The answer is 192. 3 times 4 times 2 times 8 equals 192 (you can skip the one since it doesn't change the process
teacher.
1. If the hydrogen ion concentration is a measure of the strength of an acid, how much stronger is
an acid like lemon juice with a pH of 2 than an acid like urine which has a pH of 5.5?
2. A 1998 Pontiac Grand-Am depreciates in value by 18% on average each year. If the car
originally sold for $19995 in 1998, how much would the car be worth in 2012?
3. The newest gossip spreads through Meaghann's high school like wildfire. The number of
students who have heard the news triples every two minutes, thanks mostly to texting. If the
gossip started with just one person, how long would it take before the entire school of 1200
students hears the news?
The three questions are illustrations of arithmetic operations and geometric progressions
(1) Acid concentration
The given parameters are:
pH of acid lemon juice = 2
pH of acid urine = 5.5
The difference between their pH is calculated as follows:
Difference = 5.5 - 2
Difference = 3.5
Multiply the difference by 10, to calculate the acidity
Acidity = 3.5 * 10
Acidity = 35
Hence, the acid like lemon juice is 35 times stronger than urine
(2) Depreciation
The depreciation is given as:
r = 18%
In 1998, the car's worth is $19995.
This is represented as:
a = 19995
2012 is 14 years from 1998.
This is represented as:
n = 14
So, the worth of the car in 2014 is calculated using:
[tex]\mathbf{Worth =a(1 -r)^n}[/tex]
So, we have:
[tex]\mathbf{Worth =19995 \times (1 -18\%)^{14}}[/tex]
Express percentage as decimal
[tex]\mathbf{Worth =19995 \times (1 -0.18)^{14}}[/tex]
[tex]\mathbf{Worth =19995 \times 0.82^{14}}[/tex]
Evaluate
[tex]\mathbf{Worth =1243}[/tex]
Hence, the worth of the car in 2012 is $1243
(3) Spread of Gossip
The spread of the gossip is an illustration of geometric progression, where
a = 1 ---- the first term
r = 3 --- the common ratio
L =1200 --- the last term
So, we calculate the number of terms from 1 to 1200 using the following nth terms of geometric progression
[tex]\mathbf{L = ar^{n-1}}[/tex]
This gives
[tex]\mathbf{1200 = 1 \times3^{n-1}}[/tex]
[tex]\mathbf{1200 = 3^{n-1}}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(1200) = log(3^{n-1})}[/tex]
Apply law of logarithm
[tex]\mathbf{log(1200) = (n-1)log(3)}[/tex]
Divide both sides by log(3)
[tex]\mathbf{n - 1 = log(1200) \div log(3)}[/tex]
[tex]\mathbf{n - 1 =6.45}[/tex]
Add 1 to both sides
[tex]\mathbf{n =7.45}[/tex]
Since the gossip spreads every two minutes.
The total time is:
[tex]\mathbf{Total =2minutes \times 7.45}[/tex]
[tex]\mathbf{Total =14.9\ minutes}[/tex]
Hence, it will take 14.9 minutes for the gossip to spread to 1200 students
Read more about geometric progressions at:
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Please help!! I’ll give brainliest
Answer:
4 and 2/3 from choice A on the promblem
What is 123X45 I tied but it is hard
Answer:
5,535
Step-by-step explanation:
A soft drink machine outputs a mean of 28 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of putting less than 33 ounces in a cup? Round your answer to four decimal places.
Answer:
0.7745
Step-by-step explanation:
y=-1/2x+4 y=6
solve systems of equations using substitution method
BEST ANSWER GETS BRAINLY
Margo can purchase tile at a store for $0.99 per tile and rent a tile saw for $18. At another store she can
borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the
cost to be the same at both stores?
Answer:
.79x+24=1.29
took way long then it should my fault but 1.29-.79=.5
x=18/.5
x=36 sorry for taking so long and this the answer i just answered it in a weird way sorry
Step-by-step explanation:
help me in zearn please
Answer:
Diameter: 25.6
Circumference: 80.38
125 feet in 5seconds
Answer:
25 feet in one second
Step-by-step explanation:
Since it takes 5 seconds to travel 125 feet, you would do 125 ÷ 5 to get the distance for one second, which is 25 feet.
Hope it helped!
Graph this please any math expert please thank you
Answer:
we cant see the picture but if i could i would have solved it
Step-by-step explanation:
we cant see the picture n
The owner of Bond's Gym has paid you to carry out a survey of potential customers. You asked 600 potential customers what price they would be willing to pay to join the gym. Then, the owner provided you data about the number of customers that can be admitted as members at each membership price.
This allowed you to create a combined supply and demand schedule for Bond's.
Supply and Demand Schedule
Membership Price Membership Applications Memberships Available
$0 600 0
$15 450 100
$30 300 200
$45 150 300
$60 0 400
1. Using the data in the supply and demand schedule, create demand and supply curves for Bond's Gym on the following graph. Be sure to use textboxes to label the supply curve as S and the demand curve as D. (10 points)
2. Is the demand curve shallow or steep? What does this mean about the elasticity of the demand for memberships? (5 points)
3. Is the supply curve shallow or steep? What does this mean about the elasticity of supply for memberships? (5 points)
Section 2: Equilibrium and Incentives
Now, you will graph a recommended course of action for Bond's Gym.
1. Create a graph that demonstrates equilibrium and excess demand. Make sure your graph includes the same supply and demand curves that you just created. In addition, label the point of equilibrium, draw a line showing the current price at Bond's ($10), and label the excess demand on the graph. (10 points)
2. Based upon the graph you created, what price should Bond's Gym charge for memberships in order to reach equilibrium? (5 points)
3. If Bond's Gym raises prices to your recommended price, how will this affect demand for their product? (5 points)
Answer:
Step-by-step explanation:
(b). Find the values of a and b that make f continuous everywhere.
X^2+6x + 5/x^2-3x-4, X<-1
ax^2- bx +3, -1<=x<=3
2x-a+b, x>=3
Answer:
a=-13/10
b=-5/2
Step-by-step explanation:
8 singles, 6 fives, 3 twenties, and 3 hundred dollar bills are all placed in a hat. If a
player is to reach into the hat and randomly choose one bill, what is the fair price to
play this game?
The fair price to play the game as described is therefore; $19.9.
The fair price to play the game would be the average dollar amount bill.
This can be evaluated as follows;
8 singles, 6 fives, 3 twenties, and 3 hundred dollar bills can be written as;
(8×1) + (6×5) + (3×20) + (3×100)Total amount in the hat = $398The total number of bills = 8+6+3+3 = 20The fair price = $398/20The fair price to play the game as described is therefore; $19.9.
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Note: Enter your answer and
Use matrices to solve the system.
2x + 3y = 4
5x + 8y = 11
Need help solving this
9514 1404 393
Answer:
(x, y) = (-1, 2)
Step-by-step explanation:
The augmented matrix for this system of equations is ...
[tex]\left[\begin{array}{cc|c}2&3&4\\5&8&11\end{array}\right][/tex]
Your graphing calculator or web solver will tell you the reduced row-echelon form of this matrix is ...
[tex]\left[\begin{array}{cc|c}1&0&-1\\0&1&2\end{array}\right][/tex]
The solution is (x, y) = (-1, 2).
_____
The determinant of the coefficient matrix is ...
(2)(8) -(5)(3) = 1
The inverse of the coefficient matrix is the transpose of the cofactor matrix, divided by the determinant. For a 2×2 matrix, that is the original matrix with the diagonal terms swapped, and the off-diagonal terms negated, then divided by the determinant. Since the determinant is 1, the inverse of the coefficient matrix is ...
[tex]\left[\begin{array}{cc}8&-3\\-5&2\end{array}\right][/tex]
Multiplying this by the constant vector gives the solution vector.
x = (8)(4) +(-3)(11) = 32 -33 = -1
y = (-5)(4) +(2)(11) = -20 +22 = 2
(x, y) = (-1, 2)
_____
Additional comment
Many modern calculators have so many functions that there are likely many you will never use. It is a good idea to learn to use the functions available for solving the kinds of problems you run across. Recent model calculators make it easy to enter matrices and perform various functions on them.
For solving systems of linear equations, the RREF (reduced row-echelon form) function is pretty useful. The bottom row of the result will tell you the kinds of solutions; the right column(s) will tell you what they are.
Feng is saving money each week. Feng's savings are represented by the graph below. Find the rate of change.
Answer:
I can't see the graph but to find the rate of change find the change in y over the change in x. So the difference between two y-coordinates, and the difference between two x-coordinates. It's also the same as finding the slope of the line.
Landon drove 40 miles in 1 1/4 hours. If he drove at a constant rate, how far did he travel in one hour?
9514 1404 393
Answer:
32 miles
Step-by-step explanation:
To find miles per hour, divide miles by hours.
40 mi/(1.25 h) = 32 mi/h
At that rate, Landon traveled 32 miles in 1 hour.
Pls and thank you, God bless you
Answer:
100N to the right
Step-by-step explanation:
Hope that this is helpful.
Have a great day.
change 480 cm to metres
I really need help and I would appreciate an explanation but it’s not needed thank you
What is the prime factorization of 990?
2 x 3 x 52 x 11
2 x 3 x 5x 11
2 x 32 x 5 x 11
22 x 3 x 5x 11
Answer:
2 x 3² x 5 x 11
Step-by-step explanation:
990 ÷ 2 = 495 so 2 is one factor
495 ÷ 2 = 247.5 - There is a remainder. So we can't divide by 2 anymore. Use next prime number
495 ÷ 3 = 165 - No remainder. So 3 is one factor
165 ÷ 3 = 55 - No remainder. So 3 is one factor
55 ÷ 3 = 18.3333 - There is a remainder. We can't divide by 3. Use next prime number
55 ÷ 5 = 11 - No remainder. So 5 is one factor
11 ÷ 5 = 2.2 - There is a remainder. We can't divide by 5. Use next prime number
11 ÷ 7 = 1.5714 - This has a remainder. So 7 is not a factor.
11 ÷ 11 = 1 - No remainder. SO 11 is one factor
Now put it together: 2 x 3² x 5 x 11
Factor trees also help. Have a good day or night
Sara made a withdrawal of 80$. Tom deposited 47.50.. which transactions involved more money?
Answer:
I don’t know bums
Step-by-step explanation:
y’all dum
need help ASAP it due today
Answer:
3/4
Step-by-step explanation:
How would I find the domain and range of this graph
the domain is the min/max amount of x values
the range is the min/max amount of y values
Jackson works at a company that makes widgets. If the machine he runs can make 36 widgets in 3
hours, how many hours does it take his machine to produce 66 widgets?
Answer:
Jackson needs 30 more widgets 2 hours
Step-by-step explanation:
In a class 10 students like salad. if 40% of the students like salad, how many students are in the class?
Answer:
I believe the answer is 60%
Step-by-step explanation:
Since let's think this was 10 students=100% if 40% of students went to eat salad there should only be 60% of students left.
Please mark brainliest if I helped it means a lot to me.:)
I need help I don’t understand this question
Answer:
-1
Step-by-step explanation:
0 - (-1) + (-2) = 1 - 2 = -1
19. Select numbers to create a different
expression that is equal to 7 x 9.
2
3
4
6
8
9
7x9=(x 9)+(x)
Step-by-step explanation:
7 × 9 = (? × 9) + (? × ?)
7 × 9 = (3 × 9) + (4 × 9) or (4 × 9) + (3 × 9)
The required numbers are 3, 4, and 9 to create the expression that is equal to 7 × 9.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
We have been given numbers are 2, 3, 4, 6, 8, and 9.
To determine numbers create a different expression that is equal to 7 × 9.
Here substitute the numbers 3, 4, and 9, and we get
⇒ 7 × 9 = (3 × 9) + (4 × 9) = 63
⇒ 7 × 9 = (4 × 9) + (3 × 9) = 63
Therefore, the required numbers are 3, 4, and 9 to create the expression that is equal to 7 × 9.
Learn more about the number system here:
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What is the missing constant term in the perfect square that starts with x^2+6xx
2
+6xx, squared, plus, 6, x ?
i neeeed help plz help me
Explain how the magnetic field line data supports or refutes the claim that the launcher and spacecraft magnets were misaligned in the Tuesday launch. Refer to the words and phrases below to help you write your response.
Answer:
the units were only misalignes by a few cm
(2x-6)+4(x-3)
Find the sum
Answer:
[tex](2x - 6) + 4(x - 3) \\ 2x - 6 + 4x - 12 \\ 6x - 18[/tex]
hope helpful <3
The sum of three numbers is 18. The sum of twice the first number, 5 times the second number, and 6 times the third number is 79. The difference between 8 times the first number and the second number is 43. Find the three numbers.
Answer:
The three numbers are 5,6&7
