13 results

limit - the value that a function (or sequence) approaches as the input (or index) approaches some valu

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 pe

A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same?
Let g be the number of GB.
The limited plan has a cost as follows:
C = 10(g - 5) + 55
C = 10g - 50 + 55
C = 10g + 5
We want to set the limited plan equal to the unlimited plan and solve for g:
10g + 5 = 70
Solve for [I]g[/I] in the equation 10g + 5 = 70
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 5 and 70. To do that, we subtract 5 from both sides
10g + 5 - 5 = 70 - 5
[SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE]
10g = 65
[SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE]
10g/10 = 65/10
g = [B]6.5[/B]
Check our work for g = 6.5:
10(6.5) + 5
65 + 5
70

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represe

A cup of coffee costs $1.75. A monthly unlimited coffee card costs $25.00. Which inequality represents the number x of cups of coffee you must purchase for the monthly card to be a better deal?
Let c be the number of cups. We want to know how many cups (x) where:
1.75x > 25
Using our [URL='https://www.mathcelebrity.com/interval-notation-calculator.php?num=1.75x%3E25&pl=Show+Interval+Notation']inequality solver[/URL], we see:
[B]x > 14.28[/B]

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit
a. Calculate the mean and standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+680&t=+3&pl=PDF']uniform distribution calculator[/URL], we get:
[B]Mean = 720
Standard deviation = 28.87
[/B]
b. What is the probability that X is less than 730? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+730&t=+3&pl=CDF']uniform distribution calculator[/URL], we get:
[B]0.6[/B]

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
d. In what way do you think the actual distribution of speeds differs from a normal distribution?
a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B]
b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B]
c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566
Plug into z-score formula: (x - 71)/8 = 1.281551566
[B]x = 81.25241252[/B]
d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the

Dan has a favorite fast food restaurant where he always orders French fries and a milk shake. If the fries contain 15 grams of fat and the shake contains 9 grams of fat, how many burgers, at 17 grams of fat each, can Dan add to his fries and milkshake if he wants to keep the total fat content of his meal no greater than 69 grams?
His original meal is 1 fry and 1 shake. This contains 15 + 9 = 24 grams of fat.
To limit his meal to 69 grams of fat, he has 69 - 24 = 45 grams of fat left over.
Therefore, he can consume:
17b <= 45 where b is the number of burgers
Dividing by 17, we get b = 2.65. Since he does not want to go over 45, he can eat 2 burgers.

Determine whether the random variable is discrete or continuous. In each case, state the possible v

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of customers arriving at a bank between noon and 1:00 P.M.
(i) The random variable is continuous. The possible values are x >= 0.
(ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
(iii) The random variable is continuous. The possible values are x = 0, 1, 2,...
(iv) The random variable is discrete. The possible values are x >= 0.
(b) The amount of snowfall
(i) The random variable is continuous. The possible values are s = 0, 1, 2,...
(ii) The random variable is discrete. The possible values are s >= 0.
(iii) The random variable is discrete. The possible values are s = 0, 1, 2,...
(iv) The random variable is continuous. The possible values are s >= 0.
[B](a) (ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
Discrete variables are limited in the values they can take between 9 and ∞
(b) (iv) The random variable is continuous. The possible values are s >= 0. Snowfall can be a decimal and can vary between 0 and ∞[/B]

I had a brother but my brother had no brothers. how can this be

I had a brother but my brother had no brothers. how can this be
Because "I" is a female.
To solve trick questions like this, you must expand your theory of constraints.
Most people look at this problem and see the word [I]brother [/I]twice and limit themselves to thinking in terms of men.

Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert s

Jennie and Alex both wanted to get a free ticket for a College Music concert. However, the concert staff told them the tickets were limited. Twenty people wanted to attend the concert but only 10 free tickets were left. So the concert center staff decided to use a lottery to decide who would receive the free tickets. What's the probability of Jennie and Alex both getting free tickets?
1/2 * 1/2 = 1/4 = [B]0.25[/B]

Limit of a Function

Free Limit of a Function Calculator - This lesson walks you through what limit is, how to write limit notation, and limit theorems

Normal Distribution

Free Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

Unlock Your Hidden Math Genius with Hypnosis

This hypnosis works on your subconscious by removing limiting beliefs for math. The goal for this hypnosis will be to remove anything causing you math anxiety. Since nature abhors a vacuum, the limiting beliefs fade away and you're left with positive intentions and ease to improve math grades. Unlock Your Hidden Math Genius with Hypnosis
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Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimite

Video store movie rental plans. Plan A 25 membership fee plus 1.25 for movie. Plan B 40 for unlimited rentals. What number of movies rentals is plan B less than plan A?
Let x equal the number of movies rented and C the cost for rentals
Plan A: C = 1.25x + 25
Plan B: C = 40
Set up the inequality:
1.25x + 25 > 40
Subtract 25 from each side:
1.25x > 15
Divide each side of the inequality by 1.25
x > 12
So [B]13[/B] rentals or more make Plan B less than Plan A.

X is the speed limit is a maximum 65 mph

X is the speed limit is a maximum 65 mph
A maximum of means less than or equal to. Or, no more than. So we have the inequality:
[B]X <= 65[/B]