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1 year ago

-6y + 3(12y) = 20(y - 1) + 15 is it true?

Mathematics

1 answer:

xxMikexx [17]1 year ago

5 0

Answer:

y= - 1/2 (negative half) = -0.5

Step-by-step explanation:

−6y+3(12y)=20(y−1)+15

Multiply 3 and 12 to get 36.

−6y+36y=20(y−1)+15

Combine −6y and 36y to get 30y.

30y=20(y−1)+15

Use the distributive property to multiply 20 by y−1.

30y=20y−20+15

Add −20 and 15 to get −5.

30y=20y−5

Subtract 20y from both sides.

30y−20y=−5

Combine 30y and −20y to get 10y.

10y=−5

Divide both sides by 10

y= -5/10

Reduce the fraction -5/10 = -0.5 to lowest terms by extracting and cancelling out 5 .

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Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll

JulijaS [17]

Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

So, the possibility of getting a total of 7 = $\frac{6}{36}=\frac{1}{6}$

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = $\frac{2}{36}$ = $\frac{1}{18}$

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = $\frac{28}{36}$ = $\frac{7}{9}$

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

$\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11$

$\frac{11}{3}+\frac{11}{3}-\frac{77}{9}$

$\frac{22}{3}-\frac{77}{9}$

$\frac{66-77}{9}$

$-\frac{11}{9}$

$-1.22$

Therefore the expected payoff for this game is -$1.22.

4 0

2 years ago

Parallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the

bearhunter [10]

Answer:

The corresponding angles are:

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

Step-by-step explanation:

When two parallel lines are crossed by another line, the angles in matching corners are called corresponding angles and they are equal in measures

∵ Lines s and t are parallel

∴ s // t

∵ Line r intersects lines s and t

∴ Line r is the transversal

∵ Corresponding angles are formed

- Look to the attached figure

∴ ∠ 1 ≅ ∠ 5 ⇒ corresponding angles

∴ ∠ 2 ≅ ∠ 6 ⇒ corresponding angles

∴ ∠ 3 ≅ ∠ 7 ⇒ corresponding angles

∴ ∠ 4 ≅ ∠ 8 ⇒ corresponding angles

The corresponding angles are:

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

4 0

1 year ago

Read 2 more answers

Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr

siniylev [52]

Answer:

$(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

$29619.13

Step-by-step explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then

$f(t) = 14375 (1 + \frac{5.3}{100})^{t}$ ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write

g(t) = 570 × 12t = 6840t ........ (2)

Therefore, $(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

b. So, for t = 2 years,

$(f + g)(t) = 14375 (1 + \frac{5.3}{100})^{2} + 6840 \times 2$ = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)

7 0

1 year ago

A food company originally sells cereal in boxes with dimensions 25 cm by 14 cm by 10 cm. To make more profit, the company decrea

hjlf

Answer:

1.75 cm

Step-by-step explanation:

We are given that the dimensions of the box as 25 cm by 14 cm by 10 cm.

Now, to increase the profit, the dimensions of the box by 'x' cm.

Thus, the new dimensions are (25-x) cm by (14-x) cm by (10-x) cm.

Further, it is given that the volume of the new box is 2,208 $cm^{3}$

As, Volume of the box = Length × Breadth × Height

i.e. 2208 = (25-x) × (14-x) × (10-x)

i.e. $2208 = (25-x) \times (140-24x-x^{2})$

i.e. $2208=x^{3}-x^{2}-740x+3500$

i.e. $x^{3}-x^{2}-740x+1292=0$

On solving this cubic equations, we get that, the solutions are x = 27.6, x = 1.75 and x = 26.8.

Since, the dimensions 25 cm by 14 cm by 10 cm are reduced by x cm.

Thus, if x = 27.6 or x = 26.8, then (10-x) = -17.6 or -16.8, which cannot be possible. So, x = 1.75 cm.

Hence, the dimensions were decreased by 1.75 cm.

3 0

2 years ago

Can some one please please help me? solve for x 5 /7x + 1/7 =63 enter your answer in the box below.

Soloha48 [4]

This is confusing but I think yo umean
$\frac{x+5}{7x} + \frac{1}{7} =63$
times both sides by 7x
x+5+x=441x
2x+5=441x
minus 5 both sides
2x=436
divide both sides by 2
x=218

4 0

1 year ago