Andrew is driving to visit his grandmother. He drove 171 miles in 2 hours. What was his average rate of travel for this trip?

The length of the hypotenuse of a right triangle is 157 units. The length of one leg of the triangle is 132. Lara wrote the foll

ra1l [238]

It is incorrect because the length of the unknown side is the square root of 7,225.

If you use the pythagorean theorem and plug in the values,

a^2 + 132^2 = 157^2

a^2 + 17424 = 24649
-17424 -17424
_________________
a^2 = 7225

If you square root it, the final answer would be 85.

7 0

3 years ago

Read 2 more answers

Suppose you have 3 pieces of string measuring 4 inches, 5 inches, and 10 inches. How many unique triangles can you form with the

Svet_ta [14]

I would say zero because the other strings wouldn’t be able to touch it

4 0

3 years ago

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places

NeX [460]

Answer:

θ = 0.77+6.28k, -0.77+6.28k, includes {-7.05, -5.52, -0.77, 0.77, 5.52, 7.05}

Step-by-step explanation:

The principal value of θ can be found using the inverse cosine function:

θ = arccos(0.72) ≈ 0.766994

Additional values of θ that also satisfy the equation are values that are this far away from any multiple of 2π, that is, ...

θ = ±arccos(0.72) + 2kπ ≈ ±0.77 +6.28k

Some approximate values for θ are {-7.05, -5.52, -0.77, 0.77, 5.52, 7.05}.

_____

<em>Comment on multiples of π</em>

Since π is irrational, the larger the multiple, the larger the error for any given approximation of π. One needs to be careful to use a suitable approximation for the multiple of interest. The same problem affects calculator accuracy for angles of very large magnitude.

7 0

4 years ago

A souvenir shop sells two sizes of American flags. Small flags cost $3.50 and large flags cost $6.50. On a recent day, 155 flags

Mariulka [41]

Answer:

Small flags = 108

large flags= 47

Step-by-step explanation:

Step one:

given

let the number of small lag be x

and big flags be y

so

3.5x+6.5y= 683.5----------1

x+y=155------------------------2

Step two:

from eqn 2 x= 155-y

put x= 155-y in eqn 1

3.5(155-y)+6.5y= 683.5

542.5-3.5y+6.5y=683.5

collect like terms

3y=141

divide by 3

y= 141/3

y=47

Step three:

put y= 47 in eqn 2

x+47=155

x= 155-47

x=108

3 0

3 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

kondor19780726 [428]

Answer:

The equation of the regression line is:

$y~=~234.56158 ~-~ 2.95835 \cdot x$

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

$\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}$

To find the line of best fit for the points:

Step 1: Find $X\cdot X$ and $X\cdot Y$ as it was done in the table

Step 2: Find the sum of every column:

$\sum{X} = 479 ~,~ \sum{Y} = 694 ~,~ \sum{X \cdot Y} = 32784 ~,~ \sum{X^2} = 26897$

Step 3: Use the following equations to find a and b:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}$

The graph of the regression line is:

5 0

4 years ago