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11Alexandr11 [23.1K]
3 years ago
15

If Eric can paint $3$ cars in $4$ hours and $2$ trucks in $5$ hours, then how long, in hours, would it take him to paint $4$ car

s and a truck? Express your answer as a common fraction.
Mathematics
1 answer:
deff fn [24]3 years ago
3 0

Answer:

47/6

Step-by-step explanation:

Given that :

Time taken to paint 3 cars = 4 hours

Time taken to paint 2 trucks = 5 hours

How long will it take him to paint 4 cars and a truck

If 3 cars = 4 hours ;

Then ;

1 car = (4/3)hours

If 2 trucks = 5 hours

Then;

1 truck = (5/2) hours = 2 1/2 hours

Time required To paint 4 cars :

4 × (4/3) = 16/3 hours

Time required to paint 1 truck :5/2 hours

Total time required :

(16/3 + 5/2) = (32 + 15) / 6 = 47/6

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A 6am one morning the temperature was -14 degrees by noon it rose 8 degrees and then rose another 2 degrees by 3pm. By 6pm the t
valentina_108 [34]

Answer:

-9 degrees

Step-by-step explanation:

-14 + 8 = -6

-6 + 2 = -4

-4 - 5 = -9

3 0
2 years ago
"A rectangle has a height of 5 cm and its base is increasing at a rate" of 3/2 cm/min. When its area is 60 cm2, at what rate is
sukhopar [10]

Answer:

The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

Step-by-step explanation:

Dimensions of the rectangle

Height = 5cm

Rate of base = 3/2 cm/min

Area = 60cm^2

We know the area of a rectangle of given by = base* Height

b*h = 60

b*5 = 60

b = 12cm

Applying Pythagoras theorem while drawing a diagonal to the rectangle

  b^2 +h^2 =  D^2\\

 5^2 +12^2 = 13^2

so our diagonal will be 13cm  

Upon differentiating the area of the rectangle  we get

b*h = A=60cm^2

using  the chain rule of differentiation

h*db/dt + b*dh/dt  = 0

b*dh/dt = -h*db/dt

12*dh/dt = -5*3/2

dh/dt = -5/8 cm//min

so the height of the rectangle is decreasing at the rate of -5/8cm/min

now we have all the measurements we need

b = 12 , db/dt = 3/2cm/min

h = 5 , dh/dt = -5/8 cm/min

b^2 +h^2  = D^2

Upon differentiating we get

2b*db/dt + 2h*dh/dt = 2D*dD/dt

b*db/dt + h*dh/dt = D*dD/dt

12*3/2 + 5*(-5/8) = 13*dD/dt

18 -25/8 = 13*dD/dt

\frac{144-25}{8} = 13*dD/dt

dD/dt = \frac{119}{104} cm/min

Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.

6 0
3 years ago
Out of seniors at a local high school, 60% went on the senior trip. At the hotel , one room was reserved for every 4 students .
sweet [91]

Answer:

<u>Number of rooms reserved for the students are - 90 .</u>

Step-by-step explanation:

Firstly ,

As we know 60% of the 600 students went on the trip,

Then ,

Number of students went on the trip = 60% of 600

                                                          = \frac{60}{100}\times600

                                                        = 360

Now ,

Given - One room is reserved  for 4 students ,

Therefore , Number of rooms for 360 students = \frac{360}{4}

                                                                             = 90

<u>Hence , the answer is  90 rooms reserved for the students.</u>

7 0
3 years ago
7. License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we con
sergejj [24]

Yes it is true that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars because null hypothesis is rejected.

Given among 2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticut trucks, 45 had only rear license plates.

let p_{1} be the probability that commercial cars have rear license plates and p_{2} be the probability that connected trucks have rear license plates.

                         Cars                     Trucks                         Total

Total                  2049                    334                             2383

x                          239                      45                                284

p                        0.1166                   0.1347                          0.1191

α=0.05

Hypothesis will be  :

H_{0}:p_{1} =p_{2}

H_{1} :p_{1} < p_{2}

It is a left tailed test at 0.05 significance.

Standard errors of p=\sqrt{p(1-p)/n}

=\sqrt{(0.1191*0.8809)/2383}

=\sqrt{0.1049/2383}        

=0.0066

Test statistic Z=p difference/standard error

=(0.1166-0.1347)/0.0066

=-0.0181/0.0061

=-2.967

p value=0.001505<5%

Since p is less than 5% we reject null hypothesis.

We cannot calculate standard deviation so  we cannot calculate confidence interval.

Hence there is statistical evidence at 5% significance level to support that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

Learn more about z test at brainly.com/question/14453510

#SPJ4

5 0
2 years ago
The difference of twice a number g and 10 is 24
ANTONII [103]
The number g is 7
24-10 = 14
14/2=6
8 0
3 years ago
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