(4,7 ) are solution of linear equations .
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
Solve the system of equations using elimination.
-2x + 3y = 13
x + y = 11
Multiply by 2
-2x + 3y = 13
2x + 2y = 22
5y = 35
y = 7
put in equation
x + y = 11
x = 11 - 7 = 4
so (x,y) = (4,7 )
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The accompany data represent the percentages of teenagers in various countries that have used certain drugs. Complete parts (a) through (c) below.
Country - A B C D E F G H I J K
Drug 1, x - 23 17 41 5 38 18 23 5 8 54 35
Other Drug - 3 2 21 2 15 9 15 2 2 32 25
The coefficient of determination is: 88%
How to solveThe following table shows the calculations:
X Y X^2 Y^2 XY
22 3 484 9 66
17 4 289 16 68
41 21 1681 441 861
5 1 25 1 5
36 16 1296 256 576
19 7 361 49 133
24 14 576 196 336
6 4 36 16 24
8 2 64 4 16
52 32 2704 1024 1664
35 23 1225 529 805
Total 265 127 8741 2541 4554
Sample size: n=11
Now,
Syy=1074.72727Sxx= 2356.90909Sxy = 1494.454545(a)
The coefficient of correlation is :
r=[tex]\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.94[/tex]
(b)
The slope of the regression equation is 0.63
S.
and intercept of the equation will be
[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=-3.729965\approx -3.73[/tex]
So the regression equation will be
y'=-3.73+0.63*x
(c)
The coefficient of determination is: 88%
Regression is a statistical analytical method that investigates correlations between two or more variables. Its widespread usage stems from its ability to forecast or assess the value of one contingent variable using one or many independently varying variables.
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Please help me answer this I will give you brainliest!!!!
Answer:
8) ]-infinity ,1]
9) ]-infinity,-2[
Answer:
8) x ≤ 1 9) x < -2
Hope this helps.
what is the lowest depth the diver reaches using the function d(t)=3t^2-12t+0
Answer:
12 units.
Step-by-step explanation:
Convert the expression to vertex form:
d(t)=3t^2-12t+0
= 3(t^2 - 4t)
= 3[(t - 2)^2 - 4]
= 3(t-2)^2 - 12.
Minimum value = 12.
Please solve this question!!
[tex]f(x)=\displaystyle\sum_{n=1}^{\infty}c_n\cdot x^n \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\sum_{n=1}^{\infty}c_n\cdot n\cdot x^n\implies n\sum_{n=1}^{\infty}c_n\cdot x^n\implies n\cdot f(x)\quad \textit{assuming "n" is an constant}[/tex]
You’re flying your dragon kite. it’s connected to 37 yards of string. The kite is directly above the edge of a pond. The edge of the pond is 32 yards from where the kite is tied to the ground. how high Is the kite above the edge of the pond? Round to one decimal place as needed
The kite is approximately 18.57 yards high above the edge of the pond.
How to solve for the height of the kiteThe Pythagorean theorem would be used to solve the prob;lem that we have here
The theorye tell us that the squatre of the hypotenuse is the same as the sum of the square of the other two sides
The formula is written as
c^2 = a^2 + b^2
In this case:
c = 37 yards (length of the string)
a = 32 yards (distance from where the kite is tied to the ground to the edge of the pond)
b = height of the kite above the edge of the pond (which we need to find)
Now, plug the values into the Pythagorean theorem:
37^2 = 32^2 + b^2
1369 = 1024 + b^2
Subtract 1024 from both sides:
b^2 = 345
Now, take the square root of both sides to solve for b:
b = √345
= 18.57 yards
The kite is approximately 18.57 yards high above the edge of the pond.
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Round to the nearest tenth, then find the difference. 13.56 − 10.02 = ___ pleas help I need help im in a test im sorry if 10 points is not enough.
Me podrían ayudar a resolver esto? Tengo la respuesta lo que necesito es el procedimiento. Muchas gracias
2√8p²q³r
The algebraic expression can be simplified to 4p√2q³r
How to simplify an algebraic expression?An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
The expression can be simplified as follow:
2√(8p²q³r) = 2 * √8 * √p² √(q³r)
= 2 * √(4 * 2) * p √(q³r)
= 2 * √4 * √2 * p √(q³r)
= 2 * 2 * √2 * p √(q³r)
= 4p√2q³r
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Question in English
Could you help me solve this? I have the answer what I need is the procedure. Thank you so much
2√8p²q³r
HELP
Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign?
A square shaped traffic sign is shown with the length of one side labeled as x plus 1.
x2 + 2x + 1
x2 + x + 1
x2 + 2x
x2 + 1
The expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A) [tex]x^2+2x+1[/tex].
What is area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
Here the given square shaped traffic sign side length a = x+1
We know that, area of square = [tex]a^2[/tex] square unit.
Then, area of the square shaped traffic sign is
=> A = [tex](x+1)^2[/tex]
=> A = [tex]x^2+2x+1[/tex]
Hence the expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A) [tex]x^2+2x+1[/tex].
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The city of Raleigh has 9200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 109 said they'd vote for Brown, 235 said they'd vote for Feliz, and 6 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not a percent.
That this is just an estimate of the true proportion of all voters who would vote for Brown, based on the sample of 350 voters surveyed. The true proportion could be different, due to sampling variability.
What is Statistic?
A statistic is a numerical measure that summarizes some aspect of a dataset. It is a way to describe a sample of data in a concise and meaningful way. Common examples of statistics include measures of central tendency such as the mean, median, and mode, as well as measures of variability such as the range, standard deviation, and variance.
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is the sample proportion, which is the number of voters who said they'd vote for Brown divided by the total number of voters surveyed:
Number of votes who said they'd vote for brown
total number of surveyed
= 109/350
=0.31
Therefore, based on the sample of 350 voters surveyed.
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can someone please explain how to understand where to insert the pair of brackets and why? thank you:)
Applying PEMDAS the correct expression showing where to insert brackets to make it correct are:
i. 3 × (5 + 2) + 2 = 23; ii. (12 ÷ 4) + 2 = 5
How to Apply PEMDAS in Inserting Brackets?i. 3 × (5 + 2) + 2 = 23
In this expression, we need to prioritize addition over multiplication, as per the order of operations (PEMDAS or BODMAS).
Therefore, we should add 5 and 2 first and then multiply the result by 3. Adding the brackets around 5 + 2 forces the addition to be done before multiplication, resulting in the correct answer.
ii. (12 ÷ 4) + 2 = 5
In this expression, we need to prioritize division over addition. Therefore, we should divide 12 by 4 first and then add the result to 2. Adding brackets around 12 ÷ 4 forces the division to be done before addition, resulting in the correct answer.
To understand where to insert brackets, you need to follow the order of operations, which is a set of rules that dictates the order in which arithmetic operations should be performed. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction)
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An initial amount of money is placed in an account at an interest rate of 4% per year, compounded continuously. After four years, there is $1255.66 in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.
Answer:
We can use the continuous compounding formula to solve this problem:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
1255.66 / e^0.16 = P
Using a calculator to evaluate e^0.16, we get:
1255.66 / 1.17351087099 = P
Simplifying:
P = $1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
Step-by-step explanation:
compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
P = 1255.66 / e^0.16
Using a calculator to evaluate e^0.16, we get:
P = 1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
rate 5 stars po if this helps u~ welcome po!
Answer:
We can use the continuous compounding formula to solve this problem:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
1255.66 / e^0.16 = P
Using a calculator to evaluate e^0.16, we get:
1255.66 / 1.17351087099 = P
Simplifying:
P = $1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
Step-by-step explanation:
compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.
Substituting the known values into the formula, we get:
1255.66 = Pe^(0.04*4)
Simplifying the exponent:
1255.66 = Pe^0.16
Dividing both sides by e^0.16:
P = 1255.66 / e^0.16
Using a calculator to evaluate e^0.16, we get:
P = 1069.44
Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).
rate 5 stars po if this helps u~ welcome po!
A substance with a half life is decaying exponentially. If there are initially 12 grams of the substance and after 2 hours there
are 7 grams, how many grams will remain after 3 hours? Round your answer to the nearest hundredth, and do not include
units.
Provide your answer below:
Answer:
5.35 grams
Step-by-step explanation:
Given that a 12 grams of a substance will decay exponentially to 7 grams in 2 hours, you want to know the amount remaining after 3 hours.
EquationThe amount remaining can be described by ...
remaining = (initial amount)·(decay factor)^(t/(decay interval))
remaining = 12(7/12)^(t/2) . . . . where t is in hours
ApplicationAfter 3 hours, the amount remaining is ...
remaining = 12(7/12)^(3/2) ≈ 5.35 . . . . grams
About 5.35 grams will remain after 3 hours.
__
Additional comment
The half-life is about 2.572 hours.
Ken volunteers 1hr25min each day. How many hours of volunteering is completed in 4 weeks? Enter a mixed number.
He completed volunteering in 39 hours 40 minutes in 4 weeks
How to determine this
If Ken volunteers 1 hr 25 mins each day
i.e 1 hr 25 mins = 1 days
By converting 1 hr 25 mins to mins
When 60 mins = 1 hr
1 hr 25 mins = 60 + 25 = 85 mins
How many hours of volunteering is completed in 4 weeks
Let x represent the numbers of hours
i.e x = 4 weeks
By converting 4 weeks to days
When 7 days = 1 week
4 weeks = 4 * 7 days
= 28 days
So, when 85 mins = 1 day
x mins = 28 days
x = 28 days * 85 mins/1 day
x = 2380 mins
By converting it back to hour
When 60 mins = 1 hour
2380 mins = x
x = 2380/60 hour
x = 39 hours 40 mins
Therefore, the hours that can be completed in 4 weeks is 39 hours 40 minutes
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Jonathan makes two handcrafted
wooden boxes. The volume of the
oak box is 2x³ + 5x²-3x cm³. The
volume of the maple box is 2x3 + 9x²
2x 24 cm³. In both expressions,
x represents the width of the box in
centimeters.
Which of the following is a true
statement?
statement B and D are true. to determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.
what is expressions ?
In computer programming, an expression is a combination of values, variables, and operators that produces a result or value. Expressions can be simple or complex, and they can be used in a variety of contexts, such as assigning values to variables, performing calculations, and making logical decisions.
In the given question,
To determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.
The volume of the oak box is 2x³ + 5x² - 3xc*m³.
The volume of the maple box is 2x³ + 9x² - 2x - 24c*m³.
A. The oak box has a volume 4x² + x 24c*m³ greater than the maple box.
To compare the volumes, we need to subtract the volume of the maple box from the volume of the oak box:
(2x³ + 5x² - 3xcm³) - (2x³ + 9x² - 2x - 24cm³)
= 2x³ - 4x² + 2x + 24c*m³
Therefore, statement A is not true.
B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.
To compare the volumes, we need to subtract the volume of the oak box from the volume of the maple box:
(2x³ + 9x² - 2x - 24cm³) - (2x³ + 5x² - 3xcm³)
= 4x² + x - 24c*m³
Therefore, statement B is true.
C. The total volume of 1 oak box and 1 maple box is 4x³ + 14x² + 5x + 24c*m³.
To find the total volume, we need to add the volumes of the oak and maple boxes:
(2x³ + 5x² - 3xcm³) + (2x³ + 9x² - 2x - 24cm³)
= 4x³ + 14x² - x - 27c*m³
Therefore, statement C is not true.
D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.
To find the total volume of 2 maple boxes, we need to multiply the volume of 1 maple box by 2:
2(2x³ + 9x² - 2x - 24cm³) = 4x³ + 18x² - 4x - 48cm³
Therefore, statement D is true.
In summary, the correct statements are:
B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.
D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.
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Mathematic desmos
6.7 Readiness Check
Write point P as a fraction and as a decimal.
Fraction
Decimal
The coordinates of P when written as a fraction and as a decimal, is:
Fraction - (3/4, 5/6)Decimal - (0.75, 0.83 )How to convert to fractions ?Point P has the coordinates of ( 3/4 , 5/6 ) which means that it is already in fraction form as it has both a numerator and a denominator for the x and ya values.
We can then convert these fractions to decimal form as shown :
x - value : 3 ÷ 4 = 0.75
y - value : 5 ÷ 6 = 0.83
In decimals, it is:
(0.75, 0.83)
In conclusion, as a fraction, point P is ( 3 / 4, 5 / 6 ), and as a decimal, point P is ( 0.75, 0.83 ).
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A BOAT NEEDS TO TRAVEL NORTH AT 30KM PER HOUR AND A CONSTANT CURRENT OF 4KM PER HOUR IS FLOWING IN NORTH-WEST DIRECTION WHAT IS THE EQUIVALENT SPEED IN STILL WATER TO ACHIEVE ACTUAL SPEED OF 30KM PER HOUR?
If the boat travel north at 30 km per hour . the equivalent speed in still water required to achieve an actual speed of 30 km/h is 30.1 km/h.
What is the speed?Finding the boat's true speed using Pythagoras' theorem using this formula
Speed = √((30 km/h)^2 + (4/√(2) km/h)^2)
Let plug in the formula
Speed = √(900 + 8) km/h
Speed = √(908) km/h
Speed = 30.1 km/h
Speed = 30 km/h ( Approximately)
Therefore the speed is 30km/h.
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24a + 56b= ? Using distribute law
what expression is equivalent to 91 plus 39?
Answer: 130
Step-by-step explanation:
The problem is asking for an expression that is equivalent to the addition of 91 and 39. An expression is a combination of numbers, variables, and mathematical operations that does not have an equal sign. In this case, the expression we are looking for should evaluate to the same value as the sum of 91 and 39, which is 130.
To obtain this expression, we simply add 91 and 39, since the sum of these two numbers is equivalent to the expression we are looking for. Adding 91 and 39, we get:
91 + 39 = 130
Therefore, the expression that is equivalent to 91 plus 39 is simply 130.
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z = 3x + y solve for x
Answer:
x = (y-z)/3
Step-by-step explanation:
z = 3x + y
3x = z - y
x = (z - y)/3
definition of a tangent?
Answer:
A tangent is a line that touches the curve or a circle at a point..
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume there are 360 days in a year.
P = $3000, r = 2.5%, t = 9 months
The simple interest owed for the use of the money is $56.25.
The following formula can be used to determine the simple interest due for the usage of the money:
Simple Interest = P x r x t ÷ 360
Where P is the principal amount borrowed, r is the annual interest rate as a decimal, and t is the time period in days.
In this case, the principal amount P is $3000, the interest rate r is 2.5% or 0.025 as a decimal, and the time period t is 9 months or 270 days (assuming 30 days per month).
Simple Interest (SI) = $3000 x 0.025 x 270 ÷ 360
SI = $56.25
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A rectangle's base is 3 in shorter than five times its height. The rectangle's area is 68 in?. Find this rectangle's dimensions.
The rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in, whose area is given as 68in².
What is rectangle?It has two pairs of equal-length sides that are at right angles to each other. It is the most common type of quadrilateral, and it can be found in everyday objects like windows, doors, and tabletops.
To solve this problem, we need to use the formula for the area of a rectangle (A = l x w), where A is the area, l is the length, and w is the width. We also know that the base is 3 inches shorter than 5 times the height. Therefore, we can set up the equation to solve for the height and the base of the rectangle as follows:
A = l x w
A = (h + 3) x (5h)
A = 5h² + 3h
5h² + 3h = 68
h= -2 (as height can not be in negative)
h= 2
By using the quadratic formula, we can solve for the height, h, which is equal to 2.
Therefore, the rectangle's height is 2 in, and the rectangle's base is 5 x 2+ 3 = 30 in.
This problem was solved by using the quadratic equation to solve for the height of the rectangle, which was then used to solve for the base.
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The two buses drove towards each other at constant speeds. The first left NY at 11AM and arrived in Boston at 4 PM, and the second left Boston at 12 PM and arrived in NY at 5 PM. What time did they meet?
The two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
Since the two buses are traveling towards each other at constant speeds, we can use the formula for finding the time two objects meet when traveling at constant speeds in opposite directions:
t = (d2 - d1)/(v1 + v2)
Where t is the time they meet, d1 is the distance the first bus travels, d2 is the distance the second bus travels, v1 is the speed of the first bus, and v2 is the speed of the second bus.
In this case, d1 is the distance between NY and Boston (approx. 200 miles), d2 is the distance between Boston and NY (also approx. 200 miles), v1 is the speed of the first bus (200 miles in 5 hours, or 40 miles/hour), and v2 is the speed of the second bus (200 miles in 5 hours, or 40 miles/hour).
Plugging these values into the formula, we get:
t = (200 - 200)/(40 + 40)
t = 0/80
t = 0
Hence, the two buses meet at the same time they left their respective cities, so they meet at 11 AM in NY.
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i need the answer to 1 over 3
Answer:
1 over 3 would juts be 1/3
Determine the five-number summary for the data set. 20, 26, 18, 31, 22, 28, 30
The five-number summary for the given data set is 18, 22, 26, 30, 31.
What is five-number summary?The five-number summary is a set of descriptive statistics that provides information about a dataset by summarizing the data's five most important features. It includes the minimum data point, the first quartile, the median, the third quartile, and the maximum data point.
In order to calculate the five-number summary for the given data set (20, 26, 18, 31, 22, 28, 30), we first need to arrange the data in ascending order: 18, 20, 22, 26, 28, 30, 31.
The minimum data point is 18, the first quartile is 22, the median is 26, the third quartile is 30, and the maximum data point is 31.
So, the five-number summary for the given data set is 18, 22, 26, 30, 31.
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what is the solution to the system of equations below?
y= 1/2x + 6 and y= - 3/4x - 4
(-8,2)
(-8,-1)
(8,-10)
(8,10)
Answer:
(- 8, 2 )
Step-by-step explanation:
y = [tex]\frac{1}{2}[/tex] x + 6 → (1)
y = - [tex]\frac{3}{4}[/tex] x - 4 → (2)
substitute y = [tex]\frac{1}{2}[/tex] x + 6 into (2)
[tex]\frac{1}{2}[/tex] x + 6 = - [tex]\frac{3}{4}[/tex]x - 4
multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions
2x + 24 = - 3x - 16 ( add 3x to both sides )
5x + 24 = - 16 ( subtract 24 from both sides )
5x = - 40 ( divide both sides by 5 )
x = - 8
substitute x = - 8 into either of the 2 equations and evaluate for y
substituting into (1)
y = [tex]\frac{1}{2}[/tex] (- 8) + 6 = - 4 + 6 = 2
solution is (- 8, 2 )
Find the surface area of the regular pyramid shown to the nearest whole number.
The surface area of the hexagonal pyramid is 740 metres².
How to find surface area of a pyramid?The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:
Therefore,
surface area of the hexagonal pyramid = A + 1 / 2 ps
where
A = surface areap = perimeter of the bases = slanted heightTherefore,
A = base area = 1 / 2 p a
where
a = apothemp = perimeterHence,
p = 10(6) = 60 metres
a = 5√3 metres
A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres
Therefore,
surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16
surface area of the hexagonal pyramid = 150√3 + 480
surface area of the hexagonal pyramid = 739.807621135
surface area of the hexagonal pyramid = 740 metres²
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The surface area of the hexagonal pyramid is 740 metres².
How to find surface area of a pyramid?The pyramid above is an hexagonal pyramid. The surface area of the pyramid can be found as follows:
Therefore,
surface area of the hexagonal pyramid = A + 1 / 2 ps
where
A = surface areap = perimeter of the bases = slanted heightTherefore,
A = base area = 1 / 2 p a
where
a = apothemp = perimeterHence,
p = 10(6) = 60 metres
a = 5√3 metres
A = base area = 1 / 2 × 60 × 5√3 = 150√3 metres
Therefore,
surface area of the hexagonal pyramid = 150√3 + 1 / 2 × 60 × 16
surface area of the hexagonal pyramid = 150√3 + 480
surface area of the hexagonal pyramid = 739.807621135
surface area of the hexagonal pyramid = 740 metres²
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4. How many combinations are possible on a 4 number computer cable lock. Each space can
be any number 0 - 9. The only exception is that all four numbers cannot be the same.
How many combinations are possible?
The possible number of combinations are 9,720.
What is combination?In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of selection does not matter. The number of combinations of size k that can be chosen from a set of n items is denoted by the symbol C(n,k) or sometimes by ⁿCk, and is given by the formula:
C(n,k) = n! / (k! ×(n - k)!)
Define number?A number is a mathematical concept used to represent quantity or value. It can be a whole number, such as 1, 2, 3, or a decimal, such as 1.5 or 3.14. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life for counting and measuring.
There are a total of 9,720 possible combinations for a 4-number computer cable lock where each space can be any number 0-9, except for the restriction that all four numbers cannot be the same. To arrive at this number, we can first calculate the total number of possible combinations without the restriction, which is 10⁴ = 10,000. Then we subtract the number of combinations where all four numbers are the same, which is simply 10 (i.e. 0000, 1111, 2222, etc.), to get 9,990. Finally, we subtract the number of combinations where all four numbers are the same and also subtract the number of combinations where three out of four numbers are the same (which is simply 10×4 = 40 since there are 10 possible values for the repeated number and 4 possible positions for it), which gives us a final count of 9,720.
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If the sides of a square are increased by 11, the area becomes 400. What is the length of the original side?
Answer: x = 9 units
Step-by-step explanation:
The amount of snowfall in December was 5 7/8 feet. The amount of snowball in October was 1/4 feet. How much more snowfall was there in December? Write your answer as a mixed number in simplest form.
Answer:
5 3/8 ft
Step-by-step explanation:
5 7/8 - 1/4 = 5 7/8 - 4/8 = 5 3/8