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harkovskaia [24]
3 years ago
6

1. Alex bought 2 buckets of baseballs that cost $19.49 each, a bat that cost $125.50, and 2 pair of baseball socks that totaled

$29.50. The tax on Alex's purchases equaled $16. How much change did Alex receive if he paid with three $100 bills?​
Mathematics
1 answer:
Blizzard [7]3 years ago
8 0

Answer:

$90.02

Step-by-step explanation:

<u>Solve</u>

Formula: Change money = paid money – bill. Paid money = change + bill.

Given: <em>2</em> buckets of baseballs that cost $<em>19.49</em> each

A bat that cost $<em>125.50</em>, and <em>2</em> pairs of baseball socks that totaled $<em>29.50</em>

Tax on Alex's purchases equaled $<em>16</em>.

Paid with three $<em>100</em> bills.

To find: How much change Alex received if he paid with three $100 bills

Total payment + Total Tax  -Total cost

19.49 + 125.50 + 29.50  = 174.49 (Don't add the $16 tax because that will be taken from the amount we pay)

∴, <em>three </em>100 bills is 300

So, 300 - 174.49 = 109.51

109.51 - 16 = 90.51

90.51 - 0.49 = $90.02

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Answer:

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in this problem we have

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The radius of the circle is equal to 4 units

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Work shown below!

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For A (1, –1), B (–1, 3), and C (4, –1), find a possible location of a fourth point, D, so that a parallelogram is formed using
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The possible coordinates for the vertex D of the parallelogram could be (-4, 3)

It is given that A(1, –1), B (–1, 3), and C (4, –1) are the three vertices of the parallelogram.

Let us assume that the vertices are in the order A, C, B, and D where the coordinates of D are (a, b).

In this scenario, if we join AB and CD, they will become the diagonals of the parallelogram ABCD.

According to the properties of a parallelogram, diagonals bisect each other.

Hence, mid-point of AB = mid-point of CD

Now, according to the mid-point theorem, if mid-point of AB is given as (x,y), then,

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Here, for AC,

x₁ = 1, y₁ = -1

x₂ = -1, y₂ = 3

Then, x = ( 1 - 1)/2 and y = (-1 + 3)/2

(x, y) ≡ (0, 1)  ............. (1)

Since (x, y) is also the mid-point of CD, we also have,

x₁ = 4, y₁ = -1

x₂ = a, y₂ = b

Then, x = (4 + a)/2 and y = (-1 + b)/2

(x, y) ≡ ((4 + a)/2, (-1 + b)/2) ................... (2)

From (1) and (2),

(4+a)/2 = 0 and (-1+b)/2 = 1

4+a = 0 and (-1+b) = 2

a = -4 and b = 3

Hence, the fourth vertex D of the parallelogram can be possibly located at (-4, 3)

Learn more about a parallelogram here:

brainly.com/question/1563728

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8 0
2 years ago
The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 &lt; T &lt; 36 , where T is
antoniya [11.8K]

Answer:

N(T(t)) = 1408t^2 - 385.6t - 105.52

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

N(T(t)) = 22 * (8t + 1.7)^2  - 123 * (8t + 1.7) + 40

N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40

N(T(t)) = 1408t^2 + 598.4t + 63.58 -  984t - 169.1

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Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

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1408t^2 - 385.6t - 8124.52 = 0

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

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