For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.
What is mathematical induction?An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.
Let, n = 0.
Therefore,
7⁴ - 7⁰.
= 2401 - 1.
= 2400.
= 30×80, Divisible by 30.
Similarly for n = 1 we have,
7⁵ - 7¹.
= 16807 - 7.
= 16800.
= 30×560.
Hence by induction, the cycle will continue.
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If 10x =5 what is x
Answer:
1/2
Step-by-step explanation:
Select the graph that correctly displays the solution of the system of inequalities. y > 2x – 4 y ≤ –x – 7
The solution to the system of given inequalities is (-7, 0).
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given system of inequalities are y> 2x-4 and y≤ -x-7.
The solution of the system of inequalities is the intersection region of all the solutions in the system.
x<y/2 +2 and x≤-y-7
The solution of the system of inequalities is (-7, 0)
Therefore, the solution to the system of given inequalities is (-7, 0).
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A 13-foot ladder leans against the side of a house with its base 3 feet from the house. Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house. Round your answer to the nearest hundredth.
Answer: 12.65 ft
Pythagorean theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
So, [tex]a^{2}[/tex] + [tex]3^{2}[/tex] = [tex]13^{2}[/tex]
169 - 9 = 160
[tex]\sqrt{160}[/tex] is 12.65.
Hope it helps.
When fitting a pipe into an existing fitting it allows a diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005" what's the maximum allowable pipe diameter? a. 0.496, b. 0.501, c. 0.499, d. 0.541
Considering that the diameter variance of 0.001". If the interior diameter of the pipe is 0.49" and the pipe thickness is 0.005". the maximum allowable pipe diameter is 0.501''
How to find the maximum allowable pipe thicknessThe maximum allowable pipe diameter is calculated by
finding the total thickness of pipe
= interior diameter + 2 * pipe thickness
= 0.49 + 2 * 0.005
= 0.49 + 0.01
= 0.50
The diameter variance gives the range of the allowable diameter to ± 0.001 for maximum allowable pipe diameter we use + 0.001
hence
= 0.50 + 0.001
= 0.501
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Find the 8th term of the geometric sequence 3, 12, 48, ...
You have a four color spinner and a six color spinner. Both are spun at the same time. What are the total number of possible outcomes?
Answer:
24
all u have to do is draw out a tree diagram or multiply 6*4
A salesperson uses random digit dialing to call people and try to interest them in applying for a charge card for a large department store chain. From past experience, she is successful on 2% of her cals. in typical working, she makes 50 calls. Let X be the number of calls on which she is unsuccessful.
a. This is binomial distribution. Explain using the BINS method why this is so.
b. Find the mean and standard deviation of X. Leave answer to 4 d.p
c. Find the probablity of P(X>or equal to 48)
Answer:
a)
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b) The mean is 1 and the standard deviation is 0.9899.
c) [tex]P(X \geq 48) = 0[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
From past experience, she is successful on 2% of her calls.
This means that [tex]p = 0.02[/tex]
50 calls.
This means that [tex]n = 50[/tex]
a. This is binomial distribution. Explain using the BINS method why this is so.
BINS: Binary outcomes, Independent Trials, n is fixed, and same value of p for all trials.
In this question, for each call, there are only two possible outcomes, either it is successful, or it is not, so binary outcomes. For each call, the probability of a success or failure is the same, which means that the trials are independent, having the same value of p. And the number of trials, which is 50, is fixed. This means that this is a binomial distribution.
b. Find the mean and standard deviation of X.
The mean is:
[tex]E(X) = np = 50*0.02 = 1[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.02*0.98} = 0.9899[/tex]
The mean is 1 and the standard deviation is 0.9899.
c. Find the probablity of P(X>or equal to 48)
This is:
[tex]P(X \geq 48) = P(X = 48) + P(X = 49) + P(X = 50)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 48) = C_{50,48}.(0.02)^{48}.(0.98)^{2} \approx 0[/tex]
[tex]P(X = 49) = C_{50,49}.(0.02)^{49}.(0.98)^{1} \approx 0[/tex]
[tex]P(X = 50) = C_{50,50}.(0.02)^{50}.(0.98)^{0} \approx 0[/tex]
So
[tex]P(X \geq 48) = 0[/tex]
Subtract the sum of 9 3/4 and 3 1/8 from 18 7/16
A. 5 9/16
B. 5 3/4
C. 6 9/16
D. 6 3/4
help pls
Answer:
A
Step-by-step explanation:
hope you have a great day!!
Find the product
(b+2)(-b^2+4b-3b)
Step-by-step explanation:
=>(b*-b²)+(b*4b)-(b*3b)-(2*-b²)+(2*4b)-(2*3b)
=>-b³+4b²-3b²-2b²+8b-6b
=>-b³+b²-2b²+2b
=>-b³-b²+2b
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answer:
$6.33
Step-by-step explanation:
42.40 x 0.15 = $6.33
Finding area of composite figure
Answer:
73
Step-by-step explanation:
so basically this process is rather easy, okay what u have to do is find the area but since u cant u just have to try your best and go over the answer with a friend, oh you have none? Sorry for assuming, so just ask siri if you have 0 friends, the formula should look a little like this:
A=l*w or A=b*h
which than u would have to add up the circumference (sorry for not mentioning that earlier) so the new formula would be a little like this
A+C=
than thats your answer (it should be 12.)
Evan and two friends go to a farm to pick strawberries. Evan records the number of baskets of strawberries that each person picks in a table.
Evan forgot to record how many strawberries he picked, but he knows that it was the same amount as Jerry and Ann combined.
Jerry: 2 1/3
Ann: 3 1/3
Answer:
5 2/3
Step-by-step explanation:
Hope it helps plz give brainliest ! :D
Here is a trapezium drawn on a centimetre grid (not drawn to scale) work out the area of the trapezium, stating the units of your answer
Answer: the answer is 21 squared
Answer:
21cm²,22cm (write both of them. they give you the total marks.)
Step-by-step explanation:
you can use a calculator if you want. No links please help this is very important i will give you brain thing if its correct
Answer:
6.36
Step-by-step explanation:
42.40x0.15=6.36
....
Answer:
$6.36
Step-by-step explanation:
42.4 x 0.15 = 6.36
As part of a demographic study, a college administrator needed to survey a sample of students from the college. From each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey.
Required:
What is the best description of the type of sample selected by the administrator?
Answer:
Option D is correct
Step-by-step explanation:
The options for the question is
a)cluster sample
b)convenience sample
c)simple random sample
d)stratified random sample
e)systematic random sample
Solution
The sampling here comprises of students from all the major of college. Here the major can be considered as "strata" of the educational institute. Out of these, strata or majors five students are selected on random basis.
This is a form of stratified random sample
Hence, option D is correct
1. This week Tony practiced basketball 2 hours on Tuesday, 1 hours Wednesday, and 2 hours on Friday. Next
week Tony will practice basketball for the same number of hours Tuesday, Wednesday, and Friday. What is
the total number of hours Tony will practice basketball over the 2 weeks?
For 2 weeks tony will spent time for practice basketball is 10 hours.
How do you find time in math problems?The equation for calculating time is [Time = Distance Speed]. The distance may be calculated using the time formula [Distance = Speed Time].Work completed equals Time x Rate of Work. Work Rate is equal to One/Time. Time = 1 divided by the rate of work. If a task is completed across x days, then the amount of work completed in a single day is equal to 1/x.The Greenwich hour angle, abbreviated GHA, is used to define the Equation of Time as E = GHA (apparent Sun) - GHA (mean Sun) (1). E = right ascension of the fictional mean Sun - right ascension of the apparent (real) Sun is a different formula that is frequently used in textbooks.Given data :
1st week
= Tuesday = 2 hours
= Wednesday = 1 hour
= Friday = 2 hours
same for 2nd week
so total hours = 1st week + 2nd week
= 2 + 1 + 2 + 2 + 1 + 2
= 10 hours
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verify the following -12/5 + 2/7 = 2/7 + -12/5
Answer:
yeah they are the same
Step-by-step explanation:
-2.11428571429
Step-by-step explanation:
By using the commutative property, regardless of how the numbers are listed using addition or multiplicaton, they will equal the same thing.
So, a+b=b+a, which is what is present for your question.
In a basket there are 18 tomatoes, 12 potatoes, and 8 carrots.identify the ratio of carrots and potatoes to tomatoes in all 3 forms.
Answer:
Step-by-step explanation:
Answer: 10:9, 10/9, 10 to 9.
Step-by-step explanation:
the chef mixes 12 tablespoons of flour to 8 tablespoons of sugar what fraction of the mixture is sugar.
Answer:
2/5
Step-by-step explanation:
To find the fraction that is sugar,
part sugar/ total
The total is sugar + flour = 8+12 = 20
8/20
We can simplify
Divide the top and bottom by 4
8/4 =2
20/4 = 5
The fraction is 2/5
Answer:
[tex]\sf\frac{8}{20}[/tex]
Step-by-step explanation:
First let us find the total.
Total = Flour + Sugar
Total = 12 + 8
Total = 20
Now we know that, there are 8 tablespoons of sugar in the whole mixture.
So, write it as a fraction, you have to divide the number of tablespoons of sugar by the total.
Sugar = 8/20
(0.4+ 1.6) x 6 what is it please help
Answer:
12
Step-by-step explanation:
(0.4+ 1.6) x 6 = 2 x 6 = 12
Answer:
12
Step-by-step explanation:
(0.4 + 1.6) x 6
(2) x 6
12
In a class of 55 students, 15 students liked Maths but not English and 18 students liked English but
not Maths. If 5 students did not like both, how many students liked both subjects? Represent the
above information in a Venn-diagram.
Answer:
janajaaajwjjwwjwjwuwjwjjw
You buy 4 pounds of steak at Store A for $25.50. Your friend buys 6 pounds
of steak at Store B for $40.25. Which store is cheaper?
O No answer text provided.
O They're the same
O Store A
O Store B
Question 3
Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.
At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.
At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.
Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.
Step-by-step explanation:
what do I do here..?
Answer:
Baking a cake is a chemical change.
Step-by-step explanation:
The baking powder or baking soda will undergo a chemical reaction. The heat helps baking powder or soda produce tiny bubbles of gas which makes the cake light and fluffy. That's why chemical reactions are involved in baking a cake.
Cooper has $200 in a savings account. The interest rate is 10% per year and is not compounded. How much interest will he earn in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
The interest is $20 per year
Step-by-step explanation:
Answer:
$20
Step-by-step explanation:
using the formula you gave, you can plug in the numbers, i=200 * .10 * 1 since you start with 200 dollars, have a 10% interest rate, and it has been one year, then solve to get 20
if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest
ype your answer ihto the box.
Ben bakes 30 cupcakes
A box holds 4 cupcakes
How many full boxes of cupcakes are there?
Answer:
7
Step-by-step explanation:
4 x 7 is 28
7 full boxes
random characters so I can submit this anwser to you
Answer:
90x+(-7y)=x+y
Step-by-step explanation:
i think
Research studies show that the relationship between the tire pressure of a vehicle’s tires and the life of the tires is quadratic. The following table shows the recommended tire pressure of a car’s tires (in pounds per square inch) and its anticipated tire life (in thousands of miles).
Tire Pressure Tire Life
29 46.8
32 57.6
34 58.8
36 60.0
38 58.8
40 57.0
42 52.8
Use a graphing or online regression calculator to find the quadratic function of best fit for this set of data. What is the value of a in this function?
-0.240947
-2.40947
-0.00240947
-0.0240947
Answer:
-2.40947
Step-by-step explanation:
Please complete part A.+ B. And show all work. Thank you for your help.
6 × 46 = 24 × 16
True
True
False
False
Answer:
False
Step-by-step explanation:
6x46 = 276
24x16 = 384
A students wants to write an expression for, all of the elements which are not in set A. Which expression below matches the statement A. NA (B) B (C) -A (D) A’
The expression A' represents the statement for all of the elements which are not in set A.
What is Set?A set is a collection of well defined objects.
Given that A students wants to write an expression for all of the elements which are not in set A.
The elements within set A are denoted by A.
We have to find all of the elements which are not in set A.
U represents the universal set and A is the given set.
A'=U-A
Hence, the expression A' represents the statement for all of the elements which are not in set A.
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Joseph bicycled 3 miles farther than Nickeisha. The sum of the distances they bicycled was 25 miles. How far did Nickeisha bicycle
Answer:
11 miles
Step-by-step explanation:
Let Nickeisha's distance be x
and Joseph's distance be x+3
x+(x+3) = 25
2x+3 = 25
2x=22
x=11
Nickeisha biked 11 miles.