All categories

3 years ago

Consider the rule y = 5x + 7.

Mathematics

1 answer:

maksim [4K]3 years ago

5 0

Answer:

see below

Step-by-step explanation:

Consider the rule y = 5x + 7.

a. How many tiles are in Figure 0?

In figure 0, we let x=0

y = 5*0+7 = 0+7 = 7

b. Which figure has 37 tiles?

This means y = 37

37 = 5x+7

Subtract 7 from each side

37-7 = 5x+7-7

30 = 5x

Divide by 5

30/5 = 5x/5

6 =x

Figure 6 has 37 tiles

c. In the equation y = mx + b, what do the letters m and b represent?

m is the slope or how much it is increasing each time x increases by 1 and b is how much we start with when x =0

You might be interested in

The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.9 mg and standard deviation 0.1

Ad libitum [116K]

Answer:

The answer to the question is;

The probability that the resulting sample mean of nicotine content will be less than 0.89 is 0.1587 or 15.87 %.

Step-by-step explanation:

The mean of the distribution = 0.9 mg

The standard deviation of the sample = 0.1 mg

The size of the sample = 100

The mean of he sample = 0.89

The z score for sample mean is given by

$Z =\frac{X-\mu}{\sigma/ \sqrt{n} }$ where

X = Mean of the sample

μ = Mean of the population

σ = Standard deviation of the population

Therefore Z = $\frac{0.89-0.90}{0.1/\sqrt{100} }$ = -1

From the standard probabilities table we have the probability for a z value of -1.0 = 0.1587

Therefore the probability that the resulting sample mean will be less than 0.89 = 0.1587 That is the probability that the mean is will be less than 0.89 is 15.87 % probability.

7 0

3 years ago

SOMEONE PLSSS HELPP MEE

evablogger [386]

Answer:

Step-by-step explanation:

∛6t^2= (6t^2)^1/3=

also if you want further

6^1/3 t^2/3

8 0

2 years ago

Math question down below

Alja [10]

Answer:

E is the only one that ends with 70 and is also all multiples of 6.

4 0

3 years ago

Which number sentence is not true?

Burka [1]

Answer:

Option B

Step-by-step explanation:

|-1| $\neq$ -1

|-1| = 1

8 0

2 years ago

Find the area of the region enclosed by the graphs of the functions

Vaselesa [24]

Answer:

$\displaystyle A = \frac{8}{21}$

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

Terms/Coefficients
Functions
Function Notation
Graphing
Solving systems of equations

Calculus

Area - Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

*Note:

Remember that for the Area of a Region, it is top function minus bottom function.

Step 1: Define

f(x) = x²

g(x) = x⁶

Bounded (Partitioned) by x-axis

Step 2: Identify Bounds of Integration

Find where the functions intersect (x-values) to determine the bounds of integration.

Simply graph the functions to see where the functions intersect (See Graph Attachment).

Interval: [-1, 1]

Lower bound: -1

Upper Bound: 1

Step 3: Find Area of Region

Integration

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^1_{-1} {[x^2 - x^6]} \, dx$
[Area] Rewrite [Integration Property - Subtraction]: $\displaystyle A = \int\limits^1_{-1} {x^2} \, dx - \int\limits^1_{-1} {x^6} \, dx$
[Area] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = \frac{x^3}{3} \bigg| \limit^1_{-1} - \frac{x^7}{7} \bigg| \limit^1_{-1}$
[Area] Evaluate [Integration Rule - FTC 1]: $\displaystyle A = \frac{2}{3} - \frac{2}{7}$
[Area] Subtract: $\displaystyle A = \frac{8}{21}$

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

Unit: Area Under the Curve - Area of a Region (Integration)

Book: College Calculus 10e

6 0

2 years ago