Each homeroom must send two student representatives to each student council meeting. Mrs. Lincoln has 15 girls and 10 boys in her homeroom. If she randomly selects two students to attend the next meeting, find the probability of her choosing one girl and one boy?

Answer:

Step-by-step explanation:

Amount of halloween candy bought by Jack = 5pounds

Amount he gave trick = 3pounds

Amount jack ate = 10ounces

Before we can determine the amount of halloween candy that Jack has left, we need to convert the pounds to ounces in order to make the units consistent.

given 1pound = 16ounces

5pounds = 16* 5 ounces

5pounds = 80ounces

Also;

3pounds = 16*3 ounces

3pounds = 48ounces

Total amount of halloween used up by Jack = 48ounces + 10ounces

= 58ounces

Amount of ounces of candy left = Total amount of candy bought -amount used up

Amount of ounces of candy left = 80ounces - 58ounces

Amount of ounces of candy left = 22ounces

Answer:

$90

Step-by-step explanation:

3% $500= $15

$15 times 6yrs = $90

Answer:

97.03

Step-by-step explanation:

the other guy is wrong.

Answer:

x ≈ - 0.7 ≈ 0.7; Option A

Step-by-step explanation:

Let us substitute f ( x ) with 0, as to find the " real zero value( s ) " of the function;

0 = 3x^4 + x^2 - 1 ⇒ Swap sides, as such,

3x^4 + x^2 - 1 = 0 ⇒ Rewrite equation with u being = x^2, u^2 = x^2,

3u^2 + u - 1 = 0 ⇒ And solve for u by completing the square,

3u^2 + u = 1 ⇒ Divide either side by 3,

u^2 + u / 3 = 1 / 3 ⇒ Write equation in the form x^2 + 2ax + a^2 = ( x + a )^2, solving for a,

2au = 1 / 3u,

a = ( 1 / 3u ) / 2u,

a = 1 / 6 ⇒ Add value of a^2 to either side of equation,

u^2 + u / 3 + ( 1 / 6 )^2 = 13 / 36,

( u + 1/ 6 )^2 = 13 / 36 ⇒ Solve for u,

u = ( √13 - 1 ) / 6, and u = ( - √13 - 1 ) / 6 ⇒ Substitute value of u back into first equation to solve for x,

x = √( - 1 + √13 ) / 6 ), x = - √( - 1 + √13 ) / 6 ), x = √( - 1 - √13 ) / 6 ), x = - √( - 1 - √13 ) / 6 ) ⇒ Convert to approximate decimal form,

x = 0.6589.... = - 0.6589....

Answer; x ≈ - 0.7 ≈ 0.7; Option A

Answer:PPlEASeee

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

3/11 / 3/11

=3/11 * 11/3

=1

Answer:

x = 6

Step-by-step explanation:

Answer:

an = 1.2 + (n - 1) 1.5

Step-by-step explanation: opt A on edg

Answer:

area of shaded portion=56 - 1/2 ×3×4=56-6= 50 yd^2

Answer:

A': (2, 8)

Step-by-step explanation:

I have attached the work to your problem below.

I hope this helps.

Step-by-step explanation:

4 + 3x -20 = 0

3x - 16 = 0

3x = 16

x = 16/3

Answer:

take x=2.515834 and r=14.31386

Step-by-step explanation:

Let us call the the lenght of the side of the square as x. The total lenght of the wire is 100. Note that if we have a square of side x, it has a perimeter of 4x. That means, that we need a wire of length 4x to build a square of side x. Note that if we take a wire of length 4x, we have that the remainder is 100-4x. We will use this to form a circle. As for the square, since we are using the wire of length 100-4x to build a circle, it must happen that the perimeter of the circle is 100-4x.

Recall that the perimeter of a circle of radius r is [tex]2\pi r[/tex], so in this case , we have that [tex] 2\pi r = 100-4x[/tex] which implies that [tex]r =\frac{100-4x}{2\pi}[/tex].

Now, recall that the area of a square of side x is [tex]x^2[/tex]. Also, recall that the area of a circle of radius r is [tex]\pi r^2[/tex]. In our case, the area of the circle is given by

[tex] \pi r^2 = \pi (\frac{100-4x}{2\pi})^2[/tex]

Also, we are given that the sum of the areas of both figures is 650. That is

[tex] x^2 + \pi (\frac{100-4x}{2\pi})^2 = x^2+\frac{(100-4x)^2}{4\pi}=650[/tex]

By substracting 650 on both sides and multiplying by [tex]4\pi[/tex] this equation is equivalent to

[tex]4\pi x^2 + (100-4x)^2-650\cdot 4\pi =0[/tex]

if we expand [tex](100-4x)^2[/tex] and then group each term of x, x^2 we get :

[tex](4\pi+16)x^2-800x+100^2-650\cdot 4\pi =0[/tex]

Recall that given a cuadractic equation of the form [tex]ax^2+bx+c=0[/tex] the solution is given by

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

In this case, the existence of a real solution is given by the expression [tex]b^2-4ac[/tex]. For it to have a real solution, it must happen that [tex]b^2-4ac\geq 0[/tex]

In this case, b=-800, c = 100^2-650\cdot 4\pi, a = 4\pi+16[/tex]

For this values, we get that [tex]b^2-4ac = 430681\geq 0[/tex], so the is a solution for our problem.

In this case,

[tex] x = \frac{-b - \sqrt[]{b^2-4ac}}{2a}= 2.515834[/tex]

and [tex] x = \frac{-b + \sqrt[]{b^2-4ac}}{2a}= 25.4891[/tex] are the two possible solutions for this problem. We can check that this values of x fulfill our restrictions. Note that if x=25.4891, by replacing in the value of r, we get that r=-0.3113853. Since r is the radius of the circle, it must be positive. Hence, x=25.4891 is discarted.For x=2.515834 we get a value of r=14.31386, so this is the answer

Answer:

20,701 feet

Step-by-step explanation:    

29,028-8,327= 20,701

Q 5) No. of boys = 20

Answer:

Q 6) Total time taken to answer both the quizzes = 90 minutes

Step-by-step explanation:

Q 5.

Let the number of boys = x

Therefore, number of girls = x - 5

Since,

No. of boys + No. of girls = 35

hence,

x + x- 5 = 35

2x-5 = 35

2x = 35 + 5

2x = 40

x = 40/2

x = 20

Hence 20 boys participated in the activity.

Let the time taken to answer history quiz= x min

Therefore, time taken to answer geography quiz = (x + 30) min

According to the given information:

x = 1/2(x + 30)

2x = x + 30

2x - x = 30

x = 30 min

Hence, x + 30 = 30 + 30 = 60 min

Total time taken to answer both the quizzes = 30 + 60 = 90 minutes

Answer:

Perimeter of square = [tex]12\sqrt{2}\,\,inches[/tex].

None of the given options is correct

Step-by-step explanation:

Given: Length of diagonal of the square = 6 inches

To find: perimeter of square

Solution:

Let x denotes side of square

Diagonal of square = [tex]\sqrt{2}x[/tex]

Also,  length of diagonal of the square = 6 inches

So,

[tex]x=\frac{6}{\sqrt{2}}\\=\frac{6}{\sqrt{2}}\left ( \frac{\sqrt{2}}{\sqrt{2}} \right )\\=3\sqrt{2}[/tex]

Perimeter refers to the distance around a two-dimensional shape.

Perimeter of square = 4×side

=[tex]4(3\sqrt{2})=12\sqrt{2}\,\,inches[/tex]

So, none of the given options is correct.

Answer:

x=-1      x=5

Step-by-step explanation:

f(x) =−3(x+1)(x−5)

0 = −3(x+1)(x−5)

Using the zero product property

x+1 = 0     x-5=0

x=-1      x=5

Answer:

F(1) = 7

F(2) = 14 = 7 x 2^1

F(3) = 28 = 7 x 2^2

F(4) =56 = 7 x 2^3

...

F(10) = 7 x 2^9

Hope this helps!

:)

Answer:

A) 2a + 4c = 38.00

B) 3a + 3c = 40.50

We multiply A) by -1.5

A) -3a -6c = -57 then we add B)

B) 3a + 3c = 40.50

-3c = -16.50

c = 5.50

a = 8.00

Step-by-step explanation:

Answer:

118 degrees; 30 degrees

Step-by-step explanation:

2x+14=1/2((6+14x)-58)

2x+14=1/2(-52+14x)

2x+14=-26+7x

40=5x

x=8

6+14(8)=6+112=118

2(8)+14=16+14=30

Answer:

Step-by-step explanation:

Question 6)

sin Y= m

sin Y = m/1

So, hypotenuse is 1

Since sine is opposite over hypotenuse

So XZ= m and YZ = 1

Similarly, cos Y = k

cos Y = k/1

So adjacent side of angle Y is k

So XY = k

cos z - sin z = [tex]\frac{XZ }{YZ } - \frac{XY}{YZ}[/tex]

cos z - sin z = [tex]\frac{m }{1 } - \frac{k}{1}[/tex]

cos z - sin z = m - k

Question 7)

the relationship between sine, cosine, and tangent.

tan(x) = sin(x)/cos(x) = (11/61)/(60/61)

tan(x) = 11/60

Question 8)

Start with where the shorter leg is. It must be opposite the smallest angle.

In a 30 - 60 - 90 degree triangle you have the hypotenuse to be twice as long as the shortest side. You have to read that a couple of times to make sure you understand it. 

That being said, if the shortest side is x, the hypotenuse will be 2x.

Since in this case the shortest side is 11, the hypotenuse will be 2*11 = 22

The answer is 22

Answer:

D. He distributed Negative one-fourth over (8 x + 12), distributed –1 over (Negative 2 x + 5), and then combined like terms.

Step-by-step explanation:

We know that when using the distributive property, you have to multiply the outside value with the inside value and then either subtract or add.

You can combine like terms first, but that is only if there are like terms inside the parentheses. In this case, there are not, so you would distribute first.

So, to do that, you have to first distribute -1/4 to the 8x+12 and then distribute the -1 to the -2x+5. (note that they did not include the 1, but it is still there)

So, it is D

Answer:

x² + 27x + 180

Step-by-step explanation:

(12 + x)(15 +x) = 12*15 + 12x + 15x + x² = x² + 27x + 180

Step-by-step explanation:

3/8 = 15/40= 75/200

2/5 = 16/40 = 80/200

-> 4 rational numbers between 75/200 and 80/200 are 76/200, 77/200, 78/200, 79/200

Answer:

Step-by-step explanation:

I hope it helps

Answer:

3 vases chipped.

Step-by-step explanation:

Let's use a ratio:

chipped : all

     2      :   12

     1       :    6

     3      :    18

We can expect 3 out of 18 vases to be chipped.

Answer:

1

Step-by-step explanation:

First, write the experimental probability as a fraction in simplest form.

P(chipped)

=

chipped

total

=

2

20

=

1

10

The experimental probability is

1

10

.

We can predict the outcome of the second set of trials by assuming that the ratio will be the same as in the first set of trials. Write a proportion by setting the two ratios equal to each other, then solve.

1

10

=

n

10

1

10

(1010)

=

n

10

(1010) Multiply both sides by (1010)

110

= 10n Simplify

10

= 10n Simplify

1

= n Divide both sides by 10

You would expect 1 of the next 10 vases to be chipped.

Answer: 1.16

Step-by-step explanation:

So we know [tex]\frac{3}{6} + \frac{3}{6}[/tex] will equal 1.

Now, let's take apart [tex]\frac{1}{6}[/tex] and divide it...

1 ÷ 6 = 0.16

1 + 0.16 = 1.16

[tex]\frac{3}{6} + \frac{3}{6} + \frac{1}{6} = 1.16[/tex]

I hope this helps!

Answer:

A. Figure A

Step-by-step explanation:

The protractor on the top left has an arrow halfway inbetween 50° and 60, making the angle 55°.

Therefore, the answer is Figure A.

Answer:

= 100 km

Step-by-step explanation:

Total length = 5/5

Covered length = 2/5

Remaining length = 5/5 - 2/5 = 3/5

If 3/5 = 60 km

What about 5/5 = ?

= 5/5 x 60 x 5/3 (reciprical)

= 60 x 5/3

= 300/3

= 100 km

Covered distance = 100 - 60 = 40 km