What are the quartiles of the data

Separating variables, we have

[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]

Integrate both sides.

[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]

[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]

Given that [tex]y(0)=-1[/tex], we find

[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]

Then the particular solution is

[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]

[tex]y^2 = x^2 + 1[/tex]

[tex]y = \pm\sqrt{x^2 + 1}[/tex]

and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.

[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]

Answer:

40

Step-by-step explanation:

19*2 = 38 + 2 = 40

Answer:

Step-by-step explanation:

we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16

k+3=19

 -3  -3

   k=16

Step-by-step explanation:

The value of b will be 43° as it is vertically opposite angle.. !!

\cos (\tan \left( -1\right) (\frac{x}{2}))

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Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

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\cos (\frac{\tan \left( -1\right) x}{2})

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Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

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Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]

Multiply both sides by [tex]\frac1{x^2}[/tex].

[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]

Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].

[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]

[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]

Separate the variables.

[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]

[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]

Integrate both sides

[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]

On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].

[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]

[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]

Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].

[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]

[tex]w = e^C e^{\ln|x^{-1}|}[/tex]

[tex]w = Cx^{-1}[/tex]

[tex]1 + v^2 = Cx^{-1}[/tex]

[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]

[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]

Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)

You incorrectly combine the fractions on the left side.

[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]

Answer:

-24 would be the temperature

Answer:

-24 BECAUSE I did all the math.

Information : The given hyperbola is a horizontal hylerbola with its centre (3 , -5) and one of its focus at (9 , -5) and vertex at (7 , -5) and as we can see that the focus and vertex have same y - coordinates, it must have its Transverse axis on line y = - 5.

Now,

it's vertex is given, I.e (7 , -5)

so, length of semi transverse axis will be equal to distance of vertex from centre, i.e

Now, it's focus can be represented as ;

[tex]\qquad \sf  \dashrightarrow \: (3 + ae, - 5 )[/tex]

so,

and we know, a = 4

[tex]\qquad \sf  \dashrightarrow \: 4e + 3 = 9[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4e = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: e = \cfrac{3}{2} [/tex]

Now, let's find the measure of semi - conjugate axis (b)

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = {a}^{2} ( {e}^{2} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9}{4} - 1)[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{9 - 4}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 16( \frac{5}{4} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: {b}^{2} = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: b = \sqrt{20} [/tex]

So, it's time to write the equation of hyperbola, as we already have the values of a and b ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {(x - h)}^{2} }{ {a}^{2} } - \cfrac{( {y - k)}^{2} }{ {b}^{2} } = 1[/tex]

[ plug in the values, and h = x - coordinate of centre, and k = y - coordinate of centre ]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ ({x-3)}^{2} }{ {16}^{} } - \dfrac{ {(y+5)}^{2} }{ { {20} }^{} } = 1[/tex]

Hello and Good Morning/Afternoon:

Let's solve this problem step-by-step:

Let's find the format of the standard form of hyperbole:

 [tex]\hookrightarrow \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2} =1[/tex]

Let's find the value of a, b:

             [tex]a = \sqrt{(7-3)^2+(-5--5)^2} =\sqrt{16} =4[/tex]

           ⇒value of c: distance between focus (9, -5) and center (3, -5)

                  [tex]c = \sqrt{(3-9)^2+(-5--5)^2}=\sqrt{36} =6[/tex]

            ⇒ therefore:

                  [tex]b = \sqrt{c^2-a^2} =\sqrt{6^2-4^2}=\sqrt{20}[/tex]

Let's plug everything into our standard form of the equation:

   [tex]\frac{(x-3)^2}{4^2} -\frac{(y--5)^2}{(\sqrt{20})^2 } =1\\\frac{(x-3)^2}{16} -\frac{(y+5)^2}{20 } =1[/tex] <== Answer

Hope that helps!

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Trabajando con porcentajes, concluimos que la pérdida es de $4800.

Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.

Entonces la pérdida va a ser el 8% de $60000.

Podemos escribir las relaciones:

$60000 = 100%

x = 8%

Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:

x = $60000*(8%/100%) = $60000*0.08 = $4800

Así, concluimos que la pérdida es de $4800.

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Using the Factor Theorem, the equation of h(x) is given as follows:

h(x) = -2(x³ - 2x² - 5x + 6)

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:

[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]

Then the rule is:

h(x) = a(x + 2)(x - 1)(x - 3)

h(x) = a(x² + x - 2)(x - 3)

h(x) = a(x³ - 2x² - 5x + 6)

The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:

6a = -12

a = -12/6

a = -2.

Hence the function is given by:

h(x) = -2(x³ - 2x² - 5x + 6)

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The pair of words that describe the given system of equations is: consistent and dependent.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

It demonstrates the equality of the relationship between the expressions written on the left and the right.

Given equations:

3y=9x-6

2y-6x=4

The first equation can be simplified and written as: y=3x-2

Similarly, the second equation can be written as: y-3x=2

It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.

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Answer:

B. 1

Step-by-step explanation:

-1*2 = -2

-2+1 = -1

-1+1 = 0

0+1 = 1

Answer:

X = 17√3

Y = 34

Step-by-step explanation:

TO calculate the values of X and y we use SOHCAHTOA.

tan 30 = opposite/adjacent

tan30 = 17/X

Cross multiply

tan30 ×X = 17

Divide bothsides by tan30

X = 17/1/√3

X=17√3

X = 29 ( approximately)

[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]

[tex]sin30 \times y = 17[/tex]

[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]

Answer:  89 yards

Step-by-step explanation: The perimeter is all the sides added up together. Since the width of the field is 52, the two sides are 52 yards which in total is 104 yards. 282- 104 = 178 yards. The length is 178/2 yards which is 89 yards.

Answer:

75

Step-by-step explanation:

math

Following the instructions for the inequalities gives the following results:

1. 4<7, both sides multiplied by 7

= 28<49, both sides multiplied by 6

= 168<294, both sides multiplied by 3

= 504<882, both sides multiplied by 10

= 5,040<8,820

2. 11>2, add 5 to both sides

= 16>3, add 3 to both sides

= 19>9, add -4

= 15>5

3. -4<-2, subtract 6

= -10<-8, subtract 8

= -18<-16, subtract 2

= -20<-18

4. -8<8, divide by -4

= 2>-2, divide by -2

= -1<1

5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.

Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.

Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.

Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.

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The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

In 5-card poker, find the probability of being dealt the following hand. Refer to the table.

From the table:

Total number of outcomes = 2598960

Total number of favorable outcomes = 624 + 10200 = 10824

The probability of being dealt four of a kind or a straight

P = 10824/2598960

P = 0.00416

In percentage:

P = 0.416%

Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.

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Answer:

c

Step-by-step explanation:

Answer:

268.08

Step-by-step explanation:

Answer:

803.84 m³

Step-by-step explanation:

The formula to find the volume of a sphere is:

V = 4 π r³

Given that,

radius ⇒ 4m

Let us find the volume now.

V = 4 π r³

V = 4 π × ( 4 )³

V = 4 π × 64

V = 4 π × 64

V = 12.56 × 64

V = 803.84 m³

[tex]v(x) = wlh \\ 2x {}^{3} + {x}^{2} - 16 x- 15 =(2x + 5)(x - 3)h \\ h = \frac{2x {}^{3} + x {}^{2} - 16x - 15 }{2x {}^{2} - x - 15 } \\ using \: long \: divison \\ h = x + 1[/tex]

Answer:

C...........................

Based on the given parameters, the length of c is 8.0 units

The given parameters are

Angle c = 76 degrees

Side a = 20

Side b = 13

The length of c is then calculated using the following law of sines

c^2 = a^2 + b^2 - 2absin(C)

Substitute the known values in the above equation

So, we have

c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)

Express 20^2 as 400

c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)

Express 13^2 as 169

c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)

Evaluate the product and sin(76)

c^2 = 400 + 169 - 520 * 0.9703

Evaluate the product

c^2 = 400 + 169 - 504.55

Evaluate the exponents

c^2 = 400 + 169 - 504.55

So, we have

c^2 = 64.45

Evaluate the square root

c = 8.0

Hence, the length of c is 8.0 units

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We can actually deduce here that when the tournament ended, team Olympus have tied for 13, 10, 7, 4, 1 times.

In Mathematics, inequality is used to express or show quantities that are less than, greater than, greater than or equal to,  less than or equal to.

The following can be seen in inequality expressions:

Looking at the question, we can see that each team plays exactly 19 games.

Every win (w) = 3

Every tie (t)= 1

Every loose = 0

But Olympus got a total of 28 points

Thus: 3w + t = 28 ---------(1)

Note that each team plays  19 games

Thus, T + W  ≤  19 --------------(2)

and T , W ≥ 0

Looking at equation (1) and (2)

=> 2W  ≥  9

=> W ≥ 4.5  

( match can be won in integers only )

=> W  ≥  5  

W - 5, 6, 7, 8, 9    

T - 13, 10, 7, 4, 1  

Loose - 1, 3, 5, 7, 9

Thus, team Olympus have tied for 13, 10, 7, 4, 1 times.

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Hi there,

please see below for solution steps :

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Evaluate by substituting :

[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]

Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].

I hope the answer - and steps - made sense to you !!

Happy Learning !!

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Answer:

7.....gggggggggggggggh

Answer: C

Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.

The standard deviation for the number of people with the genetic mutation is 3.77

The given parameters are:

Sample size, n = 300

Proportion that has the particular genetic mutation, p = 5%

The standard deviation for the number of people with the genetic mutation is calculated as:

Standard deviation = √np(1 - p)

Substitute the known values in the above equation

Standard deviation = √300 * 5% * (1 - 5%)

Evaluate the product

Standard deviation = √14.25

Evaluate the exponent

Standard deviation = 3.77

Hence, the standard deviation for the number of people with the genetic mutation is 3.77

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The length of segment XY is 52 units and the length of segment HD is 26 units

Secant lines (a)

To do this, we make use of the following intersecting secant theorem

VZ * VW = VY * VX

Substitute the known values in the above equation

12 * 40 = VY * 8

Divide by 8

12 * 5 = VY

Evaluate the product

VY = 60

The length VX is

XY = VY - VX

Substitute the known values in the above equation

XY = 60 - 8

Evaluate

XY = 52

Hence, the length of segment XY is 52 units

Secant lines (b)

To do this, we make use of the following intersecting secant theorem

GH^2 = HC * HD

Substitute the known values in the above equation

13^2 = 6.5 * HD

Divide by 6.5

13^2/6.5 = HD

Evaluate the quotient

26 = HD

The length HD is

HD = 26

Hence, the length of segment HD is 26 units

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Answer:

inductive reasoning

Step-by-step explanation:

By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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Step-by-step explanation:

Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating