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shepuryov [24]
3 years ago
10

Mr. Watson uses 10.5 gallons of gasoline to drive the first 313 miles of the trip. How many gallons of gasoline would he need to

drive 450 miles
Mathematics
1 answer:
adelina 88 [10]3 years ago
7 0
450/313*10.5 = 15.09.... which is approx is 15
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find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis​
stiv31 [10]

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2.  Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3.  Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5.  The y-intercept is (0, 5).

Next we find the x-intercept.  We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0).  This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5).  Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."​

3 0
3 years ago
27 over X =3 and 5y = 35 what is the value of <br> X• Y?
diamong [38]

Answer:

63

Step-by-step explanation:

\frac{27}{x} = 3

divide, 27 ÷ 3

you'll get 9, so

x = 9

Next part

5y = 35

divide both sides by 5 to isolate y,

5y ÷ 5 = 35 ÷ 5

=

y = 7

So

x = 9 and y = 7

Then let's add the numbers to our equation ( x × y)

9 × 7

=

63

7 0
2 years ago
Five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the regional science fair. Th
krok68 [10]

The theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

<h3>What is theoretical probability?</h3>

Theoretical probability of an event is the ratio of number of favourable outcome to the total expected number of outcome of that event.

Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair.

Their names are placed in a hat, and four names are chosen at random to decide who attends the fair.

  • The total number of names are 5.
  • The total number of names chosen are 4.

The total number of ways 4 names can be taken out from 5 names is,

^5C_4.

Here one spot needs to be fixed for Chandra. Now the total number of outcome remain 4 and favourable outcome remain 3.

Thus, the number of ways 4 names can be taken out such that it contains the name Chandra is

^4C_3.

The theoretical probability that Chandra will be chosen as one of the science fair participants is,

P=\dfrac{^4C3}{^5C4}\\P=\dfrac{4}{5}\\P=0.8\\P=80\%

Thus, the theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.

Learn more about the theoretical probability here;

brainly.com/question/8652467

#SPJ1

5 0
1 year ago
−3x(−4x+x)−x(−x−2x)−4x(4x+3x)
777dan777 [17]

Answer:

- 3x( - 4x + x) - x( - x - 2x) - 4x(4x + 3x) \\  \\    = 12 {x}^{2}  - 3 {x}^{2}  +  {x}^{2}  + 2 {x}^{2}  - 16 {x}^{2}  - 12 {x}^{2}  \\  \\  =  - 16{x}^{2}

7 0
2 years ago
I
Liula [17]

Answer:

2-6

Step-by-step explanation:

5 673226

8 0
2 years ago
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