The equivalent equation to Paolo's equation is,
w = Start Fraction uppercase P minus 2l Over 2 End Fraction.
What is algebraic operation?
A basic algebraic operation in mathematics is any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power).
Multiplication and division tasks should be completed first from left to right, followed by addition and subtraction tasks from left to right.
Given:
uppercase P = 2 (l + w)
Simplifying this,
uppercase P = 2l + 2w
Subtract 2l from both sides,
uppercase P - 2l = 2l + 2w - 2l
uppercase P - 2l = 2w
Divide both sides by 2,
(uppercase P - 2l) / 2 = 2w / 2
(uppercase P - 2l) / 2 = w
Hence, the equivalent equation to Paolo's equation is,
w = Start Fraction uppercase P minus 2l Over 2 End Fraction.
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stock prices used to be quoted using eights of a dollar. Find the total price of the transaction.
200 shares of national semi at 115 1/2
Answer:
Step-by-step explanation:
200 x 115.5/8 = $23,100.00
2 How much would you need to invest in a money market account if you would like to have $20,000 in the account at the end of 10 years? The account provides an APR of 2% compounded monthly.
Answer:
$16377.34---------------------------------
Use the compound interest formula:
A = P(1 + r/n)^(nt),Where A - future amount, P - invested amount, r- annual interest rate, n - number of compounds a year, t - number of years
Given:
A = $20000,r = 2% = 0.02n = 12,t = 10.Substitute known values and solve for P:
20000 = P(1 + 0.02/12)^(12*10)P = 20000/(1 + 0.01/6)^120P = 16377.34-2x-3y=48 and 7x+3y=21
Answer:
Step-by-step explanation:
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K
Fill in the blank.
The process of arriving at an approximate answer to a computation such as 0.79×403 is called
TEI
The process of arriving at an approximate answer to a computation such as 0.79 × 403 is called
A
The process of arriving at an approximate answer to a computation such as 0.79 × 403 is called estimation.
What is estimation in mathematics?Having an approximate estimate of something's worth, number, size, or extent is referred to as estimation in mathematics. When we are willing to accept a response that is extremely near to the true result, we utilize estimates of numbers to make mental computations simpler and faster.
The computation is approximate, or the number is rounded to the nearest place value.
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what is the distance between the pints (-1,2) and (2,6)
Answer:
1
Step-by-step explanation:
(-1,2) and (2,6)
d=√[2-(-1)] ^+ [2-6]^
d=√3+(-4)^
d=√-1^
d=1
Nine times the difference of 5 and y
Answer:
9(5 - y)
Step-by-step explanation:
9(?) → Nine times(? - ?) → the differenceNine times the difference of → 9(? - ?)The difference of 5 and y → (5 - y)Nine times the difference of 5 and y → 9(5 - y)- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Required answer:
9(5 - y)
Detailed explanation:
If we have the difference of two numbers, then we're subtracting these numbers. In this case, the numbers are 5 and y:
[tex]\sf{5-y}[/tex]
Next, we multiply 9 times the difference, so we put 5 - y in parentheses:
[tex]\sf{9(5-y)}[/tex]
[tex]\hrulefill[/tex]
Have a wonderful day!
PLEASE HELP 20 POINTS!
A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean ParadiseThe Caribbean Paradise has 16 more deluxe staterooms than the Pacific Paradise. The Mediterranean Paradise has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific Paradise Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the three ships is 1176
ANSWERS MUST ADD UP TO 1176
Step-by-step explanation:
x = number of deluxe staterooms on Pacific.
deluxe staterooms on Caribbean = x + 16
deluxe staterooms on Mediterranean = 4x - 28
1176 = x + (x + 16) + (4x - 28) = 6x - 12
1188 = 6x
x = 1188/6 = 198
so,
Pacific has 198 luxury staterooms.
Caribbean has 198 + 16 = 214 luxury staterooms.
Mediterranean has 4×198 - 28 = 792 - 28 = 764 luxury staterooms.
What is the surface area? 5 cm 6 cm 5 cm 7 cm 4 cm square centimeters
The surface area of the square pyramid is 224 ft²
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Surface area is the total area occupied by the surface of the object. It is gotten by summing the individual area of each surface.
For the pyramid:
Surface area = 4 * area of triangle + Area of square base
Substituting gives:
Surface area = (8 ft * 8 ft) + 4(1/2 * 8ft * 10 ft) = 224 ft²
The surface area is 224 ft²
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Answer:
Step-by-step explanation:
What is the surface area?
5 cm
6 cm
5 cm
6 cm
4 cm
square centimeters
help me with this one
Answer:
Angle A is 66°
Step-by-step explanation:
< b is equal to 57 because the opposite side lengths are equal.
The sum of the interior angles of a triangle is 180
180 - 57 - 57 = 66
PLS HELP
Use the product rule to simplify
The expression √5x × √30x is simplified using the product rule to give 12.25x
What is square root?Square root of a number can be defined as the inverse operation of the square of a number.
It is the number obtained by finding a number that when squared would give the original number.
Square root is represented using the symbol '√ '. The symbol is called a radical.
Also, the number under the symbol is called the radicand.
To multiply two square roots, we have to multiply the radicands and leave the radical sign.
From the information given, we have;
√5x × √30x
Multiply the radicands and retain the square root symbol, we have;
√150x²
Find the square root
12.25x
Hence, the value is 12.25x
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Use elimination to solve
-3x+12y = 9
x-4y=-3
Answer:
Step-by-step explanation:
Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.
In this case, we will be using elimination to solve the system of equations:
-3x + 12y = 9
x - 4y = -3
Step 1: Multiply the first equation by -1.
(Multiplying by -1 switches the sign of every number in the equation)
3x - 12y = -9
Step 2: Add the two equations together.
3x - 12y = -9
+x - 4y = -3
______________
4x - 16y = -12
Step 3: Isolate the y-variable by adding 16y to both sides of the equation.
4x - 16y = -12
+16y +16y
______________
4x = -12 + 16y
Step 4: Divide both sides of the equation by 4 to isolate the y-variable.
4x = -12 + 16y
4/4 4/4
______________
x = -3 + 4y
Therefore, the solution to the system of equations is x = -3 + 4y.
Audrey deposited $10,000 into a 3-year certificate of deposit that earned 10% annual interest, compounded annually. Audrey made no additional deposits to or withdrawals from the certificate of deposit. What was the value of the certificate of deposit at the end of the 3-year period?
A. $13,000
B. $13,300
C. $13,310
D. $13,401
Answer: C
Step-by-step explanation:
10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310
Rationalize the denominator and simplify the following expression:
fraction numerator 4 plus square root of 2 over denominator 2 space minus square root of 2 end fraction
5 plus 3 square root of 2
10 plus 6 square root of 2
2 plus 6 square root of 2
2 plus 3 square root of 2
Answer:
[tex]\textsf{A)} \quad 5+3\sqrt{2}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{4+\sqrt{2}}{2 -\sqrt{2}}[/tex]
To rationalise the denominator, multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:
[tex]2 + \sqrt{2}[/tex]Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{2}}{2 -\sqrt{2}} \cdot \dfrac{2 +\sqrt{2}}{2 +\sqrt{2}}[/tex]
Simplify:
[tex]\implies \dfrac{(4+\sqrt{2})(2 +\sqrt{2})}{(2 -\sqrt{2})(2 +\sqrt{2})}[/tex]
[tex]\implies \dfrac{8+4\sqrt{2}+2\sqrt{2}+\sqrt{2}\sqrt{2}}{4+2\sqrt{2}-2\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]
[tex]\implies \dfrac{8+6\sqrt{2}+2}{4-2}[/tex]
[tex]\implies \dfrac{10+6\sqrt{2}}{2}[/tex]
Reduce to its simplest form by dividing the numerator and the denominator by 2:
[tex]\implies 5+3\sqrt{2}[/tex]
You can hire someone without experience for $13 per hour or someone with experience for $19 per hour. You believe the
experienced person increases the sales per customer by $3. Each person handles about 12 customers per hour. Should you hire the
experienced person?
a) Yes
b) No
Answer:
a) Yes
The experienced person costs more per hour, but also increases sales per customer. To determine if it is more cost-effective to hire the experienced person, you would need to calculate the net gain or loss from hiring them.
You can do this by multiplying the increase in sales per customer by the number of customers per hour, and comparing that to the difference in hourly wages.
(12 customers/hour * $3/customer) - ($19/hour - $13/hour) = $36/hour - $6/hour = $30/hour
Since the net gain is positive, it is more cost-effective to hire the experienced person.
Slopes of parallel/Purpendicular lines - What is the slope of a line parallel to the line whose equation is x + 2y = -14
Explanation:
First we solve for y.
x + 2y = -14
2y = -14 - x
2y = -x - 14
y = (-x - 14)/2
y = -x/2 - 14/2
y = (-1/2)x - 7
The equation is in slope intercept form y = mx+b
m = -1/2 = slopeb = -7 = y interceptParallel lines have equal slopes, but different y intercepts. This means the slope of any line parallel to this given one will have a slope of -1/2
For example, y = (-1/2)x + 10 is parallel to y = (-1/2)x - 7, since both have the same slope of -1/2 but different y intercepts.
Which statement is true about the graph? Select all that apply. (Lesson 3) Long Description The ratio of the rise to the run of each triangle is the same. The smaller triangle and the larger triangle shown are similar. The slope of the line is 2. The slope of the line is −2. The corresponding sides of the two triangles are not proportional.
The correct statements about the graph are given as follows:
The ratio of the rise to the run of each triangle is the same. The smaller triangle and the larger triangle shown are similar.The slope of the line is of -2.What are the rise and the run of a graph?The rise and the run of a graph are defined as follows:
Rise: change in the output, that is, the change in y.Run: change in the input, that is, the change in x.The slope of a line is given by the change in y divided by the change in x, hence it's equation is given as follows:
Slope = Rise/Run.
For the first triangle, the rise and the run are given as follows:
Rise = -6.Run = 3.Hence the slope is of:
Slope = -6/3 = -2.
For the second triangle, the rise and the run are given as follows:
Rise = -2.Run = 1.Hence the slope is of:
Slope = -2/1 = -2.
As the ratios are the same, the triangles are similar, the line has a slope of -2, and the corresponding sides are proportional.
Missing InformationThe graph is given by the image presented at the end of the answer.
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find the property
plssss help
Subtract 7 from both sides. Subtract 7 from 23 to get 16. Divide both sides by 4. Divide 16 by 4 to get 4.
What Is Angle Congruence’s Symmetric Property?According to the symmetric property, if one geometric form is congruent to another, the second shape is likewise congruent to the first. The symmetric property of congruence states that for all angles A and B, if AB A B then BA B A.Transitive Property of Congruence. “If two shapes are congruent to the third shape, then all the shapes are congruent to each other,” asserts the transitive property of congruence.
We can solve an equation by applying the four equality properties: addition, subtraction, multiplication, and division. To get the value of an unknown variable, we simply add, subtract, multiply, or divide both sides of an equation.
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The top of a hill rises 64 feet above checkpoint -213. What is the altitude of the hill?
The top of the hill have an altitude of 1391 feet above sea level
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
From the table, checkpoint 3 is at 1327 feet above sea level. Since the top of a hill rises 64 feet above checkpoint 3, hence:
Altitude of hill = 1327 + 64 = 1391 feet
The top of the hill is 1391 feet
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CV={(Standard Deviation)/(Mean)}*100%
You are thinking about investing money in the stock market and have narrowed your choices to one of two
stocks: TD Bank or Cenovas Energy. For TD Bank you have the following statistics:
• Mean monthly closing price: $70.00
Sample standard deviation: $6.30
The monthly closing stock prices of Cenovas Energy for the last eight months is shown below:
Closing Stock Price: ($) 18.00 19.00 12.00 16.00 17.50 12.00 7.50 10.00
(a) Calculate the mean stock price of Cenovas Energy.
Answer=$
(b) Calculate the standard deviation for the sample prices of Cenovas Energy.
Answer=$
(c) What is the median stock price for Cenovas Energy?
Answer=$
(d) What is the range in Cenovas Energy's stock price?
Answer=$
(e) Calculate the coefficient of variation for each stock.
TD Bank Answer= %
Cenovas Energy Answer= %
(f) Which stock is riskier and why?
a. The mean stock price of Cenovus Energy is 15.437.
b. The standard deviation for the sample prices of Cenovus Energy is
3.93.
c. The median stock price for Cenovus Energy is 14
d. The range in Cenovus Energy's stock price is 11.5.
e. The coefficient of variation for each stock are 28.071% Cenovus Energy for % and 9% for TD Bank.
f. As the coefficient of variation is more for TD Bank it is riskier to buy.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.
a. The mean stock price of Cenovus Energy is,
= (18 + 19 + 12 + 16 + 17.50 + 12 + 7.50 + 10)/8.
= 112/8.
= 14.
b. The variance for the sample prices of Cenovus Energy is,
= [tex]\frac{1}{n}\[ \sum_{i=1}^{n}[x_i - \overline{x}]^2[/tex].
= (1/8)×[(18 - 14)² + (19 - 14)² + (14 - 12)² + (16 - 14)² +(17.50 - 14)² +(14 - 12)² +(14 - 7.50)² + (14 - 7.50)² +(14 - 10)²].
= (1/8)×[16 + 25 + 4 + 4 + 12.25 + 4 + 42.25 + 16].
= (1/8)×(123.5).
= 15.437.
Standard deviation = √(15.437).
= 3.93.
c. To find the median stock price for Cenovus Energy first we have the data set in ascending order.
7.50, 10.00, 12.00, 12.00, 16.00, 17.50, 18.00, 19.00.
So, The median of the stock price for Cenovus Energy is,
= (12 + 16)/2.
= 28/2.
= 14.
d. The range in Cenovus Energy's stock price is (19.00 - 7.50).
= 11.5.
e. The coefficient of variation for each stock is,
CV = {(Standard Deviation)/(Mean)}×100%.
CV = (3.93/14)×100%.
CV = 28.071 for Cenovus Energy.
CV = (6.30/70)×100%.
CV = 9% for TD Bank.
f. TD Bank's higher coefficient of variance makes investing riskier.
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celestine invested 1500000 simple interest at a rate of 5% per annum which amounted to 2000000. how long will it take in this investment.
The required it would take 6 years for the amount to be 2000000.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
here,
Celestine invested 1500000 simple interest at a rate of 5% per annum which amounted to 2000000.
Amount = 20,000,00
Principal = 15,000,00
Rate = 5% = 0.05
Time = n years
Amount = Principal [1 + rate×time]
20,000,00 = 15,000,00 [1 + 0.05×n]
n = 6.6 years
Thus, the required, it would take 6 years for the amount to be 2000000.
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Expand (2d - 5e)(2d - 5e)
Answer:
expanded from:4d²-20de-25e²
Edward marks exam scripts for a grade 11 extra class he charges R150 for a maths paper 1 script and R200 maths paper 2 scripts as shown below
What type of relationship is shown on the graph
The type of relationship shown on the graph that depicts Edward's exam scripts is a Linear relationship.
What is a linear relationship ?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Both a graphical representation of a linear relationship, in which the variable and constant are connected by a straight line, and a mathematical representation, in which the dependent variable is determined by multiplying the independent variable by the slope coefficient and a constant.
Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Edward's cost per math paper 1 or math paper 2 script marked will change depending on the type of paper and the number of papers. This simply means that Edward's charges are increasing per paper marked which is shown a linear relationship in the attached graph.
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Jackie wants to buy a new van for work.
She wants to borrow £7,500 to buy the van and looks at two bank loans for this amount.
an image
Formula for simple interest is: I=PRT100
I
=
P
R
T
100
Formula for compound interest is: A=P(1+r100
A
=
P
(
1
+
r
100
)n
n
What is the difference in the interest charged between the two banks?
Answer: The interest rates charged in both formulas are different.
Step-by-step explanation:
To begin with, the simple interest = PRT/100
In this, the interest is the same as the number of years.
For example, P=10,000 R=10% T=2yrs
SI = PRT/100
= 10,000*10*2/100
= 2000
This rupee 2000 is the same interest for two years.
compound interest = A= P(1+r/100)^n
In this, the interest changes every year up to the period of time.
For example, P= 10,000 R=10% N=2yrs
A= 10,000(1+10/100)^2
= 10,000*11/10*11/10
= 12100
I= A-P
=12100-10000
= 2100
This interest varies for 2 years.
Here you can see the problem in the picture
Answer:
[tex]\sqrt{6}[/tex]
Step-by-step explanation:
In a 45-45-90 triangle to find the two shorter sides (a and b) are represented as the number n in this case n is [tex]\sqrt{3\\[/tex] . The hypotenuse on the other hand is can be found by doing n[tex]\sqrt{2\\}[/tex] so you multiply [tex]\sqrt{3}(\sqrt{2} )[/tex] to get [tex]\sqrt{6}[/tex]
Simplify the following.
The value of the expression is (x∧2m-15)Yy∧5n +1). Option B
How to simplify the expression?You should understand that simplification involves making an expression more simpler to understand. Also, the expression is in index form that involves the division law of indices.
the given expression to be simplified is
(x∧3m-8)/x∧m-7) (y∧7n +1)/(y∧2n)
This can be simplifies as follows
(x∧3m-8-(m-7)(y∧7n+1(2n)
Simplify further to have the value
(x∧3n-8-m-7)(y∧7m-2n+1)
This implies that the value is
(∧2m-15)(y2n+1)
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After playing 5 games, you have 33 credits left. You play 4 more games and have 21 credits left. Write an equation that represents the number of credits y on the card after x games
Answer:
5x=33y,4x=21y I hope this is helpful
If BD=7x-10, BC=4x-29, and CD=5x-9, find each value
Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the triangle inequality theorem, we can set up the following inequality:
BD + BC > CD
7x - 10 + 4x - 29 > 5x - 9
Simplifying, we get:
11x - 39 > 5x - 9
Subtracting 5x from both sides, we get:
6x - 39 > -9
Adding 39 to both sides, we get:
6x > 30
Dividing by 6 from both sides, we get:
x > 5
So x must be greater than 5.
To find the value of BD, we can substitute the value of x in the equation:
BD = 7x - 10
BD = 7(5) - 10 = 25 - 10 = 15
To find the value of BC, we can substitute the value of x in the equation:
BC = 4x - 29
BC = 4(5) - 29 = 20 - 29 = -9
To find the value of CD, we can substitute the value of x in the equation:
CD = 5x - 9
CD = 5(5) - 9 = 25 - 9 = 16
So, BD = 15, BC = -9, CD = 16
Step-by-step explanation:
Pls help me, thanks
Given f(x) = 2x – 6, find f(10)
Answer:
14
Step-by-step explanation:
Basically, x is substituted by 10.
So if you plug that into the function, you would get
[tex]f(10)=2(10)-6[/tex]
Simplify it and you get
[tex]f(10)=14[/tex]
Simplify the following expression.
4√72
O A. 6√24
B.
144√6
OC. 24√6
D. 24√/2
O D.
The expression 4√72 can be simplified by first taking the square root of both sides, which gives us 2√72. Then, we can factor out a 6 from both sides, which gives us 24√6. Therefore, the simplified expression is 24√6.
What is expression?Expression is the process of conveying one’s thoughts, emotions, ideas, and beliefs through speech, writing, art, or any other form of communication. Expression is a form of communication that allows people to express themselves in a way that is meaningful and personal to them. It is a powerful way for individuals to express their thoughts, feelings, and opinions without fear of judgement or criticism. Expression is an important part of self-expression, and it can be used to connect with others through shared experiences, to create a sense of community, and to grow and learn from one another. Expression is an invaluable tool for self-expression, creativity, and communication.
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