy}{dx} +yP(x) = x\sin(x)[/tex]

Calculate the integrating factor I(x).

So, we have:

[tex]I(x) = e^{\int P(x) dx[/tex]

Substitute [tex]P(x) = -\frac 1x[/tex]

[tex]I(x) = e^{\int-\frac 1x dx[/tex]

Rewrite as:

[tex]I(x) = e^{-\int\frac 1x dx[/tex]

Integrate

[tex]I(x) = e^{-\ln(x)[/tex]

[tex]I(x) = \frac 1x[/tex]

So, we have:

[tex]\frac{dy}{dx} -\frac{y}{x} = x \sin(x)[/tex]

[tex][\frac{dy}{dx} -\frac{y}{x}] \frac 1x = [x \sin(x)] \frac 1x[/tex]

[tex][\frac{dy}{dx} -\frac{y}{x}] \frac 1x =\sin(x)[/tex]

Introduce [tex]I(x) = \frac 1x[/tex].

So, we have:

[tex]\frac{d}{dx}(\frac yx) = \sin(x)[/tex]

Multiply both sides by dx

[tex]d(\frac yx) = \sin(x)\ dx[/tex]

Integrate with respect to x

[tex]\frac yx = -\cos(x) + c[/tex]

Multiply through by x

[tex]y = -x\cos(x) + cx[/tex]

So, the general solution is: [tex]y = -x\cos(x) + cx[/tex], and the interval is [tex](0, \infty)[/tex]

Read more about general solution of a differential equation at:

https://brainly.com/question/4537000

ANSWER

The z-score is 2.

EXPLANATION

The z-score for a data set that is normally distributed is calculated using the formula:

[tex]z = \frac{x - \bar x}{ \sigma} [/tex]

where

[tex]\bar x[/tex]

is the mean and

[tex] \sigma[/tex]

is the standard deviation of the distribution.

From the given information the test score is 85.

This implies that,

[tex]x = 85[/tex]

The mean is 75.

[tex]\bar x = 75[/tex]

The standard deviation is 5.

We substitute the values into the formula to get,

[tex]z = \frac{85 - 75}{5} [/tex]

This implies that

[tex]z = \frac{10}{5} [/tex]

Therefore the z-score is

[tex]z = 2[/tex]

The z score for a score of 85 on the test is 2, indicating that it is 2 standard deviations above the mean.

To compute the z score value for a score of 85 on a test with a mean of 75 and a standard deviation of 5, we use the formula:

z = (x - μ) / σ

where z is the z score, x is the score, μ is the mean, and σ is the standard deviation.

Plugging in the values, we get:

z = (85 - 75) / 5 = 2

The z score for a score of 85 is 2. This means the score is 2 standard deviations above the mean.

Answer:

Vertical Angles are equal.  Therefore:

(7x -4) = (6x +8)

x = 12

answer is D

Step-by-step explanation:

Answer:

D) 12

Step-by-step explanation:

The two angles are vertical angles.  Vertical angles are equal

7x-4 = 6x+8

Subtract 6x from each side

7x-6x -4 = 6x-6x+8

x-4 = 8

Add 4 to each side

x-4+4 = 8+4

x = 12

Answer:

The price of the home = 232,000

20% is down payment.

Part A:

[tex]0.20\times232000=46400[/tex]

So, the loan amount will be =[tex]232000-46400=185600[/tex]

Loan amount or p = $185,600

Part B:

p = 185600

r = [tex]3.6/12/100=0.003[/tex]

n = [tex]10\times12=120[/tex]

The EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

Now putting the values in formula we get

[tex]\frac{185600\times 0.003\times(1+0.003)^{120} }{(1+0.003)^{120}-1 }[/tex]

=> [tex]\frac{185600\times 0.003\times(1.003)^{120} }{(1.003)^{120}-1 }[/tex]

Monthly payments = $1844.02

Part C:

p = 185600

r = [tex]3.6/12/100=0.003[/tex]

n = [tex]20\times12=240[/tex]

Now putting the values in formula we get

[tex]\frac{185600\times 0.003\times(1+0.003)^{240} }{(1+0.003)^{240}-1 }[/tex]

=> [tex]\frac{185600\times 0.003\times(1.003)^{240} }{(1.003)^{240}-1 }[/tex]

Monthly payments = $1085.96

Part D:

For 10 year loan you have to pay = [tex]120\times1844.02=221282.40[/tex]

For 20 years loan you have to pay =[tex]240\times1085.96=260630.40[/tex]

So, you ended up paying [tex]260630.40-221282.40=39348[/tex] dollars more in longer loan.

The difference is $39,348.

c. Reflection over either the x-axis or y-axis will change the graph

This is false because [tex]y=sin(x)[/tex] is an odd function, not an even one. This means that [tex]sin(-x)=-sin(x)[/tex], and a reflection over the y-axis will change the graph.

This is false because we said that [tex]sin(-x)=-sin(x)[/tex]

This is true. Since [tex]sin(x)[/tex] is an odd function, then reflection over either the x-axis or y-axis will change the graph as we said in a. So, for [tex]f(x)[/tex]:

REFLEXION IN THE X-AXIS:

[tex]h(x)=-f(x)[/tex]

REFLEXION IN THE Y-AXIS:

[tex]h(x)=f(-x)[/tex]

False by the same explanation as b.

The correct statement about the function y=sin(x) is that Reflection over either the x-axis or y-axis will change the graph. Therefore, option C is the correct answer.

The statement regarding the function y=sin(x) which is true is that reflection over either the x-axis or y-axis will change the graph.

This is because the sine function is an odd function, meaning that it has rotational symmetry about the origin. A characteristic of odd functions is that they satisfy the identity y(-x) = -y(x), not y(-x) = y(x), which describes an even function.

Therefore, the assumption Sin(x)=Sin(-x) would be incorrect, as it does not reflect the odd nature of the sine function. Thus, the correct answer is c. Reflection over either the x-axis or y-axis will change the graph.