1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
creativ13 [48]
3 years ago
10

If x is a number that satisfies 4x+3=18, can x be equal to 3? explain.

Mathematics
2 answers:
astraxan [27]3 years ago
6 0
No. 3 is an invalid number for the exponent x. If we were to plug it in like so 4(3)+3+18 it wouldn't work. Lets simplify it yea?

1. 4(3)=12
2. 12+3=15
3. 15=18 this is incorrect because 15 has a different  value than 18
Akimi4 [234]3 years ago
4 0
The answer is no. because is you substitute the value 3 in for x into the equation and solve you get,

4(3)+3=18 which says 12+3=18 15=18 and that is an untrue statement. 
Hope this helps explain the concept so you understand! Any questions feel free to ask! Please rate if I helped you! thank you so much!!
You might be interested in
I need this please help ​
Korolek [52]

Answer:

30

Step-by-step explanation:

Add all of them

5 0
3 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
A circle has a radius of 3. An arc in this circle has a central angle of 20. What is the length of the arc?
Ede4ka [16]
Circumference of whole circle =
\pi \times 3 \times 2
360÷20=18
\frac{1}{18}  \times 6\pi = \frac{1}{3} \pi
hence length of arc = 1/3 pi
5 0
3 years ago
Read 2 more answers
Evaluate 13 - 0.75w + 8x when w = 12 and x = 1/2
sashaice [31]

Answer:

8

Step-by-step explanation:

13 - 0.75 (12) + 8 (0.5)

13 - 0.75 (12) + 4

13 - 9 + 4

4 + 4

8

3 0
3 years ago
Read 2 more answers
Dominic, Ralf and Peter have just eaten a HUGE Christmas meal. Dominic now weighs half as much as Ralph, and Peter weighs three
Shtirlitz [24]
Dominic weighs 240 pounds.
6 0
3 years ago
Other questions:
  • you draw two cards from a well-shuffled deck of 52 cards. After you draw the first card, you do not replace it in the deck. What
    9·1 answer
  • Home depot has an electric drill that regularly sells for $18.50. it is on sale for 20% off. if the sales tax is 6%, what will y
    12·1 answer
  • enrollment in the ski/snowboard club increased by 30% this year. there are now 182 students in the club. how many students were
    5·1 answer
  • the rectangular grassy plot 126 m by 48m has a gravel path 1.5m wide a road 2.5m wide is constructed all around it on inside of
    8·1 answer
  • A chef is planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer. He expects 800
    13·1 answer
  • The name of your next pet is the last thing that you<br> ate. What will your next pet be called?
    9·2 answers
  • HELP ME ASAP! the quiz is timed!!!<br><br> Convert. 9 ft =_____in and round it.
    9·2 answers
  • Solve for x in the parallelogram below.
    5·1 answer
  • Solve for brainiest; thanks in advance
    13·1 answer
  • A restaurant customer left $0.70 as a tip The tax was 6% and the tip was 10% of the cost in clueing tax what did as the total bi
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!