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3 years ago

The dot plot shows a random selection of commute times in two cities.

Mathematics

1 answer:

marta [7]3 years ago

4 0

Answer:

The commute times are shorter and more predictable for City B.

Step-by-step explanation:

First, let's find the center of each set of data. We don't have to actually measure it, we can just approximate. For City A the center is around 30 minutes. For City B the center is around 15 or 20 minutes. We can clearly see that City B commute times are generally shorter than City A.

Next, let's find which city is more predictable. We can figure this out by looking at each city's range. City A has a range of 55. City B has a range of 35. Because City B has a smaller range, we can say that City B's commute times are more predictable.

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What is the diameter, circumference, and area of a circle that has the radius of 7?

user100 [1]

Answer:

the diameter is: 14

the circumference is: C≈43.98

the area is: A≈153.94

Step-by-step explanation:

4 0

4 years ago

Read 2 more answers

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

3 years ago

Black walnut trees contain chemicals that inhibit the growth of other plants. In a simple experiment to test whether this is tru

solong [7]

Answer:

Height of tomato plant is the dependent variable

Presence of walnut leaves in the soil is the independent variable

Tomato plants grown without walnut leaves is the control

Step-by-step explanation:

An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment. In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.

A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment. In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.

A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time. Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.

5 0

4 years ago

A retiree invests $5,000 in savings plan that pays 4% per year. What will the account balance be at the end of the first year ?

Ira Lisetskai [31]

$5000 + 4% = $5000.04

3 0

3 years ago

Read 2 more answers

I need help with #10!

DiKsa [7]

Answer: 6 years old.

Step-by-step explanation:

For this exercise let "x" represents your present age.

According to the information provided in the exercise, you know that In three years, Chad will be three times your present age.

Then, your age in three years can be represented with the following expression:

$x+3$

Knowing at that time Chad's age will be three times yours and you will be half as old as old as Chad, you can write the following equation to represent this situation:

$x+3=\frac{3x}{2}$

Therefore, the final step is to solve for "x" in order to find its value.

You get that this is:

$2(x+3)=3x\\\\2x+6=3x\\\\6=3x-2x\\\\x=6$

7 0

3 years ago