Here is a pattern made from sticks:
a) How many sticks would be in pattern number 6?
Answer: 32
b) How many sticks would be in pattern n?
Answer: ____
Answers
Example:
6x5= 30
30+2=32
Recursive formula of an arithmetic sequence is given by the expression,
\(T_n=a+(n-1)d\)
Where, \(T_n=\) nth term
\(a=\) First term of the sequence
\(n=\) Number of term
\(d=\) Common difference
Therefore, number of sticks in the 6th pattern are 32.
And number of sticks in the nth pattern are \(T_n=5n+2\)
From the picture attached,
Number of sticks in 1st pattern = 7
Number of sticks in 2nd pattern = 12
Number of sticks in 3rd pattern = 17
Sequence formed is 7, 12, 17..... nth term
This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.
Therefore, nth term of the sequence will be,
\(T_n=a+(n-1)d\)
\(T_n=7+(n-1)5\)
\(T_n=5n+2\)
If \(n=6,\)
\(T_n=7+(6-1)5\)
\(T_n=7+25\)
\(T_n=32\)
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Related Questions
If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.
True
False
Answers
Answer:true
Step-by-step explanation:
solve the inequality
Answers
-4 ≤ g
Graph:
put a filled in dot on -4 on the number line with the arrow facing towards the right. Aka the first option for the arrows to the left.
Hope this helps
1.you buy a car for $10,000. every year, the car loses 25% of its value. how would the function rule change if the car lost 10% of its value each year? and why does the function rule include 0.75 instead of 0.25?
2. You start a job making $10 per hour. at the end of each year, you earn a 10% raise. how will the function rule change if the annual raise is 8%?
Answers
The automobile is currently worth Rs 52,488. four years ago, it was worth 80,000.
What is Depreciation rate?The depreciation rate is the total amount depreciated each year, expressed as a percentage. For instance, if a business depreciated an asset at a rate of $15,000 per year for ten years, the total depreciation would be $100,000. This indicates that the rate would be 15% annually. To calculate depreciation using the straight-line method, the asset's salvage value, or what you expect it to be worth at the end of its useful life, must be deducted from the asset's cost.Depreciable basis, or the amount that may be written off, is the outcome. By how many years the asset will be useful, divide this sum.Present Value A = Rs. 52,488
Depreciation rate r = 10 % per annum
Time t = 4 years
Let initial value be P
We know the formula, A =\($\mathrm{P}\left(1-\frac{\mathrm{r}}{100}\right)^t$\)
We obtain by substituting the supplied values.
52,488 =\($\mathrm{P}\left[1-\frac{10}{100}\right]^4 \\\)
52,488 = \($\mathrm{P}(0.9)^4 \\\)
\($\mathrm{P}=\frac{52488}{0.6561} \\\)
P = 80,000
The complete question is:
The value of a car depreciates every year at the rate of 10% on its value at the beginning of the year. If the present value of the car is Rs 52,488 its worth four years ago was
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Write a recursive formula for the arithmetic sequence:
7,4,1,-2
Answers
a(sub)n = a(sub)n-1 - 3
(sub) indicates the values touching the parenthesis are written as a subscript.
The above would be the recursive formula as you are taking the previous number and subtracting 3 to get the next number in the sequence.
Answer:
N - 3
Step-by-step explanation:
It is a series of -3 so:
7 -3 = 4
4 - 3 = 1
1 - 3 = -2
So:
N-3
where N is the present value in the sequence.
(20 Points)
y = 4(x + 6)2 + 2
O y = -4x² + 48x + 136
O y = 4x2 + 48x + 146
O y = x² - 48x + 146
O y = -14x2 – 48x – 146
Answers
Answer:
2nd option will be the answer (y=4x²+48x+146)
Step-by-step explanation:
y=4(x+6)²+2
y=4(x²+2*x*6+6²)+2 [(a+b)²=a²+2ab+b²]
y=4(x²+12x+36)+2
y=4(x²)+4(12x)+4(36)+2
y=4x²+48x+144+2
y=4x²+48x+146
a fair, six-sided die is rolled repeatedly until either two prime numbers or two even numbers are rolled. what is the expected number of ones that are rolled?
Answers
The probability number of times to roll the number cube to result in a prime number 12 times is 24
How to determine the number of times?
The given parameters are:
Number cube = 6 sides
Number of times= 12
The probability of obtaining a prime number in a six-sided die is:
P(Prime) = 3/6
The number of times (n) is then calculated as:
p * n = 12
Substitute known values
3/6 * n = 12
Evaluate the fraction
1/2 * n = 12
Multiply both sides by 2
n = 24
Hence, the number of times is 24
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1. Which of the following linear equations has a negative slope? Circle all that apply. A. y = 2x – 5 B. y = 4– 7x C. y=-3 D. X = -1 E. y=-5/4x+2 F. y=1/2x-2
Answers
Answer:
C) y= -3, D) x= -1, E y= -5/4x +2
Step-by-step explanation:
9/10 divided by 3/5 in simplest form
Answers
Answer:
3/2
Explanation:
To divide by a fraction multiply by the reciprocal of that fraction
9/10×5/3
reduce the numbers with greatest common factor 3
3/10×5
reduce the numbers with the greatest common factor of 5
3/2 is your answer
The fraction 9/10 divided by 3/5, in simplest form, is 3/2.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 3/5 is 5/3.
So, we have:
(9/10) ÷ (3/5) = (9/10) x (5/3)
Next, we multiply the numerators and denominators:
= (9 x 5) / (10 x 3)
= 45/30
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor, which is 15:
= (45/15) / (30/15)
= 3/2
Therefore, 9/10 divided by 3/5, in simplest form, is 3/2.
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PLEASE HELP ME I CANT FAIL I WILL GIVE YOU SO MUCH POINTS IF YOU HELP! What is the product of -2 2/5 and -3 5/6?
A- -9 1/5
B- -6 7/30
C- 6 1/3
D- 9 1/5
Answers
Answer:
The answer is 9 1/5.Step-by-step explanation:
Step-1: Convert the mixed fractions into improper fractions.
=> -2 2/5 ⇒ -12/5=> -3 5/6 ⇒ -23/6Step-2: Multiply the improper fractions.
=> -12/5 x -23/6=> 12/5 x 23/6[The minuses on both fractions cancelled out because when there are 2 minuses multiplying each other, the minuses cancel out.]
=> 2/5 x 23/1=> 46/5Step-3: Convert the improper fraction into mixed fraction.
=> 46/5 = 9 1/5Hence, the answer is 9 1/5.
Hoped this helped.
\(BrainiacUser1357\)
rewrite the expression(16x^3y^2)-24x^4y^4 as a product of the greatest common factor multiplied by a binomial
Answers
The expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).
To rewrite the expression (16x^3y^2) - 24x^4y^4 as a product of the greatest common factor multiplied by a binomial, we need to find the greatest common factor of the two terms. The greatest common factor of 16x^3y^2 and 24x^4y^4 is 8x^3y^2.
We can factor out 8x^3y^2 from both terms to get:
(16x^3y^2) - (24x^4y^4) = 8x^3y^2(2 - 3x^1y^2)
Therefore, the expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).
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how many solutions are there to square root x =9
Answers
Answer:
There are 2 solutions to square root x = 9
They are 3, and -3
Step-by-step explanation:
The square root of x=9 has 2 solutions,
The square root means, for a given number, (in our case 9) what number times itself equals the given number,
Or, squaring (i.e multiplying with itself) what number would give the given number,
so, we have to find the solutions to \(\sqrt{9}\)
since we know that,
\((3)(3) = 9\\and,\\(-3)(-3) = 9\)
hence if we square either 3 or -3, we get 9
Hence the solutions are 3, and -3
a local bank reviewed its credit card policy with the intention of recalling some of its credit cards. in the past approximately 3% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. hence, management established a probability of 0.03 that any particular cardholder will default. the bank also found that the probability of missing a monthly payment is 0.21 for customers who do not default. of course, the probability of missing a monthly payment for those who default is 1. (a) given that a customer misses a monthly payment, compute the probability that the customer will default. (round your answer to 2 decimal places.) 0 changed: your submitted answer was incorrect. your current answer has not been submitted. (b) the bank plans to recall its card from customers who miss a monthly payment, if the probability those customers will default is greater than 0.20. should the bank recall its card from a customer who has missed a monthly payment? why or why not? the bank ---select--- recall its card because the probability of default for these customers is ---select--- than 0.20.
Answers
The bank should not recall its card from a customer who has missed a monthly payment, as the probability of default is less than the threshold of 0.20 set by the bank.
(a) Let D denote the event that a customer defaults and M denote the event that a customer misses a monthly payment. We need to find P(D|M). We can use Bayes' theorem to solve for this:
P(D|M) = P(M|D) * P(D) / P(M)
We know that P(D) = 0.03, P(M|D) = 1, and P(M|not D) = 0.21. To find P(M), we can use the law of total probability:
P(M) = P(M|D) * P(D) + P(M|not D) * P(not D)
= 1 * 0.03 + 0.21 * 0.97
= 0.2391
Therefore, we have:
P(D|M) = 1 * 0.03 / 0.2391
= 0.1258 or approximately 0.13 (rounded to 2 decimal places)
So the probability that a customer will default given that they have missed a monthly payment is about 0.13.
(b) The bank should recall its card from a customer who has missed a monthly payment if the probability that the customer will default is greater than 0.20. From part (a), we know that the probability of default given that a customer has missed a monthly payment is about 0.13, which is less than 0.20. Therefore, the bank should not recall its card from this customer.
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pleas help me for 20 points
Answers
Answer:
240sqin
Step-by-step explanation:
if you convert 4/3ft into inches you get 16 inches so multiplty 15x16=204sqin Hope this helps! ;-)
Answer:
234
Step-by-step explanation:
area = length × breadth
= 15.6in × 15in
= 234in²
1ft = 15in
4/3 = 15.6in
hope it helps :)
Someone help me plz.
Answers
20%
Explanation:
What we know:
- there are 25 cans in total
- 5 of them are root beer cans
Using this information, we can say that 5/25 cans are root beer cans. To find the percent, we change the fraction into a decimal and then multiply it by 100.
To change 5/25 into a decimal, we divide the numerator and denominator.
5/25=0.2
And we multiply the decimal by 100 to get the percent:
0.2*100=20
Therefore, 20% of Cam’s cans are root beer cans.
I hope this helps!
Tori bought 5 t-shirts for $35. If each t-shirt costs the same amount, how much would Tori pay for 20 t-shirts
Answers
Answer:
140
Step-by-step explanation:
Best answer gets brainliest!
Whats the question to my answer?
Answer: pickle
Whats the question?
(u can make up what the question is theres no real answer)
Answers
Answer:
If I give you a nickel, what am I wanting you to tickle? my ____
Step-by-step explanation:
Domain, range, and is it a function? SCREENSHOT BELOW!
Answers
Answer:
Domain: \((-\infty, \infty)\)Range: \((-\infty, 3]\)Function: yesStep-by-step explanation:
Domain is the set of x values, range is the set of y values.
For it to be a function, each value of x must map onto no more than one value of y.
What is 5/6 - 3/8? Chose the answer in the most simplified form. A. 1/3 B. 9/16 C. 1/12 D. 11/24
Answers
Given:
\(\frac{5}{6}-\frac{3}{8}\)We need to simplify this expression.
The least common multiple of 6 and 8 is 24.
Make the denominator of the fraction as 24.
\(\frac{5}{6}-\frac{3}{8}=\frac{5\times4}{6\times4}-\frac{3\times3}{8\times3}\)\(\frac{5}{6}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24}\)\(\frac{5}{6}-\frac{3}{8}=\frac{20-9}{24}\)\(\frac{5}{6}-\frac{3}{8}=\frac{11}{24}\)Final answer:
\(\frac{5}{6}-\frac{3}{8}=\frac{11}{24}\)
Will give brainliest
Answers
Answer:
about 15.08
Step-by-step explanation:
Angle BAC + Angle CAH = 180 (they are supplenmentary angles), which means (12x+4)+(x-20)=180
solve:
13x-16=180
13x=196
x≈15.08
Answer:
12x+4 + x-20 = 180
13x = 196
x = 15.08
Step-by-step explanation:
On a morning in December, Carl wakes up and checks the thermometer. He reads that it is -10°F. In two hours he checks and the temperature has risen 4°F. In another three hours the temperature has risen 7°F. At the last time, he checks the thermometer, what is the temperature? Also writes an addition equation that models this situation
Answers
Answer: 1 degree Fahrenheit
Step-by-step explanation:
The temperature starts at -10 degrees F, so if in two hours, the temperature has risen by 4 degrees, then the new temperature is -10 + 4 = -6 degrees F. 3 hours later, the temperature has risen another 7 degrees, so the new temperature is -6 + 7 = 1 degrees F. "addition equation" is ambiguous without knowing what class you are taking, but one such equation to represent the situation could be T = -10 + 4 + 7 = 1.
Select the true statements about the substitution method.
a. It may only be used to evaluate definite integrals
b. It is useful to solve the integral ∫2x sin x^2 dx.
c. It is based on the quotient rule for derivatives
d. It utilizes the formula ∫ f(u(x))u' (x) dx = ∫ f(u) du.
e. It is based on the chain rule for derivatives_
Answers
Options b, d, and e are the true statements about the substitution method.
b. It is useful to solve the integral ∫2x sin x^2 dx.
d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.
e. It is based on the chain rule for derivatives.
The true statements about the substitution method are:
b. It is useful to solve the integral ∫2x sin x^2 dx.
The substitution method is commonly used to simplify integrals and make them easier to evaluate. It can be applied to various types of integrals, including the given example.
d. It utilizes the formula ∫ f(u(x))u'(x) dx = ∫ f(u) du.
The substitution method involves making a substitution in the integral by introducing a new variable. This formula represents the fundamental principle of substitution, where the derivative of the substituted function appears in the integral.
e. It is based on the chain rule for derivatives.
The substitution method is based on the chain rule of derivatives. By making an appropriate substitution, the integral can be transformed into a new form that corresponds to a derivative of a simpler function.
Therefore, options b, d, and e are the true statements about the substitution method.
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Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54.
What is the oldest Kim could be? Show all your work.
I
Answers
Answer:
8
Step-by-step explanation:
Josh is 6 years older than 5 times Kim's age. The sum of their ages is less than 54. What is the oldest Kim could be?
J + k < 54 when J = 5k + 6 so:
5k + 6 + k < 54
6k + 6 < 54
subtract 6 from both sides:
6k + 6 - 6 < 54 - 6
6k < 48
divide both sides by 6:
6k/6 < 48/6
k < 8
Kim could be 8 at maximum.
Early point give away What is 100 times 10 to the 9 power.
Answers
Raven can walk 2 2/5 miles in 3/5 hour.
At this rate, how far can she walk in 1 hour?
Answers
The distance traveled by Raven in 1 hour at the given rate is 4 miles.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
Raven can walk 2 (2/5) miles in 3/5 hours.
so,
2 (2/5) = 0.6 hours.
12/5 = 0.6 hours.
2.4 = 0.6 hours.
then,
if 2.4 = 0.6 hour
for x = 1 hour
By cross multiplying:
x = 2.4/0.6 miles
= 4 miles
Hence, the distance traveled by Raven in 1 hour at the given rate is 4 miles.
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The instructions for a fruit drink say to mix one part blackcurrant juice with four parts water. I
want to make one litre of this fruit drink. How much blackcurrant juice should I use? Give your
answer in millilitres.
ml
Answers
Answer:
you should use minimum 8 black cur
Solve for the value of k.
(2k-2)
(k+2)°
Answers
Answer:
30
Step-by-step explanation:
( 2k - 2 )°, 90° and ( k + 2 )° are linear pair angles.
Sum of linear pair angle is supplementary ( that is 180 ),
2k - 2 + 90 + k + 2 = 180
2k + k + 90 = 180
3k = 180 - 90
3k = 90
k = 90/3
k = 30
Note : -
□ means 90°
Answer: b) James has a bicycle. Each wheel has a diameter of 35cm. James cycles his bicycle in a straight line in the playground. The front wheel makes 12 complete revolutions. How far does the bicycle travel? Give your answer in metres. Use π = 3.14, you must show your workings.
Answers
The bicycle travels a distance of 13.188 meters (to three decimal places).
What is the distance?
The distance traveled by the bicycle is equal to the distance traveled by one revolution of the front wheel multiplied by the number of revolutions.
The distance traveled by one revolution of the front wheel is equal to the circumference of the wheel, which is given by:
C = πd
where d is the diameter of the wheel. Therefore, the circumference of the front wheel is:
C = π × 35cm
C = 3.14 × 35cm
C = 109.9cm
Now we can calculate the distance traveled by the bicycle:
Distance = Number of revolutions × Distance traveled in one revolution
Distance = 12 × 109.9cm
Distance = 1318.8cm
Finally, we need to convert this distance to meters:
Distance = 1318.8cm ÷ 100
Distance = 13.188m
Therefore, the bicycle travels a distance of 13.188 meters (to three decimal places).
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Does anyone know what the answer is? Thanks!
Answers
Answer:
D
Step-by-step explanation:
An obtuse angle is one over 90. They both have one of them.
x Eval SR dA R १२ R= [0,3] [1,2] JO Please write clearly and Show all steps. Thanks!
Answers
integrated I(y) with respect to y, you'll get a numerical value for the double integral ∬(R) SR dA.
The specific function SR, it's not possible to provide a numerical answer.
Step-by-step explanation should help you evaluate the double integral for any given SR.
To evaluating a double integral over a region R.
Let's break it down step-by-step.
Identify the region R: R is given by the bounds [0, 3] for the x-axis and [1, 2] for the y-axis.
This defines a rectangular region in the xy-plane.
Set up the double integral:
Since the region R is a rectangle, you can write the double integral as:
∬(R) SR dA = ∫(x=0 to x=3) ∫(y=1 to y=2) SR dx dy
Here, SR represents the integrand that you need to integrate with respect to x and y.
Integrate with respect to x:
To evaluate the inner integral, integrate SR with respect to x, while keeping y constant.
Let's denote the result as I(y).
I(y) = ∫(x=0 to x=3) SR dx
Integrate with respect to y:
Now, evaluate the outer integral by integrating I(y) with respect to y over the given range [1, 2]:
∬(R) SR dA = ∫(y=1 to y=2) I(y) dy
Evaluate the integral:
Once you've integrated I(y) with respect to y, you'll get a numerical value for the double integral ∬(R) SR dA.
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ifa is a 6 4matrix, what is the smallest possible dimension of nul a?
Answers
The answer depends on the rank of A.
If the rank of A is less than 4, then the dimension of its null space is greater than or equal to 4-rank(A).
If the rank of A is 4, then the dimension of its null space is 0.
The dimension of the null space of a matrix A is given by the number of linearly independent vectors that satisfy the equation A x = 0,
where x is a column vector.
Since A is a 6x4 matrix, the equation A x = 0 represents a homogeneous system of 6 linear equations in 4 unknowns.
The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns of the matrix. Therefore, we have:
rank(A) + dim(null(A)) = 4
The rank of A is at most 4, since there are only 4 columns.
If the rank of A is 4, then the dimension of its null space is 0, because there are no linearly independent vectors that satisfy A x = 0. On the other hand, if the rank of A is less than 4, then the dimension of its null space is at least 4-rank(A).
Therefore, the smallest possible dimension of null(A) is:
dim(null(A)) = 4 - rank(A).
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The smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.
To determine the smallest possible dimension of the null space (nul A) of a 6x4 matrix A, we need to consider the rank-nullity theorem, which states:
dim(A) = rank(A) + dim(nul A)
Here, dim(A) represents the dimension of the matrix A, rank(A) represents the rank of the matrix A, and dim(nul A) represents the dimension of the null space of A.
For a 6x4 matrix A, the dim(A) is 4 since there are 4 columns. The rank(A) represents the number of linearly independent columns, and it can be at most 4 since there are 4 columns.
To find the smallest possible dimension of the null space, we need to maximize the rank(A). In this case, the maximum possible rank(A) is 4. Now, using the rank-nullity theorem:
4 = 4 + dim(nul A)
Solving for dim(nul A), we get:
dim(nul A) = 4 - 4
dim(nul A) = 0
Therefore, the smallest possible dimension of the null space (nul A) for a 6x4 matrix A is 0.
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