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3 years ago

If Mark randomly selects a boy, what is the probability that the boy's favorite food is tacos

Mathematics

1 answer:

yaroslaw [1]3 years ago

7 0

I think you’re missing a picture or additional context. You should include that!

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Line parallel to y= -2 + 7

SashulF [63]

Answer:

So, equation y=7 is parallel to x-axis. A line parallel to X axis. x axis because it is the same thing as y=0x+7 or y=7, therefore y intercept is 7 and slope is 0.

Step-by-step explanation:

5 0

3 years ago

Let t = cosA + sinA find values of t if 2 - sin2A = 2(cosA + sinA)

Zinaida [17]

$2 - \sin(2A) = 2(\cos A + \sin A)\\\\2-2\sin A\cos A=2\cos A+2\sin A\\\\2\sin A\cos A+2\cos A+2\sin A-2=0\\\\1+2\sin A\cos A+2\cos A+2\sin A-3=0\\\\\sin^2 A+\cos^2 A+2\sin A\cos A+2\cos A+2\sin A-3=0\\\\(\sin A+\cos A)^2+2\cos A+2\sin A-3=0\\\\(\sin A+\cos A)^2+2(\cos A+\sin A)-3=0\\\\\\t^2+2t-3=0\\\\t^2+2t+1-4=0\\\\(t+1)^2=4\\\\t+1=2\qquad\vee \qquad t+1=-2\\\\\\\boxed{t=1\qquad\vee\qquad t=-3}$

When $A\in\mathbb{R}$

$t=\cos A+\sin A\in[-\sqrt{2};\sqrt{2}]\approx[-1.4142;1.4142]$

and there is only one answer t = 1.

For $A\in\mathbb{C}$ both values are correct.

4 0

3 years ago

Find the distance/length of segment AB is A(2.125) and B(98, 15)

balandron [24]

Answer:

146

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point A(2, 125)

Point B(98, 15)

Step 2: Identify

A(2, 125) → x₁ = 2, y₁ = 125

B(98, 15) → x₂ = 98, y₂ = 15

Step 3: Find distance d

Substitute in coordinates [Distance Formula]: $\displaystyle d = \sqrt{(98-2)^2+(15-125)^2}$
[√Radical] (Parenthesis) Subtract: $\displaystyle d = \sqrt{(96)^2+(-110)^2}$
[√Radical] Evaluate exponents: $\displaystyle d = \sqrt{9216+12100}$
[√Radical] Add: $\displaystyle d = \sqrt{21316}$
[√Radical] Evaluate: $\displaystyle d = 146$

5 0

3 years ago

There are 25 students that would like to go on a field trip, but only 18 may go. How many different combinations of students cou

Naya [18.7K]

480700. The different combinations of students that could go on the trip with a total of 25 student, but only 18 may go, is 480700.

The key to solve this problem is using the combination formula $nC_{r}=\frac{n!}{r!(n-r)!}$ . This mean the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.