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amm1812
3 years ago
9

Zach is 6 inches shorter than two times his cousin's height, c. How tall is Zach?

Mathematics
1 answer:
Aneli [31]3 years ago
7 0

Answer:

2c - 6

Step-by-step explanation:

If it says less than the next part of the problem goes in front of the minus six.

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This month Mia read 1,240 pages
pashok25 [27]

Answer:

804

Step-by-step explanation:

1240- 436= 804

3 0
2 years ago
The average annual cost (including tuition, room, board, books and fees) to attend a public college takes nearly a third of the
Crazy boy [7]

Answer:

a) Private Colleges

Sample mean = 42.5 thousand dollars

Standard deviation = S1 = 6.62 thousand dollars.

Public colleges

Sample mean = 22.3 thousand dollars

Standard deviation = 4.34 thousand dollars

b) The difference in sample mean for both cases = 42.5 - 22.3 = 20.2 thousand dollars

The average amount of going to a Private college is 20.2 thousand dollars more than the average cost of going to public colleges

c) 95% confidence interval for a sampling distribution of the difference of the cost of private and public colleges is given as

(15.0, 25.4) thousand dollars.

Step-by-step explanation:

Private colleges.

52.8 43.2 45.0 33.3 44.0 30.6 45.8 37.8 50.5 42.0

Public colleges.

20.3 22.0 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8

a) Calculate sample mean and standard deviation for both data set.

Mean = (Σx)/N

where N = Sample size

Σx = sum of all variables

Private colleges

Σx = (52.8+43.2+45.0+33.3+44.0+30.6+45.8+37.8+50.5+42.0) = 425

N = 10

Mean = 425/10 = 42.5 thousand dollars

Standard deviation = S1 = √[Σ(x - xbar)²/N]

Σ(x - xbar)² = (52.8-42.5)² + (43.2-42.5)²

+ (45.0-42.5)² + (33.3-42.5)²

+ (44.0-42.5)² + (30.6-42.5)² + (45.8-42.5)² + (37.8-42.5)² + (50.5-42.5)² + (42.0-42.5)² = 438.56

N = 10

Standard deviation = √[Σ(x - xbar)²/N]

Standard deviation = √(438.56/10) = 6.62 thousand dollars

Public colleges

Mean = (Σx)/N

Σx =

(20.3+22.0+28.2+15.6+24.1+28.5+22.8+25.8+18.5+25.6+14.4+21.8) = 267.6

N = 12

Mean = (267.6/12) = 22.3 thousand dollars

Standard deviation = √[Σ(x - xbar)²/N]

[Σ(x - xbar)²

(20.3-22.3)² + (22.0-22.3)² + (28.2-22.3)² + (15.6-22.3)² + (24.1-22.3)² + (28.5-22.3)² + (22.8-22.3)² + (25.8-22.3)² + (18.5- 22.3)² + (25.6-22.3)² +(14.4-22.3)+(21.8-22.3) = 225.96

N = 12

standard deviation = s2 = √(225.96/12) = 4.34 thousand dollars

b) The difference in sample mean for both cases = 42.5 - 22.3 = 20.2 thousand dollars

The average amount of going to a Private college is 20.2 thousand dollars more than the average cost of going to public colleges.

c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges.

95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges.

To combine the distribution in this manner,

Sample mean of difference = 20.2 thousand dollars

Combined standard deviation of the sampling distribution = √[(S1²/n1) + (S2²/n2)]

= √[(6.62²/10) + (4.34²/12)] = 2.44 thousand dollars

Confidence interval = (Sample mean) ± (Margin of error)

Sample mean = 20.2

Margin of error = (critical value) × (standard deviation of the sampling distribution)

standard deviation of the sampling distribution = 2.44

To obtain the critical value, we need the t-score at a significance level of 5%; α/2 = 0.025

we obtain the degree of freedom too

The degree of freedom, df, is calculated in the attached image.

df = 15

t (0.025, 15) = 2.13145 from the tables

Margin of error = 2.13145 × 2.44 = 5.20

Confidence interval = (Sample mean) ± (Margin of error)

= (20.2 ± 5.2) = (15.0, 25.4)

Hope this Helps!!!

8 0
3 years ago
Part B: The length of rod PR is adjusted to 17 feet. If width PQ remains the same, what is the approximate new height QR of the
Alenkinab [10]

Answer:

9.64ft

Step-by-step explanation:

Since the diagram tends to form...a right angled triangle....;

with PR = 17ft...,PQ = 14ft

then to calculate the length of QR

we use the pythagoras theorem...which is only applicable to right angled triangles

PR^2 = PQ^2 + QR^2

(17)^2 = (14)^2 + QR^2

where we make QR the subject of formula;

QR^2 = (17)^2 - (14)^2

QR = square root of( 289 - 196)

QR = square root of( 93)

;Therefore the length of QR = 9.64ft

5 0
2 years ago
Read 2 more answers
What is the value of x
larisa86 [58]
X = 3.916
Sorry if the image is hard to read I had to smoosh it so it would fit

8 0
2 years ago
Answer all these guestions corectly and i will be so thankfull and will mark u brainiest.
Lana71 [14]
1) A = π r² = 22/7 x 10² = 314.28 in²

2)A = π r² = 22/7 x 9² = 254.57 mm²

3) radius = 1/2 diameter
r = 1/2 x 3 = 1.5 in

A = π r² = 22/7 x 1.5² = 7.07 in²


4)A = π r² = 22/7 x 14² =616 cm²


5) radius = 1/2 diameter
r = 1/2 x 1.5 = 0.75 ft

A = π r² = 22/7 x 0.75² = 1.76 ft²
4 0
3 years ago
Read 2 more answers
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