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sertanlavr [38]

3 years ago

5

You and four friends split the cost of an $80.20 dinner. How much did each person pay?

1 answer:

Ahat [919]3 years ago

8 0

Divide 80.20 by five.

80.20/5=16.04

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We have 9 pens, of which 5 are green ink, 3 are red ink, and 1 is black. If we put the pens in a line, how many arrangements are

Pavel [41]

Answer:

504 arrangements are possible

Step-by-step explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by:

$A_{n} = n!$

Arrangements of n elements, divided into groups:

The number of arrangements of n elements, divided into groups of $n_1, n_2,...,n_n$ elements is given by:

$A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}$

In this case:

9 pens, into groups of 5, 3 and 1. So

$A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504$

504 arrangements are possible

6 0

3 years ago

The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its

Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

$b = 3 + 2h$

$Area = 22$

Required

Find the length of the base

The area of a triangle is calculated as thus;

$Area = \frac{1}{2} * b * h$

Substitute 22 for Area and 3 + 2h for b

The formula becomes

$22 = \frac{1}{2} * (3 + 2h) * h$

Multiply both sides by 2

$2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h$

$44 = (3 + 2h) * h$

Open the bracket

$44 = 3 * h + 2h * h$

$44 = 3h + 2h^2$

Subtract 44 from both sides

$44 - 44 = 3h + 2h^2 - 44$

$0 = 3h + 2h^2 - 44$

Rearrange

$0 = 2h^2 +3h - 44$

$2h^2 +3h - 44 = 0$

At this point, we have a quadratic equation; which is solved as follows:

$2h^2 +3h - 44 = 0$

$2h^2 + 11h - 8h - 44 = 0$

$h(2h + 11) - 4(2h + 11) = 0$

$(h - 4)(2h + 11) = 0$

Split the above

$(h - 4) = 0\ or\ (2h + 11) = 0$

$h - 4 = 0\ or\ 2h + 11 = 0$

Solve the above linear equations separately

$h - 4 = 0$

Add 4 to both sides

$h - 4 + 4 = 0 + 4$

$h = 0 + 4$

$h = 4$ ---- <em>First value of h</em>

$2h + 11 = 0$

Subtract 11 from both sides

$2h + 11 - 11 = 0 - 11$

$2h = 0 - 11$

$2h = -11$

Divide both sides by 2

$\frac{2h}{2} = -\frac{11}{2}$

$h = -\frac{11}{2}$ <em> ------ Second value of h</em>

Since height can be negative, we'll discard $h = -\frac{11}{2}$

Hence, the usable value of height is $h = 4$

Recall that $b = 3 + 2h$

Substitute 4 for h

$b = 3 + 2(4)$

$b = 3 + 8$

$b = 11$

Hence, the length of the base is 11 meters

3 0

3 years ago

2.85 rounded to the nearest hundreth

Talja [164]

Answer:

To the nearest hundredth, 2.85

To the nearest hundred, zero

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Simplify 2^3/7 • 2^1/4

poizon [28]

Answer:

4/7Hope this helps :)

Step-by-step explanation:

Exact form:4/7

Decimal form:0.571428

7 0

2 years ago

Find the value of x.

Natasha_Volkova [10]

x is equivalent to 20

6 0

3 years ago

Read 2 more answers