A 2-column table with 5 rows. Column 1 is labeled Key Words with entries twelve, more than, quotient, a number, eight. Column 2
1 answer:
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Answer:
Following equations represents a linear function:
- y = 6x
- y = 4x - √2
- x – 4y = 6
Step-by-step explanation:
We know that a linear function is of the form
where m is the rate of change or slope and b is the y-intercept.
Please note that y = mx+b represents a straight line because the degree of a linear function is always 1.
Now, let us check whether the given functions represent the linear functions or not.
Checking y = 6x
y = 6x
comparing with the equation y = mx+b
slope = 6, and y-intercept b = 0
y = 6x is a straight line because the degree of the linear equation is always 1.
Checking x³- y = -2
x³- y = -2
As the power of x variable 3. So, its graph will no longer be a straight line,
Thus, it is not a linear function as a linear function can not have any exponent.
Hence, x³- y = -2 is not a linear function.
Checking y = 4x - √2
y = 4x - √2
comparing with the equation y = mx+b
slope = 4, and y-intercept b = -√2
Thus, y = 4x - √2 is a straight line because the degree of the linear equation is always 1. Thus, the graph of y = 4x - √2 is a straight line.
Checking x – 4y = 6
x – 4y = 6
writing the in the form y = mx+b
4y = x - 6
divide both sides by 4
4y/4 = x/4 - 6/4
y = x/4 - 3/2
comparing with the equation y = mx+b
slope = x/4, and y-intercept b = -3/2
Thus, x – 4y = 6 is a straight line because the degree of the linear equation is 1. Thus, the graph of x – 4y = 6 is a straight line.
SUMMARY:
Following equations represents a linear function:
- y = 6x
- y = 4x - √2
- x – 4y = 6
Answer:
22.96% probability that a hotel room costs between $250.00 and $285.00
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
What is the probability that a hotel room costs between $250.00 and $285.00?
This is the pvalue of Z when X = 285 subtracted by the pvalue of Z when X = 250. So
X = 285
has a pvalue of 0.7734
X = 250
has a pvalue of 0.5438
0.7734 - 0.5438 = 0.2296
22.96% probability that a hotel room costs between $250.00 and $285.00
Answer:
The first first box needs 600 more brown paper for wrapping
Step-by-step explanation:
Given:
First box:
Square base
Length of the base side = 30 cm
Height of the pyramid = 45 cm
Second Box:
octagonal base
base perimeter = 120 cm
width = 10 cm
Height = 35 cm
To Find:
Which box requires more paper to wrap, and by how much?
Solution:
To Find the amount are brown paper needed to wrap, lets find the surface area of the pyramids
Step: Finding the surface area of the box 1
The First box is square pyramid:
= base square area + 4 x area of side triangle
Base square area:
Area of the square = side x side
= 30 x 30
=900 centimetre square
Area of triangle
=
=>
=>
=>675 centimetre square
Thus the total brown paper needed for wrapping the first box
= 900 + 675
= 1575 centimetre square--------------------------------(1)
Step 2: Finding the surface area of the box 2
The second box is octagonal pyramid:
= base octagonal area + 8 x area of side triangle
Base octagonal area:
Area of the base of the octagon = 8 x area of one triangle
area of one triangle =
=
=
=75 centimetre square
Area of the base of the octagon = 8 x 75 = 600 centimetre square
Area of the side triangles
=
=
=
= 337.5 centimetre square
Thus the total surface of the octagonal pyramid is
= 600 +375
=975 centimetres square -------------------------------(2)
On comparing (1) and(2)
1575 -975 = 600
The first box requires 600 more brown paper for wrapping