2 A taxi charges $2.50 per mile in addition to a $2

Shannon buys strawberry gum in packs of 6 pieces and blueberry gum in packs of 5 pieces. If Shannon wants to buy the same amount

DIA [1.3K]

30 pieces of blueberry and 30 pieces of strawberry, therefore 5 packs of blueberry and 6 packs of strawberry

6 0

2 years ago

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The drug lorazepam, used to relieve anxiety and nervousness, has a half life of 14 hours. if a doctor prescribes one 2.5 milligr

Klio2033 [76]

$\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\dotfill &24\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ A=2.5\left( \frac{1}{2} \right)^{\frac{24}{14}}\implies A=2.5\left( \frac{1}{2} \right)^{\frac{12}{7}}\implies A\approx 0.761883533878$

4 0

2 years ago

Which statement proves that △XYZ is an isosceles right triangle? XZ ⊥ XY XZ = XY = 5 The slope of XZ is , the slope of XY is , a

Lilit [14]

Answer:

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5 ⇒ 3rd answer

Step-by-step explanation:

* Lets look to the attached figure to solve the problem

- To prove that the Δ XYZ is an isosceles right triangle, you must

find two sides the product of their slopes is -1 and they are equal

in lengths

- From the figure the vertices of the triangle are;

X = (1 , 3) , Y = (4 , -1) , Z = (5 , 6)

- The slope of the line whose endpoints are (x1 , y1) and (x2 , y2)

is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ The slope of $XY=\frac{-1-3}{4-1}=\frac{-4}{3}$

∵ The slope of $XZ=\frac{6-3}{5-1}=\frac{3}{4}$

∴ The slope of XY = -4/3 , the slope of XZ = 3/4

∵ -4/3 × 3/4 = -1

∴ XY ⊥ XZ

∴ ∠ X is a right angle

∴ Δ XYZ is a right triangle

- The distance between the two points (x1 , y1) and (x2 , y2) is

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ $XY=\sqrt{(4-1)^{2}+(-1-3)^{2}}=\sqrt{9+16}=\sqrt{25}=5$

∵ $XZ=\sqrt{(5-1)^{2}+(6-3)^{2}}=\sqrt{16+9}=\sqrt{25}=5$

∴ XY = XZ = 5

∴ Δ XYZ is an isosceles right triangle

* The statement which prove that is:

The slope of XZ is 3/4 , the slope of XY is -4/3 , and XZ = XY = 5

6 0

2 years ago

Find the distance between the points (1,5) and (10,10). Hint: Use the Pythagorean theorem.

lubasha [3.4K]

Answer:

Exact Form:

√ 106

Decimal Form:

10.29563014

5 0

2 years ago

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A bag contains four batteries, all of which are the same size and are equally likely to be selected. Each battery is a differen

GuDViN [60]

Answer:

A) 64 ways in sample space

B) 24 ways in sample space

Step-by-step explanation:

Given:-

- A bag contains 4 batteries

- We are to select 3 at random

Find:-

how many points will be in the sample space if the batteries are selected

A) with replacement

b) without replacement

Solution:-

- The counting principle says if there are "m" ways to do one thing

and "n" ways do do another, then there are (m*n) ways of doing both.

A. 4 ways to grab first battery; put battery back;

4 ways to grab second battery; put battery back;

4 ways to grab second battery

======================================

4^3 = 64 ways in the sample space.

======================================

B. 4 ways to grab first battery; DON'T put battery back; You are left with 3.

3 ways to grab second battery; DON'T put battery back; You are left with 2

2 ways to grab third battery;

======================================

4*3*2 = 24 ways in the sample space.

======================================

6 0

2 years ago

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