Answer:
f(2) means you substitute 2 with x in the function f(x) = 5x^2 - 3x + 2
Step-by-step explanation:
f(2) = 5(2)^2 - 3(2) + 2
f(2) = 5(4) - 6 + 2
f(2) = 16
An element with mass 800 grams decays by 8.2% per day. How much of the element is remaining after 15 days,
to the nearest 10th of a gram?
Given:
The initial mass of an element is 800 grams.
Decay rate = 8.2% per day
Number of days = 15
To find:
The remaining element after 15 days.
Solution:
The exponential decay model is
[tex]y=a(1-r)^t[/tex]
Where, a is the initial value r is the rate of interest and t is time period.
Putting [tex]a=800,r=0.082,t=15[/tex] in the above formula, we get
[tex]y=800(1-0.082)^{15}[/tex]
[tex]y=800(0.918)^{15}[/tex]
[tex]y=221.68188[/tex]
[tex]y\approx 221.7[/tex]
Therefore, the mass of the remaining element is 221.7 grams.
Sully is having a party and wants to fill his swimming pool. If he only uses his hose, it takes 3 hours more than if he only uses his neighbor's hose. If he uses both hoses together, the pool fills in 5 hours. How long does it take for each hose to fill the pool (in hr)?
Answer:
It takes the neighor's hose 3 hours to fill the pool and it takes Sully's hose 6 hours to fill the pool if each filled alone.
Step-by-step explanation:
This is a work problem, and the way these are done is to figure the amount that each can do based on how much can get done in a single hour.
First thing, in order to have only one variable, we have to put one hose in terms of the other hose.
We know that it takes the neighbor's hose a certain amount of time (there's our unknown) to fill the pool and that it takes Sully's hose that same time plus 3 hours.
neighbor's hose can get the job done in x time
Sully's hose can get the job done in x + 3 time
Now we will figure out how much each can do in a single hour.
If the neighbor's hose takes x hours to fill the pool, then it can get
of the pool filled in 1 hour.
If Sully's hose takes x + 3 hours to fill the pool, then it can get
of the pool filled in 1 hour.
The sum of these takes 2 hours total and 1/2 of the pool gets filled in 1 hour.
Our equation then is:
This equation states in words:
"the amount of the pool that the neighbor's hose can fill in an hour plus the amount of the pool that Sully's hose can fill in an hour will fill half the pool".
Solving for x will give us that time.
Begin to solve this by finding the LCM of those denominators and getting rid of the fractions by reducing. The LCM will be 2x(x + 3). Multiplying each term by that LCD looks like this:
In the first term the x's cancel out, in the second term the (x + 3) cancels out, and in the last term the 2's cancel out leaving us with:
and simplifying gives us:
This is a quadratic that will have to be factored to solve for those values of x. Combine like terms and get everything on one side to get:
Factor this however you find easiest to get the values:
x = 3 hours and x = -2 hours
We all know that the 2 things in math that will never EVER be negative are times and distances/measures, so we can disregard the -2 and say that
x = 3 hours.
To answer our question, then;
It takes the neighbor's hose 3 hours to fill the pool; it takes Sully's hose 3+3 hours = 6 hours to fill the pool.
HELPP CAN YOU HELP ME PLZ IF U SOLVE THIS U WILL GET 50+ EXTRA POINTS AND BRAINLIEST HELP
Answer:
Yes it is a function
Step-by-step explanation:
It is a function because a mapping diagram can be used to represent a relationship between input values and output values. A mapping diagram represents a function if each input value is paired with only one output value.
Brainliest plz?
Kym used the integer tiles to find the sum of (–3)+6.The line showed that the answer is negative 3.Which of the following does Kym need to do to get the correct answer
Answer:I need points
Step-by-step explanation:
adsfnsafasfj;ljfdksfas;lfkjdf;lksdfjsdlksfajf
Answer:
remove the zero pairs
so B
Step-by-step explanation:
The graph shows the profit, y, of a community fundraiser, with respect to the number
of tickets sold, x
Use the graph to determine the y-intercept and what it represents.
The y-intercept - -700 and represents the initial amount of expenses
The y-intercept - 35 and represents the initial amount of expenses
The y-intercept - 35 and represents the number of tickets sold
The y-intercept = -700 and represents the number of tickets sold
Answer:
A
Step-by-step explanation:
it rapresent the initial amount of expenses. the ticket sold were 0, but the profit was negative
Answer:
A
Step-by-step explanation:
What is the answer to this?
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Answer:
$125 per car
Step-by-step explanation:
The problem statement tells you Jazmin's pay goes up by $125 for each car she sells. That rate of change is $125 per car.
What is the absolute value of 8.15
Answer:
pretty sure its 8.15
Step-by-step explanation:
the question is invluded on the picture
Answer:
a is the right answer Alexis
Step-by-step explanation:
the expression (x - 0.35x) represents 35% off the cost of an item x. how is this equivalent to multiplying x by 0.65?
show full work for brainliest
Answer:
Step-by-step explanation:
x-0.35x = x(1-0.35) = x(0.65)
Si una mujer tiene en su closet 7 camisas,3 pares de zapatos y 4 pantalones ¿de cuántas formas se puede vestir?
Answer:
14 veces Step-by-step explanation:
The exterior angles of a pentagon have measures of 65 degree 86degree 104 degree 2x and 3x find the value of x
Answer:
21
Step-by-step explanation:
65+86+104+2x+3x = 360
5x = 360-65-86-104
= 105
x =21
a circular stained glass window frame with a diameter 20 inches is divided into 8 congruent find the area of 3 of the 8 panes of glass
Answer:
it would be 45
Step-by-step explanation:
What is the length of the unknown leg in the right triangle?
Answer:
There is no triangle.
Step-by-step explanation:
Answer:
Your final answer is √32 miles.
Step-by-step explanation:
This table shows how the amount Mary earns from yard work depends on the number of hours she works. Time spent (hours), x 3 4 Amount earned, y $24 $32 How much money does Mary earn per hour? $ per hour
A certain brand of candies have a mean weight of 0.8616g and a standard deviation of 0.0518 based on the sample of a package containing 447 candies. The package label stated that the net weight is 381.8g If every package has 447 candies the mean weight of the candies must exceed 381.8/447=0.8542 for the net contents to weight at least 381.8g.
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
The probability is ________.
(round to four decimal places as needed)
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
the probability that a sample of 447 candies will have a mean of 0.8542g or greater is __________.
(round to four decimal places as needed)
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Answer:
a) The probability is 0.5557 = 55.57%.
b) The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 0.8616g and a standard deviation of 0.0518
This means that [tex]\mu = 0.8616, \sigma = 0.0518[/tex]
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
This is 1 subtracted by the pvalue of Z when X = 0.8542. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0518}[/tex]
[tex]Z = -0.14[/tex]
[tex]Z = -0.14[/tex] has a pvalue of 0.4443
1 - 0.4443 = 0.5557
The probability is 0.5557 = 55.57%.
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
Sample of 447 means that [tex]n = 447, s = \frac{0.0518}{\sqrt{447}} = 0.00245[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0245}[/tex]
[tex]Z = -3.02[/tex]
[tex]Z = -3.02[/tex] has a pvalue of 0.0013
1 - 0.0013 = 0.9987
The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
What’s the answer please help me no links at all if you do I will report
Answer: 78
Step-by-step explanation:
The ideal output of a particular oil-rig in the Mexican Gulf is at least 2000 barrels per day. If the output is lesser than that, the foreman raises an red flag at the end of the day. Old Joe the Retired Statistician watches from the shore every day. After 28 days, the red flag was raised on 16 of those days. Could Joe conclude that the oil-rig is operating at a non-ideal condition most of the time
Answer:
Mexican Gulf Output of a Oil-Rig
Based on 57% red flag days, Joe, the retired statistician, who watches from the shore for the red flag every day, cannot conclude that the oil-rig is operating at a non-ideal condition most of the time, but more of the time.
Step-by-step explanation:
Ideal output of a particular oil-rig, at least = 2,000 barrels per day
When output is lesser than 2,000, a red flag is raised by the foreman
Number of days counted = 28
Number of days when red flag was raised = 16
Proportion of days when the red flag was raised = 16/28
= 0.57
or 57%
Someone please help me with this math problem
Answer: 27,600
Step-by-step explanation:
Ok, there could be two answers to this question. If the question is asking how much he would make if it was .15% more, the total would be 27,600/a year
However, if it's asking .15% of 24,000, your answer would be 3,600 ( as in the extra he would be making)
To find the answer, you would have to multiply 24,000*.15 (your starting value times how much you would like to multiply it by)Determine if each set of coordinates form a horizontal or vertical line.
a. (-3, 6) & (-3, 2)
b. (8, 4) & (-3, 4)
c. (11, -5) & (-9, -5)
d. (9, -3) & (9, -12)
Answer:
a. vertical
b. horizontal
c. horizontal
d. vertical
Step-by-step explanation:
if the x coordinate changes it's horizontal and if the y coordinate changes it's vertical
Explain how to find the area of the composite figure above in your explanation be sure to include the formulas you will need to solve the problem
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Answer:
40.5 square inches
Step-by-step explanation:
The figure appears to be a trapezoid with bases 15 inches and 12 inches, and a height of 3 inches. The formula for the area of a trapezoid is useful in this case:
A = 1/2(b1 +b2)h
A = (1/2)(15 in +12 in)(3 in) = (1/2)(27 in)(3 in) = 40.5 in²
The area of the composite figure is 40.5 square inches.
__
Additional comment
You get the same answer if you divide the figure into a rectangle and a triangle. The rectangle is 3 in high by 12 in long, so has an area of ...
A = bh = (12 in)(3 h) = 36 in²
The triangle has a base of (15 -12) = 3 in, and a height of 3 in. It has an area of ...
A = 1/2bh = 1/2(3 in)(3 in) = 4.5 in²
Then the total area is the sum of the rectangle and triangle areas:
figure area = 36 in² +4.5 in² = 40.5 in²
What is the fewest number of quarters, nickels, and pennies that can be fairly exchanged for 2 quarters, 6 nickels, and 9 pennies?
Answer:
Your answer is 3 quarters, 2 nickels, and 4 pennies
Step-by-step explanation:
2 quarters plus 6 nickels plus 9 pennies is equal to 89 cents. So if we subtract 75(3 quarters) we get 14 which is less than 25 therefore we must only use nickels and pennies from now on. If we take 14 and subtract 10(2 nickels) we get 4 which less than 5 leaving us only to use pennies, which one a piece so it must be 4 pennies. Hope this helps!
2b + 8 =? I don't know this one either
The radius of a chord and a tangent line are_ at the point of tangency
Answer:
fine
cause of it's fine point of tangency
Alexis has a bag of starbursts. After giving half of the candy to her best friend, she ate 6 starbursts.
Now, she only has 10 starbursts left. How many starbursts did Alexis start with?
Answer: 22
Step-by-step explanation:
What is the area of ACDE to the nearest whole number?
Area of ACDE =
Answer:
Step-by-step explanation:
Area of rectangle ABCD = 84.
BC=x
We can use pythagorean to find x. 12^-6^2=c^2
C=6root3
6root3*6/2 = area of triangle ABC
ABC=18root3
Area of ACDE=84-18root3 which equals about 53
Please Evaluate this expression...4a-2b for a-5 and b=3
Answer:
14
Step-by-step explanation:
(4*5)+(2*3)
20-6
14.
Each side of a square potholder is 21 centimeters long.
What is the area of the potholder?
The answer is a 441 cm area
15% of number is 54. What is 2/3 of that number?
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Answer:
240
Step-by-step explanation:
The value is proportional to the fraction:
n/(2/3) = 54/(0.15)
n = (2/3)(54/0.15) = 240 . . . . . multiply by 2/3
2/3 of the number is 240.
For what value of m does f( m) = g( m)
Answer:
Pts
Step-by-step explanation:
Need pts
solve the inequality and specify the answer
1-3x [tex]\leq[/tex]0
Interval notation
Step-by-step explanation:
hope it helps
see attached