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3 years ago

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Mathematics

1 answer:

alex41 [277]3 years ago

8 0

Answer:

y= x-3

Step-by-step explanation:

The points are ;(0, -3), (5,2), (7,4), (10,7).

Plot the coordinates on a graph tool to visualize the graph

Select two points to find the slope ; take point (5,2) and (10,7)

m=Δy/Δx

Δy = 7-2=5

Δx=10-5 = 5

m=5/5 =1

The equation of the graph will be;

m= Δy/Δx

1=y-4/x-7

x-7 = y-4

x-7+4=y

x-3=y

y= x-3

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Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,

saveliy_v [14]

Answer:

The value is $n =1351$

Step-by-step explanation:

From the question we are told that

The standard deviation is $\sigma = \$3750$

The margin of error is $E = \$ 200$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2$

=> $n = [1.96 * 3750 }{200} ] ^2$

=> $n =1351$

6 0

3 years ago

A new building is being constructed at UT Austin. It is 200 feet tall, and has a

Mariana [72]

Answer:

Walkway is 3 feet wide.

Step-by-step explanation:

Given:

Length of the building is 150 ft

width of the building is 100 ft

walkway is x ft wide.

Total area(around and including the building) = 16536 square feet

Solution:

Length of the total area will be = length of the building + width of walkway from 2 sides = $150 +2x$

Width of the total area will be = width of the building + width of walkway from 2 sides = $100 +2x$

Now Total area(around and including the building) = Length of the total area $\times$ Width of the total area

$(150+2x)\times(100+2x)=16536\\15000+300x+200x+4x^2=16536\\500x+4x^2=16536-15000\\4(125x+x^2)=1536\\125x+x^2= \frac{1536}{4}=384\\$

$x^2+125x-384=0\\x^2-3x+128x-384=0\\x(x-3)+128(x-3)=0\\(x-3)(x+128)=0\\$

Now solving for both equation we get.

$x+128=0\\x=-128\\x-3=0\\x=3$

Now, We get 2 values for x which -128 and 3 but the width of the building can't be in negative value hence we will consider value of x be 3.

∴ Width of the walkway is 3 ft.

4 0

3 years ago

Read 2 more answers

Consider a set of one-dimensional points: 6, 12, 18, 24, 30, 42, 48.

Vinvika [58]

Answer:

1) With initial centroids 10-40, final clusters are

first cluster (6,12,18,24,30)

second cluster (42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 378

2) With initial centroids 10-20, final clusters are

first cluster (6,12,18,24)

second cluster (30,42,48)

And the Sum of Squared Errors (SSE) for the clustering result is 348

Step-by-step explanation:

K-means works as follows

the points will be clustered according to their distance to the centroids.
Then centroids are updated as the cluster means.
This process continues until clusters doesn't change anymore

1) initial centroids 10-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

new centroids 15-40

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

final centroids 18-45

first cluster (6,12,18,24,30) mean:18

second cluster (42,48) mean:45

Sum of Squared errors = $(18-6)^{2}$ + $(18-12)^{2}$ + $(18-18)^{2}$ + $(18-24)^{2}$ + $(18-30)^{2}$ + $(45-42)^{2}$ + $(45-48)^{2}$ =378

2)initial centroids 10-20

first cluster (6,12) mean:9

second cluster (18,24,30,42,48) mean:32.4

new centroids 9-32.4

first cluster (6,12,18) mean:12

second cluster (24,30,42,48) mean:36

new centroids 12-36

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

final centroids 15-40

first cluster (6,12,18,24) mean:15

second cluster (30,42,48) mean:40

Sum of Squared errors = $(15-6)^{2}$ + $(15-12)^{2}$ + $(15-18)^{2}$ + $(15-24)^{2}$ + $(40-30)^{2}$ + $(40-42)^{2}$ + $(40-48)^{2}$ =348

6 0

3 years ago

A pitcher is full of lemonade. Which unit of liquid volume best describes the amount of lemonade in the pitcher? Explain.

stira [4]

I would say gallons. It honestly depends how big it is. However, the common pitcher holds about a gallon. I hope I helped!

7 0

3 years ago

There is a pic thanks and please hurry!!!

alexdok [17]

Answer:

x>7 or x≥9

I hope this helps

6 0

3 years ago

Read 2 more answers