3 decagrams = centgrams

In contract negotiations between a local government agency and its workers,

Liono4ka [1.6K]

Answer:

a. 0.4

b. Not independent.

Step-by-step explanation:

a. We use the probability table attached below for our calculations.

-the probability that an agreement is reached on both sides is obtained from the table:

$P(Agreement)=\frac{400}{1000}\\\\\\=0.4$

b. To determine whether the two events are independent, we compare the probabilities $P(s)\times P(i)$ and $P(s \ and \ i)$ where i denotes insurance and s denotes salaries:

$P(s)\times P(i)=0.5\times 0.7\\\\=0.35\\\\\\P(s \ and \ i)=0.4$

Two events are considered to be independent, if and only if:

$P(A).P(B)=P(A\ and \ B)\\\\=>P(s).P(i)\neq P(s\ and\ i)$

Hence, the events are not independent.

8 0

3 years ago

The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its areais 108cm

valentinak56 [21]

L=2w-6

area = L x W

108=(2w-6)w

108 = 2w^2-6w

2w^2-6w-108 = 0

2(w^2-3w-54)=0

2(w-9)(w+6) = 0

w=9

L= 2(9)-6 = 12

12*9 = 108

3 0

4 years ago

Solve with explanation (3)

grin007 [14]

Answer:

a = 66⁰

b = 33⁰

Step-by-step explanation:

Given;

∠ABC = 114⁰

To calculate a⁰;

a + 114 = 180⁰ (opposite angles of a quadrilateral are supplementary)

a = 180 - 114

a = 66⁰

To calculate b⁰;

Line AB = Line BC, thus, ∠BAC = ∠BCA

∠BAC = b, then ∠BCA = b

b + b + 114 = 180 (sum of angles in a triangle)

2b = 180 - 114

2b = 66

b = 66/2

b = 33⁰

4 0

3 years ago

A supermarket increases the prices of some grocery items by 10%.

Juli2301 [7.4K]

Answer:

(a) $1.98

(b) $6.30

Step-by-step explanation:

(a)

The new value =

1.80 + The value of the percentage increase =

1.80 + (10% × 1.80) =

1.80 + 10% × 1.80 =

(1 + 10%) × 1.80 =

(100% + 10%) × 1.80 =

110% × 1.80 =

110 ÷ 100 × 1.80 =

110 × 1.80 ÷ 100 =

198 ÷ 100 =

1.98

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 1.80 =

1.98 - 1.80 =

0.18

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

10% × 1.80 =

10 ÷ 100 × 1.80 =

10 × 1.80 ÷ 100 =

18 ÷ 100 =

0.18

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

1.80 increased by 10% = 1.98

The actual change:

1.98 - 1.80 = 0.18

(b)

Calculate the New value
The new value =

42.0 + The value of the percentage increase =

4.20 + (50% × 4.20) =

4.20 + 50% × 4.20 =

(1 + 50%) × 4.20 =

(100% + 50%) × 4.20 =

150% × 4.20 =

150 ÷ 100 × 4.20 =

150 × 4.20 ÷ 100 =

63,000 ÷ 100 =

630

(but its as a dollar so its 6.30)

Calculate the actual change (the absolute difference) between the two values

The actual change =

The new value - 4.20 =

6.30 - 4.20 =

2.10

Proof of calculation.

Calculate the percentage increased value...

... and see if we get as a result...

... the actual change (the absolute difference).

Calculate the percentage increased value:

The value of the percentage increase =

50% × 4.20 =

50 ÷ 100 × 4.20 =

50 × 4.20 ÷ 100 =

21,000 ÷ 100 =

210

(but its as a dollar so its 2.10)

So we have proven that the calculations are correct.

For positive numbers

The actual change =

The value of the percentage increase

The answer:

4.20 increased by 50% = 6.30

The actual change:

6.30 - 4.20 = 2.10

6 0

2 years ago

Maranda and rory are multiplying 4 1/3 by different fractions the table shows there work

topjm [15]

Fractions are numbers represented by the quotients of two integers

Rory's product is less than Maranda's because 13/9 is less than 13/3

<h3>How to determine why Rory has a lesser product</h3>

The expressions are given as:

Maranda: 4 1/3 * 4 1/3 * 1/3

Rory: 4 1/3 * 1 4/9

For Maranda, we have:

$M = 4\frac 13 * 4\frac 13$

Rewrite the fraction

$M = 4\frac 13 * \frac{13}3$

For Rory, we have:

$R = 4\frac 13 * 1\frac 49$

Rewrite the fraction

$R = 4\frac 13 * \frac {13}9$

When Maranda and Rory's expressions are compared, we have:

13/9 is less than 13/3

Hence, Rory's product is less than Maranda's because 13/9 is less than 13/3