Answer:
Nearest cent- $1.43
Step-by-step explanation:
14.25x0.10=1.425
Subtract the sum of (-82) and 43 from (-33)
Answer:
6
Step-by-step explanation:
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.
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:
https://brainly.com/question/14320920
I really need help and I would appreciate an explanation but it’s not needed thank you
5 kilograms = ...... grams (Conversion factor: 1 kg = 1,000 g)
Answer:
5000 g
Step-by-step explanation:
1 kg = 1000 g
5 kg is 5 times 1 kg
5 * 1 kg = 5 * 1000 g
5 kg = 5000 g
operación de calculo 40+30+18=
40 + 30 + 18
= 70 + 18
= 88
Answer:
88
Step-by-step explanation:
40+30+18=70+18=88
simplify this algebraic expression completely 5y - 3(y+2)
Answer: 2y - 6
Step-by-step explanation:
This problem utilizes the Distributive Property of Multiplication. It states that: a(x + y) = ax + ay.
Thus, utilizing this property (distributing -3), change the equation into:
5y - 3y - 6
Then, simply combine like terms to get:
2y - 6
Hope it helps :) and let me know if you want me to elaborate.
Write an equation in slope-intercept form for the line perpendicular to y=2x−3 that passes
through the point (−3,−3).
Answer:
y = -1/2x - 9/2
Step-by-step explanation:
If two lines are perpendicular to each other, they have opposite slopes.
The first line is y = 2x - 3. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.
Plug this value (-1/2) into your standard point-slope equation of y = mx + b.
y = -1/2x + b
To find b, we want to plug in a value that we know is on this line: in this case, it is (-3, -3). Plug in the x and y values into the x and y of the standard equation.
-3 = -1/2(-3) + b
To find b, multiply the slope and the input of x (-3)
-3 = 3/2 + b
Now, subtract 3/2 from both sides to isolate b.
-3 - 3/2 = b
-6/2 - 3/2 = b
-9/2 = b
Plug this into your standard equation.
y = -1/2x - 9/2
This equation is perpendicular to your given equation (y = 2x - 3) and contains point (-3, -3)
Hope this helps!
Solve for the measure of angle G in degrees.....
Answer:
Angle G = 76 degrees
Step-by-step explanation:
66 + 2x + x = 180
66 + 3x = 180
3x = 114
x = 38
2(38) = 76
Answer:
76 degrees is the answer hope this help if I'm wrong I'm so sorry
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
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!
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.
10,250 divided by 301
Please help!! I’ll give brainliest
Answer:
4 and 2/3 from choice A on the promblem
4. Provide an appropriate response. Round to the nearest hundredth.
(1 point)
In a certain town, 40% of adults have a college degree. If four adults from the town are
selected at random, the probabilities that 0, 1, 2, 3, or 4 of them will have college degrees are
provided in the accompanying table. Find the standard deviation for the probability
distribution
Х P(x)
0 0.1296
1 0.3456
2 0.3456
3 0.1536
4 0.0256
According to the discrete distribution given, the standard deviation is of: 0.98.
The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability, hence:
[tex]E(X) = 0.1296(0) + 0.3456(1) + 0.3456(2) + 0.1536(3) + 0.0256(4) = 1.6[/tex]
The standard deviation is the square root of the sum of the multiplication of each probability and the difference squared between the observation and the mean, hence:
[tex]\sqrt{V(X)} = \sqrt{0.1296(0-1.6)^2 + \cdots + 0.1536(3-1.6)^2 + 0.0256(4-1.6)^2} = 0.98[/tex]
The standard deviation is of 0.98.
A similar problem is given at https://brainly.com/question/25650097
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
What is 2 - (7/8- 3/4)?
Answer:
15/8
Step-by-step explanation:
2-(7/8-3/4)=
2-(1/8)=
15/8
A committee including 2 boys and 2 girls is to be formed from a group of 6 boys and 5 girls. How many different committee can be formed from the group
Step-by-step explanation:
well, we need to multiply the possibilities of forming a group of 2 boys out of 6 with the possibilities to firm a group of 2 girls out of 5.
the first is 6 over 2
6! / (2! × (6-2)!) = 6×5/2 = 3×5 = 15
the second one is 5 over 2
5! / (2! × (5-2)!) = 5×4/2 = 5×2 = 10
so, these 15 possibilities combined with the 10 possibilities makes
15×10 = 150
possibilities to form this committee.
Translate the following verbal statement into an algebraic equation and then solve:
Mariah bought a bookcase on sale for $340, which was two-fifths of the original price. What was the
original price of the bookcase?
Answer:
x times 0.4 = 340
x = 850
Step-by-step explanation:
340 / 0.4 = 850
Simplify
25⋅5⋅5⋅4
500
2000
2500
5000
Answer:
2500
Step-by-step explanation:
Use a calculator.
Answer:
5000
Step-by-step explanation:
i think this is correct if not very sorry
Please help me out guys! Giving brainliest, liking the answer, and giving a five stars to whoever gives an actual answer. (Please help my grades are closing) ty :)
Answer:
A. y = 3x
Step-by-step explanation:
A proportional relationship is described by an equation of the form ...
y = kx
The equation of answer choice A is in that form with k=3. It describes the relationship as proportional.
__
Answer choice B gives a single point on the position versus time graph. There is nothing to indicate it is part of a proportional relation.
Answer choice C tells you the relationship between time and distance (speed) is not constant. That assures you the relationship is NOT proportional.
Answer choice D does not tell you that the time starts counting when the turtle starts at the rock. It tells you the relation is linear, but does not tell you the relation is proportional.
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:
Vocabulary How do you know if a situation represents a proportional relationship?
Answer:
write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.
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.
Read more;
https://brainly.com/question/5899088
What is the least number by which 700 should be multiplied to make it a prefect cube?
The answer is Too make 700 a perfect square is 7
Help! Will give brainliest!
9514 1404 393
Answer:
$5,336
Step-by-step explanation:
The formula for an ordinary annuity is ...
A = P((1 +r)^t -1)/r
We want to find P when A=70000, r=0.059, t=10
P = Ar/((1 +r)^t -1) = 70000(0.059)/(1.059^10 -1) ≈ 5336
Owen must contribute $5,336 each year for 10 years to have $70,000.
_____
Additional comment
If this is an annuity due, with contributions made at the beginning of the year, the above contribution amount can be divided by 1.059. That will give $5038 as the contribution amount.
By which rule are these triangles congruent?
A)AAS
B)ASA
C)SAS
D)SSS
In ΔPQN and ΔSQN,
PN = SN (Given)
PQ = SQ (Given)
QN = QN (Common)
∴ ΔPQN ≅ ΔSQN (By SSS Criteria)
Option D is the correct answer.
Please mark as Brainlliest.
YALL PLS HELP IM GOVE BRAINLIST PLSSS
Answer:
If the wheels of diameter of 20 inches rotate 37 times then she will travel 2325.71 inches or 59 m.
Step-by-step explanation:
pls mark as brainliest need to rank up
A large bottle contains 1.7 liters of olive oil. A medium-sized bottle has 0.2 times the amount of olive oil as
the large bottle.
How much more olive oil does the large bottle contain than the medium-sized bottle?
There are
more liters of olive oil in the large bottle than the medium-sized bottle.
Answer:
1.36
Step-by-step explanation:
Medium Bottle hold .34. Take this and subtract from 1.7 and get 1.36
25
A man earns N 5,000.00 for 10
days work. How should he earn in
14 days, if working at the same
rate
Answer:
N 7,000.00
Step-by-step explanation:
He earns N 5,000.00 for 10 days of work so divide the 5,000.00 by 10
5,000.00/10= 500.00 ; this is the amount of money he makes in 1 day
Then multiply this amount make in 1 day by 14 to find how much the man makes in 14 days.
500.00*14=7,000.00
Therefore, the man makes N 7,000.00 in 14 days.
