answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ZanzabumX [31]
2 years ago
12

The ideal width of a safety belt strap for a certain automobile is 5 cm. An actual width can vary by at most 0.35 cm. Write and

solve an absolute value inequality for the range of acceptable widths.
Mathematics
1 answer:
notsponge [240]2 years ago
8 0

Answer:

4.65\leq x\leq 5.35

Step-by-step explanation:

Let the actual width of belt be x

we are given that the ideal width of safety belt strap is 5 cm

So, Difference between actual and ideal = (x-5)cm

We are also given that An actual width can vary by at most 0.35 cm.

So, The difference between actual and ideal width should be less than or equal to 0.35 cm

So, |x-5|\leq 0.35

We know

x-5\leq 0.35 and x-5\geq -0.35

x\leq 0.35+5 and x\geq -0.35+5

x\leq 5.35 and x\geq 4.65

So, 4.65\leq x\leq 5.35

Hence the range of acceptable widths is 4.65\leq x\leq 5.35

You might be interested in
The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.
vagabundo [1.1K]

Answer:

the ablity to choose one is the right now

Step-by-step explanation:

3 0
1 year ago
In a certain region, the number of highway accidents increased by 20% over the four years period. How many accidents were there
erma4kov [3.2K]

Equation:

a  =    5120  

r     =     1  +    .2     =     1 . 2

f (n )   =     5120 *  1 . 2^n - 1

N    =          4      years


f ( 4 )  5120 *  1 . 2^4 - 1

5120 *  1 . 2^3

We want to know, The number of Highway Accidents in Four Years.

Answer:    8,847 Highway Accidents total:






Hope that helps!!!!!!!!!!!                                                            : )


7 0
1 year ago
Barbara drives between Miami, Florida, and West Palm Beach, Florida. She drives 50 mi in clear weather and then encounters a thu
NeX [460]

Distance traveled in clear weather = 50 miles

Distance traveled in thunderstorm = 15 miles

Let speed in clear weather = x

⇒ Speed in thunderstorm = x-20

Total time taken for trip = 1.5 hours

We need to determine average speed in clear weather (i.e. x) and average speed in the thunderstorm (i.e. x-20 ).

Total time taken for trip = Time taken in clear weather + Time taken in thunderstorm

⇒ Total time taken for trip = \frac{Distance covered in clear weather}{Speed in clear weather} + \frac{Distance covered in thunderstorm}{Speed in thunderstorm}

⇒ 1.5 = \frac{50}{x} + \frac{15}{x-20}

⇒ 1.5 = \frac{50(x-20)+15(x)}{(x)(x-20)}

⇒ 15*x*(x-20) = 10*[50*(x-20)+15*x]

⇒ 15x² - 300x = 500x - 10,000 + 150x

⇒ 15x² - 300x = 650x - 10,000

⇒ 15x² - 950x + 10,000 = 0

⇒ 3x² - 190x + 2,000 = 0

The above equation is in the format of ax² + bx + c = 0

To determine the roots of the equation, we will first determine 'D'

D = b² - 4ac

⇒ D = (-190)² - 4*3*2,000

⇒ D = 36,100 - 24,000

⇒ D = 12,100

Now using the D to determine the two roots of the equation

Roots are: x₁ = \frac{-b+\sqrt{D}}{2a} ; x₂ = \frac{-b-\sqrt{D}}{2a}

⇒ x₁ = \frac{-(-190)+\sqrt{12,100}}{2*3} and x₂ = \frac{-(-190)-\sqrt{12,100}}{2*3}

⇒ x₁ = \frac{190+110}{6} and x₂ = \frac{190-110}{6}

⇒ x₁ = \frac{300}{6} and x₂ = \frac{80}{6}

⇒ x₁ = 50 and x₂ = 13.33

So speed in clear weather can be 50 mph or 13.33 mph. However, we know that in thunderstorm was 20 mph less than speed in clear weather.

If speed in clear weather is 13.33 mph then speed in thunderstorm would be negative, which is not possible since speed can't be negative.

Hence, the speed in clear weather would be 50 mph, and in thunderstorm would be 20 mph less, i.e. 30 mph.

7 0
2 years ago
Jose wants to start a restaurant and is writing a business proposal. His rent is $1,000 per month. The monthly operating costs a
Harman [31]

Answer:

Revenue =  5( 1000 + w+ k)

Step-by-step explanation:

Lets calculate expenses first

rent = $1000

wages = w

overhead cost = k

Total cost = rent + wage+ overhead

Total cost = 1000 + w+ k

Given Jose wants his monthly sales revenue, x, to be 4 times greater than the operating costs

Let revenue be R

Thus, putting the statement mathematically

revenue - total cost = 4 * operating cost

R - ( 1000 + w+ k) = 4( 1000 + w+ k)

R =  4( 1000 + w+ k) + ( 1000 + w+ k)

R =  5( 1000 + w+ k)

Thus, revenue should be  5( 1000 + w+ k).

4 0
2 years ago
Which statement correctly explains how Andre could find the solution to the following system of linear equations using eliminati
grin007 [14]

umm ,this is too long could you maybe putt it in smaller form so I can answer

7 0
1 year ago
Other questions:
  • Tom has a water tank that holds 5 gallons of water.Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces an
    11·1 answer
  • The price of a 200000 home listed by remax was reduced by 1/20. What is the new price?
    9·1 answer
  • a rectangle pyramid fits exactly on top of a rectangular prism. the prism has a length of 18 cm, a width of 6 cm, and a height o
    14·1 answer
  • As an advertising campaign, a chocolate factory places golden tickets in some of its candy bars, with the promise that a golden
    11·1 answer
  • Find the sum and express it in scientific notation. 0.00348 + (6.2 x 10-2)
    5·2 answers
  • 119.31 is 82% of what number
    9·2 answers
  • A shape is covered by 40 unit squares. What is the area of the shape
    5·1 answer
  • a bike shop rents bikes with Heights ranging from 18 in to 26 inches. The shop says that the height of the bike should be about
    8·1 answer
  • (a) Use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7 show your work
    9·1 answer
  • Which of the following terms correctly describe the figure given below?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!