Estimate the solution to the following system of equations by graphing.
9x + 8y=26
3x + 2y=9

The probability that a boy is selected is 0.5357 or 53.57%

Probability 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.

P(boy) is asking for the probability that a boy will be chosen to read a poem out loud. Since there are 15 boys, we can get the probability by dividing this by the total number of students.

This is because out of all the students, there is an equal possibility that each of the 15 boys will be chosen.

P = ( 15 ) / ( 15+13)

P = 15 / 28

P = 0.5357

Therefore the probability that a boy is selected is 0.5357 or 53.57%

To know more about probability follow

https://brainly.com/question/24756209

#SPJ1

Answer:

53.57%

Step-by-step explanation:

Answer:

237 grams

50 * 4

= 200

4 weight of 50 g

1 weight of 20g

1 weight of 10g

7 weight of 1g

Answer: (0, 1, 3)

Step-by-step explanation:

If we multiply both sides of the equation [tex]4x-2y=-2[/tex] by 7, we get [tex]28x-14y=-14[/tex].

If we multiply both sides of the equation [tex]9x-7y=-7[/tex] by 2, we get [tex]18x-14y=-14[/tex].

Subtracting the equation [tex]28x-14y=-14[/tex] from the equation [tex]18x-14y=-14[/tex], we get that [tex]-10x=0 \longrightarrow x=0[/tex].

This means that [tex]4(0)-2y=-2 \longrightarrow y=1[/tex]

And thus, [tex]4(0)-2(1)-z=-5 \longrightarrow -2-z=-5 \longrightarrow z=3[/tex].

So, the solution is (0, 1, 3).

The length of CD will be option C. 3

From given diagram, triangle ABC and EDC meet at a common vertex C.

So, triangle ABC and EDC both are congruent to each other.

Applying the similarity property of congruence, ratio of the congruent triangles' corresponding sides will be equal.

Therefore,

AB/ED = AC/EC = BC/CD

AC/EC = BC/CD

18/6 = (12 - x)/x

Simplifying the expression,

We get

18x = 6(12 - x)

Multiplicating the terms in right hand side,

18x = 72 - 6x

Solving 6x on both sides,

we get

18x + 6x = 72 - 6x + 6x

24x = 72

Dividing both the sides by 24, we get

24x/24 = 72/24

x = 3

Hence, the length of CD is 3.

Learn more about congruent triangle here:

https://brainly.com/question/2938476

#SPJ10

Answer:

The total money we have to pay is $69.

Step-by-step explanation:

MARKUP is the amount added to the cost price.

MARKUP formula = 100*profit / cost

Cost of the item = $60.00

put the value in the formula

15 = 100*profit/60

profit = 60 × 15 ÷ 100 = 9

the total money  is  cost + profit

which is 60 + 9 = $69.

So the total money we have to pay is $69.

Learn more about MARKUP here - https://brainly.com/question/23665274

#SPJ10

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Use the distributive property to distribute 3x into the term (x + 6):

[tex]3x(x+6)=-10[/tex]

[tex]3x^2+18x=-10[/tex]

To create a quadratic equation, add 10 to both sides of the equation:

[tex]3x^2+18x+10=-10+10[/tex]

[tex]3x^2+18x+10=0[/tex]

The quadratic formula is defined as:

[tex]\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

Set up the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]

Simplify the radicand:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

[tex]\sqrt{4\times51}[/tex]

Then, using the Product Property of Square Roots, break this into two radicands:

[tex]\sqrt{4} \times \sqrt{51}[/tex]

Since 4 is a perfect square, it can be evaluated:

[tex]2 \times \sqrt{51}[/tex]

To simplify further for easier reading, remove the multiplication symbol:

[tex]2\sqrt{51}[/tex]

Then, substitute for the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the roots at the plus-minus symbol:

[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]

[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]

Then, simplify the numerator of the roots by factoring 2 out:

[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]

[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]

Then, simplify the fraction by reducing 2/6 to 1/3:

[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]

[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]

The final answer to this problem is:

[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]

[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]

Answer:

37.5

Step-by-step explanation:

37.5×144/100=54 the number is 37.5

Answer:

y = 4(x+6)(x-2)

Step-by-step explanation:

y = 4x² + 16x - 48, factor out the 4

y = 4(x² + 4x - 12), find factors of 12

Factors of 12:

1*12, 2*6, 3*4; find a pair that sums to 4x or 4

6-2 = 4, since 12 is a negative number, a number in the factor must be negative, in this case, making 2 negative, would make 6-2 = 4

y = 4(x+6)(x-2)

The equation of the line is y = 3x +3 .

A straight line equation is that can be represented by y = mx +c , where m is the slope and c is the intercept on y axis.

The points given are (2,3) and (5,9)

m = (9-3)/(5-2) = 3

m = 3

Therefore the equation becomes

y = 3x +c

Te equation is given by

(y-y₁) = m(x-x₁)

y-3 = 3(x - 2)

y-3 = 3x -6

y = 3x +3

Therefore the equation of the line is y = 3x +3 .

To know more about Straight Line Equation

https://brainly.com/question/959487

#SPJ1

According to law of cosines the length of RQ can be written as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

Given the length PR is 6 , the length of RQ is p, the length of PQ is 8 and the angle RPQ is 39 degrees.

A length of the triangle can be written as according to law of cosines if sides are given and one angle is [tex]a^{2} =b^{2} +c^{2} -2bccos(A)[/tex]

We have to just put the values in the above equation.

as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

p is the side opposite to angle given , the length of other sides are 6 and 8 and angle is 39 degrees.

Hence the side can be written as according to law of cosines if the angle is 39 degrees is  as [tex]p^{2} =6^{2} +8^{2} -2*6*8cos(39)[/tex].

Learn more about trigonometric functions at https://brainly.com/question/24349828

#SPJ10

Answer: OPTION B

Step-by-step explanation:

edge22

Answer:

C

Step-by-step explanation:

HOPE THAT HELPSBDNQBDB

Answer:

Step-by-step explanation:

Open the brackets

3 x 2x = 6x

3x -3 = -9

4 x 2x= 8x

4 x 4= 16

6x - 9 = 8x + 16

Move same to same side

-16 -9 = 8x - 6x

-25 = 2x

x -25/2

x = -12.5

Answer:

Step-by-step explanation:

3*(2x - 3) = 4*(2x + 4)​

6x - 9 = 8x + 16

6x - 8x = 16 + 9

-2x = 25

x = -25/2 or -12.5

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

check

3 * (2 * (-12.5) - 3) = 4 * (2 * (-12.5) + 4)

3 * (25 - 3) = 4 * (12.5 + 4)

3 * 22 = 4 * 16.5

66 = 66

the answer is good

En una tienda se fabrican

La cantidad de mesas de 3 patas que tiene para la venta la tienda que las

fabrica es: 47

¿Qué es un sistema de ecuaciones?

Es un arreglo de ecuaciones que se caracteriza por tener el mismo número de incógnitas que de ecuaciones.

Existen diferentes métodos para su resolución:

Sustitución: se despeja de una ecuación una variable, quedando en función de otra para luego sustituirla en otra ecuación y así obtener

Igualación: se despeja la misma variable en dos de las ecuaciones y se igualan los resultados.

Eliminación: se resta o suman dos ecuaciones para que quede un resultado en función una variable y así despejarla.

Gráfico: se grafican las rectas y el punto de intersección es la solución del sistema.

¿Cuántas mesas de 3 patas se tienen para vender?

Definir;

x: mesas de 3 patas

y: mesas de 4 patas

Ecuaciones

x + y = 89

5x + y = 277

Aplicar método de eliminación;

Restar 1 - 2;

x + y = 89

-5x - y = -277

-4x + 0 = -188

Despejar x;

x = 188/4

x = 47

Sustituir;

47 + y = 89

Despejar y;

y = 89 - 47

y = 42

Learn more about En una tienda se fabrican here https://brainly.com/question/27973753

#SPJ10

The possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have a quadratic equation:

(k - 1)x² + (4k)x + k -3 = 0

Here,

a = k - 1

b = 4k

c = k - 3

As we know for distinct real roots:

D > 0

[tex]\rm {b^2-4ac}} > 0[/tex]

(4k)² - 4(k-1)(k-3) > 0

[tex]\rm 16k^2-4\left(k-1\right)\left(k-3\right) > 0[/tex]

[tex]\rm 12k^2+16k-12 > 0[/tex]

[tex]\rm 3k^2+4k-3 > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2-\dfrac{13}{3} > 0[/tex]

[tex]\rm 3\left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{3}[/tex]

[tex]\rm \left(k+\dfrac{2}{3}\right)^2 > \dfrac{13}{9}[/tex]

[tex]\rm k < \dfrac{-\sqrt{13}-2}{3}\quad \mathrm{or}\quad \:k > \dfrac{\sqrt{13}-2}{3}[/tex]

or

[tex]\rm k < -1.868 \quad \mathrm{or}\quad \:k > 0.535[/tex]

Thus, the possible values of k are k < - 1.868 or k > 0.535 in which the inequality is true.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

The amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

Gertrude has a life insurance policy that will pay her family $97,000 per year.

If interest rates are at 1.4% when the insurance company has to pay

r = 1.4%

or

r = 0.014

The amount of the lump sum that the insurance company must put into a bank account:

= 97,000/0.014

= 6928571.429 ≈ $6,928,571.43

Thus, the amount of the lump sum that the insurance company must put into a bank account is $6,928,571.43 option (B) is correct.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

Answer:

It's most likely he was charged a late fee

Answer:

the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

Answer:

4/10, 6/15, 8/20, etc.

Step-by-step explanation:

I hope you got some idea

Parallel lines are those on a plane that do not intersect while perpendicular lines are those that intersect at an angle of 90°.

Parallel lines will never intersect with each other and will maintain the same distance from each other for as long as they are on the same plane.

Perpendicular lines on the other hand will intersect each other and will do so at a 90° angle. An example of such a line is the steps on a ladder which intersect the beam at a 90° angle.

Find out more on parallel lines at https://brainly.com/question/24607467.

#SPJ1

Substitute 5 in the place of X

[tex]f(x) = \frac{1}{8} \times 4 ^{x} \\ f(5) = \frac{1}{8} \times 4 ^{5} \\ f(5) = \frac{1}{8} \times 1024 \\ f(5) = 0.125 \times 1024 \\ f(5) = 128[/tex]

The asnwer is D

PLEASE GIVE BRAINLIEST

Answer:

The volume of the pyramid with a base area of s² and the heights iss

The formula for calculating the volume of a square based pyramid is expressed as:

Volume = 1/3* Base area* Height

Since it is a square-based pyramid, the base area is calculated as:

Base Area = s ^ 2

If the height of the pyramid is equal to of the length of a side on the base, hence h = s

Substituting the base area and the height into the formula for the volume, this will give;

V = BH / 3

V = (s ^ 2 * s)/3

V = (s ^ 3)/3

V = 1/3 * s ^ 3

Hence the volume of the pyramid with a base area of s ^ 2 and the height s is 1/3 * s ^ 3

[tex]\mathsf {2(10 + 2) = 3(y + 3)}[/tex]

[tex]\mathsf {24 = 3y + 9}[/tex]

[tex]\mathsf {3y = 15}[/tex]

[tex]\textsf {y = 5}[/tex]

[tex]\textsf {The value of y will be 5. }[/tex]

Answer:

f(2) =  18

Step-by-step explanation:

Put '2' into the equation where 'x' is to get :

f(2)  =  2 (2^2) + 5 (sqrt(2+2)

        =  8        + 5 (2)   =  18

[tex]x^2-10x=30x\\x^2-40x=0\\x(x-40)=0\\x=0 \vee x=40[/tex]

Answer:

cp = rs 400

loss = 10%

Then SP = 400 - 10% of 400

= 400 - 40

= 360

Therefore SP = Rs. 360

The line of music is refered to as the bracket

It should be noted that music simply means a vocal or instrumental sounds that are combined to produce beauty of harmony and expression if emotions.

When When both of these staves are connected with this symbol, it's called a brace.

Lastly, the things inside the box are voice, piano, and guitar.

Learn more about music on:

brainly.com/question/26373912

#SPJ1

Answer:

Looks to me like it should be -2