The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
We are having digits 2,3,4,5 and 6. Numbers greater than 4000 are to be formed using these digits without repetition.
The number can have 4 digits but greater than 4000 or can have 5 digits.
The total number of 4 digits number greater than 4000 is => 3*4P3 = 3*24 = 72.
Total number of 5 digits numbers = 5P5=5!=120
So, the Total number of required numbers =120+72=192
Hence, The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
Complete question: Find the number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition.
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According to the combination method, the number of formation using the digit 4 is 192
The term combination in math is called as the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
While we looking into the four-digit has 4 digits and the first digit is the thousands place. Then the digits 2 and 3 are less than 4, here we know that they can't take the thousands place. Here we also know that the digit 4, 5, and 6 can take this place.
Here we have the remaining 4 numbers and the remaining three digits can be taken by any of them to form a number greater than 4000.
Then the number of ways is calculated as
=> 3×4×3×2 = 72
Then the number of 5 digit numbers greater than 4000.
Here we have to observe that all five-digit numbers are greater than 4000. And here we have 5 digits and hence the number of five-digit numbers is written as
=> 5×4×3×2×1 = 120
Then the total number of ways is calculated as
=> 72 + 120 = 192
Therefore the number of numbers that are greater than 4000 which can be formed using the digits 2, 3, 4, 5, 6 without repetition is 192.
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hey! i’ll give brainliest please help.
The last name I am pretty sure of it.
Answer:
Zarathustra is the answer
WILL MARK BRAINLIEST!! PLS ANSWER QUESTION!!!
Lindsey is working really hard to improve her grade. on her first quiz she scored 67 point, on her second she scored 71, and on her third she scored 75. her scores continue to increase at the same rate. write a recursive and explicit formula for this geometric sequence.
The recursive formula for Lindsey's scores is aₙ = aₙ₋₁ \(\times\) r, and the explicit formula is aₙ \(= 67 \times r^{(n-1).\)
To find the recursive and explicit formulas for the given geometric sequence, let's analyze the pattern of Lindsey's scores.
From the given information, we can observe that Lindsey's scores are increasing at the same rate.
This suggests that the scores form a geometric sequence, where each term is obtained by multiplying the previous term by a common ratio.
Let's denote the first term as a₁ = 67 and the common ratio as r.
Recursive Formula:
In a geometric sequence, the recursive formula is used to find each term based on the previous term. In this case, we can write the recursive formula as:
aₙ = aₙ₋₁ \(\times\) r
For Lindsey's scores, the recursive formula would be:
aₙ = aₙ₋₁ \(\times\) r
Explicit Formula:
The explicit formula is used to directly calculate any term of a geometric sequence without the need to calculate the previous terms.
The explicit formula for a geometric sequence is:
aₙ = a₁ \(\times r^{(n-1)\)
For Lindsey's scores, the explicit formula would be:
aₙ \(= 67 \times r^{(n-1)\)
In both formulas, 'aₙ' represents the nth term of the sequence, 'aₙ₋₁' represents the previous term, 'a₁' represents the first term, 'r' represents the common ratio, and 'n' represents the term number.
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Write a conjecture that describes the pattern in the sequence. Then use your conjecture to find the next item in the sequence. 0,2,4,6,8
The conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10
How to write a conjecture that describes the pattern in the sequence?The sequence is given as:
0, 2, 4, 6, 8
In the above sequence, we can see that each current term is 2 added to the previous term
i.e.
Tn = 2 + Tn-1
Using the above conjecture, we have
Next term = 8 + 2
Evaluate
Next term = 10
Hence, the conjecture that describes the pattern in the sequence is current term is 2 added to the previous term and the next term is 10
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Need help with problem 5, Thank you!
Sorry for the glare
Answer:
x = 57
Step-by-step explanation:
A triangles degrees add up to 180
67 + 56 = 123
180 - 123 = 57
7+42x3^2-3a=14x3^-2a+7
the answer is C a=3 for this equation
Can you guys plz help me!?
Thanks!!
PLEASE HELP:
Write an ordered-pair rule for the translation in the sequence that maps ∆EFG to ∆E'F'G'. Answer: (x, y)
Translation rule: (x, y) (x___,y____)
Fill the blanks.
Answer:
(x, y ) → (x + 4, y - 5 )
Step-by-step explanation:
Consider the coordinates of F and F'
F (1, 4 ) and F' (5, - 1 )
1 → 5 in the x- direction is + 4
4 → - 1 in the y- direction is - 5
Translation rule is (x, y ) → (x + 4, y - 5 )
Help me please this is due tonight!
Answer:
1 and 2/3 yards of material
Step-by-step explanation:
5 times 2/6 = 10/6 = 5/3 = 1 2/3
Hope this helps!! :D
6. The displacement, y(m), of a body in damped oscillation is y = 2e^-t sin 3t.
The task is to:
a) Use the Product Rule to find an equation for the velocity of the object if v =dy/dt
The equation for the velocity of the object if v =dy/dt is :
y = dy/dt = 2e-t( - sin3t + 3 cos3t)
What is the Product Rule?Calculus's "product rule" is a technique for determining the derivative of any function that is presented in the form of a product that is the result of multiplying any two differentiable functions. The derivative of a product of two differentiable functions is equal to the sum of the products of the second function with differentiation of the first function and the first function with differentiation of the second function, according to the product rule, which is expressed in terms. In other words, if we are given a function of the type f(x)g(x), we may use the product rule derivative to calculate the derivative of this function as, d/dx f(x)·g(x) = [g(x) × f'(x) + f(x) × g'(x)]Given data :
y = 2e^-t sin3t your mean is y = 2e-t * sin3t
If yes, you know the product rule is (u.v)' = u' v + uv'
in this case u = 2e-t and v= sin3t
now u' = -2 e-t and v' = 3 cos3t
y = dy/dt = -2 e-t * sin3t + 2e-t *3 cos3t
It is better you simplify! by factoring of 2e-t
y = dy/dt = 2e-t( - sin3t + 3 cos3t)
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Which of the following is not a layer of the Earth?
Answer:
Nickel is not a layer of earth. It is a white metal that belongs to the group of transition metals and is said to be present in the core of the Earth. Sial- refers to the upper layer of the Earth's crust. This layer has an abundance of minerals having aluminum and silicates.
Answer:
I dont see the following but these are the layers of the Earth
Step-by-step explanation:
found my answer im fine now
Step-by-step explanation:
X +X + X + X+X+X = 6 * x = 6x
Which expression is equivalent to 6 (3x + 4)
Answer:
E
Step-by-step explanation:
Answer:
18x+24
Step-by-step explanation:
Use the distributive property
m is directionly proptional to r squared
when r=2, m=14
A)work out the value of m when r is 12
b) work out the value or r when m is 224
9514 1404 393
Answer:
A) 504
B) 8
Step-by-step explanation:
The statement of proportionality can be written as the equation ...
m = kr²
Then we can find k from ...
k = m/r² = 14/2² = 7/2
That is, ...
m = (7/2)r²
__
Using this relation, we can find m for r=12:
m = (7/2)·12² = 7·72
m = 504 . . . for r = 12
__
And, we can use the same equation to solve for r when m=224.
224 = 7/2·r²
r² = 64
r = √64
r = 8 . . . for m = 224
Bill need to build a rectangular harp pen. The pen mut have a perimeter of 24 meter
The cost of the fence used to make the rectangular sheep pen is £57.6. The result is obtained by multiplying the perimeter by the fencing price.
How to calculate the cost for fencing a building?The cost for fencing a building can be calculated by multiplying the price of a certain size of fence by the perimeter or the length side to be fenced.
Bill builds a rectangular sheep pen.
Perimeter, P = 24 mFencing cost = £1.20 per half meterFind the total cost of the fence!
The total cost of the fence will be
= P × fencing cost
= 24 m × £1.20 / ½ m
= 24 × £2.40
= £57.6
Hence, the fence to make the sheep pen will cost £57.6.
Your question is incomplete. But most probably your full question was
Bill needs to build a rectangular sheep pen. The pen must have a perimeter of 24 m. Every half meter of fencing costs him £1.20. Work out the cost of the fence used to make the sheep pen!
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a -foot-long footbridge has two diagonal supports that meet in the center of the bridge. each support makes a angle with a short vertical support. a diagram shows the footbridge, the diagonal supports and the vertical supports create two right triangles. at the top of the diagram a horizontal line is shown and labeled 20 feet. the two right triangles are shown below this horizontal line.the two longest legs of both right triangles touch at the center of the footbridge.the shortest leg of both right triangles represents the vertical support on each end of the footbridge. the hypotenuse of both right triangles form the diagonal supports that meet at the center of the footbridge. the full length of the footbridge is 20 feet. the vertical supports are not labeled. each diagonal support is labeled x. a 65-degree-angle is formed between the short vertical support and the diagonal support on each end of the bridge. what is the length x of a diagonal support, to the nearest tenth of a foot?
The length of a diagonal support (x) is approximately 18.4 feet to the nearest tenth of a foot.
To find the length x of a diagonal support, we will use the information given about the right triangles formed by the vertical supports, diagonal supports, and the horizontal line (representing half the length of the footbridge).
Since the full length of the footbridge is 20 feet, the horizontal line in each right triangle measures half of that, which is 10 feet.
The angle formed between the short vertical support and the diagonal support is given as 65 degrees.
We'll use the sine function to find the length x of the diagonal support.
In this case, sine(65) = opposite side (vertical support) / hypotenuse (diagonal support or x).
We first need to find the length of the vertical support.
To do this, we can use the tangent function.
In this case, tangent(65) = opposite side (vertical support) / adjacent side (10 feet).
Solving for the vertical support: vertical support = 10 * tangent(65) ≈ 17.1 feet.
Now, we can plug this value back into the sine equation: sine(65) = 17.1 / x.
Solving for x (the diagonal support): x = 17.1 / sine(65) ≈ 18.4 feet.
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Which of the following represents the factorization of the polynomial below?2x2 +11x +5O A. (2x+5)(x+1)O B. (2x + 2)(x+5)C. (2x + 1)(x+5)O D. (2x+5)(x+2)
The correct option is C which is (2x+1)(x+5).
The diagram shows a circle with four special features labelled A, B, C and D.
A-
16/36 Marks
B-
a) Which feature is the centre of the circle?
b) Which feature is the diameter of the circle?
-D
(a) The feature that is the centre of the circle is A
(b) The feature that is the diameter of the circle is C
a) Which feature is the centre of the circle?From the question, we have the following parameters that can be used in our computation:
The circle
The center of the circle is a point equidistant from all points on the circumference of the circle
Using the above as a guide, we have the following:
The center of the circle is A
b) Which feature is the diameter of the circle?The diameter of the circle is a straight line that drawn through the center of the circle that touches the circumference of the circle
Using the above as a guide, we have the following:
The diameter of the circle is C
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A dentist bought 9 bags of prizes for his patients. Each bag had 12 prizes. The prizes were divided equally among 3 boxes. How many prizes were in each box?
Answer:
36
Step-by-step explanation:
A dentist bought 9 bags of prizes for his patients.
Each of the bags has 12 prizes
The first step is to calculate the total number of prizes
= 9 × 12
= 108 prizes
Since the prizes will be shared equally in 3 boxes then the number of prizes in each box can be calculated as follows
= 108/3
= 36
Hence the number of prizes in each of the 3 boxes is 36
Kirk Enterprises offers rug cleaning services to business clients. Below are the adjustments data for the year
ended July 31. Using this information along with the spreadsheet below, record the adjusting entries in proper
general journal form.
We will need to create entries for each of the specified adjustments in order to record the adjusting entries in suitable general journal form.
The notebook entries for each modification are as follows:
a) Depreciation of Equipment:
Date: July 31, 20XX
Account Debit Credit
Depreciation Expense X
Accumulated Depreciation - Equipment X
b) Accrued Wages:
Date: July 31, 20XX
Account Debit Credit
Wage Expense X
Accrued Wages X
c) Unused Supplies:
Date: July 31, 20XX
Account Debit Credit
Supplies Expense X
Supplies on Hand X
d) Earned Unearned Revenue:
Date: July 31, 20XX
Account Debit Credit
Unearned Revenue X
Service Revenue X
e) Unexpired Insurance:
Date: July 31, 20XX
Account Debit Credit
Insurance Expense X
Prepaid Insurance X
Please be aware that the question does not include the monetary amounts for each adjustment; thus, you must fill in the appropriate amounts based on the information provided. Use the correct account names according to your particular company's chart of accounts.
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The complete question is:
Kirk Enterprises offers rug cleaning services to business clients. Below is the adjustments data for the year ended July 31.
Required:
Using this information along with the spreadsheet below, record the adjusting entries in proper general journal form.
Adjustments:
a) The equipment is estimated to last for 5 years with no salvage value. The asset will be depreciated evenly over its useful life. Record one month’s depreciation.
b) Accrued wages, $2.
c) Unused supplies on hand, $8.
d) Of the unearned revenue, 75% has been earned.
e) Unexpired insurance remaining at the end of the month, $9.
How many terms are in the algebraic expression 2y+3x-5x²-g?
02
3
04
5
K
Answer:
the answer is 4 terms
Step-by-step explanation:
The algebraic expression 2y + 3x - 5x² - g consists of four terms. Each term is separated by the addition or subtraction operation. Therefore, the four terms in the expression are:
2y. .........term
3x. .......term
-5x². ........term
-g. ........term
Therefore, 4 terms in the expression
Find the length of QR
Answer:
QR = 15
Step-by-step explanation:
The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.
(QR+5) *5 = 10^2
(QR+5) *5 = 100
Divide each side by 5.
(QR+5) *5/5 = 100/5
(QR+5) = 20
Subtract 5 from each side.
QR = 20-5
QR = 15
Factor.
Z^2-9z+20
BOX METHOD WITH STEPS PLZ!!
Answer:
(z−4)(z−5)
Step-by-step explanation:
We need two numbers that...
Add together to get -9
Multiply together to get 20
-4 and -5 do just that!
So you fill in the blanks and get (z−4)(z−5)
Hope this helps :)
I need helppppppppp I d don't know what to do
EXPLANATION
The perimeter Perimeter is given by the sum of the sides as follows:
P = z + 5 + z + 5 + z + z
Substituting P=26 and adding like terms,
26 = 10 + 4z
Subtracting -10 to both sides:
26 - 10 = 10 - 10 + 4z
Simplifying:
16 = 4z
Dividing both sides by 4:
16/4 = z
Switching and simplifying:
z = 4
So,
Equation: 26 = 10 + 4z
z = 4
A wholesaler carries 6,600 different items in their store. In a normal week, demand occurs for 4,800 of these items. Of those 4,800 items, 250 are not available for the entire week and another 270 items are available for only part of the week What is the wholesaler's in-stock probability during a normal week? Note: Round your answer as a percentage rounded to 1 decimal place.
Rounded to 1 decimal place, the wholesaler's in-stock probability during a normal week is approximately 89.2%.
To calculate the wholesaler's in-stock probability during a normal week, we need to consider the number of items that are available for the entire week and divide it by the total demand.
Total demand = 4,800 items
Items not available for the entire week = 250 items
Items available for only part of the week = 270 items
Therefore, the number of items available for the entire week can be calculated as follows:
Items available for the entire week = Total demand - Items not available for the entire week - Items available for only part of the week
= 4,800 - 250 - 270
= 4,280 items
The in-stock probability can be calculated by dividing the number of items available for the entire week by the total demand and then multiplying by 100 to convert it to a percentage:
In-stock probability = (Items available for the entire week / Total demand) * 100
= (4,280 / 4,800) * 100
= 89.1666...
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I will give brainliest to whoever answers this correctly
Answer:
56
Step-by-step explanation:
40 ÷ 5 = 8
8 x 2 = 16
16 + 40 = 56
Answer:16 green grapes sold 40 red grapes sold together that makes 56
Step-by-step explanation:
Which number line shows the solutions to n<-3
Answer:
[In Picture]
Step-by-step explanation:
There are no given options.
However, I am able to recreate the best answer for the question given.
There would be arrow going to the left from -3. The arrow will include all numbers less than -3.
Since there is a less than sign, the circle at the beginning of the arrow is open.
Choose the option that closely matches the line shown.
The number line is the representation of numbers in real order.
The difference between the consecutive numbers in a number line is always positive.
The number line of n < - 3 is n less than -3.
The graph of the number line is given below.
What is a number line?It is the representation of numbers in real order.
The difference between the consecutive numbers in a number line is always positive.
We have,
n < - 3
This is read as,
n is less than -3.
The graph of the number line is given below.
Thus,
The number line of n < - 3 is n less than -3.
The graph of the number line is given below.
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[4 points.] assuming that the necessary elementary integration formulas extend to this case, find the laplace transforms of the following functions, where a and b are real constants. (a) f(t)
The question requires us to find the
Laplace transform of the function f(t), where a and b are real constants.
Let's assume that the necessary elementary
integration formulas extend to this case.
Finding the Laplace transform of f(t):
Let F(s) be the Laplace transform of f(t). Then, we have:F(s) = L{f(t)} = ∫_0^∞ e^(-st) f(t) dt
We know that the Laplace transform of a
constant function is given by:
L{1} = ∫_0^∞ e^(-st)
dt = [-1/s * e^(-st)]_0^∞ = 1/sIf
we replace the constant function 1 in the above formula with e^(at), we get:
L{e^(at)} = ∫_0^∞ e^(-st) e^(at) dt
Now, let's express f(t) as a sum of two
exponential functions
:
f(t) = e^(at) + e^(bt)
Taking the Laplace transform of both the terms separately, we get:
L{e^(at)} = 1/(s-a) and
L{e^(bt)} = 1/(s-b)
Therefore, the Laplace transform of f(t) is given by:
F(s) = L{f(t)} = L{e^(at)} + L{e^(bt)}= 1/(s-a) + 1/(s-b) = (b + a - s)/[(s - a)(s - b)]
This is the Laplace transform of the function f(t).
Hence, the required answer is:(a) f(t) = e^(at) + e^(bt) => F(s) = L{f(t)} = (b + a - s)/[(s - a)(s - b)]
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To find the Laplace transform of the function f(t) with constants a and b, substitute f(t) into the integral F(s) = ∫[0 to ∞] f(t)e^(-st) dt and evaluate it using the integration formulas mentioned.
The question asks for the Laplace transform of a function, denoted as f(t), where a and b are real constants. To find the Laplace transform of f(t), we need to apply the necessary elementary integration formulas.
The Laplace transform of a function f(t) is denoted as F(s), where s is a complex variable. It is defined by the integral:
F(s) = ∫[0 to ∞] f(t)e^(-st) dt
To find the Laplace transform of f(t), we substitute f(t) into the integral and evaluate it using the integration formulas.
The necessary elementary integration formulas include:
1. ∫ e^(at) dt = 1/a * e^(at) + C, where a is a constant and C is the constant of integration.
2. ∫ t^n dt = (1/(n+1)) * t^(n+1) + C, where n is a positive integer and C is the constant of integration.
By applying these formulas, we can find the Laplace transform of f(t) with the given values of a and b. It is important to note that the specific form of f(t) must be known in order to apply the correct integration formulas.
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Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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4x2 -28x-32 fully factored
GCF=4
4(4x^2/4+-28x/4+-32f/4)
=4(x^2-7x-8f)
Hello,
\(4x^2-28x-32\\\\=4(x^2-7x-8)\\\\=4(x^2-8x+x-8)\\\\=4[x(x-8)+1(x-8)]\\\\=4(x-8)(x+1)\\\)