What’s a situation that can represent -4?

Solve the following inequality. |3n-2|-2<1

disa [49]

Answer: $\frac{-1}{3}$ < n < $\frac{5}{3}$

Step-by-step explanation:

| 3n - 2 | - 2 < 1

+2 +2

| 3n - 2 | < 3

3n - 2 < 3 and 3n - 2 > -3

+2 +2 +2 +2

3n < 5 and 3n > -1

n < $\frac{5}{3}$ and n > $\frac{-1}{3}$

$\frac{-1}{3}$ < n < $\frac{5}{3}$

Interval Notation: $(\frac{-1}{3},$ $\frac{5}{3})$

Graph: $\frac{-1}{3}$ o--------------------o $\frac{5}{3}$

7 0

3 years ago

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Two cars start out together from the same place. they travel in opposite directions, with one of them traveling 5 miles per hou

Mashutka [201]

Annotation
General formula for distance-time-velocity relationship is as following
d = v × t
The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁.
The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.

One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car.
v₁ = v₂ + 5 (first equation)

The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below.
d₁ + d₂ = 262 (second equation)

Plug the d-v-t relationship to the second equation
d₁ + d₂ = 262
v₁ × t + v₂ × t = 262
v₁ × 2 + v₂ × 2 = 262
2v₁ + 2v₂ = 262

Plug the v₁ as (v₂+5) from the first equation
2v₁ + 2v₂ = 262
2(v₂ + 5) + 2v₂ = 262
2v₂ + 10 + 2v₂ = 262
4v₂ + 10 = 262
4v₂ = 252
v₂ = 252/4
v₂ = 63
The second car is 63 mph fast.

Find the velocity of the first car, use the first equation
v₁ = v₂ + 5
v₁ = 63 + 5
v₁ = 68
The first car is 68 mph fast.

Answer
$\boxed{\boxed{ v_{1}=68mph} }$
$\boxed{\boxed{ v_{2}=63mph} }$

7 0

3 years ago

The Scott family is trying to save as much money as possible. One way to cut back on the money they spend is by finding deals wh

avanturin [10]

Answer:

Unit price of strawberries at Grocery Mart is $ 1.495 or 150 pennies

Unit price of strawberries at Baldwin Hills Market is $ 1.33 or 133 pennies.

Step-by-step explanation:

1 dollar = 100 pennies

Given:

Cost of 2 pounds of strawberries at Grocery Mart = $ 2.99

Cost of 3 pounds of strawberries at Baldwin Hills Market = $3.99

∵ Cost of 2 pounds of strawberries at Grocery Mart = $ 2.99

∴ Cost of 1 pound of strawberries at Grocery Mart = $\frac{2.99}{2}=\$1.495=1.495\times 100\approx 150\textrm{ pennies}$

∵ Cost of 3 pounds of strawberries at Baldwin Hills Market = $3.99

Cost of 1 pound of strawberries at Baldwin Hills Market = $\frac{3.99}{3}=\$1.33= 1.33\times 100 = 133\textrm{ pennies}$

Therefore, the unit price of strawberries at each grocery store is the cost of 1 pound of strawberries. So, unit rate at Grocery Mart is 150 pennies and at Baldwin Hills Market is 133 pennies.

7 0

2 years ago

The difference of the range and the interquartile range of the data set represented by the box plot is .

Ivahew [28]

When presented with a box plot, it is better to identify the 5 numbers that are important in the box plot.

5 number summary of the boxplot.
1) minimum number - 16
2) 1st quartile - 21
3) 2nd quartile or median - 26
4) 3rd quartile - 29
5) maximum number - 34

Range is the difference of the maximum value from the minimum value of the data set.
Interquartile range is the difference of the 3rd quartile from the 1st quartile.

Range: 34 - 16 = 18
IQR: 29 - 21 = 7

6 0

3 years ago

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A rectangular room is 12.5 feet wide and 14 feet long. How many linear feet of baseboards are needed to trim the room?

QveST [7]

If you do width times length you will get 30. Good luck

8 0

3 years ago