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nirvana33 [79]
3 years ago
9

Given that (-3, 5) is on the graph of f(x), find the corresponding point for the function f(x) − 4.

Mathematics
1 answer:
hram777 [196]3 years ago
7 0
The graph of f(x) translates down 4 units to give f(x) - 4
So the x coordinate stays the same but the y coordinate is 4 units less

So the corresponding point is (-3, 1)
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Polygon ABCDE rotates 45° clockwise about point F to produce polygon FGHIJ as shown. What is mBCD?
goldfiish [28.3K]
Polygon FGHIJ is the result of the rotation of ABCDE. 

A = F ⇒ 117°
B = G ⇒ 90°
C = H ⇒ 127°
D = I ⇒ 90°
E = J ⇒ 117°

The measure of angle BCD remains the same because the rotation involves the whole polygon. Thus, it is still 127°
5 0
3 years ago
The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time).
NeX [460]

Answer:

(a) PRIVATE COLLEGES

Sample mean is $42.5 thousand

Sample standard deviation is $6.65 thousand

PUBLIC COLLEGES

Sample mean is $22.3 thousand

Sample standard deviation is $4.34 thousand

(b) Point estimate is $20.2 thousand. The mean annual cost to attend private colleges ($42.5 thousand) is more than the mean annual cost to attend public colleges ($22.3 thousand)

(c) 95% confidence interval of the difference between the mean annual cost of attending private and public colleges is $19.2 thousand to $21.2 thousand

Step-by-step explanation:

(a) PRIVATE COLLEGES

Sample mean = Total cost ÷ number of colleges = (51.8+42.2+45+34.3+44+29.6+46.8+36.8+51.5+43) ÷ 10 = 425 ÷ 10 = $42.5 thousand

Sample standard deviation = sqrt[summation (cost - sample mean)^2 ÷ number of colleges] = sqrt([(51.8-42.5)^2 + (42.2-42.5)^2 + (45-42.5)^2 + (34.3-42.5)^2 + (44-42.5)^2 + (29.6-42.5)^2 + (36.8-42.5)^2 + (51.5-42.5)^2 + (43-42.5)^2] ÷ 10) = sqrt (44.24) = $6.65 thousand

PUBLIC COLLEGES

Sample mean = (20.3+22+28.2+15.6+24.1+28.5+22.8+25.8+18.5+25.6+14.4+21.8) ÷ 12 = 267.6 ÷ 12 = $22.3 thousand

Sample standard deviation = sqrt([(20.3-22.3)^2 + (22-22.3)^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)^2 + (21.8-22.3)^2] ÷ 12) = sqrt (18.83) = $4.34 thousand

(b) Point estimate = mean annual cost of attending private colleges - mean annual cost of attending public colleges = $42.5 thousand - $22.3 thousand = $20.2 thousand.

This implies the the mean annual cost of attending private colleges is greater than the mean annual cost of attending public colleges

(c) Confidence Interval = Mean + or - Margin of error (E)

E = t×sd/√n

Mean = $42.5 - $22.3 = $20.2 thousand

sd = $6.65 - $4.34 = $2.31 thousand

n = 10+12 = 22

degree of freedom = 22-2 = 20

t-value corresponding to 20 degrees of freedom and 95% confidence level is 2.086

E = 2.086×$2.31/√22 = $1.0 thousand

Lower bound = Mean - E = $20.2 thousand - $1.0 thousand = $19.2 thousand

Upper bound = Mean + E = $20.2 thousand + $1.0 thousand = $21.2 thousand

95% confidence interval is $19.2 thousand to $21.2 thousand

6 0
3 years ago
Helppp!!!!
svetlana [45]

Answer:

1. he took 8/12 for lunch, but 1/12 is left

2. she ate 2/5, but there's 4/15 left of the whole cake that is untouched

Step-by-step explanation:

i hope this helps, the wording is a little confusing to me tho

3 0
3 years ago
Read 2 more answers
What are the coordinates of the hole in the graph of the function?
MakcuM [25]

Answer:

The hole is at (5,7)

Step-by-step explanation:

x^2 − 3x − 10

-------------------

x−5

Factor the numerator

(x-5)(x+2)

-------------------

x−5

There is a hole at x=5 since it will cancel in the numerator and the denominator

f(x) = x+2  and letting x = 5

f(5) = 5+2

The hole is at (5,7)

4 0
3 years ago
Select all of the potential solution(s) of the equation 2log5x = log54.
tankabanditka [31]

Answer:

-2 and 2

Step-by-step explanation: just did the problem

4 0
3 years ago
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