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Oksana_A [137]
2 years ago
5

Heating oil is to be poured at the constant rate of 4.5 gallons per minute into a 400-gallon tank that already contains 115 gall

ons of heating oil. What fraction of the tank's total capacity will be full in 30 minutes?
Mathematics
1 answer:
kirill [66]2 years ago
3 0

Answer:

5/8

Step-by-step explanation:

The volume after 30 minutes is:

(4.5 gal/min) (30 min) + 115 gal = 250 gal

The fraction of total capacity is:

250 gal / 400 gal = 5/8

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Find the values for k so that the intersection of x = 2k and 3x + 2y = 12 lies in the first quadrant.
RUDIKE [14]

Answer:

0 < k < 2

Step-by-step explanation:

<u>In the first quadrant both of x and y get positive values, so </u>

  • x > 0 and y > 0
  • x = 2k, k > 0

<u>And replacing x with 2k in the second equation:</u>

  • 3x + 2y = 12
  • 3*2k + 2y = 12
  • 2y= 12 - 6k
  • y = 6 - 3k

<u>Since y > 0:</u>

  • 6 - 3k> 0
  • 2 - k > 0
  • k < 2

<u>Combining both k > 0 and k < 2, we get:</u>

  • 0 < k < 2
3 0
2 years ago
Read 2 more answers
It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from
Gennadij [26K]

Answer:

correct option is  C. 3.7 km

Step-by-step explanation:

given data

A to Port B = 4.7 km

lighthouse = N73°E

lighthouse = N31°E

solution

we get here first  \angle B and  

here

\angle A = 90 - 73 = 17°

\angle B =  73 - 31 = 42°

and

sum of all angle 180° so

\angle A +  

17° + 42° +  \angle C = 180°  

solve it we get

\angle C = 121°

Now we use here sin law that is

\frac{b}{sinB} = \frac{c}{sinC}   ........................2

put here value and we get

\frac{b}{sin42} = \frac{4.7}{sin121}  

solve it we get

b = 3,7 km

so correct option is  C. 3.7 km

7 0
2 years ago
Which represents the reflection of f(x)= square root x over the x-axis?
antiseptic1488 [7]
The reflection of f(x)=sqrt(x) over x-axis will be represented by option a. This is because it is the reflection of the imaginary part of the function f(x)= sqrt(x). Hence the correct answer is a. 

8 0
2 years ago
Read 2 more answers
Solve for x. 4x−4&lt;8 AND9x+5&gt;23
djyliett [7]
I think the first one is
x<3

And the second one is
x<2
6 0
2 years ago
Read 2 more answers
A number is written with the following factorization 2x2x2x4x5. Is this factorization is prime factorization? Explain why or why
Ulleksa [173]
The number 2*2*2*4*5 is not in its prime factorization because not all the factors are prime numbers. A prime number is a number that has no other factors except for 1 and itself.
4 is not a prime number, since it can be divided by 2. The number can be broken down into its prime factors by dividing by 2, and it becomes 2*2.

Therefore, the factorization of the number 2*2*2*4*5 can be broken down to 2*2*2*2*2*5.
3 0
2 years ago
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