Mrs. Smith has a total of 28 kids in her class. There are 5 more boys than there are girls. Write a system of equations to model this.

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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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:

B. 1

Step-by-step explanation:

-1*2 = -2

-2+1 = -1

-1+1 = 0

0+1 = 1

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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[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]

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

Answer:

a=–2, 3

Step-by-step explanation:

r(a)=20

a²–a+14=20===> a²–a–6=0===> (a–3)(a+2)

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

c

o

s

(

t

a

n

(

−

1

)

(

2

)

)

Simplify

1

Combine multiplied terms into a single fraction

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

c

o

s

(

t

a

n

(

−

1

)

⋅

2

)

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

c

o

s

(

t

a

n

(

−

1

)

2

)

Solution

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

c

o

s

(

t

a

n

(

−

1

)

2

)

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]

The area of the small poster is 160 inches square

From the information given, we have the poster to take the form of a rectangle

The formula for area of a rectangle is;

Area = length × width

For the smaller poster created using a scale of factor 2/3

Length = 2/ 3 × 24

Length = 16 inches

Width = 2/ 3 × 15

Width = 10 inches

Substitute into the formula

Area = 16 × 10

Area = 160 inches square

Thus, the area of the small poster is 160 inches square

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Answer: Neither

Step-by-step explanation:

It is not an angle of the quadrilateral, so it is not an interior angle.

It does not form a linear pair with any interior angle of the quadrilateral, so it is not an exterior angle.

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.

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]

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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Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

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 !!

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

The sum notation is given as:

∞Σn=1 2(1/5)^n-1

The above notation is a geometric sequence with the following parameters

The sum is then calculated as

S = a/(1 - r)

The equation becomes

S = 2/(1 - 1/5)

Evaluate the difference

S = 2/(4/5)

Express the equation as products

S = 2 * 5/4

Solve the expression

S= 5/2

Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2

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Answer:

S = 5/2

Thank me later

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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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:

Step-by-step explanation:x+y+z=100(let x ,y,z represent the first second and third numbers respectively)

Therefore,y=2z

z=x-8

y=2x-16

substituting the values of x,y and z into the question,we have

x+(2x-16)+(x-8)=100

Simplifying,we have

4x-24=100

adding 24 to both sides of the equation,

4x=100+24

4x=124

dividing both sides of the equation by the co-efficient of x,we have

4x/4=124/4

4.31=124

therefore,x=31.

Answer:

P(B) 7

Step-by-step explanation:

The answer is P (B)

May this answers be helps you to solve

Answer:

inductive reasoning

Step-by-step explanation:

Answer:

Step-by-step explanation:

3/5 = x/10

5x = 30

x = 6

6/10

Hey there!

Original equation:

3/5 = ?/10

Convert to:

3/5 = x/10

Cross multiply the numbers:

3 * 10 = 5 * x

Simplify it:

3 * 10 = 5 * x

30 = 5x

5x = 30

Divide 5 to both sides:

5x/5 = 30/5

Simplify it:

x = 30/5

x = 6

Therefore, your mystery number should be: 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

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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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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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

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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8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent coffee A, y represent coffee B and z represent coffee C, hence:

x + y + z = 54   (1)

Also:

2x = z        (2)

And:

15.21x + 13.21y + 10.39z = 12.61(54)   (3)

x = 8.9, y = 27.3 and z = 17.8

8.9 pounds of coffee A, 27.3 pounds of coffee B and 17.8 pounds of coffee C are need to make a blend that sells for $12.61 per pound.]

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