Warm up: solve for the variable

3 = x/5

Answer:

b 18 boys

Step-by-step explanation:

In order to solve this problem we must create a system of equations.

Creating a system of equations

Let x = number of boys and y = # of girls

We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27

We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )

Solving the system

Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.

What is the substitution method?

The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )

Substitute equation 2 into equation 1

Equation 1 : x + y = 27

==> plug in x = 2y

y + 2y = 27

==> combine like terms

3y = 27

==> divide both sides by 3

y = 9

So there are 9 girls in the classroom

Solving for # of boys

To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x

equation : x + y = 27

==> plug in y = 9

x + 9 = 27

==> subtract 9 from both sides

x = 18

There are 18 boys in the classroom

Checking our work:

Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct

Equation 1 x + y = 27

==> plug in x = 18 and y = 9

18 + 9 = 27

==> simplify

27 = 27 ✓

equation 2 x = 2y

==> plug in x = 18 and y = 9

18 = 2(9)

==> multiply 2 and 9

18 = 18 ✓

Both are correct therefore we can conclude that there are 18 boys and 9 girls.

Answer: 0.8571

The explanation is in the image please

Answer:

C) V = 14130 in³

Step-by-step explanation:

Volue of a sphere: 4/3πr³

Substitute the values from above into the formula to find the volume of the sphere:

V = 4/3πr³

V = 4/3*3.14*15³

V = 4/3*3.14*3375

V = 4/3*10597.5

V = 14130 in³

Hope this helps!

Answer:

6:1. Each following term is 1 to 6 of the previous term.

Step-by-step explanation:

72/12 = 6/1

12/2 = 6/1

etc

Answer:

Yes. 3/100 = 0.3

Step-by-step explanation:

3/100 converted to decimal form equals 0.3.

Answer:

No

Step-by-step explanation:

If you divide 100 by 3 you will end up with 0.03, not 0.3.

Hope this helps!

1 is congruent to 3 and 2 is congruent to 5 because alternate interior angles are congruent.

Since 1 is congruent to 3 and to 2, then 3 is congruent to 2.

But 2 is congruent to 5, so since 3 is congruent to both 3 and 5, 3 and 5 must be congruent to each other.

Two geometric figures are said to be congruent or to be in the relation of congruence if it is possible to superpose one of them on the other so that they coincide throughout.

        The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal. For example, draw two circles of the same radius, then cut them out and place them on one another.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal.

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Answer:

$1680

Step-by-step explanation:

To find 7% of 24000, convert 7% to a decimal and multiply. Percent means per hundred, 7% is 7/100 is .07

.07 × 24000

= 1680

Answer: 60/100 or 6/10 or 3/5

Step-by-step explanation:

We get 10+20+30=60.

We Covert to a fraction, 60/100

Reduce Down. 6/10

Reduce again, 3/5

Final answer is 3/5, the chance of it not being Red, White, or Blue is 3/5.

Answer:

red 420 times

Step-by-step explanation:

The results show red (18)  out of ( 18+10+7+19+6)

  18 / 60

18/60  *   1400 = 420 times

Answer:

3/2

Step-by-step explanation:

Please give me brainlist

Using the hypergeometric distribution, it is found that there is a 0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that all of them are seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,14,3,8) = \frac{C_{8,3}C_{6,0}}{C_{14,3}} = 0.1538[/tex]

0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

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Answer:

1/4 x + 9/10

Step-by-step explanation:

[tex]=-\frac{1}{2}x+\frac{7}{10} +\frac{3}{4} x+\frac{1}{5}[/tex]

[tex]=\frac{3}{4}x-\frac{2}{4} x+\frac{7}{10} +\frac{2}{10}[/tex]

[tex]=\frac{1}{4} x+\frac{9}{10}[/tex]

Hope this helps

Answer:

D.(2, 2)

Step-by-step explanation:

The correct answer is 12:16 P.M.

According to the problem,

∴ Time at which Dev finishes her lunch =

                  9:52 A.M.  + ( 1 hour and 48 minutes +  36 minutes )

                =   11:40 A.M. +  36 minutes = 12 : 16 P.M.

∴ Deb finish eating lunch at 12:16 P.M.

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Step-by-step explanation:

for the prime number it's 1/2

Answer:

C - 35 gallons per minute

Step-by-step explanation:

350 / 10

Answer:

350/10 = 35 gallons per minute

Step-by-step explanation:

Answer:

3y(4y+9)=12y^2+27y......

The area A of the rectangular building in terms of y will be (12y² + 36y).

What is Area of rectangle?

The area of a rectangle is length time width.

Given that;

The width of rectangular building = 3y

The length of rectangular building = 4y + 9

Now,

Area of rectangle = length x width

Substitute all the values we get;

Area of a rectangle = 3y (4y + 9)

                              = 12y² + 36y

Thus, The area A of the rectangular building in terms of y will be

⇒ (12y² + 36y)

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Answer:

The expression is not factorable with rational numbers.

Hope this helps.

Answer:

-7

Step-by-step explanation: an easy way to find the y-intercept (the point at which the line crosses the y axis) is by identifying what part of the equation does not have an x value. in this problem, it would be -7. if it were to not have a number that is followed by an x the y-intercept is 0.

hope that helps!

Answer:

X= 38°

Y = 142°

Step-by-step explanation:

let the angle vertically opposite to 142° = w

therefore, w= 142° ( vertically opposite angles are equal)

hence,x+ w =180° ( two interior angles sum up to 180°)

x+ 142° = 180°

x= 180 - 142 = 48°

X = 38°

then calculating for Y

X + Y = 180° ( angles on a straight line sum up to 180°)

38+Y = 180

Y = 180- 38

Y = 142°

Answer:

5m

Step-by-step explanation:

V=whl

Solving forl

l=V

hw=70

7·2=5m

Answer:

Topics

2x-5y=4. 2x−5y=4. Add 5y to both sides. Add 5y to both sides.

2x=4+5y. 2x=4+5y. The equation is in standard form. The equation is in standard form.

2x=5y+4. 2x=5y+4. Divide both sides by 2. ...

\frac{2x}{2}=\frac{5y+4}{2} 22x​=25y+4​ Dividing by 2 undoes the multiplication by 2. ...

x=\frac{5y+4}{2} x=25y+4​ Divide 4+5y by 2.

Step-by-step explanation: How do I determine how many solutions an equation has?

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

Answer:

5

Step-by-step explanation:

[tex]\frac{25}{30}[/tex] ( divide numerator and denominator by 5 ) , then

[tex]\frac{25}{30}[/tex] = [tex]\frac{5}{6}[/tex] ( with missing number ? = 5 )

Answer:

Step-by-step explanation:

What is the missing number ?? /6 =25/30

x : 6 = 25 : 30

x = 6 * 25 : 30

x = 5

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

check

5/6 = 0.83

25/30 = 0.83

the answer is good

Answer:

u = 5 m/s

Step-by-step explanation:

Given

Required Formula

Solving

Answer: Heyaa!

A Triangle is actue! :)

Step-by-step explanation:

Hopefully this helps you!!

Answer:

it's a right triangle

Step-by-step explanation:

at the bottom left corner of the triangle, there's a square that tells u that it's a right triangle

Answer:

573440 Kg

Step-by-step explanation:

[tex]\boxed{\bf Mass = density * volume}[/tex]

Find the volume of the solid cube

          Volume of solid cube = side³

                                              = 4 * 4 * 4

                                              = 64 m³

[tex]\sf Mass = 8960* 64\\[/tex]

        = 573440 Kg

Answer:

y = 2x -23

Explanation:

Given equation: y = 2(x) + 2

Comparing with slope intercept formula: y = m(x) + b

                                             where m is slope, b is y-intercept

Here slope: 2 as parallel line has same slope

Find equation:

y - y1 = m(x-x1)

y -(-7) = 2(x-8)

y + 7 = 2x - 16

y = 2x - 16 - 7

y = 2x -23

Given graph to confirm answer:

Compare to slope intercept form

Parallel lines have slopes equal

Equation in point slope form

Answer:

about 33.9 cm

Step-by-step explanation:

[tex]2\pi(5.4) = 10.8\pi = 33.9[/tex]