How many ternary (0, 1, 2) sequences of length 10 are there without any pair of consecutive digits the same?
There are 10 spaces then the first space will be (3,1), the second one cannot be the same as the first one so it will have to be (2,1).
So it will come down to 3×2^9
There are 1536 ternary sequences of length 10 with no pair of consecutive digits the same.
Explanation:The question is asking about how many ternary sequences of length 10 there can be without any pair of consecutive digits being the same. In a sequence of length 10, each digit has 3 possible values (0, 1, 2) but cannot be the same as the digit before it. Therefore, the first digit has 3 choices, and each subsequent digit has 2 choices (since it can't be the same as the previous one). Using the multiplication principle of counting, there would be 3*2^9 = 1536 such sequences.
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y=-4x-7 in standard form
John made of a pound of fudge and Mary made of a pound of fudge. Ricky takes the sum of the two amounts of fudge and divides it into three equal portions, planning to keep one portion for himself. How much fudge does Ricky keep?
Six is less than or equal to the sum of a number n and 15
the solution is[tex]\( n \geq -9 \).[/tex]
Sure, let's break down the problem step by step.
1. The inequality given is[tex]\( 6 \leq n + 15 \).[/tex]
2. To find the value of ( n ), we'll start by isolating ( n ) on one side of the inequality.
[tex]6 &\leq n + 15 \\6 - 15 &\leq n \\-9 &\leq n[/tex]
So, the solution is[tex]\( n \geq -9 \).[/tex]
Now, let's explain the steps and the final answer in more detail.
The inequality[tex]\( 6 \leq n + 15 \)[/tex] states that "six is less than or equal to the sum of a number ( n ) and fifteen."
To solve for ( n ), we first subtract 15 from both sides of the inequality to isolate ( n ):
[tex]\[ 6 - 15 \leq n \][/tex]
This simplifies to:
[tex]\[ -9 \leq n \][/tex]
So, the solution to the inequality is[tex]\( n \geq -9 \),[/tex] which means that any number greater than or equal to -9 will satisfy the original inequality [tex]\( 6 \leq n + 15 \).[/tex]
In conclusion, the correct answer is[tex]\( n \geq -9 \)[/tex], and this means that any number greater than or equal to -9 makes the statement "six is less than or equal to the sum of that number and fifteen" true.
complete question
Six is less than or equal to the sum of a number n and 15
The price of an item has risen to $156 today. Yesterday it was $65 . Find the percentage increase.
What is the value of ▲ in the equation shown?
7 x 9 = (7 x 10) - (7 x ▲)
=_____
A box contains 4 bags of sugar,The total mass of all 4 bags is 6 kg. What is the mass of each bag in grams?
Answer:
1500 g.
Step-by-step explanation:
So i'll start by converting 6 kg to grams. Which is 6000 g.
There are four bags so i will do 6000 divided by 4 which equals 1500.
So the answer is 1500. each bag weighs 1500 g.
Your welcome hope this was helpful!
A fence around a square garden is made up of 4 equal sized pieces that are each 5 1/2 feet long. Matt decided to make the sides 2 1/2 times longer. How much fencing does he need in all?
kenneth earns a commission of 4 1/2 on total sales plus a weekly salary of $350. What is his gross pay if his sales are 4500 this week?
Answer:
gross pay = $552.50
Step-by-step explanation:
Kenneth earns a commission on his total sales = [tex]4\frac{1}{2}[/tex] %
= [tex]\frac{9}{2}[/tex] %
= 4.5%
If his sales are 4500 this week.
His commission would be = 4.5% × 4500
= [tex]\frac{4.5}{100}\times 4500[/tex]
= 0.045 × 4500
= $202.50
His weekly salary is $350
Gross pay = 350 + 202.50 = $552.50
Kenneth's gross pay would be $552.50 this week.
There are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred. Julia says it is one thousand, five hundred. Kim says it is 15 hundreds. Who is correct? Explain your thinking.
Answer:
They are both correct.
Step-by-step explanation:
SInce they both are saying the same amount of pages just in different ways, Kim is saying a thousand plus five hundred, that is 1500, and Kim says 15 hundred, which is basically 1500, so they are both rounding up the number to the nearest cent correctly just are expressing the number in different ways.
What integer represents the change in balance from Monday to Tuesday?
The integer represents the change in balance from Monday to Tuesday is -34
What is integer?Zero, a positive natural number, or a negative integer are all considered integers. The equivalent positive numbers' additive inverses are represented by the negative numbers. The boldface Z or blackboard bold is frequently used to represent the set of all numbers.
Based on the question, there is a change in balance from Monday to Tuesday , then
monday=-21
Tuesday = -55
The change =-55 - (-12)
=-55+12
=-34
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Write an equation of the line through (-2,-1) having slope 4/13 Give the answer in standared form
Ambrose has an indifference curve with equation x2= 20 − 4 x 1/21. when ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.
An indifference curve is used in economics to show different combinations of goods that provide equal satisfaction to a consumer. Ambrose's indifference curve equation and marginal rate of substitution are given, representing his willingness to trade one good for another while holding utility constant.
Explanation:An indifference curve is a graphical representation used in economics to show the different combinations of two goods that provide equal satisfaction or utility to a consumer. In this case, Ambrose has an indifference curve with the equation x2 = 20 - 4x1/21. To find his marginal rate of substitution (MRS), we need to calculate the slope of the indifference curve at the point (4, 16). The MRS is given as 25/4, which means that Ambrose is willing to give up 25/4 units of x1 in exchange for 1 unit of x2, while keeping his utility constant.
A 27 oz bottle of a new soda costs $2.25. What is the unit rate, rounded to the nearest tenth of a cent?
Upon decomposition, one sample of magnesium fluoride produced 1.65 kg of magnesium and 2.57 kg of fluorine. a second sample produced 1.32 kg of magnesium. how much fluorine (in grams) did the second sample produce?
The amount of fluorine (in grams) on second sample is,
⇒ 2062.5 g.
Here,
On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.
And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.
We have to find the amount of fluorine (in grams) on second sample.
What is Ratio?
Ratios compare two numbers, usually by dividing them.
Now,
On Sample one, 1.65 kg Magnesium and 2.57 kg Fluorine.
And, On second sample, 1.37 kg of magnesium and let x kg of fluorine.
Hence,
The ratio from sample one,
⇒ 1.65kg / 2.57kg = 0.64
The ratio of second sample,
⇒ 1.3 kg / x kg
Now, Using Law of define properties of ratio, the first and second should have the same ratio.
Hence,
1.3 kg / x kg F = 0.64
x = 2.0315 kg F
x = 2031.2 g F
Therefore, The amount of fluorine (in grams) on second sample is,
⇒ 2062.5 g.
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The distributive property combines_____________and _____________ to make multiplying whole numbers simpler.
45 points for first most detailed / accurate answer:
You are planning to make and sell 3 different sizes of cylindrical candles. You buy 1 cubic foot of candle wax for $20 to make 24 candles (8 per 3 sizes).
a. Design the candles what dimensions are each size of candle? (Remember, 3sizes)
b. You want to make a profit of $100. Decide on a price for each size of candle.
c. Did you set the prices so that they are proportional to the volume of each size of candle? Why/Why not?
What are other names for a trapezoid
Final answer:
The term 'trapezoid' refers to a four-sided figure with at least one pair of parallel sides in American English, while 'trapezium' is the equivalent term in British English.
Explanation:
Other names for a trapezoid include trapezium in British English. The term trapezoid is commonly used in American English to describe a four-sided figure with at least one pair of parallel sides. In contrast, British English refers to the same shape as a trapezium. It is important not to confuse these terms with trapezius, which is a muscle in the human body, or other unrelated terms such as triad or tricarboxylic acid cycle (TCA).
In isosceles triangle the length of the base is twice shorter than the length of a leg. The perimeter of this triangle is 50cm. Find the lengths of all sides.
Answer:
yes
Step-by-step explanation:
Jogging is one of the few sports that has been consistently increasing over the past few years. the number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y equals x plus 26y=x+26, where x is the number of years after 2000.
How many hours between 8:30 am to 5:30 pm
There are 9 hours between 8:30 am to 5:30 pm
How many hours between 8:30 am to 5:30 pmFrom the question, we have the following parameters that can be used in our computation:
Initial time = 8:30 am
Final time = 5:30 pm
using the above as a guide, we have the following:
Number of hours = Final time - Initial time
substitute the known values in the above equation, so, we have the following representation
Number of hours = 5:30 pm - 8:30 am
Evaluate
Number of hours = 9 hours
Hence, there are 9 hours between 8:30 am to 5:30 pm
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Teddy was having trouble fitting into his clothes due to weight gain. In January he weighed 180 lbs 6 oz. He gain 3lbs 9 oz , 5 lbs 12 oz and 6 lbs 11 oz in the next 3 months how much does teddy weigh now
A) 196 lbs 6 oz
B) 196 lbs 8 oz
C) 194 lbs 6 oz
D) none
E) 194 lbs 8 oz
Which equation has solution x = -3?
A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x + 8 = 10
D) 1/2 (2x - 6) = -6
Given that events a and b are independent and that p(a) = 0.8 and p(b|a) = 0.4, then p(a and
b.= 0.32.
a. True
b. False
Hayden is 59 inches tall and is standing on top of a ladder that is 2 yards tall. In inches, what is the distance from the top of Hayden's head to the ground?
when a decimal is written in word form,what indicates that the equivalent form is a mixed number and not a fraction
Final answer:
A decimal written in word form represents a mixed number if there's a whole number followed by 'and', then the fractional part, such as 'two and three tenths' for 2.3.
Explanation:
When a decimal is written in word form, the indication that the equivalent form is a mixed number rather than a fraction is the presence of a whole number followed by the word 'and', then the fractional part.
For example, 'two and three tenths' (2.3 in numeric form) is a mixed number, as it has a whole number 'two' and the fractional part 'three tenths'. In contrast, a number written solely as 'three tenths' would represent just a fraction (0.3 in numeric form).
The total cost of four pens and seven mechanical pencils is $13.25. The cost of each pencil is 75 cents.
a. Using an arithmetic approach, find the cost of a pen.
b. Let the cost of a pen be dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of .
c. Write an equation that could be used to find the cost of a pen.
d. Determine a value for for which the equation you wrote in part (b) is true.
Answer:
Step-by-step explanation:
4x+7(0.75)=13.25
4x+5.25=13.25
4x=13.25-5.25
4x=8
X=$2 each
Let f(x)= x+3 and g(x)= 4x-3. Find (f+g)(3).
A hypothesis _____.
A. must be tested
B. is supported by large amounts of data
C. is accepted by the scientific community
B. must be proven true for an experiment to be worthwhile
factor the expression 10x+40
Final answer:
To factor the expression 10x + 40, we can factor out the greatest common factor (GCF) of 10 from both terms, resulting in 10(x + 4).
Explanation:
To factor the expression 10x + 40, we can first find the common factor for both terms, which is 10. Factoring out 10, we get 10(x + 4). This expression represents the original 10x + 40. In simpler terms, we've taken out the common factor of 10 from both terms, leaving us with 10 multiplied by the quantity (x + 4). This factored form is useful for simplifying expressions or solving equations. Essentially, factoring helps us break down a more complex expression into simpler parts, making it easier to work with and understand in various mathematical contexts.