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3 years ago

30 treadmills to 36 elliptical machines the ratio in simplest form

1 answer:

4 0

30 treadmills : 36 ellipticals
this could be written in a few ways, but i am going to write it as a fraction. since treadmills come first, you put 30/36.

now that you have your fraction you have to find the GCF (greatest common factor) of the two numbers. the GCF is 6, so you have to divide 30 treadmills by 6, and 36 ellipticals by 6.
30/6=5
36/6=6

5/6 or 5:6 is the simplified ratio of treadmills to ellipticals

comment for any questions!!

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The sum of three consecutive even numbers is-138. What is the smallest of the 3 numbers?

Vlada [557]

Answer:

the smallest of the three consecutive even numbers is 44

Step-by-step explanation:

44+46+48=138

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2 years ago

What is the range for y=x^2-7x-8 ?

gtnhenbr [62]

Answer:

[-20.25;+∞).

Step-by-step explanation:

1) according to the properties of the given parabola the minimum is:

$x_0=-\frac{-7}{2}=3.5; \ y_0=-20.25;$

2) y₀=-20.25 means, the value -20.25 is minimum of the range, the maximum →+∞;

3) finally, the range y≥-20.25.

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1 year ago

(6z 2 - 4z + 1)(8 - 3z).

Yakvenalex [24]

Distributive property
a(b+c)+ab+ac
a(b-c)=ab-ac

(6z^2-4z+1)(8-3z)
move for nicety
(8-3z)(6z^2-4z+1)
distribute
8(6z^2-4z+1)-3z(6z^2-4z+1)=
48z^2-32z+8-18z^3+12z^2-3z=
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3 years ago

Solution for 18-3.8t=7.36-1.98

ohaa [14]

$\text{Hello there!}\\\\\text{Solve for t:}\\\\18-3.8t=7.36-1.98\\\\18-3.8t=5.38\\\\\text{Subtract 18 from both sides}\\\\-3.8t=-12.62\\\\\text{Divide both sides by -3.8}\\\\t=3.321053\\\\\text{Round to the nearest hundredths}\\\\\boxed{t=3.32}$

3 0

2 years ago

Arm Span(x) Height(y)

natita [175]

Answer:

Here's what I get.

Step-by-step explanation:

1. Representation of data

I used Excel to create a scatterplot of the data, draw the line of best fit, and print the regression equation.

2. Line of best fit

(a) Variables

I chose arm span as the dependent variable (y-axis) and height as the independent variable (x-axis).

It seems to me that arm span depends on your height rather than the other way around.

(b) Regression equation

The calculation is easy but tedious, so I asked Excel to do it.

For the equation y = ax + b, the formulas are

$a = \dfrac{\sum y \sum x^{2} - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}}$

This gave the regression equation:

y = 1.0595x - 4.1524

(c) Interpretation

The line shows how arm span depends on height.

The slope of the line says that arm span increases about 6 % faster than height.

The y-intercept is -4. If your height is zero, your arm length is -4 in (both are impossible).

(d) Residuals

$\begin{array}{cccr}&\textbf{Arm Span} & \textbf{Arm Span}&\\\textbf{Height/in} &\textbf{Actual} & \textbf{Predicted}&\textbf{Residual}\\25 & 19 & 22.3 & -3.3\\40 & 41 & 38.2 & 2.8\\55 & 51 & 54.1 & -3.1\\65 & 67 & 62.6 & 4.4\\ \end{array}$

The residuals appear to be evenly distributed above and below the predicted values.

A graph of all the residuals confirms this observation.

The equation usually predicts arm span to within 4 in.

(e) Predictions

(i) Height of person with 66 in arm span

$\begin{array}{rcl}y& = & 1.0595x - 4.1524\\66 & = & 1.0595x - 4.1524\\70.1524 & = & 1.0595x\\x & = & \dfrac{70.1524}{1.0595}\\\\& = & \textbf{66 in}\\\end{array}\\\text{A person with an arm span of 66 in should have a height of about $\large \boxed{\textbf{66 in}}$}$

(ii) Arm span of 74 in tall person

$\begin{array}{rcl}y& = & 1.0595x - 4.1524\\& = & 1.0595\times74 - 4.1524\\& = & 78.4030 - 4.1524\\& = & \textbf{74 in}\\\end{array}\\\text{ A person who is 74 in tall should have an arm span of $\large \boxed{\textbf{74 in}}$}$

6 0

3 years ago