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aleksandrvk [35]
1 year ago
15

club a raised $168 by washing 42 cars. club b raised $152 by washing 38 cars. are these fundraising rates equivalent ? explain y

our reasoning.​
Mathematics
1 answer:
uysha [10]1 year ago
6 0

Answer:

The two rates are equivalent.

Step-by-step explanation:

Here we'll find the respective unit rates and then compare those rates:

$168

----------- = $4/car

42 cars

$152

----------- = $4/car

38 cars

These two rates are precisely the same.  Thus, we conclude that they are equivalent.

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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of
Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2  are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j

The unit vector in the direction of force will be

\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}

The magnitude of the force is 40lb, so the force will be

F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k

\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}

The magnitude of the force is 60lb, so the force will be

F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)

The resultant of the two forces is

F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k

The magnitude force will be

|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469

The angle formed by F and y axis

\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=

The angle formed by F and z axis

\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359

8 0
1 year ago
The Weston Laundry washes all the linens for local hotels. In 7 days, they washed 285.38 pounds of towels and 353.47 pounds of s
Serhud [2]
In the problem it is already given that Weston Laundry washed 285.38 pounds of towel and 353.47 pounds of sheets from local hotels in 1 day. Firstly we have to find the total pounds of linens that Weston Laundry has washed in 7 days. Then only will it be possible to find the amount of linen washed in a day.
Then t
Total linen washed by Weston Laundry in 7 days = (285.38 + 353.47) pounds
                                                                               = 638.85 pounds.
Then
The amount of linen washed by Weston Laundry in 1 day = 638.85/7
                                                                                             = 91.26 pounds
So Weston Laundry washed about 91.26 pounds of linen each day.


4 0
1 year ago
A random sample of 25 roundtrip flights between Philadelphia and Dallas has an average airfare of $393.50 with a sample standard
Sauron [17]

Answer:

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $393.50

Standard deviation r = $50.30

Number of samples n = 25

Confidence interval = 95%

z value(at 95% confidence) = 1.96

Substituting the values we have;

$393.50+/-1.96($50.30/√25)

$393.50+/-1.96($10.06)

$393.50+/-$19.7176

$393.50+/-$19.72

= ( $373.78, $413.22)

Therefore, the 95% confidence interval (a,b) = ($373.78, $413.22)

5 0
1 year ago
What is the area of a square, in square feet, whose perimeter is 20 feet
geniusboy [140]
Perimeter of a square = 20 feet = 4a
=>4a = 20
=>a = 20/4
=>a = 5 feet
Area of a square = a²
=>a² = 5²
=>a = 25 square feet
3 0
2 years ago
What is the range of the function y = 2 e Superscript x Baseline minus 1
pishuonlain [190]

Answer:

I may be able to help you I need a image though

6 0
1 year ago
Read 2 more answers
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