Sarah has an unorganized sock drawer. There are 24 loose socks in her drawer. If there are 10 black socks, 3 green socks , 8 white socks, 2 blue socks and 1 red sock sock, what is the probability of pulling out 2 socks in a row that are both black?

Answer:

a) 7000 x 1.06^t

b) 11156

Step-by-step explanation:

a) This is quite a case of compound interest where you begin with a value (7000) and every year (t) it goes up by a set amount (6%). To mathematically convert this you put 7000 at the start and you convert the 6% into 1.06 since 0.06 is the amount it increases by and the 1 adds the 0.06 to the previous value. The 't' makes it so each year the value increases so 1.06^t where t is 2 would mean 1.06 x 1.06 which is basically what happens every year.

b) Since it is 8 years later (2008 - 2000), you substitute t for 8 to find the range which is 7000 x 1.06^8 = 11156.9365 which rounds down to 11156 as that's what you do when talking with whole numbers as a new fox isn't quite there yet.

Answer:

20 m/hr

Step-by-step explanation:

distance / rate = time

24 miles / 9 miles/hr  = 2 2/3 hr

(24 + 20 miles) / 12 miles/hr = 3 2/3 hr

3 2/3  -  2 2/3 = 1 hour to ride the next 20 miles   means  20 m/hr

Answer:

  c.  3a^2b^11/2

Step-by-step explanation:

The applicable rule of exponents is ...

  (a^b)/(a^c) = a^(b-c)

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 [tex]\dfrac{-18a^{-2}b^5}{-12a^{-4}b^{-6}}=\dfrac{-18}{-12}a^{-2-(-4)}b^{5-(-6)}=\boxed{\dfrac{3a^2b^{11}}{2}}[/tex]

Answer:

Step-by-step explanation:

For mixture problems, it is convenient to let the variable represent the quantity of the high-value contributor.

Here, we can let x represent the number of quarters. Then the number of nickels is (52-x), and the total value of the coins is ...

  0.25x +0.05(52 -x) = 6.40

  0.20x +2.60 = 6.40 . . . . . . . . simplify

  0.20x = 3.80 . . . . . . . . . . . subtract 2.60

  x = 3.80/0.20 = 19 . . . . divide by the coefficient of x

The number of quarters is 19. The number of nickels is 52-19 = 33.

Answer:

Step-by-step explanation:

Its a linear function it goes throw the y-x Axis and is in a striaght line.

Answer:

y = [tex]\frac{5}{2}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = [tex]\frac{5}{2}[/tex] x + 5 ← equation of line

Answer:

____________

3748 x 4 = (3000+700+40+8) x 4

(3000 x 4) + (700 x 4) + (40 x 4) + (8 x 4)

12000 + 2800 + 160 + 32

= 14992

Step-by-step explanation with answer:

3748x4 = (3000+700+40+8) x 4

= 3000x4 + 700x4 + 40x4 +8x4

=12000+2800+160+32

=14992

Answer:

Step-by-step explanation:

you can think of it backwards,

-50 = 3x - 8y

x = 6y

X x 3 = 3x

6y x 3 = 18y

3x = 18y

18y - 8y = -50

10y = -50

y = -5

6 x -5 = -30

x = -30

The length of DE in centimetres is 12 .

The following proportion can be established as follow:

AB / DE = BC  / EF = AC / DF

Therefore,

let's find DE as follows;

AB  / DE = BC / EF

4 / DE = 3 / 9

cross multiply

9 × 4 = 3DE

divide both sides by 3

DE = 36 / 3

DE = 12 cm

learn more: https://brainly.com/question/22808925?referrer=searchResults

Answer: t=2

Step-by-step explanation:

add the t's and calculate

Step-by-step explanation:

If you were to round 398 to the nearest hundred, you would get 400. that's only 2 off of 398. when you add 400 + 257 that would equal 857 because 4 + 2= 6 and then the other two digits on 400 are zeros so 5 and 7 stay the same. with 857, you must now subtract 2 because you added 2 earlier. 857 - 2 = 855.

Answer:

Step 1. Rewrite in the form of y=mx+b

Step 2. Find and plot 2 points (x and y-intercepts)

Step 3. Connect dots

y=mx+b

y - 5x = -2

y = 5x - 2

Find 2 points

y-intecept = (0, -2)

x-intercept = ?

0 = 5x - 2

2 = 5x

x = 2/5

x-intercept = (2/5, 0)

Answer:

Step-by-step explanation:

Point P is marked in the expanded view on the 7th mark of the 10 marks between 5×10^-3 and 6×10^-3. That means it is representing ...

  (5 +7/10)×10^-3 = 5.7×10^-3 . . . . scientific notation

__

The -3 exponent of 10 means the multiplier of the value is 1 in the 3rd place to the right of the decimal point: 0.001. So, the standard form of the number is ...

  5.7×0.001 = 0.0057 . . . . . standard form

Answer:

(-2,1)

Step-by-step explanation:

The solution of a system of equations is wherever the two lines intersect. So, this is quite easy. We can see they intersect at (-2,1). We can tell it is (-2,1) becuase it is two units left and one units up from the origin.

That is the solution.

(-2,1)

Answer:

The answer is (-2,1). Hope this helps :)

Step-by-step explanation:

Answer:

The answers are:x = ±7/4x = ±3/2x = ±11/8

yww:)

Answer:

Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Step-by-step explanation:

Step 1:  Add 144 to both sides

[tex]64x^2 - 144 = -23[/tex]

[tex]64x^2 - 144 + 144 = -23 + 144[/tex]

[tex]64x^2 = 121[/tex]

Step 2:  Divide both sides by 64

[tex]\frac{64x^2}{64} = \frac{121}{64}[/tex]

[tex]x^2 = 1.890625[/tex]

Step 3:  Square root both sides

[tex]\sqrt{x^2} = \sqrt{1.890625}[/tex]

[tex]x =[/tex] ± [tex]1.375[/tex]

[tex]x =[/tex] ± [tex]11/8[/tex]

Answer: Option A, [tex]x =[/tex] ± [tex]11/8[/tex]

Answer:

B. 2.365

Step-by-step explanation:

Divide total distance by total people in order to get distance each person traveled.

28.375 miles / 12 = 2.36458333.......

If you round taht to nearest thousandth of a mile, the answer is: 2.365

Answer:

D

Step-by-step explanation:

since Δ QRS is isosceles then the base angles are congruent , that is

∠ RQS = ∠ RSQ = (180 - ∠ QRS ) ÷ 2 = (180 - 32)° ÷ 2 = 148° ÷ 2 = 74°

the sum of the 3 angles in Δ SPQ = 180° , then

∠ PQS = 180° - ∠ SPQ - ∠ PSQ = 180° - 36° - 90° = 54°

Then

∠ PQR = ∠ RQS + ∠ PQS = 74° + 54° = 128°

Step-by-step explanation:

problem 10 is function

but problem 9 is not

Answer:

Step-by-step explanation:

You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.

__

The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).

The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).

The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).

__

Additional comment

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

Answer:

x=75

Step-by-step explanation:

99/66=1.5

30x1.5=45

30+45 =75

[tex]\text{Given that,} ~f(x) = 2x-4~~ \text{and}~~ g(x) = 2x+8\\\\ g(f(3))\\\\=g(2\cdot 3 -4)\\\\=g(2)\\\\=2(2)+8\\\\=4+8\\\\=12[/tex]

Answer:60 pages

Step-by-step explanation:

first take away the zero then devide by 2 then add the zero the the number that your left with.

Answer:

24

Step-by-step explanation:

Lets start by working out 80% of 30

80% x 30=24

so the student answered 24 questions correctly

Answer:

3:2

Step-by-step explanation:

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60

using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:

0.9/0.6 = 1.5

1.5 x 2 = 3

this gives 3/2 = 1.5

so we know that the ratio is 3:2 and this is the smallest whole number that it could be

Answer:

Linear expression

Step-by-step explanation:

The greateest exponent on a variable is 1 on x, so it is a linear expression,

Answer: Linear expression

Answer:

m = 3a

Step-by-step explanation:

The number of pieces of candy eaten by Alex is not important.

The only thing that matters is that Marisol eats 3 times as many pieces of candy.

If a is the number eaten by Andy, then 3 times a equals the number of pieces of candy eaten by Marisol, or m=3a

281.2 units³

volume of Prism: Base Area x Height

Here given:

Base Area: 38 units²

Height: 7.4 units

Solve for volume:

38 x 7.4

281.2 units³

Volume:-

Answer:

$31,500

Step-by-step explanation:

10% = 0.1

100% = 1

1 - 0.1 = 0.9

35,000 x 0.9 = 31,500

Answer: A. Complex

Step-by-step explanation: hope this helps!

Answer:

Step-by-step explanation:

In this question we have provided an equation that is 9 ( 3x - 16 ) + 15 = 6x - 24 . And we are asked to write the steps to solve the equation with explanation and to find the value of X .

Solution : -

[tex] \longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24[/tex]

Step 1 : Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :

[tex] \longmapsto \quad \:27x - \bold{144 }+ \bold{15 }= 6x - 24[/tex]

Step 2 : Solving like terms on left side that are -144 and 15 :

[tex] \longmapsto \quad \:27x -129 = 6x - 24[/tex]

Step 3 : Adding 129 on both sides :

[tex] \longmapsto \quad \:27x - \cancel{129} - \cancel{129} = 6x \bold{ - 24 } + \bold{129}[/tex]

Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :

[tex] \longmapsto \quad \:27x = 6x + 105[/tex]

Step 4 : Subtracting with 6x on both sides :

[tex] \longmapsto \quad \: \bold{27x} - \bold{6x} = \cancel{6x} +105 - \cancel{ 6x}[/tex]

On calculating further, We get :

[tex] \longmapsto \quad \:21x = 105[/tex]

Step 5 : Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :

[tex] \longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}} = \dfrac{105}{ 21} [/tex]

Now , by cancelling 21 with 21 on left side , We get :

[tex] \longmapsto \quad \:x = \cancel{\dfrac{105}{21}} [/tex]

Step 6 : Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :

[tex] \longmapsto \quad \: \purple{\underline{\boxed{\frak{ x = 5 }}}}[/tex]

Verifying : -

Now we are verifying our answer by substituting value of x in the given equation . So ,

Therefore, our value for x is correct that means it'll makes the equation true .