Three red balls, 5 green balls and a number of blue balls are put together in a sac. One ball is picked at random from the sac. If the probability of picking a red ball is 1|6, find the a) The number of blue balls in sac. B) the probability of picking a green ball. ​

Answer:

Step-by-step explanation:

The easiest way to do this is to complete the square on the quadratic. This allows us to see what the vertex is and answer the question without having to plug in a ton of numbers to see what the max y value is. Completing the square will naturally put the equation into vertex form:

[tex]y=-a(x-h)^2+k[/tex] where h will be the time it takes to get to a height of k.

Begin by setting the quadratic equal to 0 and then moving over the constant, like this:

[tex]-4.9t^2+19.6t=-58.8[/tex] and the rule is that the leading coefficient has to be a 1. Ours is a -4.9 so we have to factor it out:

[tex]-4.9(t^2-4t)=-58.8[/tex] Now take half the linear term, square it, and add it to both sides. Our linear term is a -4, from -4t. Half of -4 is -2, and -2 squared is 4, so we add a 4 to both sides. BUT on the left we have that -4.9 out front there as a multiplier, so we ACTUALLY added on to the left was -4.9(4) which is -19.6:

[tex]-4.9(t^2-4t+4)=-58.8-19.6[/tex] and now we have to clean this up. The right side is easy, that is -78.4. The left side...not so much.

The reason we complete the square is to create a perfect square binomial, which is the [tex](x-h)^2[/tex] part from above. Completing the square does this naturally, now it's just up to us to write the binomial created during the process:

[tex]-4.9(t-2)^2=-78.4[/tex] Now, move the constant back over and set the equation back equal to y:

[tex]-4.9(t-2)^2+78.4=s(t)[/tex] and we see that the vertex is (2, 78.4). That means that 2 seconds after launch, the object reached its max height of 78.4 meters, the third choice down.

Answer:

Step-by-step explanation:

[tex]Mean=\frac{all.ages.added.together.of.all.kids}{total.number.of.kids}[/tex] Hopefully, that makes sense! To get the numerator of that problem, we take the number of kids and multiply it by the corresponding age and add them all together. To get the denominator, we add the total number of kids together. That will look like this mathematically, setting the mean equal to 14.44, as stated:

[tex]14.44=\frac{13(15)+14(42)+15X+16(10)+17(3)}{15+42+X+10+3}[/tex] and simplify that a bit to

[tex]14.44=\frac{195+588+15X+160+51}{70+X}[/tex] and a bit more to

[tex]14.44=\frac{994+15X}{70+X}[/tex] and cross multiply

14.44(70 + X) = 994 + 15X and

1010.8 + 14.44X = 994 + 15X and

16.8 = .56X so

X = 30

30 kids are 15 years old for the mean age to be 14.44

d.30

Answer:

Solution given:

x. [tex] \:\:\:[/tex] f. [tex] \:\:\:[/tex] fx

13. [tex] \:\:\:[/tex] 15. [tex] \:\:\:[/tex] 195

14.[tex] \:\:\:[/tex] 42 [tex] \:\:\:[/tex] 588

15. [tex] \:\:\:[/tex] x. [tex] \:\:\:[/tex] 15x

16. [tex] \:\:\:[/tex] 10. [tex] \:\:\:[/tex] 160

17. [tex] \:\:\:[/tex] 3. [tex] \:\:\:[/tex] 51

. n=70+x. [tex]\sum[/tex]=994+15x

we have

mean=sum/n

14.44=[tex]\bold{\frac{\sum}{n}}[/tex]

14.44=[tex]\bold{\frac{994+15x}{70+x}}[/tex]

doing crisscrossed multiplication

(70+x)*14.44=994+15x

1010.8+14.44x=994+15x

15x-14.44x=1010.8-994

0.56x=16.8

x=16.8/0.56

x=30

Answer:

30 degrees.

Step-by-step explanation:

Let the acute angle be x.

Then as the 2 acute angles in a right triangle sum to 90 degrees,

x = 90 - 60

= 30.

We used the information we know to give us this equation.

90°+60°+x=180°

We add 90° and 60° to give 150°

150°+x=180°

Answer:

[tex]6(3f-15)=90[/tex]

[tex]3f=90/6+15=30[/tex]

[tex]f=10[/tex]

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

Hope it helps...

Have a great day!!

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{6(3f - 15) = 90^\circ}\\\\\huge\text{DISTRIBUTE}\\\\\mathsf{6(3f) + 6(-15) = 90^\circ}\\\\\mathsf{18f - 90 = 90^\circ}[/tex]

[tex]\text{NEW EQUATION: }\mathsf{18f - 90 = 90}[/tex]

[tex]\huge\text{ADD 90 to BOTH SIDES}[/tex]

[tex]\mathsf{18f - 90 + 90 = 90 + 90}[/tex]

[tex]\textsf{CANCEL out: -90 + 90 because that gives the number of 0}[/tex]

[tex]\textsf{KEEP: 90 + 90 because it helps solve for the f-value}[/tex]

[tex]\mathsf{90 + 90 = \bf 180}[/tex]

[tex]\huge\text{NEW EQUATION:\textsf{ 18f = 180}}[/tex]

[tex]\huge\text{DIVIDE 18 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{18f}{18}=\dfrac{180}{18}}[/tex]

[tex]\mathsf{CANCEL \ out: \dfrac{18}{18}\ because \ that \ gives \ the \ number \ of\ 1}[/tex]

[tex]\mathsf{KEEP: \dfrac{180}{18} \ because \ that \ gives \ the\ f-value \ result}[/tex]

[tex]\mathsf{f = \dfrac{180}{18}}[/tex]

[tex]\huge\text{SOLVE ABOVE \& YOU HAVE THE RESULT}[/tex][tex]\huge\text{OF THE F-VALUE}[/tex]

[tex]\mathsf{\dfrac{180}{18}}[/tex]

[tex]\mathsf{= \bf 18}[/tex]

[tex]\boxed{\boxed{\huge\textsf{Therefore, your ANSWER is: \bf f = 10}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

A

Step-by-step explanation:

A compressed by a factor of 1/4 in the y or vertical direction

Total gasoline = 10 gallons

Gasoline left after 100 miles = 5 gallons

Gasoline used in 100 miles

= Total gasoline - Gasoline left after 100 miles

= 10 gallons - 5 gallons

= 5 gallons

Gasoline used in 1 mile

= Gasoline used in 100 miles/100

= 5 gallons/100

= 0.05 gallons

Answer:

m<EFG = 72°

m<GFH = 108°

Step-by-step explanation:

m<EFG = 2n + 16

m<GFH = 3n + 24

Linear pairs are supplementary, therefore,

m<EFG + m<GFH = 180°

Substitute

2n + 16 + 3n + 24 = 180

Add like terms

5n + 40 = 180

5n + 40 - 40 = 180 - 40 (subtraction property of equality)

5n = 140

5n/5 = 140/5 (division property of equality)

n = 28

✔️m<EFG = 2n + 16

Plug in the value of n

m<EFG = 2(28) + 16 = 72°

✔️m<GFH = 3n + 24

Plug in the value of n

m<GFH = 3(28) + 24 = 108°

Answer:

e s r

Step-by-step explanation:

The graph above or below should answer the question.

Answer: He bought 6 pounds of coffee.

Step-by-step explanation:

Money he have = 70

money he used to buy = 70.00 - 23.62 = 46.38

so

7.73 dollar = 1 pound

1 dollar = 1/(7.73) = 100/773 pound

46.38 dollar = (100/773) * 46.38 = 6 pound

Answer:

DE ║ BC

BC = 2(DE)

Step-by-step explanation:

From the picture attached,

AD = DB [Given]

AE = EC [Given]

Therefore, points D and E will be the midpoints of the sides AB and AC.

By midsegment theorem,

Segment joining midpoints of the two sides of a triangle is parallel and measures the half of the third side of the triangle.

DE ║ BC

DE = [tex]\frac{1}{2}(BC)[/tex]

BC = 2(DE)

Answer:

DF

Step-by-step explanation:

The side opposite the largest angle has the longest measurement

<E has  the largest measurement so DF is the longest side

Answer:

what is that? I can't understand it.

Lets do

[tex] \\ \sf \longmapsto \: 3(x + 5) - 7 = 2(x +2) \\ \\ \sf \longmapsto \: 3x + 15 - 7 = 2x + 4 \\ \\ \sf \longmapsto \: 3x + 8 = 2x + 4 \\ \\ \sf \longmapsto \: 3x - 2x = 4 - 8 \\ \\ \sf \longmapsto \: x = - 4[/tex]

Answer:

tan x = c/b

cos x = b/a

sin x = c/a

Step-by-step explanation:

an easy way to memorize it would be SOH CAH TOA

SOH = sin, opposite, hypotunese

-- you find the angle and you divide it's opposite and hypotunese when it asks for sin

CAH = cos, adjacent, hypotunese

-- you find the angle's adjacent side and hypotunese, then divide

TOA = tan, opposite, adjacent

-- you find the angle's opposite side and divide it by the adjacent side

Answer:

The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b.

Step-by-step explanation:

Answer:

The line of reflection in [tex]y=mx+b[/tex] form is [tex]y=\frac{1}{3} x-2[/tex]

Step-by-step explanation:

Answer:

c = 21

Step-by-step explanation:

**I assume that side WX in my diagram (attached as an image below) is the value of C that we're looking for. ALSO, the sizes and lengths of the parallelograms are NOT to scale.**

If two parallelograms are similar, that means the lengths of the corresponding sides have EQUAL ratios.

PL corresponds with WZ. To get from 15 to 45, you would multiply 15 by 3, so the ratio of the legnths of the corresponding sides between these two parallelograms is 1:3.

With that in mind, we can apply this ratio to find WX.

We know that AP has a length of 7, so we will multiply that by 3, getting a value of 21, and 7:21 ratio is the same as 1:3.

c = 21

Hope this helps (●'◡'●)

Answer:

i guess Bis the answer bcuz, A sample space is a collection or a set of possible outcomes of a random experiment

Statement B is correct, which best defines the sample space that is " a sample space is the set of all possible outcomes for the a given situation".

A sample space is a collection or a set of possible outcomes of a random experiment. It is represented by using the symbol "s".

For example,

When we flip or toss a coin, two outcomes are possible such as head and tail. Therefore the sample space for this experiment is given as

Sample space, S = {H, T} = {Head, Tail}

According to the given option

Option B is correct. That is a sample space is the set of all possible outcomes for a given situation.

Learn more about sample space here:

https://brainly.com/question/17144524

#SPJ2

Answer:

72√2

Step-by-step explanation:

3√2 × 2√8 × √3 × √6

The above can be simplified as follow:

3√2 × 2√8 × √3 × √6

Recall

a√c × b√d = (a×b)√(c×d)

3√2 × 2√8 × √3 × √6 = (3×2)√(2×8×3×6)

= 6√288

Recall

288 = 144 × 2

6√288 = 6√(144 × 2)

Recall

√(a×b) = √a × √b

6√(144 × 2) = 6 × √144 × √2

= 6 × 12 × √2

= 72√2

Therefore,

3√2 × 2√8 × √3 × √6 = 72√2

Answer:

1/4

Step-by-step explanation:

a^2

Let a= 1/2

(1/2)^2

(1/4)

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{a^2}\\\\\mathsf{= \ (\dfrac{1}{2})^2}\\\\\mathsf{= \ \dfrac{1}{2}\times\dfrac{1}{2}}\\\\\mathsf{= \ \dfrac{1\times1}{2\times2}}\\\\\mathsf{= \ \bf \dfrac{1}{4}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, the ANSWER is: }\boxed{\mathsf{\bf \dfrac{1}{4}}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

78

Step-by-step explanation:

For every 1 bout Lina makes, Harry makes two boats.

1 + 2 is 3.

117 divided by 3 = 39, which is how many boats Lina made.

39 x 2 = 78, which is how many boats Harry made.

To check our answer, 39 + 78 = 117, which is how many boats they made altogether, so the answer is correct.

Answer:

78

Step-by-step explanation:

My knowledge!!

Hope it helps!

Answer:

option A is write answer

I hope you help

Answer:

none of these

Step-by-step explanation:

it's 96000 so none

Answer:

[tex]\frac{-1}{30} a - \frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

x1 y1 x2 y2

-2 -2 0 3

ΔY 5

ΔX 2

slope= 2 1/2

B= 3

Y =2.5X +3

Answer:

a =2 5

b =50

Step-by-step explanation:

We have

(a + bx) / (a - bx) = (b + cx) / (b - cx)

==>   (a + bx) (b - cx) = (a - bx) (b + cx)

==>   ab + (b ² - ac) x - bcx ² = ab + (ac - b ²) x - bcx ²

==>   (b ² - ac) x = (ac - b ²) x

==>   b ² - ac = ac - b ²

==>   2b ² = 2ac

==>   b ² = ac … … … [1]

Similarly, you would find

(a + bx) / (a - bx) = (c + dx) / (c - dx)

==>   ad = bc … … … [2]

and

(b + cx) / (b - cx) = (c + dx) / (c - dx)

==>   c ² = bd … … … [3]

Now:

c ² = bd   ==>   b = c ² / d

b ² = ac   ==>   c = b ² / a

ad = bc   ==>   d = bc / a

and we find

d / c = (bc / a) / (b ² / a) = c / b

and

c / b = (b ² / a) / (c ² / d) = (b ² d) / (a c ²) = b / a

which is to say, the ratio between d and c is equal to the ratio between c and b, and also equal to the ratio between b and a. Therefore (a, b, c, d) are in a geometric progression.

Answer:

10%

Step-by-step explanation:

Answer:

given that the only one that actually adds up to 65%

is B....

B. 25% + 10% + 10% + 10% + 10%

Step-by-step explanation: