Find the general solution of the following differential equation. Primes denote derivatives with respect to x.(x+2y)y'=2x-yleft parenthesis x plus 2 y right parenthesis y prime equals 2 x minus y

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.

[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex]  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation [tex]4x+3y=1[/tex]  by 2.

[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]

Now we can add these equations

[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]

------------------------

[tex]5x = 5[/tex]

Dividing both sides by 5, we get [tex]x = 1[/tex].

Now we can substitute x into an equation to find y.

[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]

Hope this helped!

Answer:

g = [tex]\frac{1}{24}[/tex]

Step-by-step explanation:

Given

[tex]\frac{5}{2}[/tex] + 6g = [tex]\frac{11}{4}[/tex]

Multiply through by 4 to clear the fractions

10 + 24g = 11 ( subtract 10 from both sides )

24g = 1 ( divide both sides by 24 )

g = [tex]\frac{1}{24}[/tex]

Answer:

Step-by-step explanation:

2a is the middle term of a quadratic expression.  2 is the coefficient of a to the first power.

Not much more you can say about this.

Please, if the original question includes answer choices, share those choices.  Thank you.

Step-by-step explanation:

Suppose, John walks with a speed x

Then, John can jog at a speed 2x

[tex]total \: time \: = \frac{total \: distance}{average \: speed} [/tex]

TOTAL TIME

[tex]0.9 = \frac{5}{2x} + \frac{2}{x} [/tex]

Further solving :

x = 5 mph

Average jogging speed (2x) = 10 mph

Answer:

10mph

Step-by-step explanation:

We know that John's total trip is 0.9 hours, so let's try to figure out how much of that time is spent jogging, and how much of it is spent walking.

We can do that by naming the time he takes to jog a mile y.

An equation would be:

5y+2(2y)=0.9

5y+4y=0.9

y=0.1

It takes him 0.1 hours, or 6 minutes to jog a mile.

Since he jogged 5 miles, his jogging time is 0.5 hours, or 30 minutes.

Now,

Let's name the speed he jogs x (miles per hour)

This allows us to set up another equation.

Note that:

Speed=distance/time

His jogging speed is x.

x=5/0.5

x=10

His average jogging speed is 10 miles an hour.

Answer:

Step-by-step explanation:

Given sinα=−2/3, before we can get secα, we need to get the value of α first from  sinα=−2/3.

[tex]sin \alpha = -2/3[/tex]

Taking the arcsin of both sides

[tex]sin^{-1}(sin\alpha) = sin^{-1} -2/3\\ \\\alpha = sin^{-1} -2/3\\ \\\alpha = -41.8^0[/tex]

Since sin is negative in the 3rd and 4th quadrant. In the 3rd quadrant;

α = 180°+41.8°

α = 221.8° which is between the range 270°<α<360°

secα = sec 221.8°

secα = 1/cos 221.8

secα = 1.34

Answer:

L = 13.3649

Step-by-step explanation:

We are given;

x = t − 2 sin(t)

dx/dt = 1 - 2 cos(t)

Also, y = 1 − 2 cos(t)

dy/dt = 2 sin(t)

0 ≤ t ≤ 2π

The arc length formula is;

L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt

Where α and β are the boundary points. Thus, applying this to our question, we have;

L = (0,2π)∫√((1 - 2 cos(t))² + (2 sin(t))²)dt

L = (0,2π)∫√(1 - 4cos(t) + 4cos²(t) + 4sin²(t))dt

L = (0,2π)∫√(1 - 4cos(t) + 4(cos²(t) + sin²(t)))dt

From trigonometry, we know that;

cos²t + sin²t = 1.

Thus;

L = (0,2π)∫√(1 - 4cos(t) + 4)dt

L = (0,2π)∫√(5 - 4cos(t))dt

Using online integral calculator, we have;

L = 13.3649

This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).

Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.

Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.

Answer:

A

Step-by-step explanation:

because it has a + sign

Answer:

120%

Step-by-step explanation:

First pair of equations :

[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]x+2y=30\ ..(iii)[/tex]

By Elimination Method, Add (i) and (ii) (term with x eliminate), we get

[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]

put y= 14.4 in (iii), we get

[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]

hence, x=1.2 and y =14.4

Second pair of equations :

[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]

Elimination Method, Add (i) and (ii) (term with y eliminate) , we get

[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]

put [tex]x=\dfrac{18}{13}[/tex]   in (i), we get

[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]

hence, [tex]x=\dfrac{18}{13}[/tex]   and [tex]y=\dfrac{-45}{13}[/tex] .

Answer:

False

Step-by-step explanation:

the answer is false because

year 1 to 2 is $18

year 2 to 3 is $17

year 3 to 4 is $18

year 4 to 5 is $17

false because simple interest always has the same money not a pattern

Answer:

0.9938

Step-by-step explanation:

We can find this probability using a test statistic.

The test statistic to use is the z-scores

Mathematically;

z-score = (x-mean)/SD/√n

from the question, x = 119 , mean = 117 , SD = 6.4 and n = 64

Plugging these values in the z-score equation above, we have;

z-score = (119-117)/6.4/√64

z-score = 2/6.4/8

z-score = 2.5

The probability we want to find is;

P(z < 2.5)

we can get this value from the standard normal distribution table

Thus; P(z < 2.5) = 0.99379

Which to four decimal places = 0.9938

Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2

The sum of the two would be:

X + 5(x-2) = -244

Simplify:

X + 5x -10

Combine like terms

6x -10 = -244

Add 10 to both sides:

6x = -234

Divide both sides by 6

X = -234/6

X = -39

The smallest number is x-2 = -39-2 = -41

The answer is -41

Answer:

h = 5 cm

Step-by-step explanation:

Given that,

The volume of ice-cream in the cone is half the volume of the cone.

Volume of cone is given by :

[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]

r is radius of cone, r = 3 cm

h is height of cone, h = 6 cm

So,

[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]

Let [tex]V_i[/tex] is the volume of icecream in the cone. So,

[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]

Let H be the depth of the icecream.

Two triangles formed by the cone and the icecream will be similiar. SO,

[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]

So, volume of icecream in the cone is :

[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]

or

h = 5 cm

So, the depth of the ice-cream is 5 cm.

Answer:

Step-by-step explanation:

probabilty distribution= interval of x/total area of the distribution

OR  P(x)= frequency of x/total frequency(N)*the interval of x(w)

x                   f                   probabilty f/N*w

16                 10                  0.2

17                  16                  0.32

18                  20                  0.4

19                    4                   0.08

w is the width of the bar( interval) 17-16=1

N=10+16+20+4=50

( only need to draw histogram)

Answer:

(x+4)/3. When x is 5 the answer is 3

Step-by-step explanation:

Answer:

-1 and 1

Step-by-step explanation:

Reciprocal means "one divided by...".

1/-1 = -1 and 1/1 = 1

33/64 cups of sugar does snoopy scoop out.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

The amount of sugar needed = 2 3/4 cups

Amount of sugar per scoop = 5 1/3 cups/scoop

So, number of cups of sugar scoops

= cups of sugar needed/ cups of sugar per scoop                                                                              

                                   =11/4 /16/3

                                     =11/4 *3/16

                                     =33/64

Hence, 33/64 cups of sugar does snoopy scoop out.

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Answer:

A. 1

B. -1

C. -1.67

D. 0.67

E. 3.33

Step-by-step explanation:

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 20 , SD = 3 while x represents the individual values

A. 23

Z = (23-20)/3 = 3/3 = 1

B. 17

z = (17-20)/3 = -3/3 = -1

C. 15

z = (15-20)/3 = -5/3 = -1.67

D. 22

z = (22-20)/3 = 2/3 = 0.67

E. 30

z = (30-20)/3 = 10/3 = 3.33

Answer:

The  condition  are

           The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

           The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

The  check revealed that

             There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons

Step-by-step explanation:

From the question we are told that

     The  population mean is  [tex]\mu = 5 \ year[/tex]

      The sample size is  n =  20

      The sample mean is  [tex]\= x = 4.6 \ years[/tex]

       The  standard deviation is [tex]\sigma = 2.2 \ years[/tex]

   The  Null hypothesis is  [tex]H_o : \mu = 5[/tex]

   The  Alternative hypothesis is  [tex]H_a : \mu < 5[/tex]

So i will be making use of  [tex]\alpha = 0.05[/tex] level of significance to test this claim

    The critical value of  [tex]\alpha[/tex] from the normal distribution table is  [tex]Z_\alpha = 1.645[/tex]

Generally the test statistics is mathematically evaluated as

                 [tex]t = \frac{\= x - \mu}{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

                 [tex]t = \frac{ 4.6 - 5}{ \frac{2.2}{\sqrt{20} } }[/tex]

                [tex]t = -0.8131[/tex]

Looking at the value of  t and [tex]Z_{\alpha }[/tex] we see that  [tex]t < Z_{\alpha }[/tex] so we fail to reject the null hypothesis  

  This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.

Answer:

[tex] \boxed{\sf Instantaneous \ velocity \ (v) = -3} [/tex]

Given:

Relation between position of an object at time t is given by:

s(t) = -9 - 3t

To Find:

Instantaneous velocity (v) at t = 8

Step-by-step explanation:

To find instantaneous velocity we will differentiate relation between position of an object at time t by t:

[tex] \sf \implies v = \frac{d}{dt} (s(t))[/tex]

[tex] \sf \implies v = \frac{d}{dt} ( - 9 - 3t)[/tex]

Differentiate the sum term by term and factor out constants:

[tex] \sf \implies v = \frac{d}{dt} ( - 9) - 3 (\frac{d}{dt} (t))[/tex]

The derivative of -9 is zero:

[tex] \sf \implies v = - 3( \frac{d}{dt} (t)) + 0[/tex]

Simplify the expression:

[tex] \sf \implies v = - 3( \frac{d}{dt} (t))[/tex]

The derivative of t is 1:

[tex] \sf \implies v = - 3 \times 1[/tex]

Simplify the expression:

[tex] \sf \implies v = - 3 [/tex]

(As, there is no variable after differentiating the relation between position of an object at time t by t so at time t = 8 is of no use.)

So,

Instantaneous velocity (v) at t = 8 is -3

Answer:

  A. rectangle

  B. any of triangle, quadrilateral, pentagon, hexagon

Step-by-step explanation:

A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.

__

B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...

Answer:

(2-j)(4-y)

Step-by-step explanation:

Factoring using grouping,

(2-j)(4-y)

Answer:

The unit price of the 20 pack is $0.79 and the unit price for the 8 pack is $0.80.

Step-by-step explanation:

Simply Take the price of the pack of batteries divided by the number within the pack.

$6.40 / 8 == $0.80

$15.80 / 20 == $0.79

Cheers.

The question is incomplete. You can find the missing content below.

A package of 8-count AA batteries costs $6.40. A package of 20-count Of batteries costs $15.80. Which statement about the unit prices is true?

A) The 8-count pack of AA batteries has a lower unit price of $0.79 per battery.

B) The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.

C) The 8-count pack of AA batteries has a lower unit prices of $0.80 per battery.

D) The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

The correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

Inequality is the relation between two numbers or variables or expressions showing relationships like greater than, greater than equals to, lesser than equals to, lesser than, etc.

For example 2<9

A package of 8-count AA batteries has cost = $6.40.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $6.40/8= $0.8

A package of 20-count AA batteries has cost = $15.80.

cost per unit count AA batteries will be= total cost of AA batteries/ number of AA batteries

= $15.80/20= $0.79

As 0.79<0.8

cost of 20-count AA batteries <  cost of 8-count AA batteries

Therefore the correct option is Option D: The 20-count pack of AA batteries has the lower price of $0.79 per battery.

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Answer:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The answer is C.

Step-by-step explanation:

We are given the rational function:

[tex]\displaystyle f(x) = \frac{x-3}{4x-1}[/tex]

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

[tex]\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}[/tex]

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

[tex](-\infty,1/4)\cup(1/4,\infty)[/tex]

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.  

In conclusion, our answer is C.

Answer:

The third one

Step-by-step explanation:

Complete Question

Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.

Answer:

The probability is  [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Step-by-step explanation:

From the question we are told that

   The standard deviation is  σ = 15.

    The mean μ= 100

     The range we are considering is [tex]x_1 = 81 , \ x_2 = 119[/tex]

Now given that IQ scores are normally distributed

    Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as

               [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )[/tex]

 Generally

                [tex]\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )[/tex]

So

              [tex]P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )[/tex]

substituting values

               [tex]P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )[/tex]

               [tex]P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )[/tex]

               [tex]P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )[/tex]

From the standardized Z table

               [tex]P(Z <-1.2667 ) = 0.10263[/tex]

And        [tex]P(Z <1.2667 ) = 0.89737[/tex]

So

            [tex]P( x_1 < X < x_2) = 0.89737 - 0.10263[/tex]

            [tex]P( x_1 < X < x_2) = 0.79474[/tex]

Answer:

y - 5 = -1/4(x - 4)

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

To find the point slope form, plug in the point given and the slope.

y - y1 = m(x - x1)

y - 5 = -1/4(x - 4)

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation:

Answer:

The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.

Step-by-step explanation:

Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.

Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.

Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)

We know that :

7.518 - 1.236 = 6.282 = ( About ) 2π

5.047 + 1.236 = 6.283 = ( About ) 2π

1.236 + 1.906 = 3.142 = ( About ) 2π

Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).