The ratio of the number of people at a dinner to the number invited was 106 to 100. Express this as a percent

What is the first step in solving this equation? 3(2x+6)-4x 2(5x- 2) +6 Use the subtraction property of equality to subtract 6 f

LekaFEV [45]

Answer:

Use the distributive property on each side of the equation.

Explanation:

PEMDAS

5 0

3 years ago

A closed box with a square base is to have a volume of 13 comma 500 cm cubed. The material for the top and bottom of the box cos

andrezito [222]

Answer:

x = 1,5 cm

h = 6 cm

C(min) = 135 $

Step-by-step explanation:

Volume of the box is :

V(b) = 13,5 cm³

Aea of the top is equal to area of the base,

Let call " x " side of the base then as it is square area is A₁ = x²

Sides areas are 4 each one equal to x * h (where h is the high of the box)

And volume of the box is 13,5 cm³ = x²*h

Then h = 13,5/x²

Side area is : A₂ = x* 13,5/x²

A(b) = A₁ + A₂

Total area of the box as functon of x is:

A(x) = 2*x² + 4* 13,5 / x

And finally cost of the box is

C(x) = 10*2*x² + 2.50*4*13.5/x

C(x) = 20*x² + 135/x

Taking derivatives on both sides of the equation:

C´(x) = 40*x - 135*/x²

C´(x) = 0 ⇒ 40*x - 135*/x² = 0 ⇒ 40*x³ = 135

x³ = 3.375

x = 1,5 cm

And h = 13,5/x² ⇒ h = 13,5/ (1,5)²

h = 6 cm

C(min) = 20*x² + 135/x

C(min) = 45 + 90

C(min) = 135 $

8 0

3 years ago

Write an equation for the nth term of the arithmetic sequence −15, −33, −51, −69, .... An equation for the nth term of the

stira [4]

Given:

The arithmetic sequence is −15, −33, −51, −69.

To find:

The nth term of the arithmetic sequence.

Solution:

We have,

−15, −33, −51, −69

Here,

First term: a = -15

Common difference is

$d = -33-(-15)$

$d = -33+15$

$d = -18$

Now, nth term of an arithmetic sequence is

$a_n=a+(n-1)d$

Substitute a=-15 and d=-18.

$a_n=-15+(n-1)(-18)$

$a_n=-15-18n+18$

$a_n=-18n+3$

Therefore, the nth term of the given arithmetic sequence is $a_n=-18n+3$ .

4 0

3 years ago

The temperature is 45°F. The temperature will decrease by 2°F each hour. Let h be the number of hours.

Varvara68 [4.7K]

45 - 2t < 32 ( where t is time and you can replace it with x or h if you prefer)
Solving for t you get:
45 - 2t - 32 < 0
45 - 32 < 2t
13 < 2t
13/2 < t
Or the temperature will drop below 32F after 6 and a half hours

8 0

3 years ago

Hostoso

Softa [21]

Answer:

B

Step-by-step explanation:

0.12 is 12 percent we also have the 0.06 percent which would just be 6 percent we need to add up those percentages to get 18 percent, for the people surveyed that cannot swim would be 18 percent.

6 0

2 years ago