I need help with these three questions

Number Frequency 1,400 3 1,450 7 1,500 7 1,550 5 1,600 4 1,650 2 1,700 1 What is the mode?

poizon [28]

Mode is the number that shows up the most

in this case, it is 71,500 which shows up twice, one more than any of the other numbers

hope this helps

3 0

2 years ago

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Factorise y^2 - 16 (y squared)

cricket20 [7]

$y^2-16=y^2-4^2=(y-4)(y+4)\\\\\text{used}\ a^2-b^2=(a-b)(a+b)$

8 0

2 years ago

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2748 mile flight 6 hours

Karo-lina-s [1.5K]

We Know, speed = Distance / Time
Here, Distance = 2748 miles
Time = 6 hours

Substitute their values in to the expression,
Speed = 2748 / 6 = 458 Miles / Hour

So, the speed would be: 458 miles/hour

Hope this helps!

7 0

2 years ago

The curve

kherson [118]

Answer:

Point N(4, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$

y-coordinate

Substitute in x [Function]: $\displaystyle y = \sqrt{4 - 3}$
[√Radical] Subtract: $\displaystyle y = \sqrt{1}$
[√Radical] Evaluate: $\displaystyle y = 1$

∴ Coordinates of Point N is (4, 1).

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Derivatives

Book: College Calculus 10e

4 0

2 years ago

Question: (Graph photo attached)

Anna11 [10]

The double bar graph shows the number of imports and exports for a company in a certain week.

On how many days was the number of exports greater than the number of imports?

Answer: From the given double bar graph, we clearly see:

Number of imports for a company on Monday = 15

Number of exports for a company on Monday = 7

Number of imports for a company on Tuesday = 18

Number of exports for a company on Tuesday = 9

Number of imports for a company on Wednesday = 14

Number of exports for a company on Wednesday = 14

Number of imports for a company on Thursday = 15

Number of exports for a company on Thursday = 6

Number of imports for a company on Friday = 9

Number of exports for a company on Friday = 19

From the above information, we clearly see that only on Friday the number of exports are greater than number of imports. Therefore, there is only 1 day when the number of exports greater than the number of imports.

Hence the option D. 1 is correct

8 0

2 years ago