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maw [93]
3 years ago
8

At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. if the car starts with a full 12 gallon

tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank? (a) 3/25 (b) 11/36 (c) 7/12 (d) 2/3 (e) 25/36
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
4 0

First find the total amount of miles traveled: 50*5=250

Then divide how many gallons of gas used per mile by total miles traveled: 30/250= 3/25

your answer: 3/25

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Identify the error or errors in this argument that supposedly shows that if ∃xp (x) ∧ ∃xq(x) is true then ∃x(p (x) ∧ q(x)) is tr
Ymorist [56]

The mistake lies in steps 3 and 5.

In fact, you know that there exists some element that satisfies p(x), and some element that satisfies q(x), but you can't assume that the same element satisfies p(x) and q(x) at the same time.

So, you are only allowed to say

p(c) existential instantiation from (2)

q(d) existential instantiation from (4)

and so you can't do the conjunction in step 6 anymore.


Here's an example: if you follow this logic, you would say something like:

"There exists a person who is born in Italy and there exists a person who is born in the USA. Therefore, there exists a person who is born in both Italy and the USA"

which is clearly false: altought there exists a person for each proposition, they are not the same person.


This is even easier if q is the negation of p:

"There exists a number greater than 10, and there exists a number lesser than 10. Therefore, there exists a number that is greater than and lesser than 10 at the same time"

which is clearly absurd

8 0
3 years ago
Bill buys the pizza shown below.
Elza [17]
The answer is <span>circumference</span>
7 0
3 years ago
Read 2 more answers
Marc can wash the cars in 4 hours alone and Madison can wash the same cars in 2 hours alone how long would it take if they worke
skelet666 [1.2K]

Answer:

My answer 2 hour

Step-by-step explanation:

If whats-his-face can do it in 4 and girl can do it in 2 divide 4 and 2 and get 2.

Hope you get it right tell me if this is correct or not.

6 0
3 years ago
Using triangle A B C as the pre-image and the origin as the center of dilation, which coordinate point is not a coordinate of a
Ostrovityanka [42]

Answer:

The correct option is:

begin ordered pair 4 comma 12 end ordered pair i.e. (4,12).

Step-by-step explanation:

We are given the coordinates of the point A,B and C of the triangle ΔABC as:

A(-1,3) , B(2,1) and C(-2,-1).

Now it is given that there is dilation of this triangle about the origin with a scale factor of 4.

This means that the change in the coordinates after the transformation is given by the rule:

(x,y) → (4x,4y)

As A → A' , B → B' and C → C'

Hence the coordinates A',B' and C' are given by:

A' are (4×-1,4×3)=(-4,12)

B' are (4×2,4×1)=(8,4)

and C' are (4×-2,4×-1)=(-8,-4).

<em>Hence the coordinate point which is not a coordinate of dilation is:</em>

<em>begin ordered pair 4 comma 12 end ordered pair  i.e. (4,12)</em>

3 0
3 years ago
Help!!!!!!!!!!!!!!!!​
kaheart [24]

Answer:

\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)

Step-by-step explanation:

First, simplify each term:

\sin\left(\dfrac{\pi}{2}+\alpha\right)=\cos \alpha\\ \\\cos \left(\dfrac{\pi}{2}+\alpha\right)=-\sin \alpha\\ \\\cos \left(\alpha-\dfrac{3\pi}{2}\right)=-\sin \alpha\\ \\\sin \left(\dfrac{3\pi}{2}+\alpha\right)=-\cos \alpha

Then given expression is equivalent to

\cos ^3\alpha+(-\sin \alpha)^3-(-\sin \alpha)+(-\cos \alpha)\\ \\=\cos ^3\alpha-\sin^3 \alpha+\sin \alpha-\cos \alpha\\ \\=(\cos\alpha-\sin\alpha)(\cos^2\alpha+\cos\alpha\sin\alpha+\sin^2\alpha)-(\cos\alpha-\sin\alpha)\\ \\=(\cos\alpha-\sin\alpha)(1+\cos\alpha\sin\alpha-1)\ \ [\cos^2\alpha+\sin^2\alpha=1]\\ \\=\cos\alpha\sin\alpha(\cos\alpha-\sin\alpha)

6 0
3 years ago
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