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3 years ago

9

Mr and Mrs Carlton are taking John and Mrs carltons parents kn a 3 day colorado ski trip. They will travel 1,000 miles in Me. Ca

rltons car, which gets 30 miles per gallon of gasoline. How many gallons of gasoline will he need to purchase during the trip? (Round the quotient to the nearest hundredth)

1 answer:

Rashid [163]3 years ago

5 0

Answer:

33.33 gallons

Step-by-step explanation:

1000 miles divided by 30 miles per gallon.

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Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

How is dividing mixed numbers related to dividing whole numbers

Taya2010 [7]

Answer:

Dividing mixed numbers is very similar to multiplying mixed numbers. You just add one step—after changing the divisor into an improper fraction, you then find its reciprocal and multiply. ... First step: Write the whole number and the mixed number as improper fractions.

Step-by-step explanation:

4 0

3 years ago

Viefleur [7K]

Answer:

2625 cubic meters

Step-by-step explanation:

the volume of a rectangle is V = length x width x height (depth in this case)

so, 50m x 30m x 1.75m = 2625m^3

7 0

3 years ago

Read 2 more answers

Really struggling on this

navik [9.2K]

Angle 4 would be 77degrees because angle two is vertical to angle four.

Angle 3 and Angle 1 are equal because they are vertical to each other.

You would subtract 180 (degrees) minus 77 (degrees) and get 103 (degrees).

So Angle 3 and Angle 1 would both be 103 degrees.

You would get 180 degrees from the line.

5 0

2 years ago

Mr.yueng graded his students math quizzes students came up with four different answers when solving the equation x3=22. Which an

alex41 [277]

The question is incomplete. Here is the complete question:

Mr.yueng graded his students math quizzes students came up with four different answers when solving the equation x3=22. Which answers is correct.

(A) $\frac{22}{3}$

(B) $\sqrt[3]{22}$

(C) $\pm \sqrt[3]{22}$

(D) $\sqrt{22}$

Answer:

(B) $\sqrt[3]{22}$

Step-by-step explanation:

Given:

The equation to solve is given as:

$x^3=22$

Here, the left hand side of the equation has a variable 'x' in exponent form. So, in order to solve for 'x', we have to eliminate the exponent.

For removing the exponent, we have to take cubic root on both the sides. As we know that,

$\sqrt[n]{x^n} =x$

So, taking cubic root on both the sides, we get

$\sqrt[3]{x^3}=\sqrt[3]{22}\\\\x=\sqrt[3]{22}$

Therefore, the second student has written the correct answer and hence the correct option is (B).

6 0

3 years ago

Read 2 more answers