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bixtya [17]
3 years ago
10

The local train heading for Westford at 60km/h and the express train heading for Eastford at 80 km/h pass each other at Centervi

lle while heading in opposite directions along a straight roadbed. Westford and Eastford are 195 km apart, and if the local train makes one additional 15 minute stop after passing Centerville the express completes its run before the local does. What is the maximum distance to the nearest kilometer between Westford and Centerville?
Mathematics
1 answer:
Wewaii [24]3 years ago
3 0

Answer:

The maximum distance to the nearest kilometer between Westford and Centerville is 111.43 km.

Step-by-step explanation:

Local train stats:

Rate = 60 km/h

Distance = x km

Time = x/60 hours

Express train stats:

Rate = 80 km/h

Distance = (195-x) km

Time = (195-x)/80 hours

Now we will equate both the times.

x/60 =(195-x)/80

x/3= (195-x)/4

4x= 585-3x

7x= 585

x = 83.57 km

195-x=195-83.57= 111.43 km

Hence, the maximum distance to the nearest kilometer between Westford and Centerville is 111.43 km.

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A rectangle measured 2 ⅔ inches by 1 5/9 inches what is its area
andre [41]

Answer:

4 4/27 sq inches

Step-by-step explanation:

the area is 2⅔ × 1 5/9 = 8/3 × 14/9

= 112/27 = 4 4/27

5 0
3 years ago
Garth has a summer job and earns $9.32 per hour. One week, he works 16 34 3 4 hours. He deposits $150 in a bank and decides to u
trasher [3.6K]

Answer:

762 raffle tickets

Step-by-step explanation:

16×9.32= 149.12

34×9.32= 316.88

3×9.32= 27.96

4×9.32= 37.28

add them all up= 531.24

531.24-150=381.24

381.24÷.50=762.48

answer: 762 raffle tickets

5 0
3 years ago
Social media is popular around the world. Statista provides estimate of the number of social media users in various countries in
amm1812

Answer:

Kindly check explanation

Step-by-step explanation:

The data table :

Use of SM _UK _China _ Russia _US _ col total

Yes ______480 __215 ___343 __640 _ 1678

No _______320 _ 285 ___357__ 360 _ 1322

Row Total__ 800 _500 __ 700_ 1000_ 3000

H0 : p1 = p2 = p3 = p4

H1 : p1 ≠ p2 ≠ p3 ≠ p4

Test statistic :

χ² = Σ(observed - Expected)² / Expected

Expected value of each cell = (Row total * column total) / N

N = grand total

Expected Values:

447.467 _279.667 _ 391.533 _ 559.333

352.533 _ 220.333 _ 308.467 _ 440.667

χ²=(2.36536+14.9527+6.01605+11.6337+3.00232 18.9793+7.63611+14.7665) = 79.352

Degree of freedom, df = (row-1)*(column-1) = (2 - 1) * (4 - 1) = 1 * 3 = 3

Using the Pvalue from Chisquare calculator :

Pvalue(79.352, 3) = 0.00000000001

Decision region :

Reject H0 ; If Pvalue < α

α = 0.05

Since 0.000000001 < 0.05 ; Reject H0 and conclude that not all population proportion are equal.

Sample proportion :

Phat = number of yes, x / total

For UK, Phat = 480/800 = 0.6

For China , Phat = 215/500 = 0.43

For Russia , Phat = 343/700 = 0.49

For US, Phat = 640/1000 = 0.64

7 0
3 years ago
The coordinates of each rectangle ABCD are A (0,2) B (2,4) C (3,3) D (1,1). Find the distance of each side of the rectangle then
EastWind [94]

AB = CD = √8 ≈ 2.8 units

BC = AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = 3.92 units²

Perimeter of the rectangle ABCD = 8.4 units

<h3>How to Find the Area and Perimeter of a Rectangle?</h3>

Given the coordinates of vertices of rectangle ABCD as:

  • A(0,2)
  • B(2,4)
  • C(3,3)
  • D(1,1)

To find the area and perimeter, use the distance formula to find the distance between A and B, and B and C.

Using the distance formula, we have the following:

AB = √[(2−0)² + (4−2)²]

AB = √[(2)² + (2)²]

AB = √8 ≈ 2.8 units

CD = √8 ≈ 2.8 units

BC = √[(2−3)² + (4−3)²]

BC = √[(−1)² + (1)²]

BC = √2 ≈ 1.4 units

AD = √2 ≈ 1.4 units

Area of the rectangle ABCD = (AB)(BC) = (2.8)(1.4) = 3.92 units²

Perimeter of the rectangle ABCD = 2(AB + BC) = 2(2.8 + 1.4) = 8.4 units

Learn more about the area and perimeter of rectangle on:

brainly.com/question/24571594

#SPJ1

5 0
1 year ago
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly ge
snow_tiger [21]
Kelly should get back $6.72.

To get this answer, start by adding 16.79 and 28.49. The answer you should get is 45.28. Next, subtract 45.28 from 50 and your total should be 6.72. Hope this helped!
5 0
3 years ago
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