6. Jack buys a 6 pound bag of sand to put in his two fish tanks.

Nady [450]

To simplify 7C4 we use the combination formula given by:
nCr=n!/[(n-r)!r!]
thus:
In our case we shall have:
n=7 and r=4
7C4
=7!/[(7-4)!4!]
=5040/[6×24]
=5040/144
=35

The answer is 35

6 0

2 years ago

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator.

mart [117]

Answer:

$\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$ .

Step-by-step explanation:

The given expression is

$\dfrac{3y^{\frac{1}{4}}}{4x^{-\frac{2}{3}}y^{\frac{3}{2}}\cdot 3y^{\frac{1}{2}}}$

We need to simplify the expression such that answer should contain only positive exponents with no fractional exponents in the denominator.

Using properties of exponents, we get

$\dfrac{3}{4\cdot 3}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{\frac{3}{2}+\frac{1}{2}}}$ $[\because a^ma^n=a^{m+n}]$

$\dfrac{1}{4}\cdot \dfrac{y^{\frac{1}{4}}}{x^{-\frac{2}{3}}y^{2}}$

$\dfrac{1}{4}\cdot \dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{y^{2}}$ $[\because a^{-n}=\dfrac{1}{a^n}]$

$\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$

We can not simplify further because on further simplification we get negative exponents in numerator or fractional exponents in the denominator.

Therefore, the required expression is $\dfrac{x^{\frac{2}{3}}y^{\frac{1}{4}}}{4y^{2}}$ .

5 0

3 years ago

Fifty students are going on a field trip. Twenty of the students are boys. What percent of the students are girls?

Vilka [71]

Answer:

60% would be the correct answer

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Identify the property used in each step of solving the inequality 3x-2>-4.

WARRIOR [948]

Addition property of equality

Division property of equality

Solution:

Given inequality is:

3x - 2 > 4

$\mathrm{Add\:}2\mathrm{\:to\:both\:sides}$

Here, Addition property of equality is used

When the same amount is added to both sides of an inequality, then the inequality is still true

3x - 2 + 2 > 4 + 2

3x > 6

$\mathrm{Divide\:both\:sides\:by\:}3$

Here, Division property of equality is used

When we divide both sides of an equation by the same nonzero number, the sides remain equal.

$\frac{3x}{3}>\frac{6}{3}\\\\x > 2$

Thus the property used in each step of solving the inequality is found

8 0

2 years ago

What equation makes the line go through the following points. (11, -3) and (7, 9)

Brums [2.3K]

Answer:

y = -3x + 30

Step-by-step explanation:

First, find the slope using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (9 - (-3)) / (7 - 11)

m = -12/4

m = -3

Next, find the y-intercept by substituding one of the two points into what the equation is so far:

y = -3x + b

(7, 9)

9 = -3(7) + b

9 = -21 + b

30 = b

Now you have the full equation:

y = -3x + 30

5 0

2 years ago